tag:blogger.com,1999:blog-138170572024-03-07T21:42:10.645-05:00JC's BlogOn this blog, I often discuss the evolution vs. creation debate. With my background in information technology and computer design, I find fault with evolution and defend the creationist viewpoint. I'm also interested in gardening, birdwatching, origami, hiking, physics, programming, recreational mathematics, photography, Bible study.. And this is a good place to record those favorite stories that I've told my children. All sorts of things may show up here.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.comBlogger91125tag:blogger.com,1999:blog-13817057.post-47151816604808808812021-09-02T00:27:00.001-04:002021-09-02T00:27:52.302-04:00Twin Poems<p></p><div class="separator" style="clear: both; text-align: left;"><span style="font-size: large;"></span><blockquote><span style="font-size: large;">This was scanned from a small notebook of my poetry:</span></blockquote></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdcY3GHgHTYi8oiLHh0i62Rs5WCHtoXNjp-otW1xWAx5qFz7UHGo2Jys6gUXQ7KIPWsoKrNcdiMHrX6mgaSoKZvcI_jx74o1kmxOgbPbsXGGIqa1QirJcchTRfWiuzv2y4CVXSWA/s1996/Twin+Poems.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1996" data-original-width="1108" height="636" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdcY3GHgHTYi8oiLHh0i62Rs5WCHtoXNjp-otW1xWAx5qFz7UHGo2Jys6gUXQ7KIPWsoKrNcdiMHrX6mgaSoKZvcI_jx74o1kmxOgbPbsXGGIqa1QirJcchTRfWiuzv2y4CVXSWA/w354-h636/Twin+Poems.jpg" width="354" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /> <p></p>JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-4841354841770818112021-09-01T23:33:00.002-04:002021-09-01T23:33:54.187-04:00Puppet Props - Cuckoo ClockI made this Black Forest style Cuckoo Clock for an Oktoberfest-themed puppet show.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFAq8OXlnW14fkwu6J5K0c8SSu1LODu9U-1ifiuqeTffzOF76GtT4eC6AcCPfPF-7EdMGchccludX_6Cyli3Xd0DJMf4IrIXvkg5W4SZIPU37DZK0P33fi9HeBoimeBlXnP4hcKg/s1600/PA090721.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFAq8OXlnW14fkwu6J5K0c8SSu1LODu9U-1ifiuqeTffzOF76GtT4eC6AcCPfPF-7EdMGchccludX_6Cyli3Xd0DJMf4IrIXvkg5W4SZIPU37DZK0P33fi9HeBoimeBlXnP4hcKg/s1600/PA090721.JPG" height="640" width="476" /></a></div>
The sticks at the bottom are part of the support system. I split a photo of the clock three times (into 8 equal parts of about 8.5 x 11 inches each) to make it about 22 x 34 inches. The parts were pasted onto foam-core board, and to counteract curling of the board, blank paper was pasted on the back side. The shape was cut out and the edges colored brown to hide the white color of the foam core.<br />
<br />
A double door 4.5 inches wide and high was cut into the area above the clock face. The hinge areas were reinforced with clear plastic packing tape. The cuts for the door were widened a bit to eliminate friction on the door edges. A puppet bird can push the doors open, and when the bird withdraws, the doors are pulled closed by a weighted string.<br />
<br />
Here are two views of the back side:<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDiWt9MGzjTuiXKZ8aaBWx9f7w4FiP0dGlvsrnFdog8bMSKLuRiiBusRNsztWY_5SF81jWbwYlH487-MA6wvNM_AUnhTd_whKSe_jXkfJ5xMAQGlx-syvw71uDw2U_u_14UFCocA/s1600/PA090722.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDiWt9MGzjTuiXKZ8aaBWx9f7w4FiP0dGlvsrnFdog8bMSKLuRiiBusRNsztWY_5SF81jWbwYlH487-MA6wvNM_AUnhTd_whKSe_jXkfJ5xMAQGlx-syvw71uDw2U_u_14UFCocA/s1600/PA090722.JPG" height="640" width="478" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEVh0n1__eWoNvKzmOhOIvhuOIgJEo0PrxpgFZpTZe-eTp2PKSKHjLEVwS6Lt1ww_QGqAeAL92KtA0wu5XZ0hYHI6kGM_5wHzxNaOc3AKO2HSelSep1X-O9ivJ2mJ2BVK1hOxdkA/s1600/PA090726.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEVh0n1__eWoNvKzmOhOIvhuOIgJEo0PrxpgFZpTZe-eTp2PKSKHjLEVwS6Lt1ww_QGqAeAL92KtA0wu5XZ0hYHI6kGM_5wHzxNaOc3AKO2HSelSep1X-O9ivJ2mJ2BVK1hOxdkA/s1600/PA090726.JPG" height="296" width="400" /></a></div>
<br />
Popsicle sticks were glued on the back to strengthen some narrow areas. Two wire hooks with attached wood sticks enable the clock to hang on the top rail of the puppet stage in front of the top curtain. The big sticks go down between the top curtain and the top script rail, preventing the clock from tipping forward, especially when a puppet bird thrusts its head through the door. (A script rail holds a row of four open three-ring binders across the 7-foot width of the stage.)<br />
<br />
The vertical narrow box between the two big sticks encloses the weights that pull the doors closed. This box and the foam-core ridges on either side of the two big sticks push the clock away from the top rail and the top curtain so that the top rail and curtain do not interfere with the rise and fall of the weights. More details on the door-closing mechanism next.<br />
<br />
The next views show the doors held open by a tissue box:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjM0G6-NzskQu1MHBwpfYm9rvcDEX4nyH_Uach3w7GPhBkPTXhibARLl6f7vBqe8mVCw1wQJmIbpIsboqWt8FsTdnEaecD6LB3vFHPEiGdyON6_vWizgQhXOk9RLLOXpTAbeAGhLg/s1600/PA090723.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjM0G6-NzskQu1MHBwpfYm9rvcDEX4nyH_Uach3w7GPhBkPTXhibARLl6f7vBqe8mVCw1wQJmIbpIsboqWt8FsTdnEaecD6LB3vFHPEiGdyON6_vWizgQhXOk9RLLOXpTAbeAGhLg/s1600/PA090723.JPG" height="297" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpp_7OvRg-WtKzUnsc0JDkpLRIQy3Ywfad4ic0J1Y7wJy-kHd1rE7YTIyMTt8I9TX-mKGHcxFANm0FO6_sdczvDZ1h-u5jay0TrX2UtfhCClXpkB0EHgTTcAH6Qm9yMnOaUASgUw/s1600/PA090724.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpp_7OvRg-WtKzUnsc0JDkpLRIQy3Ywfad4ic0J1Y7wJy-kHd1rE7YTIyMTt8I9TX-mKGHcxFANm0FO6_sdczvDZ1h-u5jay0TrX2UtfhCClXpkB0EHgTTcAH6Qm9yMnOaUASgUw/s1600/PA090724.JPG" height="298" width="400" /></a></div>
<br />
Each door has a wire taped to its back side, but extending on the outside about two inches below the door. A string attached to each wire passes through a grommet hole on one side of the "XII" of the clock face. These two strings are actually the ends of one loop of string from which the weights hang. Thus the weights pull equally on both doors, whether one is open or both.<br />
<br />
The next view shows a few other details:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAlcMW2KGQN0KF6GyhF4iBEnzI_10h5DKGNrsNweQwp1xFPOYjCRoxDYm-O8rypke1SCI7Lrv0aOy9-XZOUu668Tn93Moao3-I_AzlFGNQVkSvGAOwjvMpX6zQAxT5KZ6xmayklg/s1600/PA090725.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAlcMW2KGQN0KF6GyhF4iBEnzI_10h5DKGNrsNweQwp1xFPOYjCRoxDYm-O8rypke1SCI7Lrv0aOy9-XZOUu668Tn93Moao3-I_AzlFGNQVkSvGAOwjvMpX6zQAxT5KZ6xmayklg/s1600/PA090725.JPG" height="298" width="400" /></a></div>
You can see the string loop from the grommets going into the box that allow the weights to slide freely without pressure or friction from the stage curtain. You can also see the heavy wire pieces that anchor the top of one of the wire hooks that hang on the top rail of the puppet stage. The wire loop that passes through the foam core board is painted brown on the front side. The colored paper on the back of each door covers the wire that is taped onto the back of the door.<br />
<br />JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-77946435070110096002021-09-01T23:31:00.000-04:002021-09-01T23:31:48.627-04:00Automatic Garden Watering Systems<div>For those who might consider how they might reduce the work and worry of keeping their garden watered, I will show here, in words and photos, how our garden is automatically watered. I have installed three kinds of watering systems, and I will discuss the differences. One uses 'soaker' hoses, another drip hoses, and another is a modified drip system running from a rain barrel.
The soaker system starts at an outside faucet, with a pressure reducer, timer, and Y connectors:
<table style="WIDTH: auto">
<tbody>
<tr>
<td><a href="http://picasaweb.google.com/lh/photo/O-c0_DQimS3k8NimF5Lw9A?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNSTQr5F0Kq8mfjr7i-aLu5KpJ-ugjSSOQMQBy-UVLzyr1Ak2dSMMfMCEvcwimlvPVBQ0iFy2gPt_d7JGH7-BbPgaYjMvXC4hU-yvIqiiDWhWmiXmYEXqopk-f9sjZFEusr1vMJQ/s400/P6190668.JPG" /></a></td></tr>
<tr>
<td style="TEXT-ALIGN: right; FONT-FAMILY: arial, sans-serif; FONT-SIZE: 11px">From <a href="http://picasaweb.google.com/James.m.clark5/AutomaticGardenWateringSystems?feat=embedwebsite">Automatic Garden Watering Systems</a></td></tr></tbody></table>
The pressure reducer saves wear and tear on the system, and minimizes the flow if there is a breakage or leak.
The timer controls how often the water is turned on, when the timing cycle starts, and how long the water will be on each time that it is turned on. There is a manual mode to over-ride the set timing cycle, but if you turn the water on in manual mode and forget to turn the water off, it will tun off automatically after two hours. The timer used a 9 volt battery, which will last one season.
Two Y splitters provide two more outlets from the timer. The levers on these Y splitters are valves that can be used to shut off individual outlets when desired. Short sections of standard garden hose lead from each outlet to a soaker hose. In this case, one zig-zags south through the garden on the east side of the house, one winds westward on the north side of the house, and one goes northward under the lawn to the L-shaped fence garden. The underground part is regular garden hose,
The line on the north side of the house needs to cross the sidewark at the bottom of the front steps. So the soaker hose on one side connects to regular hose to cross the sidewark, and then back to soaker hose. The hose crossing the sidewalk is painted to blend in with the sidewalk color, and tucked close to the steps so that it is not a tripping hazard.
Installing hose underground is easier than you might think. You only need to split the ground open with a straight shovel -- no ditch-digging. Work the shovel down as deep as you can and rock it back and forth to open widen the crack. Make this crack as long as needed to reach your destination. Push the hose down into the crack as far as you can, using a scrap of one-inch lumber or an old broom handle or such. Stomp on each side of the crack to close it up. In a few days the lawn will heal and the path of the hose will be invisible. The next photo shows the texhnique with 1/4-inch drip hose, but it works with garden hose, too.
<table style="WIDTH: auto">
<tbody>
<tr>
<td><a href="http://picasaweb.google.com/lh/photo/e-I3cos9lZZiePy654E2mg?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjn0Yu47HvOICrtYqtq5CWgJyL4bsi9rMii7_AgWDWL_lPd63dpKrVk0uxjHiVDtjeGlbjdUve7iYpTGtQnF1kyqkPDFJJtA23MoyolPRPS8fpmHrPAc6UaInI0lu1fBq5X87fn5w/s400/P7300204.JPG" /></a></td></tr>
<tr>
<td style="TEXT-ALIGN: right; FONT-FAMILY: arial,sans-serif; FONT-SIZE: 11px">From <a href="http://picasaweb.google.com/James.m.clark5/AutomaticBirdBath?feat=embedwebsite">Automatic Bird Bath</a></td></tr></tbody></table>
The soaker hoses are made from recycled tires, and are porous, allowing water to slowly ooze out along the length of the hose. The soaker hoses, available in 25-ft and 50-ft lengths, can be strung in a sequence with a cap on the end of the last one.
The next photo shows where the underground hose (orange, at right) ends. It has gone under part of one garden, some lawn, and a peony, and surfaces here, at a cluster of four Y splitters, connecting to five soaker hoses. One curls around the peony, and the other four run in parallel the length of the fence garden: one outside the fence, one under the fence, and two in the wider strip inside the fence.
<table style="WIDTH: auto">
<tbody>
<tr>
<td><a href="http://picasaweb.google.com/lh/photo/cIuaYuTIBdkHWw3qQjauvw?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZXHBrenkNXAgHLHKN2xkp1W8pO7o2XBZ6xzgPM6pxDT00c04TTCczDnaN_bvbnZOADVbvVYUatgOGYYqjwxbKLAw2eWzKbGhLIo-FDvBSlJh-JOCIkw9I2bDeMmw3rhYiRDw-nQ/s400/P6190669.JPG" /></a></td></tr>
<tr>
<td style="TEXT-ALIGN: right; FONT-FAMILY: arial, sans-serif; FONT-SIZE: 11px">From <a href="http://picasaweb.google.com/James.m.clark5/AutomaticGardenWateringSystems?feat=embedwebsite">Automatic Garden Watering Systems</a></td></tr></tbody></table>
The drip system serves two different kinds of gardening: container gardening, and an herb garden in a raised bed. I'll compare them later. The drip system starts with a Y connector, a pressure reducer, and a timer inside the storage/shop area:
<table style="WIDTH: auto">
<tbody>
<tr>
<td><a href="http://picasaweb.google.com/lh/photo/thqV3rDAWkyotSyqGRUMMA?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFCdNXxltlDDs2ONnAoHJ0RVKXFDaZsvnjhH0Z2ysxM6dsWqimPUfol_xY5f1GAUAYd_PX8WOppAdujxbIMFtnz2S5fWEcRdDBil8oYK403SdkPcONBzC12JsRlXecU-K1RT9GMg/s400/P6210706.JPG" /></a></td></tr>
<tr>
<td style="TEXT-ALIGN: right; FONT-FAMILY: arial, sans-serif; FONT-SIZE: 11px">From <a href="http://picasaweb.google.com/James.m.clark5/AutomaticGardenWateringSystems?feat=embedwebsite">Automatic Garden Watering Systems</a></td></tr></tbody></table>
The Y connector provides an extra untimed outlet for filling a watering can for occasional spot watering or other uses. The pressure rducer is especially needed for the drip system, because its parts are not designed for high pressure. (The green hose on the left is used for filling the rain barrel in a dry spell.)
The hose from the bottom of the timer goes down and through the wall to the outside. First, it waters the herb garden - sandy soil in a raised bed for good drainage. Then it turns the corner of the house and climbs up the the rear deck to water flowers on the railing. Along the way, lines extend under the decorative stone to reach potted plants.
<table style="WIDTH: auto">
<tbody>
<tr>
<td><a href="http://picasaweb.google.com/lh/photo/NAmTqga4Z2bltJGP73bgKA?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWAs-zGdMBM9ulaPw8zUuLpbRRtdKss9-x6eRkKsDTVlHoyshM6JGnldubsMItTP17BE9ifDz_emhuZtz20yo8npcmWn2miFkw_TNoh3LgWEFzCkKJpdDzLUJhvrXTDE3p44kaxw/s400/P6210708.JPG" /></a></td></tr>
<tr>
<td style="TEXT-ALIGN: right; FONT-FAMILY: arial, sans-serif; FONT-SIZE: 11px">From <a href="http://picasaweb.google.com/James.m.clark5/AutomaticGardenWateringSystems?feat=embedwebsite">Automatic Garden Watering Systems</a></td></tr></tbody></table>
<p>The main line is a stiff black hose about the same size as regular garden hose, running behind the trellis behind the herb garden. (The trellis hides an air conditioning compressor and some garbage cans.) Here is a view behind the trellis:
</p>
<table style="WIDTH: auto">
<tbody>
<tr>
<td><a href="http://picasaweb.google.com/lh/photo/5V9eW_-4rVvtaxSo1jDBJw?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJg1XZK8tb-FiekZ9A5DoFgBvwwcCfwevi4KkLybXwa89K3X3C0IZd2pqJTkV9j7a_q_vjfF9u4aPDpSU7D2nHhE504_RcSVAqFAKfWR_OC1xI6zT7Y5-OcJj8ogTGtYwI_Z-9ww/s400/P6210707.JPG" /></a></td></tr>
<tr>
<td style="TEXT-ALIGN: right; FONT-FAMILY: arial, sans-serif; FONT-SIZE: 11px">From <a href="http://picasaweb.google.com/James.m.clark5/AutomaticGardenWateringSystems?feat=embedwebsite">Automatic Garden Watering Systems</a></td></tr></tbody></table>
<p>The main line hugs the wall on the left, and quarter-inch hoses are connected to the main line. A hole is punched in the main line, and a flow-control button is plugged into the hole. You can get buttons for different flow rates such as 0.5, 1, or 2 gallons per hour. For example, at 1 gal/hr, dripping for 4 minutes will deliver about 1 cup of water at a designated spot.</p>
<p>Using a T connector, I joined two buttons to one hose to burrow under the stones and then go through the lattice to the herb bed. After going through the lattice, another T connector divides the flow to reach two drip locations. This pattern is repeated several times along the length of the lattice and herb bed.</p></div>JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-24945619268288120852019-07-30T17:21:00.000-04:002019-07-30T18:35:54.368-04:00How to Make an Automatic Bird Bath<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<h4>
In a <a href="https://jamesmclark.blogspot.com/2005/06/automatic-birdbath.html" target="_blank">previous blog</a>, I briefly described my Automatic Bird Bath, and I will give more details here, especially how to make one.</h4>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVFPPSqCJtlX3hGgmZQIeWLM70mqI3RN0hPnr7sStlesBF6rBhdggJlZ2BtTjS5P3TsopJiICOSGGGq_0mXZBJBfqgIJZ9_V1_H6GAmZAdSpqtuiXg5053cGyan1cr7t4vzMP3kQ/s1600/P7180090.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1197" data-original-width="1600" height="149" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVFPPSqCJtlX3hGgmZQIeWLM70mqI3RN0hPnr7sStlesBF6rBhdggJlZ2BtTjS5P3TsopJiICOSGGGq_0mXZBJBfqgIJZ9_V1_H6GAmZAdSpqtuiXg5053cGyan1cr7t4vzMP3kQ/s200/P7180090.JPG" width="200" /> </a></div>
<h4>
Controlled by a timer, any debris accumulated during the day (fallen from trees or left by birds) is flushed out of the bowl of the bird bath at the end of the day. I recommend setting the time to late in the evening when it is highly unlikely that a bird will be using it. We don't want a bird to be suddenly and forcefully swept out while bathing!</h4>
<h4>
The force of the flushing operation will leave the bowl nearly empty; but overnight, the dripper will refill the bowl. During the day, the dripper will not only make a sound that advertises a source of water for the birds, but will also keep the bowl filled as the sun evaporates the water and as the birds splash some of the water out.</h4>
The next photo views the bird bath from the side, labeling some of the parts. We will detail the hardware parts later.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyVHTY-0PvrQ2-CFSvr0Q31ClcD8uWG6_xH_sbsdMp_xakDS3BHFRsENw46LNTytdN0w7c-qnW7T7AcMblVVWNKYxixlsoL42553RONvr3y3ET5xzm6-vLrWZFFXkX2BU9oOaCNA/s1600/P4270143.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1036" data-original-width="1600" height="257" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyVHTY-0PvrQ2-CFSvr0Q31ClcD8uWG6_xH_sbsdMp_xakDS3BHFRsENw46LNTytdN0w7c-qnW7T7AcMblVVWNKYxixlsoL42553RONvr3y3ET5xzm6-vLrWZFFXkX2BU9oOaCNA/s400/P4270143.JPG" width="400" /></a></div>
I have supported the parts with a "shepherd's crook" pole, the kind typically used to support a hanging flower pot. But the bent "crook" is not used, so any sturdy pole will do.<br />
<br />
A bent <b>metal strap </b>is fastened to the pole with U-hooks <b>U1 </b>and <b>U2</b>, and to the hose with U-hooks <b>U3 </b>and <b>U4</b>. The hose is a sturdy watering hose, The usual male connector at the end of the hose is removed by cutting the hose with a hack-saw. Clamp <b>C </b>flattens the end of the hose so that the water comes out as a flat, fan-shaped spray. Before you adjust the angle and position of the bent metal strap, you should experiment with this fan-shaped spray to find the best angle and position of the hose to sweep out the bowl, tossing some debris into the bowl as part of the test.<br />
<br />
The <b>dripper D</b> is just quarter-inch hose, the kind used for drip watering. The drip hose is fastened to the pole with twist-ties or plastic tape. The <b>valve V </b>in the photo is used to adjust the drip rate. You can buy the valve from places that sell drip watering parts. The part of the drip hose that arches from the pole over the center of the bird bath needs to be stiffened. I wrapped wire around a wood dowel to make a spiral, which I slipped over the drip hose. One end of the same wire that was not wrapped around the dowel was wrapped around the pole to anchor the drip hose. The drip hose should be high enough to give large birds enough room for splashing. Then bend the stiffened part of the drip hose so that it will drip near the center of the bowl.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi97U4EyCE8zbAyazJVJddD5385JLBcNXAATWbrIPaGCCliajHVG3tThe2yY_uhRyvTt-MRgWr86Gi7C35s4XGW4_AaE-TJuzIlMyuRyezDzcnIguLsR4-oYv9sOqsOoibjc1XC3w/s1600/bb_hw.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="300" data-original-width="407" height="235" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi97U4EyCE8zbAyazJVJddD5385JLBcNXAATWbrIPaGCCliajHVG3tThe2yY_uhRyvTt-MRgWr86Gi7C35s4XGW4_AaE-TJuzIlMyuRyezDzcnIguLsR4-oYv9sOqsOoibjc1XC3w/s320/bb_hw.jpg" width="320" /></a></div>
<br />
The <b>hardware parts </b>are shown in the next diagram. I bought one-inch wide steel material as thick as a typical steel hinge at a hardware store and cut it to the lengths indicated here. I bought the U-bolts and small straps used with them as-is at the hardware store. The U-bolts must be large enough to fit around the watering hose, and this will generally be large enough to fit around the pole.<br />
<br />
The <b>long strap </b>must be bent on an angle at its center. The angle is needed so that the hose can pass by one side of the pole. To assure yourself of the correct angle, make a 'dummy' strap of cardboard, then hold the hose at the desired angle alongside of the pole, and bend the 'dummy' strap so that one half is parallel to the pole and the other half is parallel to the hose. Note the angle of the bend (about 50 degrees) and how far it is bent (about 80 degrees). <br />
<br />
Use a <b>sturdy vise </b>mounted on a work bench to bend the strap. Mark the location and angle of the bend, and clamp the strap in the vise with the bend line at the edge of the vice jaws. Then hit the strap near the bend line with a hammer until it is bent the right amount by your best estimate. You can adjust this later.<br />
<br />
The <b>short strap </b>can be bent by a similar method. I recommend drilling the holes after bending, as this will make it easier make the holes aligned. Here it is more important that the bend is centered, so that the two ends will come close together. So reversing the strap in the vice after partly bending it can help. Also, because the strap will wrap around a partly flattened hose, we don't want the bend the strap too sharply. Clamping a big nail or small bolt alongside the strap near the edge of the clamp will promote a 'softer' bend (more like a U, less like a V). Try how it fits over the end of the hose, flattening the hose, but not so much that water flow is shut off. Drill a hole through both ends of the strap large enough for a bolt to go through the holes. The short strap should not be bent too much; the two sides should be about 1/2 inch apart, and it should need the bolt and a nut to pull the strap a little more to make the two sides of the strap parallel on either side of the flattened hose.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS2hjFdUKIzxQuVcr9pH1PHPRjJW38zEIAS9q9fQSuu3u60MtMfusVyh49eb9x6WAofwLApITBaK8c9t5zBUUEDKKOaX7XTQJB0IxT-ywlgqpZamXA_rX-2v3huj6qxjo4xDeoGg/s1600/dsc_213c.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="275" data-original-width="397" height="221" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS2hjFdUKIzxQuVcr9pH1PHPRjJW38zEIAS9q9fQSuu3u60MtMfusVyh49eb9x6WAofwLApITBaK8c9t5zBUUEDKKOaX7XTQJB0IxT-ywlgqpZamXA_rX-2v3huj6qxjo4xDeoGg/s320/dsc_213c.jpg" width="320" /></a></div>
<br />
Here are the controls. A Y-connector divides the water supply for the flushing function and for the dripper. <br />
<br />
The flushing is controlled by a water timer to turn on at 10 pm so no birds will be flushed out of the bird bath. Three seconds is sufficient to flush the bird bath, by most water timers cannot be programmed for intervals that short, so it is set for the shortest possible interval (one minute). When on, the water flows at full pressure.<br />
<br />
Drip systems are not designed to operate at full water pressure. So on the right side of the Y-connector, we have a pressure reducer and an adapter that adapts the 3/4 inch hose hardware to the 1/4 inch drip hose. You can also insert a flow-control button in the 1/4 inch drip hose line. These can be bought where drip system parts are sold.<br />
<br />
My bird feeders and bird bath are at the back edge of my back lawn, near scrubs and trees, an ideal location because birds want a place that feels safe from predators, at the boundary of a <b>place to hide</b> in foliage (but close enough to look for an opportunity to visit the feeders or bath) and an <b>open area to flee </b>if needed. Because it is near trees, the bath tends to collect debris from the trees; and because the water supply and controls are near the house, the flush and drip hoses must cross the lawn.<br />
<br />
My method of burying a hose under a lawn is fast and simple. I thrust a flat shovel as deep as I can into the grass, and tilt it forward and back to wedge open a narrow trench, repeating this along a mostly straight line. Then I push the hose down into the trench as far as I can, using a broom handle or long scrap of 3/4 inch lumber. Then stepping on either side of the trench pushes the grass back into place, closing the crevice. Within a week, all evidence of the crevice will disappear. Winter freezing is not a problem when the water is turned off, because the hose is soft, not rigid like metal pipes.<br />
<div style="text-align: center;">
_____________________</div>
<br />
I have acquired 45 patents during my 43-year career, all of which are expired by now. But in my retirement, I am too lazy to file for a patent for my automatic bird bath. I know how much work it takes, even with the help of a patent lawyer. I have preferred to put it in the "public domain" for any one to use.<br />
<br />
Not everyone has the tools and muscle to make the straps. But if you are willing to make these or more parts of my design for others, leave me a comment with your contact information, and I will publish it here. But I won't get involved with any financial arrangements.<br />
<br />
One reader of this blog makes and sells his own patented design, which automatically cleans and refills, but does not include a dripper. See <a href="http://selfcleaningbirdbath.com/">http://selfcleaningbirdbath.com/</a> .<br />
<br />
<br />JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-18900698447382936432019-02-19T11:52:00.000-05:002019-02-19T11:52:14.023-05:00The Ingraham CircusI was watching the <i><b>Ingraham Angle</b></i> last night, and in the introductory monologue, it was indicated that "transgender women" in sports would be discussed.<br />
<br />
Now it may seem silly, but I feel that a review of basic English grammar is needed before I proceed.<br />
<br />
English has nouns and adjectives. "Women" is a noun. "Transgender" is an adjective. "Transgender Women" are women that are transgender. People that are described as transgender are invariably confused about their gender. So "transgender women" means gender-confused women. In normal English, that is.<br />
<br />
But when Laura Ingraham said that transgender women were a trouble in women's sports, I suspected that something was wrong, because I knew it was the transgender, that is, gender-confused <b>men</b> that were making trouble in women's sports. It soon became apparent that Laura was speaking in Gender-confused English.<br />
<br />
In Gender-confused English, the word 'transgender' is a special adjective that triggers novel rules of grammar never seen before in the long history of the English language. It has the power to reverse the gender of any noun to which it is attached. Moreover, it has the power to not only modify the grammar of sentences, but even paragraphs, because the gender of all pronouns that refer to such a gender-reversed noun must likewise be reversed. In short, when you speak Gender-confused English, you sound like you are pretending to be as confused as the transgender people you are talking about.<br />
<br />
The show became more interesting, astounding I thought, when Laura began to interview Martina Navratilova on the subject. Martina was speaking normal English while Laura spoke in Gender-confused English, one saying "men" and the other saying "transgender women" to refer to the same trouble-makers. They must have understood each other in spite of this, because they acted like they heartily agreed. It was quite a circus, more entertaining than the traditional bearded lady.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-73697214525273944842019-02-14T21:29:00.000-05:002019-02-14T21:33:23.592-05:00How do you write "Jim Clark" in Chinese?I have a funny story about a Chinese friend that I knew where I worked before I retired. I knew that Chinese writing is "ideographic", meaning that the symbols represent ideas, not sounds. For example, the symbols for 'sun' and 'moon' are combined to make the word for 'light'. So one day I asked him how do they write a name like "Jim Clark" in Chinese, because who knows what 'Jim' and 'Clark' mean?<br />
<br />
He said that they find Chinese words that sound like the name, and combine them. He thought for a minute, and thought of Chinese words that sounded to me like 'jin', 'kar', and 'lok'. He told me what the words meant, but I forget, except that one meant a small dish used for offerings to idols. He wrote it on the blackboard, and I asked him to teach me how to write it.<br />
<br />
He told me to first see each stroke in my head, then write it with a quick, chopping motion. I memorized it, practiced it, and wrote it on a small slip of paper so that I would not forget it.<br />
<br />
About a week later, a couple of engineers were in my office, and we started talking about languages. I told them that I knew a few words of German, Greek, and Latin, and that I could write my name in Chinese. They said that they could believe me about the German, Greek, and Latin, but about the Chinese, I was a bragging liar. <br />
<br />
I protested, "no, I really can". I wrote it on the blackboard with quick, confident strokes. They still did not believe me.<br />
<br />
They said, "It LOOKS like Chinese, but it is fake. We can prove that you are a liar. We will go get an expert." They left the room, and a minute later came back with their 'expert'.<br />
<br />
As they entered, I saw that the 'expert' was my Chinese friend. He gave me a quick smile when they were not looking.<br />
<br />
"Don't say one word", they warned me. Then pointing to what I had written on the blackboard, they asked the expert, "What does that say?"<br />
<br />
He answered, "It means Jim Clark", and their mouths dropped open. Then my Chinese friend and I laughed, and we explained how he had taught me a week ago.<br />
<br />
Unfortunately, I have lost that small slip of paper with my name written in Chinese.<br />
<br />
Does someone know Chinese well enough that they can tell what "Jim Clark" looks like, as my friend probably told me?<br />
<div>
<br /></div>
JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-63809247437751262452019-01-04T02:22:00.000-05:002019-01-04T03:00:31.752-05:00The Geometry of the Times Square BallAfter watching the traditional New Year's Day ball drop in New York City (on television; I wouldn't stand in the rain for hours even if I were capable of doing so), I became curious about the construction of the ball, and did some research on the Internet, finding <a href="https://www.azocleantech.com/article.aspx?ArticleID=311">https://www.azocleantech.com/article.aspx?ArticleID=311</a> and other descriptions. <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCSBwBG8tYh2aE4xOocS0dB0-eIb5IxBM0xAZVuQM_Y0_04C7IH-LpT15SMOHMNopSPwlH6U1L1Sp_axN7x82vDtIkZITcQ07gI_hTQYc_YLbFcILascTKPVM9pCNByakqSlHupw/s1600/Times_Square_Ball_2010_c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="621" data-original-width="614" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCSBwBG8tYh2aE4xOocS0dB0-eIb5IxBM0xAZVuQM_Y0_04C7IH-LpT15SMOHMNopSPwlH6U1L1Sp_axN7x82vDtIkZITcQ07gI_hTQYc_YLbFcILascTKPVM9pCNByakqSlHupw/s320/Times_Square_Ball_2010_c.jpg" width="316" /></a> </div>
<div class="separator" style="clear: both; text-align: center;">
<span style="font-size: x-small;">[Images derived from Times_Square_Ball_2010.jpg by Susan Serra, CKD from Long Island, USA - 222 (2), CC BY-SA 2.0, https://commons.wikimedia.org/w/index.php?curid=23313305]</span></div>
<br />
It is described as having "a diameter of 12 feet and weighing 11,575 pounds" and is "covered with 2,688 Waterford Crystals", also called "triangular crystal panels". It has a total of "32,256 Philips Luxeon Rebel energy-saving LEDs", and from this I figured that there are 12 LEDs per triangular crystal panel.<br />
<br />
There are 672 "LED units", each having 48 LED lights, 12 each of "red, blue, green and white colors". 672 times 48 is 32256, confirming the total LEDs. We can also conclude that each "LED unit" has 4 triangular crystal panels, because there are 12 LEDs per crystal panel.<br />
<br />
In the photo of the Times Square Ball, we can see triangles framed by the black aluminum struts; we will call these 'frame' triangles. Each frame triangle is divided into four 'color' triangles which apparently have independently selectable colors. And if you look carefully, each color triangle is divided into four 'tiny' triangles. So which of these triangle sizes is a "crystal panel"?<br />
<br />
Geodesic spheres are nearly always based on the geometry of an icosahedron, generally by dividing its triangular faces into smaller triangles. There are 20 triangles in a icosahedron; 12 vertices, and 30 edges, and 5 edges meet at each vertex. A typical geodesic sphere is full of triangles, and in most places, a cluster of six triangles around a vertex form a hexagon. But in rare places, a cluster of five triangles around a vertex will form a pentagon.<br />
<br />
Finding these pentagons is the trick to discovering the icosahedron from which the geodesic sphere was formed, because the centers of these pentagons are the vertices of the icosahedron. You can impress your friends by 'counting' the number of triangles in the complete 'sphere' that you see (even though it is not actually complete or not all visible) in two or three seconds, as follows: Find two pentagons and along the line that connects their centers, count the number of edges of the small triangles. Square this number and multiply by 20. That's it. If you counted 10 edges, the answer is 10x10x20=2000. In a few seconds, you have 'counted' 2000 triangles!<br />
<br />
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiDc3RhEYh-WWHQ3i7_VZiDdo5zxD_YMVpTrpVYdcpdIE6j-_rLyBHJ2REwxluxdcs5IWVxHvYMZcaNVQnUQpSe4-9-qe73F0qjTYAE4LUbea1jqjNTfkoQvhrgtekncUW_a34uw/s1600/Times_Square_Ball_2010_c36.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="621" data-original-width="614" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiDc3RhEYh-WWHQ3i7_VZiDdo5zxD_YMVpTrpVYdcpdIE6j-_rLyBHJ2REwxluxdcs5IWVxHvYMZcaNVQnUQpSe4-9-qe73F0qjTYAE4LUbea1jqjNTfkoQvhrgtekncUW_a34uw/s200/Times_Square_Ball_2010_c36.jpg" width="196" /></a>In the photo at right, we have located the centers of three pentagons, and thus one triangle of the icosahedron. Three struts make one side of this triangle of the icosahedron, making 3x3=9 frame triangles in one triangle of the icosahedron, or 9x20=180 frame triangles in the complete geodesic sphere, not enough for "672 LED units". But there are four color triangles in each frame triangle, so there are 4x180=720 color triangles in the complete geodesic sphere, 48 more than the "672 LED units". But there must be two holes in the sphere to allow it to slide down the supporting pole, so we can guess that each hole must account for 24 color triangles, or 24 "LED units", or 24/4=6 frame triangles. A hexagon of 6 frame triangles is marked on the next photo below, which looks plausibly the right size for a hole. A study of the symmetries of the icosahedron confirms that such a hexagon is matched by one on the opposite side of the sphere.</div>
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6ThSYnV8NJm8ukiaV9ewTA5_h7O9zgRBFRVKrCNUyPoRAnmf6797uW8FAyxc5AfjFMBBK_99Q2O2Uc4VraN0VXRuX2YclkJgFXg5187jSU8WAZ4A5-kCvfFdVwctAErD5LmEgOA/s1600/Times_Square_Ball_2010_c24.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="621" data-original-width="614" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6ThSYnV8NJm8ukiaV9ewTA5_h7O9zgRBFRVKrCNUyPoRAnmf6797uW8FAyxc5AfjFMBBK_99Q2O2Uc4VraN0VXRuX2YclkJgFXg5187jSU8WAZ4A5-kCvfFdVwctAErD5LmEgOA/s200/Times_Square_Ball_2010_c24.jpg" width="196" /></a><br />
So we conclude that each color triangle corresponds to an LED unit, which has 48 LED lights. And each tiny triangle must correspond to a Waterford crystal panel, which has 12 LED lights, 3 LEDs of each color, which can be neatly arranged in a triangle. I have seen a number of products using LEDs which embed LEDs in a plastic sheet to distribute the light over the area; so I guess that LEDs are similarly embedded in the Waterford Crystals.<br />
<br />
We have been ignoring one small but interesting detail. When a flat triangle of an icosahedron is divided into smaller triangles (144 Waterford Crystals in this case) by dividing the edge length by an integer value (12 in this case), the big triangle remains flat. What is actually done is that the smaller triangles are made a tiny bit larger; making the big triangle bulge out just enough so that all the triangle corners (vertices) lie perfectly on a spherical surface; which is how geodesic spheres look almost like real spheres. The calculation of this adjustment involves trigonometry; need I say more?<br />
<div>
<br /></div>
JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-45388874477084511412018-06-01T19:17:00.000-04:002018-06-01T19:33:27.917-04:00Trellis Project<br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The Situation</span></h4>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgex8yerMx-HgwQTP8aGG7Figa56m51mZpaGCDbr62mwQzA8GK7b-jR3JKYiIoO7SpWDuEBolRX_SV_MRhHkTnD0FTBHHjBVgBraegAx4oT1ox0nnfaopiT8MCGSmLFOmrq3bcnwQ/s1600/aP7060010.JPG" imageanchor="1" style="clear: right; display: inline !important; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="297" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgex8yerMx-HgwQTP8aGG7Figa56m51mZpaGCDbr62mwQzA8GK7b-jR3JKYiIoO7SpWDuEBolRX_SV_MRhHkTnD0FTBHHjBVgBraegAx4oT1ox0nnfaopiT8MCGSmLFOmrq3bcnwQ/s400/aP7060010.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">When a former owner of my house decided to add an extension at the back, he decided to minimize the cost by using a corrugated plastic material for the side wall of the unfinished space below the new master bedroom. Over the years, this material became grimy-looking, which became more evident when new siding was put on the house.</span><br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The Plan</span></h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">I didn't want to paint this wall, because the material is translucent, and allows daylight to illuminate the storage and shop area inside. Instead, I decided to hide the ugly wall and the air-conditioner compressor behind a trellis. Garbage cans could also be hidden behind the left side of the trellis. This was also an opportunity to make a raised bed for an herb garden. The trellis would rest on the back edge of the raised bed. Clematis could also be planted in the raised bed and allowed to climb on the trellis. Hinged 'gates' at either end of the trellis would allow access to the garbage cans and to the AC compressor. (The white space at the bottom right of the diagram represents the neighbor's fence.)</span><br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVblcRiYfWerKKaP8cEH0405M6UK2KFSdBM83drpl6ypDzOKp06MepZ4fhiDUdezeQzA-zjo4Raql4tphOpxOaxw2G1m-fXXq3MTlOCdXmMAqigVDvcZk3A7YfPCSNq7IluTrWLA/s1600/bTrellis-Plan.BMP.GIF.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="392" data-original-width="817" height="305" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVblcRiYfWerKKaP8cEH0405M6UK2KFSdBM83drpl6ypDzOKp06MepZ4fhiDUdezeQzA-zjo4Raql4tphOpxOaxw2G1m-fXXq3MTlOCdXmMAqigVDvcZk3A7YfPCSNq7IluTrWLA/s640/bTrellis-Plan.BMP.GIF.jpg" width="640" /></a></div>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;"><br /></span>
<br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;"><br /></span></h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Notice that the gates at either end of the trellis are co-linear with the angled ends of the raised bed, both at 45-degree angles. (The angle of the lawn edge is parallel to this angle on the right side.) The trellis has five panels: two gates, two wide panels, and one narrow center panel.</span><br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Phase One</span></h4>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE3590ZJILhEhSv-MWCF7_pn-b521q62eKZvtwrfaTnFodaF0UqWTGhCzi-tAdc_rHi-sqa7YhVzHJ4lOLgbmlfiobPSy23DGyHzis5oz4rP2_atC8FtEKRD_3PUFANEcyQIzt3A/s1600/cP7040286.JPG" imageanchor="1" style="clear: right; display: inline !important; float: right; font-family: Georgia, 'Times New Roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE3590ZJILhEhSv-MWCF7_pn-b521q62eKZvtwrfaTnFodaF0UqWTGhCzi-tAdc_rHi-sqa7YhVzHJ4lOLgbmlfiobPSy23DGyHzis5oz4rP2_atC8FtEKRD_3PUFANEcyQIzt3A/s400/cP7040286.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The first phase was to re-locate the step-stones further away from the house and to re-shape the lawn edge to make two 45-degree turns instead of one 90-degree turn. The white stones were washed, and new weed-stop fabric was installed under the white stones and step-stones.</span><br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Phase Two</span></h4>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRE2LCj1lLuf6AdEM1g6OmSEZ4NASSybAy-LVi5nxxckEP7v6wKPrInYj8sCHyVEfxxSp9WCAA5cRAt1bdk5MWFHPEQGu-Gg9crVtL0ZKyyH8B0qFAr6oAtJWWwx5LD0DyLnW7jA/s1600/dP7160343.JPG" imageanchor="1" style="clear: right; display: inline !important; float: right; font-family: Georgia, 'Times New Roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRE2LCj1lLuf6AdEM1g6OmSEZ4NASSybAy-LVi5nxxckEP7v6wKPrInYj8sCHyVEfxxSp9WCAA5cRAt1bdk5MWFHPEQGu-Gg9crVtL0ZKyyH8B0qFAr6oAtJWWwx5LD0DyLnW7jA/s400/dP7160343.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The second phase was to build the raised bed for the herb garden, filling the bed (including two feet deep below ground level) with good loam-rich soil mixed with plenty of sand for good drainage.</span><br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Phase Three</span></h4>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5IE41VxA1rQGlMpe6a3Qdhij0uM6DoJvJCdS1dkRPgdpetZeoYcYm2wmCRe1zJX4Vb_ECiaF7fFDvsVa0skuFDO7el08Q1mV9dgsBLyCchE2qUH8OrzfBJhq9Xq1kC_4KQWVGBA/s1600/eP7270396.JPG" imageanchor="1" style="clear: right; display: inline !important; float: right; font-family: Georgia, 'Times New Roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5IE41VxA1rQGlMpe6a3Qdhij0uM6DoJvJCdS1dkRPgdpetZeoYcYm2wmCRe1zJX4Vb_ECiaF7fFDvsVa0skuFDO7el08Q1mV9dgsBLyCchE2qUH8OrzfBJhq9Xq1kC_4KQWVGBA/s400/eP7270396.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The last phase was to build the trellis, fastened</span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;"> to the back edge of the raised bed, and kept from tipping over by braces fastened to the bottom of the siding.. Notice that the holes in the trellis are larger at the top and sides. </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Next, </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">we will describe this phase in more detail.</span><br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Pre-assembly</span></h4>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzuhqhPxkChUiCmZHgVUlHIkAgi1zfDWjGs3onhzlqlfuDrZm_g6zphCKU0fQQPp0OrCOhCvaPtpdyfnJarS99ICYS62GNr0WlaEiWIrdCdYkC9QadEcMFgWgSPEMdwSPplV5QPg/s1600/fP7240390.JPG" imageanchor="1" style="clear: right; display: inline !important; float: right; font-family: Georgia, 'Times New Roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzuhqhPxkChUiCmZHgVUlHIkAgi1zfDWjGs3onhzlqlfuDrZm_g6zphCKU0fQQPp0OrCOhCvaPtpdyfnJarS99ICYS62GNr0WlaEiWIrdCdYkC9QadEcMFgWgSPEMdwSPplV5QPg/s400/fP7240390.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The frames of the various panels were pre-assembled from 2-by-3-inch lumber and painted before </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">the</span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;"> </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">final assembly. There is no </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">pre-assembled frame for the narrow center panel because it is just the space between the two wide panels. (It only needs top and bottom frame pieces.)</span><br />
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;"><br /></span>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAWqlcWN8JZZKp9X-JWM5v51FNFDqfPZB1B61s6o0uxrKKR2UKKtAX7nlqSwPMWgUR6RovvqUgEAmPWKbcaCZBpFBDjeU681c293aAxkWbJnIccJ0_3FVsl7wo8xrZKIGWvfIZOQ/s1600/gP7260394.JPG" imageanchor="1" style="clear: right; float: right; font-family: Georgia, 'Times New Roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAWqlcWN8JZZKp9X-JWM5v51FNFDqfPZB1B61s6o0uxrKKR2UKKtAX7nlqSwPMWgUR6RovvqUgEAmPWKbcaCZBpFBDjeU681c293aAxkWbJnIccJ0_3FVsl7wo8xrZKIGWvfIZOQ/s400/gP7260394.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">After painting, the vinyl channel strips were screwed onto the wood frames, holding the vinyl trellis panels in place. The channels are supposed to allow for the expansion and contraction of </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">the vinyl trellis panels due to temperature changes. But adjusting the channel positions is tricky: Where is the current temperature relative to the minimum and maximum temperatures?</span><br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Tip-over Bracing</span></h4>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPbS_jg6o8xp0Qeh_74VkqoM85bwgs8lobkrG0jTRFbICJvLP6p3fr3R_4xgeB-txeelNFsWl7RqaeUAsv6OnuURFxgdNXvvdOqUGvffXljjjYtvQhBRowugjC5kHZVV9aywvgYA/s1600/hP7260395.JPG" imageanchor="1" style="clear: right; float: right; font-family: Georgia, 'Times New Roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPbS_jg6o8xp0Qeh_74VkqoM85bwgs8lobkrG0jTRFbICJvLP6p3fr3R_4xgeB-txeelNFsWl7RqaeUAsv6OnuURFxgdNXvvdOqUGvffXljjjYtvQhBRowugjC5kHZVV9aywvgYA/s400/hP7260395.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The trellis is </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">kept from tipping over by braces (made of 3/4-by-2-inch wood) fastened to the top of the trellis and the bottom of the siding on the house, as shown here.</span><br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The Center Panel</span></h4>
<div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCeSrXQx7uVfOJQ_tqelIpvzyVNxfaeln1h0pVZqqSotHCl5Wa38MNLpQg61HKmRdqm0iNEpQ6ga7Tnb9BHNyfSt_9-ZWjH_d0Z6F-3yOtsGrI2dn0RUbIMEbRsLDKFnDwV3yenQ/s1600/iP7280406.JPG" imageanchor="1" style="clear: right; display: inline !important; float: right; font-family: georgia, 'times new roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCeSrXQx7uVfOJQ_tqelIpvzyVNxfaeln1h0pVZqqSotHCl5Wa38MNLpQg61HKmRdqm0iNEpQ6ga7Tnb9BHNyfSt_9-ZWjH_d0Z6F-3yOtsGrI2dn0RUbIMEbRsLDKFnDwV3yenQ/s400/iP7280406.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The center panel only needs top, middle, and bottom horizontal frame pieces, because it shares the vertical pieces of the wide panels on its left and right. These horizontal pieces are fastened on the back side by metal straps with built-in 'nails'.</span></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCeSrXQx7uVfOJQ_tqelIpvzyVNxfaeln1h0pVZqqSotHCl5Wa38MNLpQg61HKmRdqm0iNEpQ6ga7Tnb9BHNyfSt_9-ZWjH_d0Z6F-3yOtsGrI2dn0RUbIMEbRsLDKFnDwV3yenQ/s1600/iP7280406.JPG" imageanchor="1" style="clear: right; float: right; font-family: Georgia, 'Times New Roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><br /></a>
<br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The Gate Hinges</span></h4>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhx8jDEIFc0wSg55KJXORBtsV_E9lBTYSst9SECLUBCvcHspnuAjEIJZhHjM6B7dgwdbUvseBjRtK5cwmFfrhZDHI4_DhTMkabxA87ab0c28q0tQyHFwHEjGL2iEJSy_XUeJQht-g/s1600/jP7300408.JPG" imageanchor="1" style="clear: right; display: inline !important; float: right; font-family: georgia, 'times new roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhx8jDEIFc0wSg55KJXORBtsV_E9lBTYSst9SECLUBCvcHspnuAjEIJZhHjM6B7dgwdbUvseBjRtK5cwmFfrhZDHI4_DhTMkabxA87ab0c28q0tQyHFwHEjGL2iEJSy_XUeJQht-g/s400/jP7300408.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Each gate is allowed to turn inward by 45 degrees by rip-cutting a 2-by-3-inch piece of lumber on a diagonal, making two 22.5-degree wedges, and adding a wedge to the hinge side of each frame. This photo also shows the ends of two channel pieces, and the strap fastening one end of a brace.</span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjEwUtsq8ZAn_mmnA1aAzdC-ImX0d_JHia0mTeY6a1v3yQhvAeTc5HO19s7PaQunJEyofQIi4etEJSSiIwYFTiqNlqNyoo4fE1-tl3W-IHxx6ujawkjVfm97R8dHEZzePTdCQqsQ/s1600/kP7280402.JPG" imageanchor="1" style="clear: right; float: right; font-family: georgia, 'times new roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjEwUtsq8ZAn_mmnA1aAzdC-ImX0d_JHia0mTeY6a1v3yQhvAeTc5HO19s7PaQunJEyofQIi4etEJSSiIwYFTiqNlqNyoo4fE1-tl3W-IHxx6ujawkjVfm97R8dHEZzePTdCQqsQ/s400/kP7280402.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Each strap hinge is positioned to allow the gate to swing open all the way (180+45 degrees). The straps were too long, so each strap was cut shorter and a new beveled hole added.</span><br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Square-angle Bracing</span></h4>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoorMRcqMJ3cvtOCFVu62_0fZ9ESXfNWlZrqO-hCv11MbghoCYsEzVorQl1a1AFMOz7vMVevTBfz4hJFt0D4s6rZv5TwQrm2Bxj2Ni4zed2TPxgeMjinsbkGuJaFxZsK9PbwOeOw/s1600/lP7280405.JPG" imageanchor="1" style="clear: right; float: right; font-family: georgia, 'times new roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoorMRcqMJ3cvtOCFVu62_0fZ9ESXfNWlZrqO-hCv11MbghoCYsEzVorQl1a1AFMOz7vMVevTBfz4hJFt0D4s6rZv5TwQrm2Bxj2Ni4zed2TPxgeMjinsbkGuJaFxZsK9PbwOeOw/s400/lP7280405.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">To keep each rectangular panel 'square', that is, with square corners, heavy wires were installed diagonally, anchored by eye-screws, to pull opposite corners toward each other.</span><br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGDMbyabKURv7Ga1vlwQmejsnmyTQ1n4MJwz0t92nLrucpFyGwIWXBrnFADY17BVRyNQ5NIilPoS5zOkaGiWDtVAb9tVCBAESH15VjBGOsrK4TXf-XrXeLxK5w6sM1DcB9DbCYxQ/s1600/mP7280404.JPG" imageanchor="1" style="clear: right; display: inline !important; float: right; font-family: georgia, 'times new roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGDMbyabKURv7Ga1vlwQmejsnmyTQ1n4MJwz0t92nLrucpFyGwIWXBrnFADY17BVRyNQ5NIilPoS5zOkaGiWDtVAb9tVCBAESH15VjBGOsrK4TXf-XrXeLxK5w6sM1DcB9DbCYxQ/s400/mP7280404.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;"><br /></span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Since each gate is supported only on the hinge side, only one diagonal wire was installed, to keep the outer edge from sagging.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;"><br /></span>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCOHFZOzHuS5u5_yERg7udpRQzX1mHoEpfW5emV6wyH5iP5alEav0IqJs_HGdANJcQL14i2bSDBNJt3nnqzhNmKBkx0E2wKp0ydUnNw7H7LBjVV29kmLLb5F9r_36XsM9tAze-KA/s1600/tension+adjuster.jpg" imageanchor="1" style="clear: right; display: inline !important; float: right; font-family: georgia, 'times new roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="90" data-original-width="498" height="57" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCOHFZOzHuS5u5_yERg7udpRQzX1mHoEpfW5emV6wyH5iP5alEav0IqJs_HGdANJcQL14i2bSDBNJt3nnqzhNmKBkx0E2wKp0ydUnNw7H7LBjVV29kmLLb5F9r_36XsM9tAze-KA/s320/tension+adjuster.jpg" width="320" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The tension of the bracing wires will be more easily adjusted by using a tension adjuster like that shown here. Left- and right-handed threads enable turning of the joining part to change the tension without turning either end of the device.</span><br />
<h4>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Gate Latches</span></h4>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7EXrotQwftz_bak8BjXjKpCYkFDAf78qP-vToZ9OX0iiDcJwmdcPiIt_IbVnRCGZMhsdfX65B44-sOC0kI3m6EUF9MdPkgxdDZZGG3DRcks-o7BvxLEa2anV38tBWmuZNb17KWw/s1600/nP7300410.JPG" imageanchor="1" style="clear: right; float: right; font-family: georgia, 'times new roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="885" data-original-width="1182" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7EXrotQwftz_bak8BjXjKpCYkFDAf78qP-vToZ9OX0iiDcJwmdcPiIt_IbVnRCGZMhsdfX65B44-sOC0kI3m6EUF9MdPkgxdDZZGG3DRcks-o7BvxLEa2anV38tBWmuZNb17KWw/s400/nP7300410.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Each gate is held closed by a latch-bar, seen here at the top of the gate. Lifting the end of the latch bar releases the gate. The latch bars are made of the same material as the bracing bars.</span><br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ6_gKfSJzmRAaqscgZvD6Cxc9jpAGZE4vD3FVyc8vVveL9NBhPqKAEFUg9P-MIgE_PsJzEHuAm9gU9244Cno81LBG0bAwy_VgeGT9oPh90EhEY-r2wHcXdkxVjANAWAR6-6Y0iw/s1600/oP7310414.JPG" imageanchor="1" style="clear: right; float: right; font-family: georgia, 'times new roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ6_gKfSJzmRAaqscgZvD6Cxc9jpAGZE4vD3FVyc8vVveL9NBhPqKAEFUg9P-MIgE_PsJzEHuAm9gU9244Cno81LBG0bAwy_VgeGT9oPh90EhEY-r2wHcXdkxVjANAWAR6-6Y0iw/s400/oP7310414.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">A piece of wedge material is added to the top of each gate, the wide side of the wedge toward the outside.</span><br />
<br />
<div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcknefwiwLjzcCfNy48kCkb7q0VdgF19CePO0NhEchhF-o6HrQ0YyGzg2BkEWuFmGn1SmLKF4Zgx_8RzfEl8CrgyQS3licvNjBODzCVz3NqNs6sJzEp8sdtlie1tLoOczcSKf8sA/s1600/pP7310413.JPG" imageanchor="1" style="clear: right; float: right; font-family: georgia, 'times new roman', serif; font-size: x-large; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="843" data-original-width="1125" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcknefwiwLjzcCfNy48kCkb7q0VdgF19CePO0NhEchhF-o6HrQ0YyGzg2BkEWuFmGn1SmLKF4Zgx_8RzfEl8CrgyQS3licvNjBODzCVz3NqNs6sJzEp8sdtlie1tLoOczcSKf8sA/s400/pP7310413.JPG" width="400" /></a><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">The latch-bar is notched at the bottom to catch the wedge on the top of the gate, and an eye-screw is positioned on the bottom of the latch-bar to prevent the gate from swinging inward too far. The bottom of the latch bar is beveled at the end to help ease the latch bar over the wedge </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">on the top of the gate.</span></div>
<div>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: x-small;"><br /></span></div>
<div>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">Each latch bar crosses a brace bar, and they are fastened at the crossing point by a screw. The flexibility of the latch bar is used to apply pressure at the notch. A natural bend in one of the latch bars was used to choose and adjust the position of the latch bar.</span><br />
<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS6V0KZJcn4hcsFReVIjeTJ9QpjeA9Md6tLBa6BUjsmABuaGpBuz6UDuq3Gmpx6yf5jXRnTPb4K4Aqh0_yuXWLhpAXk9boLGtn0kKP57zUUmRlSpunvuxa8o10LnMr1SRfOBm7gg/s1600/qP7300411.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="843" data-original-width="1125" height="148" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS6V0KZJcn4hcsFReVIjeTJ9QpjeA9Md6tLBa6BUjsmABuaGpBuz6UDuq3Gmpx6yf5jXRnTPb4K4Aqh0_yuXWLhpAXk9boLGtn0kKP57zUUmRlSpunvuxa8o10LnMr1SRfOBm7gg/s200/qP7300411.JPG" width="200" /></a> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEif7cXEDYmfe10a6TZHkC0ir24LdOP9ehsNjh9wDw6xs7B0vcS0CKuKEC802prgNGsb-XgxFe62uZ9YMnWUbazBNarVa8XFX_AOjlMYL-iEyBnO-FSomTZ7DsfAKyE3rexxz1_iAw/s1600/rP7300412.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="843" data-original-width="1125" height="148" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEif7cXEDYmfe10a6TZHkC0ir24LdOP9ehsNjh9wDw6xs7B0vcS0CKuKEC802prgNGsb-XgxFe62uZ9YMnWUbazBNarVa8XFX_AOjlMYL-iEyBnO-FSomTZ7DsfAKyE3rexxz1_iAw/s200/rP7300412.JPG" width="200" /></a></span></div>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">
</span></div>
<div>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;"></span><br />
<div>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">_____________________________________</span></div>
<span style="font-family: "georgia" , "times new roman" , serif; font-size: large;">
</span></div>
JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-78589405723284623272014-12-15T01:05:00.001-05:002014-12-15T01:05:40.993-05:00Someone gave me the following link to an article listing "Seven mind-scrambling science ideas only geniuses can understand". <br /><a href="http://metro.co.uk/2014/12/13/seven-mind-scrambling-science-ideas-only-geniuses-can-understand-4985026/">http://metro.co.uk/2014/12/13/seven-mind-scrambling-science-ideas-only-geniuses-can-understand-4985026/</a><br /><br />The article said that "The worldās scientists donāt just sit around doing really hard maths for fun ā they also believe some truly crazy ideas."<br /><br />My comments on these seven ideas follow. but first, keep in mind that science does not explain everything; we must also deal with metaphysics, philosophy, and theology here. Science has been defined as the study of all that is material (mass-energy-space-time), so only materialists, those that ascribe to the metaphysical notion that everything is material (non-material things are imaginary) -- only materialists believe that science can explain everything.<br /><br />In this modern era, we also study information just as intently, but information is not made of mass-energy-space-time -- mass and energy are only used in arbitrarily different ways for tranport of information through either space (communication) or time (storage). Information is observed only where life is observed. This frustrates the materialists, who resort to all kinds of stupidity trying to explain life. (For more on this, read my blogs such as <a href="http://jamesmclark.blogspot.com/2005/07/in-beginning-was-information.html">http://jamesmclark.blogspot.com/2005/07/in-beginning-was-information.html</a>, <br />
<a href="http://jamesmclark.blogspot.com/2007/06/is-encoded-information-essential-part.html,">http://jamesmclark.blogspot.com/2007/06/is-encoded-information-essential-part.html,</a> <a href="http://jamesmclark.blogspot.com/2008/09/life-is-more-than-chemistry.html">http://jamesmclark.blogspot.com/2008/09/life-is-more-than-chemistry.html</a>, and.<a href="http://jamesmclark.blogspot.com/2010/03/digital-control-of-life.html">http://jamesmclark.blogspot.com/2010/03/digital-control-of-life.html</a>.) To define information theory as part of science, you either have to change the definition of 'material' or stop being a materialist.<br /><br />1. Time goes slower on the Space Station<br /><br />"This isnāt just theory ā itās actually measurable."<br /><br />A proven fact. From working on GPS, I know that when we make and test the time-keeping system of a GPS satellite on the ground, we have to 'set the clock' a little faster on the ground so that after it is launched, it will agree with our global time-keeping system on the ground. The 'correction' is mostly to account for the speed of the satellite (a 12-hour orbit), but also to account for the decreased gravity (altitude).<br /><br />2. We are almost certainly living in the Matrix<br /><br />"British philosopher Nick Bostrom claims that we are probably living inside a Matrix-style simulation."<br /><br />A conjecture. I think that if Nick Bostrom studied complexity theory, he would change his mind.<br /><br />3. In a class of 25 children, two will probably share a birthday<br /><br />"But itās actually more likely than not that two will share a birthday ā a chance of 57%."<br /><br />Yes, the probabilty is closest to 50% for a class of 23; for 25, the probability goes up a little. As I recall, it is a difficult calculation requiring surprisingly high precision. <br /><br />4. There is more than one universe<br /><br />"There are billions, according to a theory which is accepted by ānearly allā cosmologists."<br /><br />A conjecture. This is based on the accepted fact that the universe that we observe is finite. Most people would think that this requires that the universe has an edge, or boundary. But topologists know that a 3D space can be folded on itself edgelessly, like the 2D surface of a sphere, for example. So, some far-away galaxy might be our local galaxy (the Milky Way) many, many years ago. This conjecture is scientifically unprovable, but many Christians assume that heaven is in another universe. (We really don't know.)<br /><br />5. There are more than four dimensions<br /><br />"...there are either dimensions too small for us to see, or that our 4D world exists on a ābraneā which floats in another, higher-dimensional world."<br /><br />Only in subatomic physics. The extra dimensions 'fold up' within the tiny spaces of atoms.<br /><br />6. No one knows what a computer is<br /><br />"Computing professors worry about this stuff. Is an abacus a computer? Is a sundial?"<br /><br />This is really just saying that there isn't yet a universally agreed definition of a computer, especially of very small ones. I once designed a computer with only one bit of internal memory and unlimited external memory, which I started to build but never finished. It would have been practically useless, taking a very long time to compute something very small.<br /><br />7. The universe should not exist at all<br /><br />"The universe may not have started with a Big Bang", the article says.<br /><br />
<blockquote class="tr_bq">
"Prof Mersini-Houghtonās calculations seem to prove that when a dying star collapses in on itself, it does not shrink down to become a āsingularityā, ... what we know as a black hole.<br /><br />Instead, the radiation that escapes from dying stars robs them of their mass, so they never have enough gravity to form black holes.<br /><br />This creates a major problem. The āfuseā that lit the Big Bang is supposed to have been a singularity ā something which has now been proven not to exist."</blockquote>
<br />I think this conundrum is a consequence of relying only on science. In other words, it results from an inherent limitation of science. It demonstrates a fundamental question that science alone cannot explain. All you can conclude is that something outside of science created the universe. If you add information theory to your thinking toolbox, you can conclude that 'that something' had an enormous amount of information, since we know that the material universe can destroy information but can never create it. And since information is observed only where life is observed, we can also conclude that 'that something' is living. It takes theology to go further than that, and the Bible to go in the right direction.<br />JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-53668612507248106642014-06-02T10:45:00.000-04:002014-06-10T10:46:59.252-04:00How to use the "WHAT IS NUMBER" T-shirt<div align="LEFT" style="margin-bottom: 0in;">
<span style="font-size: medium;">I have created T-shirt designs with a mathematical theme, and I sell them on <a href="http://www.zazzle.com/mathart">http://www.zazzle.com/mathart</a>. Lately, I created a magic trick using mathematics and some other tricks for 'guessing' a number that a volunteer has secretly chosen. Then I adapted this magic trick, in a simpler form, for a T-shirt design. For those who buy the "WHAT IS NUMBER" T-shirt (or receive one as a gift), here is an explanation of how to use the T-shirt as a magic prop. To buy the T-shirt, go to <a href="http://www.zazzle.com/what_number_magic_shirt-235678841307212061?rf=238851269352169293">http://www.zazzle.com/what_number_magic_shirt-235678841307212061?rf=238851269352169293</a> (you can customize the shirt.)</span></div>
<div align="LEFT" style="margin-bottom: 0in;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0in;">
<span style="font-size: medium;">You
ask a volunteer to choose a number in the range 1 to 144, but to keep
it secret. You ask him to find his number on the front of the shirt,
and to tell you the letter in the same box as his number. For
example, he tells you "U". You ask him to also find his
number on the back of the shirt, and to tell you the corresponding
letter. While he is finding his number on the back, you translate
the "U" to 4, using the mnemonic "foUr", and
multiply the 4 by 12, getting 48. He reports "S" for the
back, and you translate the "S" to 6, using the mnemonic
"Six", and add the 6 to the 48, getting 54. You tell him
his number is 54, without (of course) telling him how you derived
that number, and he is amazed. </span>
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4-ebyldsffkzG7MEgOjt0v-4DBLkS2O4cSE2y8t-fztMD8pTmYg3NJyWFrcwN8-niXE09lQ37wNFnN4GrwtXxcdZDqsSwywtRk7PXaLskorCqWM99zTBtoboFDdNBNlPzulLgkw/s1600/WhatNumber_U_S.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4-ebyldsffkzG7MEgOjt0v-4DBLkS2O4cSE2y8t-fztMD8pTmYg3NJyWFrcwN8-niXE09lQ37wNFnN4GrwtXxcdZDqsSwywtRk7PXaLskorCqWM99zTBtoboFDdNBNlPzulLgkw/s1600/WhatNumber_U_S.jpg" height="240" width="320" /></a></div>
<div align="LEFT" style="margin-bottom: 0in;">
<span style="font-size: medium;">Optionally, you may ask the volunteer to write down his number on a card and to show the card to others nearby. This allows others to participate by verifying that your 'guess' is correct. It is obvious that you cannot see the back of the T-shirt, but you should not look down at the front of the T-shirt, either. Look straight at the volunteer, or the audience, or look up, or close your eyes, or be blindfolded. The audience may think you have the entire shirt memorized, but that is not necessary.</span></div>
<div align="LEFT" style="margin-bottom: 0in;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0in;">
<span style="font-size: medium;">What
is the complete method, and how does it work? The method is based on
the following matrix and the cipher that follows.</span></div>
<div align="LEFT" style="margin-bottom: 0in;">
<br /></div>
<h3 align="CENTER" style="margin-bottom: 0in;">
<span style="font-size: medium;">Matrix
of numbers 1 to 144 with rows and columns labelled</span></h3>
<div lang="zxx" style="margin-bottom: 0in;">
<br /></div>
<table border="0" cellpadding="0" cellspacing="0" style="page-break-inside: avoid; width: 100%px;">
<colgroup><col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
<col width="20*"></col>
</colgroup><tbody>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<br /></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">B</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">I</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">W</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">H</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">U</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">R</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">S</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">E</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">A</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">N</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">T</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">M</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">B</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">144</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">1</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">2</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">3</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">4</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">5</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">6</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">7</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">8</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">9</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">10</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">11</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">I</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">12</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">13</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">14</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">15</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">16</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">17</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">18</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">19</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">20</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">21</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">22</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">23</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">W</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">24</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">25</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">26</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">27</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">28</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">29</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">30</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">31</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">32</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">33</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">34</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">35</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">H</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">36</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">37</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">38</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">39</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">40</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">41</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">42</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">43</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">44</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">45</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">46</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">47</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">U</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">48</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">49</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">50</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">51</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">52</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">53</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">54</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">55</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">56</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">57</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">58</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">59</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">R</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">60</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">61</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">62</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">63</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">64</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">65</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">66</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">67</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">68</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">69</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">70</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">71</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">S</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">72</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">73</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">74</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">75</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">76</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">77</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">78</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">79</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">80</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">81</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">82</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">83</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">E</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">84</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">85</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">86</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">87</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">88</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">89</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">90</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">91</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">92</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">93</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">94</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">95</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">A</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">96</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">97</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">98</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">99</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">100</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">101</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">102</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">103</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">104</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">105</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">106</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">107</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">N</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">108</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">109</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">110</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">111</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">112</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">113</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">114</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">115</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">116</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">117</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">118</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">119</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">T</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">120</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">121</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">122</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">123</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">124</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">125</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">126</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">127</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">128</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">129</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">130</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">131</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">M</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">132</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">133</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">134</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">135</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">136</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">137</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">138</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">139</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">140</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">141</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">142</span></div>
</td>
<td width="8%"><div lang="zxx">
<span style="font-size: medium;">143</span></div>
</td>
</tr>
</tbody></table>
<div lang="zxx" style="margin-bottom: 0in;">
<br /></div>
<div style="margin-bottom: 0in;">
<span style="font-size: medium;">The
front of the T-shirt indicates which row, and the back of the T-shirt
indicates which column. The letters are translated to numbers
according to the following cipher. The mnemonics are an aid to
memorizing the cipher.</span></div>
<h3 align="CENTER" style="margin-bottom: 0in;">
<span style="font-size: medium;">Cipher
and mnemonics:</span></h3>
<div style="margin-bottom: 0in;">
<br /></div>
<table border="0" cellpadding="0" cellspacing="0" style="page-break-inside: avoid; width: 100%px;"><tbody>
<tr valign="TOP"><td width="10%"><div lang="zxx">
<span style="font-size: medium;">W</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">2</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">tWo, first
spelled number with W </span>
</div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">H</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">3</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">tHree, first
spelled number with H</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">A</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">8</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">sounds like Ate
</span>
</div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">T</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">10</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">Ten, fourth
spelled number with T</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">I</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">1</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">I looks like 1</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">S</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">6</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">Six, first
spelled number with S</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">N</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">9</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">NiNe, first
spelled number with two N's</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">U</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">4</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">foUr, first
spelled number with U</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">M</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">11</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">eleven ā
Melvin (similar sound)</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">B</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">0</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">B00, surprise,
O looks like 0</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">E</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">7</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">sEvEn, first
spelled number with two separate E's</span></div>
</td>
</tr>
<tr valign="TOP">
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">R</span></div>
</td>
<td width="10%"><div lang="zxx">
<span style="font-size: medium;">5</span></div>
</td>
<td width="80%"><div lang="zxx">
<span style="font-size: medium;">fiveR, slang
for 5-dollar bill</span></div>
</td>
</tr>
</tbody></table>
<div align="LEFT" lang="zxx" style="margin-bottom: 0in;">
<br /></div>
<div align="LEFT" style="margin-bottom: 0in;">
<span style="font-size: medium;">After
translating the front and back letters to numbers Fr and Bk,
calculate this in your head:</span></div>
<div align="CENTER" style="margin-bottom: 0in;">
<br />
<span style="font-size: medium;">Result
= 12 * Fr + Bk</span></div>
<br />
<span style="font-size: medium;">You can calculate the 12 * Fr
part while the back number is being found.</span><br />
<div align="LEFT" style="margin-bottom: 0in;">
<br /></div>
<b>EXCEPTION: </b><span style="font-size: medium;">If
the Result is zero, change it to 144. </span><br />
<div align="LEFT" style="margin-bottom: 0in;">
<br /></div>
<h3 style="text-align: center;">
<span style="font-size: medium;">The Reverse Trick </span></h3>
<span style="font-size: medium;">You can do the magic trick in reverse. That is, given 54, for example, you can determine where it is found without looking. You divide 54 by 12, getting the quotient 4 and remainder 6. Using the cipher, you convert the </span><span style="font-size: medium;">quotient 4 to U, the position on the front of the shirt, and you</span> <span style="font-size: medium;">convert the </span><span style="font-size: medium;"><span style="font-size: medium;">remainder 6</span> to S, the position on the back of the shirt.</span><br />
<div align="LEFT" style="margin-bottom: 0in;">
<br /></div>
<h3 style="text-align: center;">
<span style="font-size: medium;"><b>Another Trick</b> </span></h3>
<span style="font-size: medium;">For any letter, there is a number that appears under that letter on both the front and the back of the T-shirt. So you can ask a volunteer to choose a letter, and then you choose a number that </span><span style="font-size: medium;">appears under that letter on both the front and the back. To do this, it will help to be familiar with the multiples of 13. (Most people are not, and as a result, think that 91 is a prime number.)</span><br />
<span style="font-size: medium;"><br /></span>
<span style="font-size: medium;">Given a letter, use the cipher to convert the letter to a number, then multiply the number by 13. For example, suppose the letter is E. According to the cipher, the corresponding number is 7. 7 times 13 is 91, so you declare that 91 is found in box E </span><span style="font-size: medium;">on both the front and the back of the T-shirt.</span><br />
<br />
<span style="font-size: medium;">The equivalence of 0 and 144 applies to all tricks. </span>JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-70536289644363395922012-01-20T20:39:00.003-05:002012-01-20T20:54:31.908-05:00God Is On FacebookI know, He doesn't have a profile with "Work and Education", "Philosophy", "Arts and Entertainment" interests, etc. He doesn't have a friends list or photo albums; but He definitely IS on Facebook.<br /><br />When Christian friends share their hopes, concerns, blessings, problems, questions, and opinions on Facebook -- whenever the Bible is quoted or referenced, then God's viewpoint is heard. Sometimes it is a doctrinal issue that is discussed, and obviously God's Word must predominate. But it can be ANY kind of situation that comes our way along life's journey, and there is always something in God's Word to provide guidance and a foundation for understanding and dealing with the situation.<br /><br />God's Word itself claims that it is relevant for all kinds of things:<br /><br />"For the word of God is quick, and powerful, and sharper than any twoedged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart." (Hebrews 4:12)<br /><br />"...the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus. All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: That the man of God may be perfect, throughly furnished unto all good works." (2 Timothy 3:15-17)<br /><br />"For whatsoever things were written aforetime were written for our learning, that we through patience and comfort of the scriptures might have hope." (Romans 15:4)<br /><br />"Wherefore take unto you the whole armour of God, that ye may be able to withstand in the evil day, and having done all, to stand. And take ... the sword of the Spirit, which is the word of God." (Ephesians 6:13, 17)<br /><br />"I have more understanding than all my teachers: for thy testimonies are my meditation." (Psalm 119:99)<br /><br />I have found that when there are discussions (yes, even arguments) on Facebook, it is often just one opinion vs. another opinion. And when I feel the urge to offer my opinion, I think, "Why should they listen to me? I'm just another opinion. I'm not an authority." Then my mind turns to The Authority, The Creator, The Lord of Lords and King of Kings (MY Lord, my Creator, and my Authority), the One that challenged Job with questions like these --<br /><br />"Where were you when I laid the foundations of the earth? Tell Me, if you have understanding. Who determined its measurements?" (Job 38:4-5)<br />"Who has put wisdom in the mind? Or who has given understanding to the heart?" (Job 38:36)<br />"Does the hawk fly by your wisdom, and spread its wings toward the south? Does the eagle mount up at your command, and make its nest on high?" (Job 39:26-27)<br /><br />-- and many others in chapters 38 and 39 of Job.<br /><br />And so I quote the Bible, and let God interject His opinion into the conversation. And I encourage others to do the same, and many do, without my encouragement.<br /><br />And so, God is on Facebook.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com1tag:blogger.com,1999:blog-13817057.post-12119349986575050982011-09-29T09:41:00.002-04:002020-09-18T00:56:29.825-04:00When I Disappear<div style="text-align: center;"><i><b>(updated by recent events)</b></i></div><div style="text-align: center;"><i><b><br /></b></i></div>If you find that I, and many other Bible-believing Christians, have disappeared from the earth, leaving behind all our earthly possessions, even the clothes we wear, you will wonder what has happened. What has happened is the Rapture (snatching away) of believers that the Bible has predicted. Believers that have died will be resurrected and joined by those alive, all receiving in an instant new bodies like the resurrection body of Jesus, meeting Jesus in the air and going to heaven with Him. <div><br />1 Thessalonians 4:15-17 --
āFor this we say to you by the word of the Lord, that we who are alive and remain until the coming of the Lord will by no means precede those who are asleep [dead].
16 For the Lord Himself will descend from heaven with a shout, with the voice of an archangel, and with the trumpet of God. And the dead in Christ will rise first.
17 Then we who are alive and remain shall be caught up together with them in the clouds to meet the Lord in the air. And thus we shall always be with the Lord.ā </div><div><br /></div><div>1 Corinthians 15:51-53 --
āBehold, I tell you a mystery: We shall not all sleep, but we shall all be changed --
52 in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised incorruptible, and we shall be changed.
53 For this corruptible must put on incorruption, and this mortal must put on immortality.ā </div><div><br /></div><div>We believe this will happen shortly before God pours out His wrath to judge the earth, because the Bible says: </div><div><br /></div><div>1 Thessalonians 5:9-10 --
āFor God did not appoint us to wrath, but to obtain salvation through our Lord Jesus Christ, 10 who died for us, that whether we wake or sleep, we should live together with Him.ā </div><div><br /></div><div>Those resurrected and raptured will include all those that trust that the death of Jesus Christ on the cross is entirely sufficient to pay for all their sins, not relying on anything that they do; not those that call themselves 'Christian', but follow the traditions of men rather than the Word of God, the Bible.
Some time later (perhaps a few weeks), a leader in Europe will come to prominence and "confirm a covenant" with Israel for seven years, bringing peace to the world.</div><div><br /></div><div><b><i>Notice that the Bible says "confirm" (or strengthen), not "make" a covenant. Recently, President Trump <span style="background-color: white; color: #222222; font-family: georgia;">brokered</span><span style="background-color: white; color: #222222; font-family: georgia;"> peace agreements </span><span style="background-color: white; color: #222222; font-family: georgia;">between Israel and the United Arab Emirates and </span><span style="background-color: white; color: #222222; font-family: georgia;">between</span><span style="background-color: white; color: #222222; font-family: georgia;"> </span><span style="background-color: white; color: #222222; font-family: georgia;">Israel and Bahrain that many believe will soon lead to a more complete agreement. So now (or soon) we have a covenant that can be confirmed or strengthened. </span></i></b></div><div><br /></div><div>This leader will be welcomed as the Messiah by many so-called 'Christian' leaders, and as the Mahdi by Muslim leaders, but the Bible says he is the Antichrist (false Messiah) and also calls him āthe beastā, and the Bible calls the leader of the 'Christian' world that endorses him the āfalse prophetā. The real Messiah (Jesus Christ) will not come to the earth until after the seven years. In the middle of the seven years, the Antichrist will break his covenant with Israel, and world calamities will increase greatly as never before, as God judges the earth. The Antichrist will do miraculous things, but he is controlled by Satan, not God.
It will be far better to trust the real Jesus and die (but have eternal life after resurrection) than to worship the image of the Antichrist or to accept the mark that the Antichrist will require: </div><div><br /></div><div>Revelation 13:15-17 --
āHe was granted power to give breath to the image of the beast, that the image of the beast should both speak and cause as many as would not worship the image of the beast to be killed.
16 He causes all, both small and great, rich and poor, free and slave, to receive a mark on their right hand or on their foreheads,
17 and that no one may buy or sell except one who has the mark or the name of the beast, or the number of his name.ā
</div><div><br /></div><div><i><b>In recent years, the technologies for such a "mark" have been developed, but are not yet combined into the "mark". One is the technology of digital currency, which is absolutely resistant to counterfeiting, but is not yet required to replace traditional currency. The other is the technology of ID tagging (embedded chips), which absolutely prevents identity theft. The embedded chips need a source of energy to recharge their tiny batteries. The chip inventor decided that the energy would come from changes in body temperature. The inventor's research showed that the best places for this are the <u>right hand</u> and the <u>forehead</u>.</b></i></div><div><br /></div><div>Revelation 14:9b-11 --
āIf anyone worships the beast and his image, and receives his mark on his forehead or on his hand,
10 he himself shall also drink of the wine of the wrath of God, which is poured out full strength into the cup of His indignation. He shall be tormented with fire and brimstone in the presence of the holy angels and in the presence of the Lamb.
11 And the smoke of their torment ascends forever and ever; and they have no rest day or night, who worship the beast and his image, and whoever receives the mark of his name." </div><div><br /></div><div>Revelation 20:4b --
āThen I saw the souls of those who had been beheaded for their witness to Jesus and for the word of God, who had not worshiped the beast or his image, and had not received his mark on their foreheads or on their hands. And they lived and reigned with Christ for a thousand years.ā </div><div><br /></div><div>As Jesus said in Matthew 10:28 --
āAnd fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.ā </div><div><br /></div><div>Call on the name of Jesus (the name means savior) for salvation:
</div><div><br /></div><div>Romans 10:13 --
āFor whosoever shall call upon the name of the Lord shall be saved.ā </div><div><br /></div><div>Ephesians 2:8-9
āFor by grace are ye saved through faith; and that [grace] not of yourselves: it is the gift of God: 9 Not of works, lest any man should boast.ā </div><div><br /></div><div>If you read this before the Rapture, trust Jesus now to save you.
If you have questions, see <a href="http://www.gotquestions.org/">http://www.GotQuestions.org</a> .</div>JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-44175816474898678402011-07-27T17:40:00.002-04:002011-07-27T17:59:32.011-04:00Science and the BibleA Christian friend asked me, "What are the boundaries between all science theories and the Bible? As a Christian, to me, the Bible is the truth. So what position and conclusion do we give to these theories?"<br /><br />That's an interesting question, and I'll try to answer it here.<br /><br />A Christian scientist (not the cult that calls themslves that) realizes that he is examining God's creation. The facts never contradict the Bible, but give glory to God. It is the theories that are sometimes the problem. When the theories are based on non-biblical principles, the Christian should doubt them. So we must know what is the basis for the theories and put biblical principles first.<br /><br />In my blog, <em><strong><a href="http://jamesmclark.blogspot.com/2011/07/thinking-outside-box.html">Thinking Outside the Box</a></strong></em>, I said "Evolutionists don't want to think outside the box of materialism." They like the definition of science as "systematic knowledge of the physical or material world", because materialists believe that everything is material, and that science explains everything.<br /><br />But there is a broader definition of science: "a study dealing with a body of facts or truths systematically arranged and showing the operation of general laws". Science actually includes immaterial things like information, and abstract mathematical concepts.<br /><br />And Christians know that there is a spiritual realm that is part of God's creation, but beyond the reach of science. And of course, God is also beyond the reach of science, because He exists outside of His creation. Yet He can reach inside His creation to communicate with His creatures and to intervene in our affairs. The epitome of that was when He made himself a human body in the womb of a virgin, and putting aside His power and glory for a while, indwelt that body as Jesus.<br /><br />So Christians see science as an incomplete study of God's creation -- we can study some parts in enough detail that we can partly understand and thus enjoy and use.<br /><br />We realize that science doesn't explain everything. We don't even claim that it potentially could explain everything, given enough time for study. We realize that there are things outside the scope of science, even important things that our Creator has revealed to us.<br /><br />The Bereans were commended for comparing the apostle Paul's preaching to the Scriptures, to check whether they should believe what he said (Acts 17:10-11). And Christians today should also check Bible teachers against the Bible. Likewise, Christians should check scientific ideas against God's Word, knowing that science is incomplete and developed by fallible men, but the Bible was inspired by God. In fact, scientific theories should also be checked against scientific facts, because some theories are inspired by political or philosophical agendas.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-11304305609328130702011-07-08T17:07:00.005-04:002011-07-08T18:29:20.126-04:00Thinking Outside the Box<strong>Synopsis</strong><br />First, I'll explain how, I think, the expression "thinking outside the box" originated. Then I'll give two examples of how great strides in math / science / engineering were accomplished by "thinking outside the box". But the most important point that I want to make is that evolutionists are stuck inside the box of materialism because they are afraid to think outside the box. I discuss a vibrating string as an example of the limitations of materialism. Outside the box of materialism (but not outside science) is information theory, and in particular, the structured information of design. Here, the evolutionists are "out of their element".<br /><br /><strong>The Puzzle</strong><br />I think that the expression "thinking outside the box" was inspired by the following puzzle. You are presented with an array of nine spots arranged as shown below on the left, and are challenged to draw a sequence of four connected straight lines such that they will pass over all of the spots, touching each spot only once. The lines must be connected end-to-end, and are allowed to cross over each other, for example, as shown on the right.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4I1ZJ-oTBy97_KBDCJ3KEQta2hkMKJ3wKQhe0y1AUmwecbQjqStHv65sUKEFw8A7u3UUW7eg2__-kIwRv7jKb5m-9ZgUR_QqKsta5MPU2K-_8uAPMIZKW9CgAaByLkbUcKdilyw/s1600/box1.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 277px; height: 139px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4I1ZJ-oTBy97_KBDCJ3KEQta2hkMKJ3wKQhe0y1AUmwecbQjqStHv65sUKEFw8A7u3UUW7eg2__-kIwRv7jKb5m-9ZgUR_QqKsta5MPU2K-_8uAPMIZKW9CgAaByLkbUcKdilyw/s320/box1.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5627095970026803042" /></a><br />It was reported that the puzzle is difficult for most people because they mentally think of the array of nine spots as defining a square area as depicted in the next diagram, and they assume that the puzzle operates within this area.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDT7pz8zmPyg1ObXIhlmbkaFcP_fVqO20qWa2Wr7SyVRNclhWymQqlpMsFlfFnn5osYUcrATEBl05Bl6HdM-UFhat0nmddATuaAA_zZjIHS98RAMYEJ0lapQP1HTEBTmBLj_kFaw/s1600/box2.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 139px; height: 139px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDT7pz8zmPyg1ObXIhlmbkaFcP_fVqO20qWa2Wr7SyVRNclhWymQqlpMsFlfFnn5osYUcrATEBl05Bl6HdM-UFhat0nmddATuaAA_zZjIHS98RAMYEJ0lapQP1HTEBTmBLj_kFaw/s320/box2.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5627096287923492050" /></a><br />The puzzle does not require the lines to stay inside this assumed 'box'. Adding this restriction prevents a solution, because the puzzle solution must go "outside the box", as shown next.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyjxcGI2PeOaEpj-KIWBbHlrKPLoYc4ojM-8YB3JP402BN0EMfKhDcga5IQWRMHjAZf1q6CotmkNJcn3NpPWYYo9O9EHKQ2D6PFRkh9Nl0FvHu2mbWqcdJGTGDFb_g7daFi85KWg/s1600/box3.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 185px; height: 185px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyjxcGI2PeOaEpj-KIWBbHlrKPLoYc4ojM-8YB3JP402BN0EMfKhDcga5IQWRMHjAZf1q6CotmkNJcn3NpPWYYo9O9EHKQ2D6PFRkh9Nl0FvHu2mbWqcdJGTGDFb_g7daFi85KWg/s320/box3.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5627096692246138306" /></a><br />Science and mathematics have grown by "thinking outside the box". <br /><br /><strong>Imaginary Numbers</strong><br />For example, it was once thought that it was meaningless to speak of the square root of a negative number. It could be proved, for example, that the square root of minus one, if it had a value, could not equal any known numeric value. But if we IMAGINE that it had a value -- call this value 'i' (for Imaginary) -- then, logically, we could compute the square root of any other negative number. The square root of -9 would equal the square root of 9 (that is, 3) times i. So 3i would be an "imaginary" number, while 4 is a "real" number.<br /><br />But then it was reasoned that we could think of these out-of-the-box numbers as newly discovered numbers rather than "imaginary" numbers. We could even add "real" and "imaginary" numbers to create "complex" numbers. It all made sense (it didn't lead to contradictions), and it opened up a new world of mathematical discovery. At first, it appeared that this branch of mathematics was an abstract, theoretical-only world unrelated to the physical world; but scientists and engineers found that it could precisely describe the behaviour of resonant electronic circuits. Our modern electronic devices could not be designed without the aid of this out-of-the-box mathematics.<br /><br /><strong>Finite Numbers</strong><br />I'll give one more example from mathematics and engineering, but I'll keep it extremely simple. We are all familiar with doing arithmetic with integers (whole numbers), and we know that we have an infinite supply of integers, because no matter how large an integer we might be given, we can always add one to it and get a larger integer. Wouldn't it be weird if we had a finite supply of numbers, and no matter what arithmetic operation (add, subtract, multiply, or divide) we did with any two of them, the result would be found in our finite supply of numbers? Well, mathemeticians have discovered how to construct a finite set (of any size) of 'numbers' with associated arithmetic operations that operate like this. (They are called finite fields, a kind of finite algebras. Math geeks, see http://mathworld.wolfram.com/Ring.html) The arithmetic is weird, but easy to learn to do in most cases.<br /><br />Like the "imaginary" numbers, these weird systems of arithmetic seem like mathematical toys or games that bear no resemblance or relationship to the real world. Why don't we stick to normal math that describes how the real world operates? But engineers have used this weird math to construct codes used to detect and correct errors that occur in the communication or storage of digital data. For example, CDs and DVDs would not function without Reed-Solomon error-correction codes, which are based on these "finite fields".<br /><br /><strong>The Box of Materialism</strong><br />Evolutionists don't want to think outside the box of materialism. One of the definitions of science (from dictionary.com), is "systematic knowledge of the physical or material world gained through observation and experimentation", which limits the scope of science to the material world. <br /><br />Of course, evolutionists have a problem with the "observation" part, because nobody has observed genetic changes from one kind of creature to a completely different kind (such as dog to horse, rather than dog to another kind of dog). So they mostly content themselves with inferring (by theory) past events from current observations.<br /><br />And of course, evolutionists also have a problem with the "experimentation" part, because a true experiment requires control over the conditions of the experiment. Their experiments only show things such as that one can breed flies just like one can breed dogs, not major changes of kind. Even by broadening the concept of experiment so that "predictions" can be made and tested regarding past events fails. For example, evolution predicts that there should be millions of intermediate forms ("missing links"), but none are found.<br /><br />But the evolutionist argues, and rightly so, that the creationist also has similar problems with the "observation" and "experimentation" parts of the definition of science, and thus feels that he is on a 'level playing field' with his game of 'my story is more plausible than your story'. (He considers this story-telling to be "science", but if it weren't based on a theological / philosophical battle, it would be called "science fiction" instead.)<br /><br />But the evolutionist thinks that the "physical or material world" part of the definition of science works to his advantage, because it rules out the supernatural, which is the essential part of the creationist's "theory". And, after all, his main objective is to rule out God. But is it honest to 'win' an argument by virtue of a definition?<br /><br /><strong>Vibrating String Example</strong><br />Consider, for example, the vibration of a guitar string. If we know certain characteristics of the string, we can apply the laws of physics by means of a branch of mathematics called differential calculus to determine how the string will vibrate, and the nature of the sound that it will produce. We need to know:<br /><br />(1) the weight (such as ounces per foot) of the string<br />(2) the tension (such as pounds of force) of the string<br />(3) the length (between fixed points: a fret and the bridge) of the string<br /><br />These, which can all be measured, suffice to compute the 'steady state' vibration of the string. To determine the initial 'transient' component of the vibration that quickly fades before settling into the 'steady state', we would also need to know if the string were plucked or struck, and where on the string. To know the intial amplitude and how quickly the vibration will fade, we would also need to know how hard the string was plucked or struck, and other details.<br /><br />So by observing (measuring) a guitar string, we can use science to predict precisely what will happen when we pluck the string. But what if we are not in control? <br /><br />First, we have a 'future' problem. We might observe the string vibrating and make a prediction, only to find that the guitarist (the one in control) stops the vibration, without our permission, before our prediction can be fulfilled. <br /><br />Second, we have a 'past' problem. If our observation of the string began after the 'transient' component of the vibration has faded, we will have insufficient data to determine when the vibration started, and we will be unable to determine if it were plucked or struck, or were given its inital energy some other way.<br /><br />Note that our problem, essentially, is not that the guitarist is a material object too complex for us to analyze, but rather that the guitarist has a mind outside of the scope of our observation and control. If the guitarist were a robot, our problem would be difficult, but not impossible.<br /><br />So what do we learn from this vibrating string parable?<br /><br />We realize that the size and age of the material world makes nearly all of it beyond the scope of our observation and control. And science that is limited by definition to apply only to the material world is, by definition, limited in its application. Defining this box does not prove that there is nothing outside the box. If there is a Creator outside the box who is ultimately in control, and if you want to be the one in control, you may be inclined to hide inside your box, but you can't make God go away.<br /><br /><strong>A Broader Definition of Science</strong><br />Dictionary.com gives a broader definition of science, one that precedes the definition that we quoted earlier: "a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws: the mathematical sciences." So more generally, science is not limited to material things, but anything that can be studied "systematically" such that it can be explained in terms of "the operation of general laws". For greater clarity, "mathematical sciences" is mentioned, indicating that there should be sufficient precision that the language and methods of mathematics can be applied.<br /><br />So what is immaterial that can be included in this broader definition of science? Information is immaterial, and is studied systematically and operates in accordance with specific laws with sufficient precision so that the language and methods of mathematics are applied. This area of science consists of information theory and related theories of formal languages, algorithms, etc., and the corresponding applied science consists of the technologies of information storage, communication, and processing.<br /><br />In a previous blog, <a href="http://jamesmclark.blogspot.com/2005/08/all-things.html">ALL Things</a>, I made the case that the material world consists of four interrelated elements: matter, energy, space, and time. Then in a later blog, <a href="http://jamesmclark.blogspot.com/2007/06/is-encoded-information-essential-part.html">Is Encoded Information an Essential Part of the Universe?</a>, I made the case that encoded information is an optional fifth element, not required by the laws of physics, but nonetheless present where (and only where) life is present. The reason why information is found only where life is found is that the design paradigm of life is chemistry guided by DNA information, as I explained in the blog, <a href="http://jamesmclark.blogspot.com/2008/09/life-is-more-than-chemistry.html">Life is more than chemistry</a>. Without the guiding information, chemistry can only make inorganic molecules. DNA information is needed to make organic molecules, which are much larger and more complex. (Some simple molecules such as certain amino acids are traditionally classified as 'organic' if they are used as components of large organic molecules, but that is like listing raw iron as a machine part, along with the nuts, bolts, and cotter pins.)<br /><br /><strong>Information Outside the Box</strong><br />Before the functions of DNA and RNA, and the genetic code were discovered, evolutionists could take advantage of the mystery of genetics to tell imaginative stories of how evolution might operate. But these discoveries irreversibly brought information theory into the scientific arena of the creationism / evolutionism debate. Just as someone caught in a lie feels forced to tell new lies or to modify the first lie to maintain credibilty, the evolutionists felt compelled to change their story; and just as a gang of liars are not likely to agree except on their innocence, the evolutionists don't agree except that God is not involved.<br /><br />Some evolutionists insist that there is no information in DNA and RNA, as though closing their eyes will make the information bogeyman go away. Some insist that information theory is not a valid science (because information is not material). Some claim that information can come from nothing, or from randomness (which is zero information according to information theory), attempting to prove this by equating patterns and information. And some claim that new information can be generated by random re-arrangements of scraps of information, as though it were possible that if you scrambled parts of the Koran long enough, you might end up with the Bible. Even those that admit that information always originates from intelligence deny that God is a plausible source of that intelligence, but prefer an "extraterrestrial" source, replacing the question "How did life information originate on earth?" with the question "How did life information originate on planet X?" (Do I need to explain the fallacy of that logic?)<br /><br />So the evolutionists that dare to wander outside the box of materialism either flounder like someone diving into water without learning to swim first, or they retreat to the more comfortable zone of materialism.<br /><br />But that is only the beginning of the problems for the materialists. The information in DNA is not just information, but more specificly, DESIGN information. And here the evolutionists are completely lost in an unfamiliar world. Most of the contributors to the science of intelligent design have a background in the applied science of engineering, because this is familiar territory that they understand.<br /><br /><strong>Structured Information (Top-Down Design) Outside the Box</strong><br />The key to understanding the evolutionary problem is that design information is <strong>structured information</strong>. Let me give a simple example to make this clear. In a book, whether fiction or nonfiction, letters are arranged to make words, words arranged to make phrases, phrases arranged to make clauses, clauses arranged to make sentences, sentences arranged to make paragraphs, and paragraphs arranged to make make chapters. Does any author start with letters and play with different sequences to make words, etc., finally making chapters? No, the author starts with an array of related concepts, and starts at some high level of organization and works downward, finally working out the details of how best to arrange a sentence and how to spell the words. Rarely does the author accomplish the final work in one pass, but each revision starts with a new concept at some level and works downward.<br /><br />Does a designer start with an assortment of parts, like a box of legos, and wonder what he might do with them? No, he starts with a concept, such as using suction to remove household dirt, and designs a vaccuum cleaner "top down", as designers like to say. He may begin with a simple set of features, and add features such as exchangeable attachments, but additions and revisions are always "top down". For example, when he decides that he needs a hose to connect attachments to the vaccuum pump, he first determines its desired properties (lightweight, flexible, does not collapse like a fire hose, etc.) and then works out the details, such as using a wire coil to keep the hose from collapsing. <br /><br />Unlike the book example, a design typically mixes different technologies. For example, the engineer needs to choose appropriate materials, and so depends on experts in metallurgy, plastics, etc. Or he needs a motor, and orders one meeting his specications designed by a specialist.<br /><br />Living things, even single-celled organisms, are likewise complex designs, systems made of subsystems that are made of sub-subsystems, etc. And they mix mechanical, chemical, electrical, communication, etc. 'technologies' to acheive coordinated purposes.<br /><br />So, the evolutionist, in re-telling his story to adapt to the undeniable presence of design, imagines that accidental genetic changes can modify designs to make new designs. But experienced designers recognize this as "bottom-up" design: that is, a foolish, unworkable strategy. Fiddling with the details never makes a truly new design; it only 'tunes up' or adjusts a design.<br /><br />For example, the first television sets had about a dozen adjustment knobs in front, which was dangerous, because people that had no clue about the internal technology would fiddle with them with disasterous results. It took a while for the engineers to design automatic adjustment mechanisms to replace all of those knobs except for the channel selector and the volume control. But note that a billion adjustment knobs on the television will never suffice to make it function like a cell phone or a vaccuum cleaner.<br /><br />Complex systems generally require many automatic adjustment mechanisms. And that is exactly what scientists observe in biology. Genetic adjustment (adaptation) is just one category of these mechanisms. So species are designed to adapt to environmental changes, and we can influence the process by breeding (outside intelligence). But breeding dogs to make horses takes a leap of imagination, and supposing that inorganic matter can turn into human beings with no outside intelligence in something less than an eternity takes a enormous leap of faith.<br /><br />So if and when evolutionists dare to wander outside the box of materialism, they are likely to discover that evolution is a religion, after all, not a science. That is, if they are willing to be honest with themselves.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-23016057799407344472011-05-10T19:42:00.133-04:002011-05-15T02:35:03.146-04:00Origami Water Lilly and Lilly-Pad<strong>Overview</strong><br /><br />This blog article provides instructions for folding origami Water Lillies and Lilly-Pads designed by Jim Clark. It is a modular design: each lilly is made of 6 squares of various sizes plus two octagons of slightly differing sizes. The lilly-pad is made of one square. The design is not pure origami, because there is some use of glue and cutting, but origami is the main method.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNEuZ-PPwjBOAg_IuGgD2TE1SCkc40yX9Nl866MO7yV8nLrefT3sABYtsfFEpsUbwEFObElcPKnA5GWz3qeUAqSowF_8Ohq1-oj0tjJi54RFugBiqQTipFxkaO9UU5dzuZ_JJNAg/s1600/water_lilly_1.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNEuZ-PPwjBOAg_IuGgD2TE1SCkc40yX9Nl866MO7yV8nLrefT3sABYtsfFEpsUbwEFObElcPKnA5GWz3qeUAqSowF_8Ohq1-oj0tjJi54RFugBiqQTipFxkaO9UU5dzuZ_JJNAg/s200/water_lilly_1.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5605240288616836402" /></a>I used photos of real water lillies such as this > one as a guide to the design. Some water lillies have wider petals than this.<br /><br />(Click on any photo here to see a larger copy.)<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvfRcJ1BcxvdaK-yzNx5PbX34xiQO5j-zl_QGTndIqech5raUJO0v4lWPLZWNqdpRkZW-hQBepNfb8rtvzVkfVoWuSYK1g0A7oUQIEzrDzEvyISUpXb4ADun2LkH4svjnOWOo0VA/s1600/P4011625.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvfRcJ1BcxvdaK-yzNx5PbX34xiQO5j-zl_QGTndIqech5raUJO0v4lWPLZWNqdpRkZW-hQBepNfb8rtvzVkfVoWuSYK1g0A7oUQIEzrDzEvyISUpXb4ADun2LkH4svjnOWOo0VA/s200/P4011625.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605250508901527122" /></a>I made two table centerpieces like the one in < this photo. Each centerpiece had three lillies, one lilly-pad, and one 'puddle'. The blue foil of the 'puddle' simulates water by providibg a reflection of the lillies. I didn't include photo instructions for the 'puddle' because it is so simple and almost obvious. You start by folding the corners of a square of foil underneath, two opposite corners more than the other two, to approximate an oval shape; then fold more corners under to get a smoother, rounded shape.<br /><br />In the instructions, I provide recommended sizes and colors, but you can vary these as you like after you learn the design.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKUhQtLs9gFzhcfZhW9wwyRT-IlPKt-hegdAm1aZPXVAYpTyzJE5SqjMTjSoAHTPGhSIK-HNOZT_uSn-8bh8uy0Nw8pjTby-hu9_tgb6TnSMYl17TRdq8h4cTshe2pEX2g0nUZPg/s1600/P3231587.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKUhQtLs9gFzhcfZhW9wwyRT-IlPKt-hegdAm1aZPXVAYpTyzJE5SqjMTjSoAHTPGhSIK-HNOZT_uSn-8bh8uy0Nw8pjTby-hu9_tgb6TnSMYl17TRdq8h4cTshe2pEX2g0nUZPg/s200/P3231587.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605252509207110562" /></a><strong>The Water Lilly (<a href= "#pad">Skip to Lilly Pad</a>)</strong><br /><br />Here > is the origami water lilly. It has 24 petals and about 200 or more stamens in the center. It is made from 6 white squares of various sizes (white on both sides), and 2 yellow octagons (yellow on both sides).<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX9q5SaYOBHZNkalyj8sTDqzrXAT83CYEWeUQeF-V9lDfrK8SphTBFNv9RKNhO4vpnvxPtoqLAJ2ENdarsWjAknWYC_9oXY1rkolasmAJcZMWroOrMOx_7q9VlZwnVErZKSKkAFg/s1600/P3221509.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX9q5SaYOBHZNkalyj8sTDqzrXAT83CYEWeUQeF-V9lDfrK8SphTBFNv9RKNhO4vpnvxPtoqLAJ2ENdarsWjAknWYC_9oXY1rkolasmAJcZMWroOrMOx_7q9VlZwnVErZKSKkAFg/s200/P3221509.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605253677506175314" /></a>< For the petals, you need squares of 5.25, 5.0, 4.5, 4.0, 3.5, and 3.25 inches on a side; 6 squares, or 1 of each size. Use the 'A' design for the 2 smallest squares, and the 'B' design for the 4 largest squares. The 'AB' steps are for both 'A' and 'B' designs. <br /><br /><strong>Four-Petal Unit ('A' and 'B' Petal Designs)</strong><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI8HQrmYVSX_Fyuy0iFrg98klse4vTfbucykEyUVXOkrM8r2jYYkOQ6heNphZhLYsZPtxMa7rwBDB-ILds56DZqczqCv9dAp6WLeKfprtmUS6xQTFY5ONaYYDvF13s1C6UFNkHRw/s1600/P3221510.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI8HQrmYVSX_Fyuy0iFrg98klse4vTfbucykEyUVXOkrM8r2jYYkOQ6heNphZhLYsZPtxMa7rwBDB-ILds56DZqczqCv9dAp6WLeKfprtmUS6xQTFY5ONaYYDvF13s1C6UFNkHRw/s200/P3221510.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605254186845221378" /></a>AB1. Valley-fold the two diagonals, and mountain-fold in half (twice) parallel to the sides, like this > <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgufN2HcDT53ORAbebQHmYbaxqGRXmPRohdheoRoPc6xoVhxzLLzumN_4WR1qIARNmq3QrG3WW2mj_rVxA4jGLLks85t9PjdXd0WDmbhxvRI3Nbfw7ve1ZUVyGXGpD826JjiDPZrA/s1600/P3221512.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgufN2HcDT53ORAbebQHmYbaxqGRXmPRohdheoRoPc6xoVhxzLLzumN_4WR1qIARNmq3QrG3WW2mj_rVxA4jGLLks85t9PjdXd0WDmbhxvRI3Nbfw7ve1ZUVyGXGpD826JjiDPZrA/s200/P3221512.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605255666151142818" /></a>< AB2. Fold flat into a square shape (preliminary base) like this. (After this, the A and B designs differ. Go to A3 or B3. For the center of the lilly, start at C1. For a lilly-pad, start at P1.) <br /><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie4lIWJVjWLk9sJ6tHlAbIS3g9iVsWWLojNZdoz_yY8QCCz1YKCTl4Kr3K3tOT2kkH2qH1HiJedKAfwYlsYaLvIF1gRgoPrqFklak34KkmmnXBGRVpir80fv3DiMDlpGT1Xd79dA/s1600/P3221513.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie4lIWJVjWLk9sJ6tHlAbIS3g9iVsWWLojNZdoz_yY8QCCz1YKCTl4Kr3K3tOT2kkH2qH1HiJedKAfwYlsYaLvIF1gRgoPrqFklak34KkmmnXBGRVpir80fv3DiMDlpGT1Xd79dA/s200/P3221513.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605256861972347186" /></a><strong>'A' Petal Design</strong><br /><br />A3. > Raise one 'wing' and fold another wing up against it like this. The narrow end of the new triangle must be toward the open corner. Using the raised wing as a guide prevents the folded wing from going past the center. We want a small gap at the center.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtoKemhAHjMVOmTsgZTpvaORNCyDZ1ub8VZ6XiU4F9N3orzfx8qRnrk1DcztBbpO3e9qH1IrcdNnIEg7nKeNVyzIdvva6LBM9XjwEVjUX59Oe5CLpTT5uWzrXLy87msiJBaK75xg/s1600/P3221518.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtoKemhAHjMVOmTsgZTpvaORNCyDZ1ub8VZ6XiU4F9N3orzfx8qRnrk1DcztBbpO3e9qH1IrcdNnIEg7nKeNVyzIdvva6LBM9XjwEVjUX59Oe5CLpTT5uWzrXLy87msiJBaK75xg/s200/P3221518.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605287143803469634" /></a>< A4. Repeat A3 on the other side. There should be a small gap at the center. <br /><br><br><br><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqYx4dwVLhyphenhyphen0FF1YYxqD5I4d8h-HiChWVIH_kWv0kOlOLNkcmGQhe0AWcH5IR2ZLwWWXnvEVKOMpggn1S-aM5NDYeTB6VQMXGjmSc2yQlfQ9GGAoWC0uL7uP_kZrmn4psQpAaRrw/s1600/P3221520.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqYx4dwVLhyphenhyphen0FF1YYxqD5I4d8h-HiChWVIH_kWv0kOlOLNkcmGQhe0AWcH5IR2ZLwWWXnvEVKOMpggn1S-aM5NDYeTB6VQMXGjmSc2yQlfQ9GGAoWC0uL7uP_kZrmn4psQpAaRrw/s200/P3221520.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605287586628370898" /></a>A5. > Turn the model over and repeat A3-A4 on the remaining 2 wings to get this. Then unfold to AB2 and flex all the creases made in A3-A5 both ways.<br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQiBWxvseB9TwkKxeEIc3rzdGe9wEyWMdMtVWCGo5PukFqa1ataPzd9UQiVUK50JnTlVFlKWa6a5NNj0rpUJUTNr7zG9wwjIjj4BFDqxNBw7IZdJnKBh01X7oTpt8KcV7AWKrgbg/s1600/P3221522.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQiBWxvseB9TwkKxeEIc3rzdGe9wEyWMdMtVWCGo5PukFqa1ataPzd9UQiVUK50JnTlVFlKWa6a5NNj0rpUJUTNr7zG9wwjIjj4BFDqxNBw7IZdJnKBh01X7oTpt8KcV7AWKrgbg/s200/P3221522.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605287996757950242" /></a>< A6. Push the model into this shape. <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgV7U95zzX4pgLpJEOX_Y3ChXHOy4EolimTEBMwsDJiGGKslgFJMsjgvWYRRCo52tHxgDErLHC6I019V_BMrv_JgfVU6tcjX-QiY_ZSRjTgA9tH1eq-Jtkwd6ma-o-3jiww07tdTQ/s1600/P3221524.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgV7U95zzX4pgLpJEOX_Y3ChXHOy4EolimTEBMwsDJiGGKslgFJMsjgvWYRRCo52tHxgDErLHC6I019V_BMrv_JgfVU6tcjX-QiY_ZSRjTgA9tH1eq-Jtkwd6ma-o-3jiww07tdTQ/s200/P3221524.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605288454352885298" /></a>A7. > Fold the top and bottom edges inward on existing creases. <BR><br /><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZ3j3vZTzcme3v3B00ZtwUV1eUVwULHIGRFzQRpU9Z78I9DyWREFn4vQTf-fcWYH1tOhkP9jhDlH4_0iLCeHGaQbTfySjqROB86l6VLvl0_C41cvVsB6ur5-KbF6HVzgugYOoWzQ/s1600/P3221527.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZ3j3vZTzcme3v3B00ZtwUV1eUVwULHIGRFzQRpU9Z78I9DyWREFn4vQTf-fcWYH1tOhkP9jhDlH4_0iLCeHGaQbTfySjqROB86l6VLvl0_C41cvVsB6ur5-KbF6HVzgugYOoWzQ/s200/P3221527.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605288810591517234" /></a>< A8. Push the left and right sides together, like this. <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKW09YMBNe_Wtl-0IAZmrF2WOmtDyOWpXBBbxX5adkQSKFZYtbjSuOs0UUK9v-6xgtwxhAb6kqCIBca_1dWeFzWUWQXnJhlwYnojg3AC75p1u1fPXpoC9tuNJfDUzkt3zA4G8e_g/s1600/P3221529.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKW09YMBNe_Wtl-0IAZmrF2WOmtDyOWpXBBbxX5adkQSKFZYtbjSuOs0UUK9v-6xgtwxhAb6kqCIBca_1dWeFzWUWQXnJhlwYnojg3AC75p1u1fPXpoC9tuNJfDUzkt3zA4G8e_g/s200/P3221529.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605291690879758722" /></a>A9. > Hold the 2 wings that were folded narrower and pull apart to get this.<br /><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt-mMRdryoi-qpEfypKRjJxe_SzQcPN_zKUZ9VuARJxgwiJtC7DWKdWShU09O7MjmYlKRuKL4IaiQ2amqjDAKY04AzC25f3M3D7xpmvD-SI7q8I37QUhIJm0h9KCDgWX675bSFtg/s1600/P3221531.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt-mMRdryoi-qpEfypKRjJxe_SzQcPN_zKUZ9VuARJxgwiJtC7DWKdWShU09O7MjmYlKRuKL4IaiQ2amqjDAKY04AzC25f3M3D7xpmvD-SI7q8I37QUhIJm0h9KCDgWX675bSFtg/s200/P3221531.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605291989403302050" /></a>< A10. Fold the top and bottom edges inward on existing creases (as in A7) to get this. Then swing the left and right ends together. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRJbNr32L3b7cmBvSzoxOMhDdr9l-3ozdU7cYkU_1HzMlVGfXlPOQDbJK_Wh5t8hZYgl_URv9E66G8Y_jeCB4BoPUuDOerE6G3bj8NgIL0U19Y54PFpjFTZFLyU9rSyvHl2cGfmQ/s1600/P3221533.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRJbNr32L3b7cmBvSzoxOMhDdr9l-3ozdU7cYkU_1HzMlVGfXlPOQDbJK_Wh5t8hZYgl_URv9E66G8Y_jeCB4BoPUuDOerE6G3bj8NgIL0U19Y54PFpjFTZFLyU9rSyvHl2cGfmQ/s200/P3221533.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605292429807465442" /></a>A11. > This paper form with 4-way symmetry is called a bird base, because it's often used to fold birds. (But sometimes fish are folded from a bird base and birds from a fish base.) I'll call the 4 bottom points 'legs', the top point 'head', and the 4 side points 'shoulders'.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinUwdtm2t1y4gGc1IZIrcJ9Id96JDRKFX_0l0FvBRGjLZUBFM_q0aB55dIL31ZMKOfoZNlEMufzcO5MEO5qQ6F_t208J2J0rHBoIxK-jRJ7RtVXHMrljmwAqU24XHhnKVnNJkTlg/s1600/P3221535.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinUwdtm2t1y4gGc1IZIrcJ9Id96JDRKFX_0l0FvBRGjLZUBFM_q0aB55dIL31ZMKOfoZNlEMufzcO5MEO5qQ6F_t208J2J0rHBoIxK-jRJ7RtVXHMrljmwAqU24XHhnKVnNJkTlg/s200/P3221535.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605292726536386306" /></a>< A12. Pull 2 opposite 'legs' past the 'head' as far as they can go, and flatten. Each new crease will be between 2 'shoulder' points. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMSx9cCQJSGsfYn8pIKdunqBTSgwgn1M4v9BLpA4Uzmx4cxrPvAG19O7_sRM_FDTaA2fRrbG9ymvfN7CIt-ZsVGUy1ePN55JlRmnVrKcFVLhSao1jTOCWPfageZ7IPSNy1_nLPQQ/s1600/P3221537.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMSx9cCQJSGsfYn8pIKdunqBTSgwgn1M4v9BLpA4Uzmx4cxrPvAG19O7_sRM_FDTaA2fRrbG9ymvfN7CIt-ZsVGUy1ePN55JlRmnVrKcFVLhSao1jTOCWPfageZ7IPSNy1_nLPQQ/s200/P3221537.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605293042487756930" /></a>A13. > With one 'leg' point raised, fold the 'head' point to the center of the crease at the base of the raised 'leg', like this. Then unfold, flatten, turn the model over and repeat from the other side.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF3A7B-sXscsT978Go0qIPkNYn7f5tP34tFXUorioEca50_4rIUb2BJRUHFamFXbiuRVwn5klIRmQ0s6ARqJgzDEk4wtEoNJJtm9dsLmoBRvO59lwBukZCYnmPE2vEOxmOArZb9g/s1600/P3231539.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF3A7B-sXscsT978Go0qIPkNYn7f5tP34tFXUorioEca50_4rIUb2BJRUHFamFXbiuRVwn5klIRmQ0s6ARqJgzDEk4wtEoNJJtm9dsLmoBRvO59lwBukZCYnmPE2vEOxmOArZb9g/s200/P3231539.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605293342476226962" /></a>< A14. Returning to the A11 position, notice the creases made by step A12. (In this view, notice the crease between 'shoulder' points on the right side, but no similar crease on the left.) Turn the model and repeat step A12 to get 2 more creases between 'shoulder' points. Also, fold the 'head' point both ways as in A13 in this position.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkRqikTKfAmv5FP1QLFZ2NNsDdUCJQqLTL6haXRTLGhTLFlFkXQ3tXaZ8KSznHq3BPpE31cplFKXKuu8hBSnpS4he9N_ywD2nDbTd_nP_n0Bbya0ariiv6GBGxJah4S-3-Baqf7Q/s1600/P3231541.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkRqikTKfAmv5FP1QLFZ2NNsDdUCJQqLTL6haXRTLGhTLFlFkXQ3tXaZ8KSznHq3BPpE31cplFKXKuu8hBSnpS4he9N_ywD2nDbTd_nP_n0Bbya0ariiv6GBGxJah4S-3-Baqf7Q/s200/P3231541.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605294179623593538" /></a>A15. > Returning to the A11 position, flatten the paper around the 'head' point along the creases made by the folding the 'head' point in step A13, forming a flat square on existing creases, like this. (This prepares for a 'sink' fold.)<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizUbpUTDFQWfxUloWp-o0LHJZB56mXNkQWSIue1OlzrVgVogQXwp-n2gX75-Z1A88lFV-Uog-_b0xdOkCL9uHPX3FsyZRy7_1fqH8XNEh1Sgvi1oYEoC1NWqm5baDVv_R2vhkOcQ/s1600/P3231543.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizUbpUTDFQWfxUloWp-o0LHJZB56mXNkQWSIue1OlzrVgVogQXwp-n2gX75-Z1A88lFV-Uog-_b0xdOkCL9uHPX3FsyZRy7_1fqH8XNEh1Sgvi1oYEoC1NWqm5baDVv_R2vhkOcQ/s200/P3231543.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605294572331358146" /></a>< A16. Now, the sink fold: Push down on the diagonals of the new square and push inward the middles of the sides of the square, making all folds on existing creases.<br /><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpKxi6G-oGVjQ4z-iABW3Lexud4AC4hXMl9rtxmbhhFba9PvKrB5PpFns2DGiHjTFyB9cCkm3zIMsQbDD8zlFoaaL5fsCQnVBaRy9ctCVNw0CLvvuMcKvwfhKSm1vUZjkJy7ZfPQ/s1600/P3231545.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpKxi6G-oGVjQ4z-iABW3Lexud4AC4hXMl9rtxmbhhFba9PvKrB5PpFns2DGiHjTFyB9cCkm3zIMsQbDD8zlFoaaL5fsCQnVBaRy9ctCVNw0CLvvuMcKvwfhKSm1vUZjkJy7ZfPQ/s200/P3231545.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605294954258319922" /></a>A17. > Flatten the sink fold, like this. <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyPvFtitVHpDnmC-04oCk1-8YCVtZQMWY-_QvyAWDqwGkqAxdWnQvpglK-E3iE7MFyDqR7_dgmj3S1S5YEoWI20KppwVmv92gZYbis1Xgri0sbT7Ps7OMt1T9JLlASVTPlUvoEvw/s1600/P3231547.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyPvFtitVHpDnmC-04oCk1-8YCVtZQMWY-_QvyAWDqwGkqAxdWnQvpglK-E3iE7MFyDqR7_dgmj3S1S5YEoWI20KppwVmv92gZYbis1Xgri0sbT7Ps7OMt1T9JLlASVTPlUvoEvw/s200/P3231547.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605303783697455730" /></a>< A18. Raise 2 opposite 'legs' as in step A12, and fold each raised leg in half, to get this position. <br /><br><br><br><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgW-5FemEbzBOd4AWE79NKvauCqlBo5tnJXAufBtkNGMM48u9QVcWgMnGzP3FZ2NCxonxWCKYmHWeSucRbLaRf-THYQbcK0s72qcGOm2B_bbQ8Mo2TFP9eV46oHksjV_CBCEcLqeA/s1600/P3231549.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgW-5FemEbzBOd4AWE79NKvauCqlBo5tnJXAufBtkNGMM48u9QVcWgMnGzP3FZ2NCxonxWCKYmHWeSucRbLaRf-THYQbcK0s72qcGOm2B_bbQ8Mo2TFP9eV46oHksjV_CBCEcLqeA/s200/P3231549.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605305694109168754" /></a>A19. > Holding one of the raised 'legs' in its folded-in-half shape. pull it half-way back to line up with 2 'shoulder' points, like this. Check that the pivot point inside is at a crease intersection. This makes the creases shown in view A20. Repeat on the other raised 'leg'.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSdDlVqG__cl4IrQKaVGedSgdca2e63RP4H7wntBRfvtywqXGB50UXmnZl-DQ72RgacGmiifEbuMUz39MBZg0ATosok9E8EH2DEY2rfv8aaB8usSqBORgJRzWPumc3RrRayC6kbg/s1600/P3231551.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSdDlVqG__cl4IrQKaVGedSgdca2e63RP4H7wntBRfvtywqXGB50UXmnZl-DQ72RgacGmiifEbuMUz39MBZg0ATosok9E8EH2DEY2rfv8aaB8usSqBORgJRzWPumc3RrRayC6kbg/s200/P3231551.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605306016096879442" /></a>< A20. Returning to the A17 position, the new creases form an up-side-down V crossing the vertical and horizontal creases, as seen here. Rotate the model to repeat step A19 on the remaining 2 'legs'.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijdqrCBK4ao49hYLmMkxlbCR7LurPALsTeN0ziNPBsmAOddYOXEbt8WtG6GDgtgX9EfWWuvDUxvafxXfRhQNJp1-wMVGEK79IlZngH78ZtYNpTeFzjoEvPuKEUS7bBXHjLhMyZaA/s1600/P3231554.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijdqrCBK4ao49hYLmMkxlbCR7LurPALsTeN0ziNPBsmAOddYOXEbt8WtG6GDgtgX9EfWWuvDUxvafxXfRhQNJp1-wMVGEK79IlZngH78ZtYNpTeFzjoEvPuKEUS7bBXHjLhMyZaA/s200/P3231554.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605306462521645490" /></a>A21. > The model has 4 'sides', each with one 'leg' point and 2 'shoulder' points. Flatten one side, then flatten a second nearby side so that its left shoulder lands on the center crease of the first side, as shown here.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6IZqCaD19bjwxgObrxjqY2JrV0dFh4oqvuqNghadp2LDhFhZffKVJgWBYwkz8jc8xX49rXE-ePE_F-Sf7XlqW1LuamBB1EX27bS9Wp477E4ZOj5t5j-xkqUnWGuv48hnFTy9c6A/s1600/P3231556.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6IZqCaD19bjwxgObrxjqY2JrV0dFh4oqvuqNghadp2LDhFhZffKVJgWBYwkz8jc8xX49rXE-ePE_F-Sf7XlqW1LuamBB1EX27bS9Wp477E4ZOj5t5j-xkqUnWGuv48hnFTy9c6A/s200/P3231556.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605306770993872450" /></a>< A22. Holding the alignment of sides 1 and 2 (pointing left and down in this view), align side 3 (pointing right here) with side 2 in a similar way. (The sink fold in the center will begin to open.)<br /><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSD-nqPOuqG9npeyMIxHiV57Azq7SfbBVTRx5jmmgK-zUe57I9FwnNIM7qUu1xWb-t6gRXKTSalURuanwU_Bia3OJnKGUwPh_F6dWo3Q1uUSdC0Ai1a822P4ijuACWa3379-VvOA/s1600/P3231557.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSD-nqPOuqG9npeyMIxHiV57Azq7SfbBVTRx5jmmgK-zUe57I9FwnNIM7qUu1xWb-t6gRXKTSalURuanwU_Bia3OJnKGUwPh_F6dWo3Q1uUSdC0Ai1a822P4ijuACWa3379-VvOA/s200/P3231557.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605307116592271282" /></a>A23. > Align side 4 with side 3 in a similar way. (The sink fold in the center will open more.) <br /><br><br><br><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDeNSbORLxunpyRwd4sTIPjbtZsegZZpSPzAQF9rcLfo-FuLsYvE0Czy8EEn9U3bxUCW9myX7Gz3D7g6qx-kqfjkEM23gqaZqWSq_5zWW_ejaKUesko8RvgYfL0NRfZL5DQv9EpQ/s1600/P3231558.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDeNSbORLxunpyRwd4sTIPjbtZsegZZpSPzAQF9rcLfo-FuLsYvE0Czy8EEn9U3bxUCW9myX7Gz3D7g6qx-kqfjkEM23gqaZqWSq_5zWW_ejaKUesko8RvgYfL0NRfZL5DQv9EpQ/s200/P3231558.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605307396362760066" /></a>< A24. Open the sink fold completely and flatten. (I 'iron' it with the back of a fingernail.) This forms a square 'button' at the center. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOzxM_eqehIVr5va_f73b_B5jR5gNY3gpznMh3sgHP-fDJepXv7_QlRA6I10xZnPBsdmCrWef1kfd4Wo6MGx6esQxVfcJSVmU9YL1kqap7fG5Xncna8baJCTSpWtsT8eMKpHA4Hg/s1600/P3231562.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOzxM_eqehIVr5va_f73b_B5jR5gNY3gpznMh3sgHP-fDJepXv7_QlRA6I10xZnPBsdmCrWef1kfd4Wo6MGx6esQxVfcJSVmU9YL1kqap7fG5Xncna8baJCTSpWtsT8eMKpHA4Hg/s200/P3231562.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605307824960520610" /></a>A25. > Raise one of the 'shoulder' points up against the nearest edge of the square 'button', creasing it along the edge of the square, like this. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYEoxFARw87nurRnNYCQUc5RYIkOiG_2nsma3k-9ZnAZ4zYMs0J_aDPDyFgQVoPCKSXccYynQAq2W20xfxS-UA0vGkmaFPnYysubtWzJzhDL0_dT5a67B-1NXkHPuleMP4pb1H7g/s1600/P3231564.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYEoxFARw87nurRnNYCQUc5RYIkOiG_2nsma3k-9ZnAZ4zYMs0J_aDPDyFgQVoPCKSXccYynQAq2W20xfxS-UA0vGkmaFPnYysubtWzJzhDL0_dT5a67B-1NXkHPuleMP4pb1H7g/s200/P3231564.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605308736775870242" /></a>< A26. The 'shoulder' point should land on the center of the square. Part the paper from the center of the square to the corner of the square, but allow the paper to be curled past the corner, like this.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNsl4uKqXjGriF9FLVSvFlvTootZwkwgZC_D_idyH9FWN26eP7ejI-IjNGCsKj4mK4G84zSNQucr8rdc_RN1xF7NZQ856fqhhX3xIo8_NXiDrwy9jG2XVpeSN59I-ikG_1gG-WgA/s1600/P3231566.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNsl4uKqXjGriF9FLVSvFlvTootZwkwgZC_D_idyH9FWN26eP7ejI-IjNGCsKj4mK4G84zSNQucr8rdc_RN1xF7NZQ856fqhhX3xIo8_NXiDrwy9jG2XVpeSN59I-ikG_1gG-WgA/s200/P3231566.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5605309268040395938" /></a>A27. > Lift the side of the square button and slip the new fold under the button, like this. <br /><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1waqtjJ_xb11tfeMxFh_5IrEI2JLI6fvmmStx_1lZntvSBctVIvNWkB5-i1q7fl5vYeVxEkI41ccVtftP8Mpr3iZeKQLmAKF4ZlgID7DYNTu4_RAflNpxPAlsJJz30L3sJ6Hqlw/s1600/P3231568.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1waqtjJ_xb11tfeMxFh_5IrEI2JLI6fvmmStx_1lZntvSBctVIvNWkB5-i1q7fl5vYeVxEkI41ccVtftP8Mpr3iZeKQLmAKF4ZlgID7DYNTu4_RAflNpxPAlsJJz30L3sJ6Hqlw/s200/P3231568.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606385909468743538" /></a>< A28. Repeat steps A25 through A27 on the remaining 3 'shoulder' points to get this. (The curled areas will be creased later.) These are four petals.<br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgj336uTHpae4pzJowOlY9vXrXB0cbqm4EWgv4o50-KIKrx_HzigakUPJuNvSR_YmOxKsD3UfgpWBE8pg6zFrZlBD0ae8wE5Lq0aS3iYOcUSjK4VIXGQY068aUaVkgPWXc842IO3A/s1600/P3231570.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgj336uTHpae4pzJowOlY9vXrXB0cbqm4EWgv4o50-KIKrx_HzigakUPJuNvSR_YmOxKsD3UfgpWBE8pg6zFrZlBD0ae8wE5Lq0aS3iYOcUSjK4VIXGQY068aUaVkgPWXc842IO3A/s200/P3231570.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606386763635832018" /></a>A29. > The bottom side looks like this. <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8T5rhTl6Pm53UAOK5YKVln0Anw53cXhQrY9PW571crkWIAyb7oJpwUyJ-ZA5XH4uCPmlXuhGqC6UFyK4sTO3CsbVgikFc-WuAZy74UKuYldpBIZ-smZQDoP7eoTR8jb0sZ-vwjw/s1600/P3231572.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8T5rhTl6Pm53UAOK5YKVln0Anw53cXhQrY9PW571crkWIAyb7oJpwUyJ-ZA5XH4uCPmlXuhGqC6UFyK4sTO3CsbVgikFc-WuAZy74UKuYldpBIZ-smZQDoP7eoTR8jb0sZ-vwjw/s200/P3231572.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606387092480550082" /></a>< A30. Looking at the bottom, mountain-fold a petal on two angled creases while valley-folding on the center crease from where the angled creases meet to the center of the model. The angle of the new creases should be sharper for the smaller squares (inner petals) to make these petals stand higher, and should be blunter for the larger squares (outer petals) to make these petals lean out more.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPgf0-tMzgh5y-Q6iNe1HwY1D8rIJfSgPl43ywTENsGSowxyIUx49TNCEXkf0lOLSmbHOeNNK8CZv-CHoGvzvHL8n63ZbAX4z5JQs4navTVlvlB2ApDI6Cz3iWB_BQWkQRIGxq8A/s1600/P3231574.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPgf0-tMzgh5y-Q6iNe1HwY1D8rIJfSgPl43ywTENsGSowxyIUx49TNCEXkf0lOLSmbHOeNNK8CZv-CHoGvzvHL8n63ZbAX4z5JQs4navTVlvlB2ApDI6Cz3iWB_BQWkQRIGxq8A/s200/P3231574.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606389233162811378" /></a>A31. > Repeat step A30 on the remaining 3 petals to get this (bottom view). <br /><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBqsCL4qA8DbU2K4_NhsGRwE7wCVshq58u6zjh6BsoqE6U8oURaZrPV5Yl9m_ML-kemXlmZUAdh3pp2gsczLW3KqL7lI6LRw-dK3JVgJM6wbpkzKF2ihfsDyG39UC8r6XsFGIaCw/s1600/P3231576.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBqsCL4qA8DbU2K4_NhsGRwE7wCVshq58u6zjh6BsoqE6U8oURaZrPV5Yl9m_ML-kemXlmZUAdh3pp2gsczLW3KqL7lI6LRw-dK3JVgJM6wbpkzKF2ihfsDyG39UC8r6XsFGIaCw/s200/P3231576.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606390284789543938" /></a>< A32. Top view of a set of 4 petals. Press the curled paper areas against the creases made in step A30. Curl each petal so that it is curved rather than simply folded on its center line. <br /><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLYjG7EygNPP_ab3qjQL3YximkmSnOXuWA8k8oHbFAXJpZoa12oNhm9hlYGCLbyXP5FhKB1_4lPG2n6L-PO_RScPjp0FnjYVZSS-XYjYcTm6i9AlY5K4IchHBjt7N_gMI3rG2Xww/s1600/P3231578.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLYjG7EygNPP_ab3qjQL3YximkmSnOXuWA8k8oHbFAXJpZoa12oNhm9hlYGCLbyXP5FhKB1_4lPG2n6L-PO_RScPjp0FnjYVZSS-XYjYcTm6i9AlY5K4IchHBjt7N_gMI3rG2Xww/s200/P3231578.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606390696945908930" /></a>A33. > To make a set of inner (smaller) petals stand more erect, form a cup with your fist, and stuff the petals into the cup; then put a finger inside and smooth the paper against the cup (inside of fist). <a href="#AB35"><strong>Skip to step AB35.</strong></a><br /><br /><strong>'B' Petal Design</strong><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvSWHGsSDTV3kgMCYBjhw7CYZrzxGHWM-c8j8m4D0pJqowcOKhDYfcpflqswrTo7NCY-FuAaDbuUEHb2TMckMQuPkGO4zRTWusNZrJZFDUNbauUVmjPNlDKGuDbl4P-74xy5iIug/s1600/P3221514.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvSWHGsSDTV3kgMCYBjhw7CYZrzxGHWM-c8j8m4D0pJqowcOKhDYfcpflqswrTo7NCY-FuAaDbuUEHb2TMckMQuPkGO4zRTWusNZrJZFDUNbauUVmjPNlDKGuDbl4P-74xy5iIug/s200/P3221514.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606391171392589650" /></a>< B3. Fold (softly) a wing over and past the center line so that the top surface and the exposed surfaces on the left have equal angles (3 x 30 degrees = 90). Do not press down hard on the new crease yet.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMTr_bGHKxfN_6ODM6v2tiGwywxJ8hJIzoJ8FZ2_OaOA-RHrQwJriibQxJRR7-9eBdYlFqv_-MJZCghpooQmHWm4aNlIETcbS024ZnAUZ8PBGhwpB7hUBzAs9HvqRFC2qLG8Tu8w/s1600/P3221517.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMTr_bGHKxfN_6ODM6v2tiGwywxJ8hJIzoJ8FZ2_OaOA-RHrQwJriibQxJRR7-9eBdYlFqv_-MJZCghpooQmHWm4aNlIETcbS024ZnAUZ8PBGhwpB7hUBzAs9HvqRFC2qLG8Tu8w/s200/P3221517.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606393552728149634" /></a>B4. > Fold the wing on the other side over the first wing. Adjust so that the first (bottom) wing is tucked close to the crease of the second wing, and the second wing NEARLY reaches the crease of the first wing. After adjusting, press down hard on both new creases.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbRLf6xSao80P_xIt9FLOOdu5S4NAQolngQuZZbSd93RQCUYYVi_RnlM71ymxpVsPSSArnIns4UsToLr_B_czHol117BLCTSMoJSWlGayhQcyDyAnuDAlAb61mOU9mVYv2CHxcRw/s1600/P3221519.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbRLf6xSao80P_xIt9FLOOdu5S4NAQolngQuZZbSd93RQCUYYVi_RnlM71ymxpVsPSSArnIns4UsToLr_B_czHol117BLCTSMoJSWlGayhQcyDyAnuDAlAb61mOU9mVYv2CHxcRw/s200/P3221519.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606393922291957794" /></a>< B5. Fold the raw edge of each wing back to the previous crease. There should be a small gap at the center. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtz4N-TnUWBDZ8jdQImXewix9Pb01ycaG8hPoadjXrCVYHoY-s-Rqdlxgxbs651qZ2-zpcNxfDx7oEj8GWBFIxPx0_ktlsx65sOy1gVxcWvDxAxx-xKNxJX7K5MIVC5UF9SXe4Eg/s1600/P3221521.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtz4N-TnUWBDZ8jdQImXewix9Pb01ycaG8hPoadjXrCVYHoY-s-Rqdlxgxbs651qZ2-zpcNxfDx7oEj8GWBFIxPx0_ktlsx65sOy1gVxcWvDxAxx-xKNxJX7K5MIVC5UF9SXe4Eg/s200/P3221521.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606394350268718770" /></a>B6. > Turn the model over and repeat B3-B5 on the remaining 2 wings to get this. Then unfold to AB2 and flex all the creases made in B3-B6 both ways. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw2n3Yk8QT75v8vZaBDN0-jvKC8q0HqYqvkxFqVMZOeaZGJD2et4g-rinoFfxzenjYQcQSt2J0d-2ghyPh02rmoUDxD_3EyrF4aAc7qQGzTr4OqdazmlUX5IoxKOaqBSKbFHnpBQ/s1600/P3221523.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw2n3Yk8QT75v8vZaBDN0-jvKC8q0HqYqvkxFqVMZOeaZGJD2et4g-rinoFfxzenjYQcQSt2J0d-2ghyPh02rmoUDxD_3EyrF4aAc7qQGzTr4OqdazmlUX5IoxKOaqBSKbFHnpBQ/s200/P3221523.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606394652381305426" /></a>< B7. Push the model into this shape. <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizgB5nku7XRbCN03UoHlqGFQQKyM0J1swTPpwT5sdzLFC6wjqtk2thXZejApMjiM1z8zL-RcnPkQSDAScf19TD3Vj5yY9SPpLplcv6ZaI-_Rdqbt0TbOnS3UP_V8eDj5Atx6LBLw/s1600/P3221525.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizgB5nku7XRbCN03UoHlqGFQQKyM0J1swTPpwT5sdzLFC6wjqtk2thXZejApMjiM1z8zL-RcnPkQSDAScf19TD3Vj5yY9SPpLplcv6ZaI-_Rdqbt0TbOnS3UP_V8eDj5Atx6LBLw/s200/P3221525.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606397382610378754" /></a>B8. > At the top, fold inward on the existing crease closest to the center of the paper (back), then fold outward on the existing crease farthest from the center of the paper (front).<br /><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4I25NSP8WKo_-X_i0Fadbcg0pQ3NNHGfWC0e3giL6e1F0semuG1IKLmnOPnrQp-vTJ1Ds08lL9RbEK7qxQkCuBiGJ8xFz4Y5BnLnkAy5QuFfaiMG_hbk3cCbq4ckPyYVzmKTJKw/s1600/P3221526.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4I25NSP8WKo_-X_i0Fadbcg0pQ3NNHGfWC0e3giL6e1F0semuG1IKLmnOPnrQp-vTJ1Ds08lL9RbEK7qxQkCuBiGJ8xFz4Y5BnLnkAy5QuFfaiMG_hbk3cCbq4ckPyYVzmKTJKw/s200/P3221526.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606398188235366002" /></a>< B9. Repeat B8 on the bottom. <br /><br><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIluB2bTh8PcAwubfZ7hAYjXouoXL8TWPwpQGg8DCPZzOlo109J4zixGKmuvnRn5IsBSk_Baq0ajma0_F_Au08xEt0gO0Z4u9fTW6a_MCICsbzQTcn33jlJ5er3nRwtwp-6mLT0Q/s1600/P3221528.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIluB2bTh8PcAwubfZ7hAYjXouoXL8TWPwpQGg8DCPZzOlo109J4zixGKmuvnRn5IsBSk_Baq0ajma0_F_Au08xEt0gO0Z4u9fTW6a_MCICsbzQTcn33jlJ5er3nRwtwp-6mLT0Q/s200/P3221528.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606398523814217682" /></a>B10. > Push the left and right sides together, like this. <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8-ug9z_1MA_arawTHZFVAKteyXlSrnpXAdXdytY1EehN1MHhg89Y88OXmI9nGYLhyQ06oyJXnnlJb5LnRgrDpMd_Puw1fNw15GxGWsGC5ktQkDjRotrZoaijf5S_-Nkmuv4OayQ/s1600/P3221530.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8-ug9z_1MA_arawTHZFVAKteyXlSrnpXAdXdytY1EehN1MHhg89Y88OXmI9nGYLhyQ06oyJXnnlJb5LnRgrDpMd_Puw1fNw15GxGWsGC5ktQkDjRotrZoaijf5S_-Nkmuv4OayQ/s200/P3221530.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606398920148762370" /></a>< B11. Hold the 2 wings that were folded narrower and pull apart to get this. <br /><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibExoAbqmtbCtRGWoD-Sn-Qn6stvfjISWmqYIWdIomSgWUJM7QLKmIzcBNrxzzXefAJ852pj7Jo8FCwZlzMjvjCLENn2T7jh9UgJVFk8dTiKWkkK09kBJAfed78iHd9c7QDpQ2Dg/s1600/P3221532.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibExoAbqmtbCtRGWoD-Sn-Qn6stvfjISWmqYIWdIomSgWUJM7QLKmIzcBNrxzzXefAJ852pj7Jo8FCwZlzMjvjCLENn2T7jh9UgJVFk8dTiKWkkK09kBJAfed78iHd9c7QDpQ2Dg/s200/P3221532.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606399221141794578" /></a>B12. > Fold the top and bottom edges inward on the existing creases closest to the center of the paper, then fold outward on the existing creases farthest from the center of the paper (as in B8 and B9) to get this.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQfXV284BQCnON77eM-4Xg-xez8yIs4sSjkUZDcYztkuzFnPNWXVOiiSWuB-81jUUmdQB-3WRSBadHTVwLVLoU9iiz5xKJmFxe4rB3u9oPSdqhL88ojCIPfD1QMuXMXfx3XfG9PQ/s1600/P3221534.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQfXV284BQCnON77eM-4Xg-xez8yIs4sSjkUZDcYztkuzFnPNWXVOiiSWuB-81jUUmdQB-3WRSBadHTVwLVLoU9iiz5xKJmFxe4rB3u9oPSdqhL88ojCIPfD1QMuXMXfx3XfG9PQ/s200/P3221534.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606399491812784546" /></a>< B13. This modification of the bird base I call a 'skinny bird base'. (I haven't tried folding skinny birds yet.) I'll call the 4 bottom points 'legs', the top point 'head', and the 4 side points 'shoulders'.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh82NuQ2dzz6JKBLYZs__DiSc5tgvDVyb_hf5f_wfYpNuqZVPvSX_Yu5sgrm_DcGPTzvqCPlP3IzjfqqFQbNHgyxrYPWebFgcE9P3YOd8N8g0kAo9YRsF3kJeyFzkFAdAlDS_USTg/s1600/P3221536.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh82NuQ2dzz6JKBLYZs__DiSc5tgvDVyb_hf5f_wfYpNuqZVPvSX_Yu5sgrm_DcGPTzvqCPlP3IzjfqqFQbNHgyxrYPWebFgcE9P3YOd8N8g0kAo9YRsF3kJeyFzkFAdAlDS_USTg/s200/P3221536.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606399800154965346" /></a>B14. > Pull 2 opposite 'legs' past the 'head' as far as they can go (but don't pull too hard!), and flatten. Each new crease will NOT be between 2 'shoulder' points, as for the unmodified bird base. Instead, the folding is limited by lower points ('armpits'?!), so be careful. <br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcpBVV4Uy4B_yzegBT4BVXnaBqy66l9r4eeV-PyahaWsKeEFgcpWulJB4J1cndAawge2uxLhV4JX6qDrK_0BHocUTe-t5jQqNWXlJDFUIsniBmrOqKvXWtVXP0ou0SBgq0BowcnQ/s1600/P3231538.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcpBVV4Uy4B_yzegBT4BVXnaBqy66l9r4eeV-PyahaWsKeEFgcpWulJB4J1cndAawge2uxLhV4JX6qDrK_0BHocUTe-t5jQqNWXlJDFUIsniBmrOqKvXWtVXP0ou0SBgq0BowcnQ/s200/P3231538.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606400170520858754" /></a>< B15. With one 'leg' point raised, fold the 'head' point to the center of the crease at the base of the raised 'leg', like this. Then unfold, flatten, turn the model over and repeat from the other side.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjc7RYo5hPHJJsSjTMjI6fF4XNIUxcIyQZDKdE0InZdmS3PFzm13gkgWfMHvefo-4hEGxCUPknZicOZ7jiE3pcl3FvTtgl3FsflTNScWA4FjZGrwWAgi8jVZsTwySpVIoN5Yq_-g/s1600/P3231540.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjc7RYo5hPHJJsSjTMjI6fF4XNIUxcIyQZDKdE0InZdmS3PFzm13gkgWfMHvefo-4hEGxCUPknZicOZ7jiE3pcl3FvTtgl3FsflTNScWA4FjZGrwWAgi8jVZsTwySpVIoN5Yq_-g/s200/P3231540.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606400490191055090" /></a>B16. > Returning to the B13 position, notice the creases made by step B14. (In this view, notice the crease on the right side below the shoulder points, but no similar crease on the left.) Turn the model and repeat step B14 to get 2 more creases between 'shoulder' points. Also, fold the 'head' point both ways as in B15 in this position.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHQyEwudnrxYNfBPyuXNUVDCYc4G37TQHs-Gglu-_e1txkO2-YqDxyWyzdDvfb0oWbIvEyVt0gCJ2tcYUBMPg2Oj1qq_aekj9sRd3W1YZk4-QQnes3ZoMnAxYPO3bufAKtnDWkPg/s1600/P3231542.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHQyEwudnrxYNfBPyuXNUVDCYc4G37TQHs-Gglu-_e1txkO2-YqDxyWyzdDvfb0oWbIvEyVt0gCJ2tcYUBMPg2Oj1qq_aekj9sRd3W1YZk4-QQnes3ZoMnAxYPO3bufAKtnDWkPg/s200/P3231542.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606400754267185154" /></a>< B17. Returning to the B13 position, flatten the paper around the 'head' point along the creases made by the folding the 'head' point in step B15, forming a flat square on existing creases, like this. (This prepares for a 'sink' fold.) <br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuhU7rnEnm1GwDE9ohf_-oA-qYmU7kzC6SIV9RbrB66tOEJSAcKa-o-9XZVNpTwPd608iwxuOf4GaSY8ZoZ-l83v09v1R2PLsV8xGaizPYw7FUjpC431aD97-Ly_YImCips1FlvQ/s1600/P3231544.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuhU7rnEnm1GwDE9ohf_-oA-qYmU7kzC6SIV9RbrB66tOEJSAcKa-o-9XZVNpTwPd608iwxuOf4GaSY8ZoZ-l83v09v1R2PLsV8xGaizPYw7FUjpC431aD97-Ly_YImCips1FlvQ/s200/P3231544.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606402539087313794" /></a>B18. > Now, the sink fold: Push down on the diagonals of the new square and push inward the middles of the sides of the square, making all folds on existing creases.<br /><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGkoQrxAFAKi142tRx2qgKlblVg3eexZcYuHWc5AacX7YXygzOV4tQqggyNwGLXD7UZ_vBC3NSwS39Xl0o723VC5VlJPY5yz0_ngSbaHQC1OkPlVu7gOSBskZjuTV1XY34lcnHYQ/s1600/P3231546.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGkoQrxAFAKi142tRx2qgKlblVg3eexZcYuHWc5AacX7YXygzOV4tQqggyNwGLXD7UZ_vBC3NSwS39Xl0o723VC5VlJPY5yz0_ngSbaHQC1OkPlVu7gOSBskZjuTV1XY34lcnHYQ/s200/P3231546.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606402862437602002" /></a>< B19. Flatten the sink fold, like this. <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhefZW3OLH-sS0KT6uPO26MrBm-XHEuKQyxR_4c-IVk62SLBAwmx524BcHhkW8rWyubq3TNaDbh3mWdGZNhnHrTlgYNTUb7RvjOEhM9Pzg9JTNao1lWHviM6aa3opErK3JFL240qg/s1600/P3231548.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhefZW3OLH-sS0KT6uPO26MrBm-XHEuKQyxR_4c-IVk62SLBAwmx524BcHhkW8rWyubq3TNaDbh3mWdGZNhnHrTlgYNTUb7RvjOEhM9Pzg9JTNao1lWHviM6aa3opErK3JFL240qg/s200/P3231548.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606403253071584402" /></a>B20. > Raise 2 opposite 'legs' as in step B14, and fold each raised leg in half, to get this position. <br /><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXFnppBup9Pnq4sknQ11ZFbn_gP_1hju2fEiVdTqcz6Z_Kx8_6VaQQykNsCGqT720xy3J9GgQSZ7EnbUmxndX_F9z4P-dtWsxiBV0FZPmlaVTmBEgSUOTawj1UArCKFMYe8VHKCQ/s1600/P3231550.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXFnppBup9Pnq4sknQ11ZFbn_gP_1hju2fEiVdTqcz6Z_Kx8_6VaQQykNsCGqT720xy3J9GgQSZ7EnbUmxndX_F9z4P-dtWsxiBV0FZPmlaVTmBEgSUOTawj1UArCKFMYe8VHKCQ/s200/P3231550.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606403550674786370" /></a>< B21. Holding one of the raised 'legs' in its folded-in-half shape. pull it half-way back to line up with the crease used to raise the 'leg', like this. Check that the pivot point inside is at a crease intersection. This makes the creases shown in view B22. Repeat on the other raised 'leg'.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaSUAbVs0dwYHhAGB0LWihS9eul6JqoaQqHzPcq4L3NBx_7KHKiaUVd6Tmt_kJKJgIVQxscxlxqG-6wlibL4V3N-8v_1NrxV7VGgEbHxZkVhXsuxX7n0xMCP03pykmm5ZLB3KeTA/s1600/P3231552.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaSUAbVs0dwYHhAGB0LWihS9eul6JqoaQqHzPcq4L3NBx_7KHKiaUVd6Tmt_kJKJgIVQxscxlxqG-6wlibL4V3N-8v_1NrxV7VGgEbHxZkVhXsuxX7n0xMCP03pykmm5ZLB3KeTA/s200/P3231552.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606404096270454066" /></a>B22. > Returning to the B19 position, the new creases form an up-side-down V crossing the vertical and horizontal creases, as seen here. Rotate the model to repeat step B21 on the remaining 2 'legs'.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKoJOsiLvCQSgiTTsfm3jPesMyrEHh9_K2nTWqW36m2DDMDNyKTlahq3p0ov7g_tvmkYw4pu_szuLnwylH9muheMWwJG4HrYD6rXcZe9ECNiUQCdhovgrXL8B2tdsX1tB1LIHQ3g/s1600/P3231553.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKoJOsiLvCQSgiTTsfm3jPesMyrEHh9_K2nTWqW36m2DDMDNyKTlahq3p0ov7g_tvmkYw4pu_szuLnwylH9muheMWwJG4HrYD6rXcZe9ECNiUQCdhovgrXL8B2tdsX1tB1LIHQ3g/s200/P3231553.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606404521205773602" /></a>< B23. For EACH of the FOUR 'V' creases, continue one side of the V over to a 'shoulder' point by creasing like this. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5zlq-PHF4S3ASCY_6VK9Bbx-SZbgLxfmDMQGcfPAXjZb_BI4mWC7CX4qeOgEictJVQznTFwz-K4mmaGlSYi_8sV06LCkkpr_GxozRKZ2End_Kbx8pZpUw9M0Hd0Iv2xIEI91qWA/s1600/P3231555.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5zlq-PHF4S3ASCY_6VK9Bbx-SZbgLxfmDMQGcfPAXjZb_BI4mWC7CX4qeOgEictJVQznTFwz-K4mmaGlSYi_8sV06LCkkpr_GxozRKZ2End_Kbx8pZpUw9M0Hd0Iv2xIEI91qWA/s200/P3231555.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606404918566836242" /></a>B24. > The model has 4 'sides', each with one 'leg' point and 2 'shoulder' points, and a 'cross' crease that is used whenever the side is raised (prominent in view B19). Flatten one side, then flatten a second nearby side so that its 'cross' crease aligns with the center crease of the first side.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG5WuhfslaHw2JxAtTS1waw7CoHxBbroc9uBHIL1as3cw4aXHJraUx6t8FMKHdfWxN_59DW6TwpkZLmSktjftpqjjr3XkyV580EHQjUpG1x_xeSnBxUaf3NSBuydbRTYgFSmP7jg/s1600/P3231559.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG5WuhfslaHw2JxAtTS1waw7CoHxBbroc9uBHIL1as3cw4aXHJraUx6t8FMKHdfWxN_59DW6TwpkZLmSktjftpqjjr3XkyV580EHQjUpG1x_xeSnBxUaf3NSBuydbRTYgFSmP7jg/s200/P3231559.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606716241368324354" /></a>< B25. Holding the alignment of sides 1 and 2 (pointing left-down and down-right in this view), align side 3 (pointing right-up here) with side 2 in a similar way. (The sink fold in the center will begin to open.)<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHDeDsWAVS4O1D2o7fOsJ7gNx-mg-Bwr2gKpC11kh2v46oZOkSXN8coCUCuAAXwMjctsF5N87L2QdHnDT8Lykiu45aWKtrtm7p4ublK94AHa0_nUOe1X04CPk7TKN6-I7Rpft2eg/s1600/P3231560.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHDeDsWAVS4O1D2o7fOsJ7gNx-mg-Bwr2gKpC11kh2v46oZOkSXN8coCUCuAAXwMjctsF5N87L2QdHnDT8Lykiu45aWKtrtm7p4ublK94AHa0_nUOe1X04CPk7TKN6-I7Rpft2eg/s200/P3231560.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606718207329128034" /></a>B26. > Align side 4 with side 3 in a similar way. (The sink fold in the center will open more.) <br /><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8bvKG6gNvQpghpmsdEdxLBRh5cGXwF4EOZQJ-cHpRnJRA9e9hxiVEviMXCQtf28JrkQBdKBfdoX79LGoIUvqBgD1BB_lmSD1xrEoW04BliyIVmX2Ua7bt44Trmu20bIXW5PdpEw/s1600/P3231561.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8bvKG6gNvQpghpmsdEdxLBRh5cGXwF4EOZQJ-cHpRnJRA9e9hxiVEviMXCQtf28JrkQBdKBfdoX79LGoIUvqBgD1BB_lmSD1xrEoW04BliyIVmX2Ua7bt44Trmu20bIXW5PdpEw/s200/P3231561.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606718554070131474" /></a>< B27. Open the sink fold completely and flatten. (I 'iron' it with the back of a fingernail.) This forms a square 'button' at the center. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKslXpe0VXSMrteI23NgzkbUcFqrlvdb2wHVDez7_-aeY7YY9TpZgEL1Akn_6bqTaRuegwD4Fli5TuLbG74WUfdisvUM7KsxiLU1UZQbkOx5Lbi258DE3ZfUN0OuY6WEQMmnvOHA/s1600/P3231563.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKslXpe0VXSMrteI23NgzkbUcFqrlvdb2wHVDez7_-aeY7YY9TpZgEL1Akn_6bqTaRuegwD4Fli5TuLbG74WUfdisvUM7KsxiLU1UZQbkOx5Lbi258DE3ZfUN0OuY6WEQMmnvOHA/s200/P3231563.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606718948490853474" /></a>B28. > Raise one of the 'shoulder' points up against the nearest edge of the square 'button', creasing it along the edge of the square, like this. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGqx9kREBVhPbdF8ZRXqsfTaaLHnIzLtfHVk2CUkKcOqyCpVHLonvUHM7jVEIpdueyeZdF6zgnsemcPqDVwJE6lIrtFoUwL_1xSJBWMjeytN0PCVlKvCBA7xfuJj9lRtxivBAebw/s1600/P3231567.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGqx9kREBVhPbdF8ZRXqsfTaaLHnIzLtfHVk2CUkKcOqyCpVHLonvUHM7jVEIpdueyeZdF6zgnsemcPqDVwJE6lIrtFoUwL_1xSJBWMjeytN0PCVlKvCBA7xfuJj9lRtxivBAebw/s200/P3231567.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606719376445732114" /></a>< B29. Lift the side of the button and fold the shoulder point under the button, like this. <br /><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMEiXtCulyq6EjMusCXWsYLNSFo_TgSGVzeHtPCZII7pyqh2NlQkoKt6R1LBIGaKyCaQAmgfSKxh7ZKyiikI7ZW1qTEb2SWC67K33_YTM5sFFI7Hk5xnqWaPBTgEXQypY__k6Ttw/s1600/P3231569.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMEiXtCulyq6EjMusCXWsYLNSFo_TgSGVzeHtPCZII7pyqh2NlQkoKt6R1LBIGaKyCaQAmgfSKxh7ZKyiikI7ZW1qTEb2SWC67K33_YTM5sFFI7Hk5xnqWaPBTgEXQypY__k6Ttw/s200/P3231569.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606719771314247666" /></a>B30. > Repeat steps B28 and B29 on the remaining 3 'shoulder' points to get this. These are four petals. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLsAIuJIFXg6hFem0AA2ZLZKZsFYDcoLNk9jZ7hNV3FFdcEXNjAP2P9Xp13zYtLaV5A-84ptcEwQeQ2hinlNHLL_47Y4f1doey560Oe9rPwdM6iu5Zrk_AEkKRR9QSxM4nxHybKQ/s1600/P3231571.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLsAIuJIFXg6hFem0AA2ZLZKZsFYDcoLNk9jZ7hNV3FFdcEXNjAP2P9Xp13zYtLaV5A-84ptcEwQeQ2hinlNHLL_47Y4f1doey560Oe9rPwdM6iu5Zrk_AEkKRR9QSxM4nxHybKQ/s200/P3231571.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606720165204827106" /></a>< B31. The bottom side looks like this. <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2ffE1sYB9NFs_MJ8P1oONCPcF1mGie9et352ec_7L_r1Be6jP3pNz5yZTObwOLqb5_l2ssKPHZGwzd9gNVFLNnLMkIdsp3hnJ6V-1CocQ6zbFxwPQlfJrRiD-UeWJ7Qlz_xnmPg/s1600/P3231573.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2ffE1sYB9NFs_MJ8P1oONCPcF1mGie9et352ec_7L_r1Be6jP3pNz5yZTObwOLqb5_l2ssKPHZGwzd9gNVFLNnLMkIdsp3hnJ6V-1CocQ6zbFxwPQlfJrRiD-UeWJ7Qlz_xnmPg/s200/P3231573.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606720662705848066" /></a>B32. > Looking at the bottom, mountain-fold a petal on two angled creases while valley-folding on the center crease from where the angled creases meet to the center of the model. The angle of the new creases should be sharper for the smaller squares (inner petals) to make these petals stand higher, and should be blunter for the larger squares (outer petals) to make these petals lean out more.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2vwX4puLi_3ozwOKCERUo_d-QvuafkY5uzTcR_8HEf2kDJJqua7w4yclUx6jsM5BSXhee43U2NeYjbOoOcndu0KkI3Y9Xf6lTl84sLTvdQ2nuu66vVgtrNfNH89B9o7GbCkKb9Q/s1600/P3231575.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2vwX4puLi_3ozwOKCERUo_d-QvuafkY5uzTcR_8HEf2kDJJqua7w4yclUx6jsM5BSXhee43U2NeYjbOoOcndu0KkI3Y9Xf6lTl84sLTvdQ2nuu66vVgtrNfNH89B9o7GbCkKb9Q/s200/P3231575.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606720951952416770" /></a>< B33. Repeat step B32 on the remaining 3 petals to get this (bottom view). <br /><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3Ww1XJWvChy85xZzratDmFqPWhwNF7_TdRxjUxbA1ilxsEmqLOHadw493iyl-fQPUyAewYcvShYoJIy71KSnOjzSsdwL9PM2xE13IYvCQNwYuqJD6cCX4MR76Esdb1GLZFephDw/s1600/P3231577.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3Ww1XJWvChy85xZzratDmFqPWhwNF7_TdRxjUxbA1ilxsEmqLOHadw493iyl-fQPUyAewYcvShYoJIy71KSnOjzSsdwL9PM2xE13IYvCQNwYuqJD6cCX4MR76Esdb1GLZFephDw/s200/P3231577.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606721250236990674" /></a>B34. > Top view of a set of 4 petals. Curl each petal so that it is curved rather than simply folded on its cemter line. Press inward at each notch between petals, blunting each corner of the square button. <br /><br /><a name="AB35"><strong>Petal Assembly</strong></a><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLPH_AJYWqV6wo6WVCPcljYFiShH7ry2uqmJynjv6k_9C4flKLB4-KMb5nRICS9SMLNt6Dq0rLy8Zn-WXTHLQLJiOmbqiPxGBofK8If85NoYVflNqIa7_3yNiw0stzm5hHYhPkpg/s1600/P3231579.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLPH_AJYWqV6wo6WVCPcljYFiShH7ry2uqmJynjv6k_9C4flKLB4-KMb5nRICS9SMLNt6Dq0rLy8Zn-WXTHLQLJiOmbqiPxGBofK8If85NoYVflNqIa7_3yNiw0stzm5hHYhPkpg/s200/P3231579.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606721736943013458" /></a><strong>AB35.</strong> Stack the 4-petal units, starting with the smallest (on top) and proceeding to the largest, using glue on the central square between units.<br /><br />< Here we show the first 2 (smallest) units. Notice that the gaps between petals at top, bottom, left, and right are a little larger than the other 4 gaps. This slight assymetry or 'imperfection' provides a more natural look. The petals of the next (3rd) unit (underneath) should be placed approximately at the larger gaps. The petals of the 4th unit should be placed under the smaller gaps seen here. In general, each set of petals should be placed approximately under the largest gaps currently seen. (See the view of the finished water lilly.)<br /><br /><strong>Lilly Center</strong><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3LCJNO7i6Ne1r3cX1kkCil9BCYUYEjnQuqMB7xaIziMdouViqKIrgFg2JtkK9uXqF8ElZUQQB24BioNv-qY5qizd2DKIsc8rhwlTgknAn39-4m4coCdyM1T9qGxHi0xNHxDg1Mw/s1600/P3231580.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3LCJNO7i6Ne1r3cX1kkCil9BCYUYEjnQuqMB7xaIziMdouViqKIrgFg2JtkK9uXqF8ElZUQQB24BioNv-qY5qizd2DKIsc8rhwlTgknAn39-4m4coCdyM1T9qGxHi0xNHxDg1Mw/s200/P3231580.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606729174023515394" /></a>C1. > For the center of the lilly, use 2 squares of a contrasting color (color on both sides of the paper). One square should about 1/16 inch more than 2 inches on a side, and the other about 1/16 inch less than 2 inches on a side. Cut enough off of each corner that the all 8 sides are approximately equal (octagon). Draw a circle in the middle with a diameter about 1/3 of the width of the paper. A lipstick container or toothpaste cap may be the right size to make a smooth circle. (The circle will be hidden later.)<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrBwt5Z_EVrxhgiUJbPOzhrb69k872DBKRL8xSD2fcfW6RJwmECTVZLBcdP9UyUFYb8PtWVY86byLxdorBoQmyndeGLUeX-1MOlea1Ns6xMlSCXsSivr2jJFfw3wcnWMzsQ7Kviw/s1600/P3231581.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrBwt5Z_EVrxhgiUJbPOzhrb69k872DBKRL8xSD2fcfW6RJwmECTVZLBcdP9UyUFYb8PtWVY86byLxdorBoQmyndeGLUeX-1MOlea1Ns6xMlSCXsSivr2jJFfw3wcnWMzsQ7Kviw/s200/P3231581.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606745141681976626" /></a>< C2. Cut slivers as narrow as you can all around, from the edge of the paper to the edge of the circle. Each sliver will be wider at the outside end and narrow at the inner end. Aim the scissors towards the center of the circle, and watch the circle edge for spacing the cuts. Don't worry if 2 or 3 slivers fall off; you can easily get over 100 slivers.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPcPnMua6oQqUH3xwVuN5yMwCP0yeYCY483UD3LnUWUtJYhqAnbe26l_5NcGmXsJgmwc8qvvRQRy2tlZuahrlUyfKMjeHav4vGdI2NpJ330WVAdLYRO92FZhik8am6liK3993bMw/s1600/P3231582.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPcPnMua6oQqUH3xwVuN5yMwCP0yeYCY483UD3LnUWUtJYhqAnbe26l_5NcGmXsJgmwc8qvvRQRy2tlZuahrlUyfKMjeHav4vGdI2NpJ330WVAdLYRO92FZhik8am6liK3993bMw/s200/P3231582.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606745551373638482" /></a>C3. > Stack the smaller octagon on top of the larger one, with the drawn circles hidden between them, and a spot of glue between them, and with the octagon corners NOT aligned (for a more natural, random look).<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2X5w1dNP__eQaJUNFGcm6SEXjH-L7T7GEcI53Dcb0k08o7phKunhK9Qy0RKOxPTdPPnM_MlEOmhvktGFwpIfuqavaAkvTbqnFqNj5jzwn-AnMjm3QO_l4t-BMuqK-4C2TKnwXpw/s1600/P3231585.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2X5w1dNP__eQaJUNFGcm6SEXjH-L7T7GEcI53Dcb0k08o7phKunhK9Qy0RKOxPTdPPnM_MlEOmhvktGFwpIfuqavaAkvTbqnFqNj5jzwn-AnMjm3QO_l4t-BMuqK-4C2TKnwXpw/s200/P3231585.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606746039520031458" /></a>< C4. Bend all the slivers toward the side with the smaller unit, and pinch the circular edge all around to get a good crease. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjusyGPcCjkq77AHM1w9y8nzbYjp89Cm-wlS__USjDTpZa-v14w3BdjT3xXQfrqz9jcaTTVI7CoEGjxDRTWXS6r8loDj1aqYO0MxamSacB1tHX5VTQuLMyfuf2B5UMX6ncUIqT9_Q/s1600/P3231584.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjusyGPcCjkq77AHM1w9y8nzbYjp89Cm-wlS__USjDTpZa-v14w3BdjT3xXQfrqz9jcaTTVI7CoEGjxDRTWXS6r8loDj1aqYO0MxamSacB1tHX5VTQuLMyfuf2B5UMX6ncUIqT9_Q/s200/P3231584.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606746648381147266" /></a>C5. > Holding the center with one hand, stir the slivers (stamens) into random positions by pushing them up and down and sideways repeatedly. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidprVEjY1RRBoCsj5URHM99LEfNw5cXCKUNJ2Hu6BjywIGICs2fGtaS5gVHrPgg45uiekiFeQUgWOHy_8Jqx5yz3itSB_0TPO5Y8kAmtgZFErU9B5VGPx5d4IYa3Cz_G8LbjjITA/s1600/P3231583.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidprVEjY1RRBoCsj5URHM99LEfNw5cXCKUNJ2Hu6BjywIGICs2fGtaS5gVHrPgg45uiekiFeQUgWOHy_8Jqx5yz3itSB_0TPO5Y8kAmtgZFErU9B5VGPx5d4IYa3Cz_G8LbjjITA/s200/P3231583.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606746984337837090" /></a>< C6. Form a cup shape. Some water lillies have a noticable hole in the middle of the stamens, like this. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsWHdF3KOD8uKk35aL86zKqB2NclG0E9EE3c2MscqzGSRIzlnJG90NmA6g9Oaswy5hp-wcFovGqJPMuwalRzMOHA9KTB0aeLUUmTqRwhQrUmYjPqiqEVvCFfkg0UEqDgAaVljVtw/s1600/P3231586.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsWHdF3KOD8uKk35aL86zKqB2NclG0E9EE3c2MscqzGSRIzlnJG90NmA6g9Oaswy5hp-wcFovGqJPMuwalRzMOHA9KTB0aeLUUmTqRwhQrUmYjPqiqEVvCFfkg0UEqDgAaVljVtw/s200/P3231586.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606747413916213506" /></a>C7. > Some water lillies have a barely noticable hole in the middle of the stamens, like this. Glue the stamens unit in the center of the lilly. For a tiny hole, you may need the eraser end of a pencil to press the stamens unit down until the glue sets. <br /><br /><a name="pad"><strong>Lilly Pad</strong></a><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3qc3BcPIZlNJUS4pJL12sU-s2fQOwtwitquc8kxUSh-2RKN5cO0NCF1RSL1-ySI2uAFI44sNiYGOx1MDRAdo_6mKlqEOuSRkDxSumO7hKhlEdUvjShZGyrdXA5N5R01autLpp1g/s1600/P3251588.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3qc3BcPIZlNJUS4pJL12sU-s2fQOwtwitquc8kxUSh-2RKN5cO0NCF1RSL1-ySI2uAFI44sNiYGOx1MDRAdo_6mKlqEOuSRkDxSumO7hKhlEdUvjShZGyrdXA5N5R01autLpp1g/s200/P3251588.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606747850750549298" /></a>< P1. For a lilly-pad, start with a 7 to 8.5 inch square of green paper. Mine is green on both sides, but you can use paper that is green on one side only. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizI7P4nlxQHqy9igAjRLI_nyUDAKtvULT3h-WZD8KdhBskJIcNE7QaTXiSpaOlYqAnF-xUp7MTG0BvwOfhpO1_Xw-FCrKYdiFAOe8Va90zLAbtfOgTXicpiIfTpfJz7C9lP8Nwkw/s1600/P3251589.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizI7P4nlxQHqy9igAjRLI_nyUDAKtvULT3h-WZD8KdhBskJIcNE7QaTXiSpaOlYqAnF-xUp7MTG0BvwOfhpO1_Xw-FCrKYdiFAOe8Va90zLAbtfOgTXicpiIfTpfJz7C9lP8Nwkw/s200/P3251589.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606749907829843490" /></a>P2. > Fold in half parallel to an edge, like this. If green on one side only, the green should be inside here. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw-nzcdqGNaSaAHcrkaKhY8VmAKZIt6f5JDnwoFM_5Y3iqbDrBIyYRVwY66xHzMt49yUcfyRX49b0pemIyr1Ox532BL2PMUNXzAGWQYd-zZ55HsCOcCIXSnreC79lOmH7D5e0XlQ/s1600/P3251590.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw-nzcdqGNaSaAHcrkaKhY8VmAKZIt6f5JDnwoFM_5Y3iqbDrBIyYRVwY66xHzMt49yUcfyRX49b0pemIyr1Ox532BL2PMUNXzAGWQYd-zZ55HsCOcCIXSnreC79lOmH7D5e0XlQ/s200/P3251590.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606750294013782498" /></a>< P3. Fold the bottom-left and top-left corners of the top layer over to the center of the right folded edge. Two raw edges should land on the folded edge on the right, and two raw edges should meet in the middle.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXuzjZ9LQigVyb9OeuySsyY4X1_pRkhJvPBIgeDh6B5oN2BwF-KhJ4EwFF2IGfMkrGeBdSMmxB2yZIj1w1Qn62uBifmSZ0MeFK53f1pDVjxmX5CYr0sbY4WTNUSKxwLFhDOkTvyw/s1600/P3251591.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXuzjZ9LQigVyb9OeuySsyY4X1_pRkhJvPBIgeDh6B5oN2BwF-KhJ4EwFF2IGfMkrGeBdSMmxB2yZIj1w1Qn62uBifmSZ0MeFK53f1pDVjxmX5CYr0sbY4WTNUSKxwLFhDOkTvyw/s200/P3251591.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606750829750769170" /></a>P4. > Turn over and repeat step P3 on the other side. <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFtj42KeA_wwhI1njyllEqb2OwGCmMBB-OAbMVJG_toFUGPizR1y-9gci_x8EbjnFE6Zi9RI3K4-SQoybrQYDk9r3fUSXlk8yoN8gSkPL54xMJWqrCHnqTyCXeW1jA99iFD6-4Pw/s1600/P3251592.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFtj42KeA_wwhI1njyllEqb2OwGCmMBB-OAbMVJG_toFUGPizR1y-9gci_x8EbjnFE6Zi9RI3K4-SQoybrQYDk9r3fUSXlk8yoN8gSkPL54xMJWqrCHnqTyCXeW1jA99iFD6-4Pw/s200/P3251592.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606751146898369970" /></a>< P5. Unfold the first fold, and you have a blintz base. (Named after the Jewish pastry that is folded this way.) <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiekP5_iOM0FjXUaAWgi6i7aFhXIoY_cM26nw8clNsGN9juFICCARvF1Uja2Y7PxUuBQbo0EaPAYMNN5giRkTq3FoHTMB3dpzmvatDrRqXvEnFV4zCd3IEwc75v2OcFh8RZrUr2g/s1600/P3251593.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiekP5_iOM0FjXUaAWgi6i7aFhXIoY_cM26nw8clNsGN9juFICCARvF1Uja2Y7PxUuBQbo0EaPAYMNN5giRkTq3FoHTMB3dpzmvatDrRqXvEnFV4zCd3IEwc75v2OcFh8RZrUr2g/s200/P3251593.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606751509959370434" /></a>P6. > Mountain-crease as shown here, by twice folding one side over to the opposite side and unfolding. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOAqU4iey50Gb744PYFjmbq5-a9cCCtbR-fNqIfHyMmDawiK323fOItkOvVoGPy8wd_14WafEnaZDRBDf5UaxBzgjbDZPpv7Y5xgQh93COJQFIF9n1xheNH2BnG6Z8t0fsaLcsUA/s1600/P3251594.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOAqU4iey50Gb744PYFjmbq5-a9cCCtbR-fNqIfHyMmDawiK323fOItkOvVoGPy8wd_14WafEnaZDRBDf5UaxBzgjbDZPpv7Y5xgQh93COJQFIF9n1xheNH2BnG6Z8t0fsaLcsUA/s200/P3251594.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606751756108352146" /></a>< P7. Make a valley crease by bringing two mountain creases together. Do on opposite sides, as shown here. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoa9C74VbLM4ymE2oaw42iQQY1dMpSd0vpuRprejLsZhPmHtfFzqoeX515RzV_DRikPDLomRq1ROyBJM05d8GodGO5O_Lbi_67A60hOoeBWAyQGSmc7uJNZpm7IzP-8_y6THQn2Q/s1600/P3251595.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoa9C74VbLM4ymE2oaw42iQQY1dMpSd0vpuRprejLsZhPmHtfFzqoeX515RzV_DRikPDLomRq1ROyBJM05d8GodGO5O_Lbi_67A60hOoeBWAyQGSmc7uJNZpm7IzP-8_y6THQn2Q/s200/P3251595.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606752037876474786" /></a>P8. > Rotate the model 90 degrees and repeat step P7 to get a total of 4 valley creases equally spaced around the center. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB-Hpo2EYXFNPpKS7l2zK5cj7XTlWLrtWNaX7T525UsuwlJaItUF5M0bbOIZEb4u0d_QOS7MTnlQh3L68CkE6RT4WHr59lZl0TigAfcLE2aIRO5c6DDN5h_ZTNjmWG8ra_HF3mkw/s1600/P3251596.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB-Hpo2EYXFNPpKS7l2zK5cj7XTlWLrtWNaX7T525UsuwlJaItUF5M0bbOIZEb4u0d_QOS7MTnlQh3L68CkE6RT4WHr59lZl0TigAfcLE2aIRO5c6DDN5h_ZTNjmWG8ra_HF3mkw/s200/P3251596.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606752278241531394" /></a>< P9. Using the end-points of the last valley creases as a guide, fold the 4 corners toward the center. Each new crease starts at an end-point of one of the previous valley creases, and the corner should land on a diagonal.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJyhmuFRWvVx46RYFgmcsehZ2-6egm3ecgPVI1SUHnkC4yiHVn_FRYZCe89Ux9KSS-4A7jL2IKUY0RiDNkfxlKnHJ2wCVw4QVDrL4AgAdUnym4pDF-k1D3XXErtKB1vWu45fNEvg/s1600/P3251597.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJyhmuFRWvVx46RYFgmcsehZ2-6egm3ecgPVI1SUHnkC4yiHVn_FRYZCe89Ux9KSS-4A7jL2IKUY0RiDNkfxlKnHJ2wCVw4QVDrL4AgAdUnym4pDF-k1D3XXErtKB1vWu45fNEvg/s200/P3251597.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606752608928374674" /></a>P10. > Turn the previous corner folds inside-out as shown here progressing clockwise:<br />9-o'clock - the original position;<br />12-o'clock - opened up;<br />3-o'clock - corner pushed in;<br />6-o'clock - closed (all folds on existing creases).<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYT2xT5Ir5ZK8plp-hDnsJBPktIwFkF-ePE9Ph7015pqU8vjgXKC34P_187niecCuyDV8W3UNYAhyphenhyphenPLwA_JDnttm8oHIFBHPEuiDcOykWx-9guwvf5Z4dq65r041UXd6_k-ZFZbQ/s1600/P3251598.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYT2xT5Ir5ZK8plp-hDnsJBPktIwFkF-ePE9Ph7015pqU8vjgXKC34P_187niecCuyDV8W3UNYAhyphenhyphenPLwA_JDnttm8oHIFBHPEuiDcOykWx-9guwvf5Z4dq65r041UXd6_k-ZFZbQ/s200/P3251598.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606753724677777122" /></a>< P11. Do the process P10 on all 4 corners, like this. This side, with the 4 'cracks', is the bottom of the lilly-pad. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0dbo8WV0cyzY2Ww0sDJY6B1G7QlOnc5cqledpjA0847DDTZyE5M59HGoLx9MlLPyJthVShSJ0_9yKzAgyvqdWmtCDjtGTNMkKN8z8grjdSHdfl6VKqAKtUxGWISOXrKoOfL44_g/s1600/P3251599.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0dbo8WV0cyzY2Ww0sDJY6B1G7QlOnc5cqledpjA0847DDTZyE5M59HGoLx9MlLPyJthVShSJ0_9yKzAgyvqdWmtCDjtGTNMkKN8z8grjdSHdfl6VKqAKtUxGWISOXrKoOfL44_g/s200/P3251599.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606754223521270306" /></a>P12. > Here's the view from the opposite side. It is an octagon (8 equal sides). This side, with no 'cracks', is the top of the lilly-pad. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnBCz4f40F4gR9LA0QyV5TCvFpNFdv0U_yDZ-ynmvcCay7eOWk2JrO0-s53faet2ruSlE6Z3bKbXUPZbWX4s_sD8KZIAL6dDKxdw7gRHJB_khyHSK8g8EVbU7M6lV7H_klntjOsg/s1600/P3251600.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnBCz4f40F4gR9LA0QyV5TCvFpNFdv0U_yDZ-ynmvcCay7eOWk2JrO0-s53faet2ruSlE6Z3bKbXUPZbWX4s_sD8KZIAL6dDKxdw7gRHJB_khyHSK8g8EVbU7M6lV7H_klntjOsg/s200/P3251600.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606754474035799058" /></a>< P13. Bottom side up. For this step, consider each of the 8 sides to be each 4 units long. Fold each of the 8 corners inward, each fold extending 1 unit on each side of the corner. (The width of each fold is equal to the space between folds.)<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjN9YAHfhEnaWqGtfEIXvuYhbhXVzXg5e-N2-GtZaeT1bL10z6TOI06kIaXZAQsKDUcUVXfXk4vMVHS1t1JB3vjQqoxbmWutbN-ipFF1u0INQ8L87HYiwzAKMs0VNJdqM-y2KZh2A/s1600/P3251601.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjN9YAHfhEnaWqGtfEIXvuYhbhXVzXg5e-N2-GtZaeT1bL10z6TOI06kIaXZAQsKDUcUVXfXk4vMVHS1t1JB3vjQqoxbmWutbN-ipFF1u0INQ8L87HYiwzAKMs0VNJdqM-y2KZh2A/s200/P3251601.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606754761890262226" /></a>P14. > Top side up. We now have a polygon of 16 sides, which nearly looks like a circle. <br /><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBGURGXrTldoLUPLMDvneioapGqCO7uTrqCqnP-ps_m59D0hbLcBS0v8Sz50-tfVnBdQLzfwf3eF9ne3wNvmYw1kwMbszFIjc8eGnE7wuNkBfFXihAKThMyYERX7HqDa8LqydczA/s1600/P3251602.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBGURGXrTldoLUPLMDvneioapGqCO7uTrqCqnP-ps_m59D0hbLcBS0v8Sz50-tfVnBdQLzfwf3eF9ne3wNvmYw1kwMbszFIjc8eGnE7wuNkBfFXihAKThMyYERX7HqDa8LqydczA/s200/P3251602.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606755039586596770" /></a>< P15. Open up two of the folds made in step P13 on either side of a 'crack'. Folding on existing creases, flatten an 'arrow-head'-shaped area, as shown here on the left, then push in the angle-dividing creases as shown on the right. (All folds are on existing creases.) Then pinch closed. These are called 'sink' folds.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7F7Obp9jKpSVVFKrvXrkXsjiRcE3RiXqVX2VFj4gv-TvuHeHvm2qfc_wQsXxrNDE9jlhNWd7yUtEqW2nTCDMeo5RmanmShyphenhyphen-rSnbrQ8LU6DtsIcKT9OwZkher0KA63iy23B_ynw/s1600/P3251603.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7F7Obp9jKpSVVFKrvXrkXsjiRcE3RiXqVX2VFj4gv-TvuHeHvm2qfc_wQsXxrNDE9jlhNWd7yUtEqW2nTCDMeo5RmanmShyphenhyphen-rSnbrQ8LU6DtsIcKT9OwZkher0KA63iy23B_ynw/s200/P3251603.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606755442930652050" /></a>P16. > The 2 sink folds seen edge-on. Do 3 more pairs of 2 sink folds, for a total of 8 sink folds. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVu2GBlcqBm_s9gg_uM1i4C_4gPwloRi-mOZT9NK5wsu6o6Qo5cIMkjww9FGHF97Q8NHWgGtAnRex3s35V1Kybehq1n4ZBubNjG_yt_Rr3gDOe3pnu4VcIuWWX1e3AdTe-KB98tQ/s1600/P3251604.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVu2GBlcqBm_s9gg_uM1i4C_4gPwloRi-mOZT9NK5wsu6o6Qo5cIMkjww9FGHF97Q8NHWgGtAnRex3s35V1Kybehq1n4ZBubNjG_yt_Rr3gDOe3pnu4VcIuWWX1e3AdTe-KB98tQ/s200/P3251604.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606755752360977858" /></a>< P17. Bottom-side view when all 8 sink folds are done. <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyVV_X5C_DcgiiY_NOnbvyM8f4vGCBALW0PTM6Hb4vRUgVO5l0Xm2cPj1gOQfuKcJWf51B6LLAGa3aXfAYoc1v6l6M5-323InYNVlaJdgeNVHUU_Y-Hw7MwIP1EimREbO9Ujp0Lg/s1600/P3251606.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyVV_X5C_DcgiiY_NOnbvyM8f4vGCBALW0PTM6Hb4vRUgVO5l0Xm2cPj1gOQfuKcJWf51B6LLAGa3aXfAYoc1v6l6M5-323InYNVlaJdgeNVHUU_Y-Hw7MwIP1EimREbO9Ujp0Lg/s200/P3251606.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606756118306454786" /></a>P18. > Along one of the 4 'cracks' on the bottom, cut the top layer from the outside to the center. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZy7ld7ChD1zhm430tHMk7ae0P7X0-yUGMGoXBrkpBH7LAc8ZDM8VBubyAqgRFnnvZz20hGE7FYLIE7BZQDr_Sqk_xHsqXJCgC51dYrRUAUyHUUWZkNsZ_dmPd8CAtrXGYOtovSA/s1600/P3251607.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZy7ld7ChD1zhm430tHMk7ae0P7X0-yUGMGoXBrkpBH7LAc8ZDM8VBubyAqgRFnnvZz20hGE7FYLIE7BZQDr_Sqk_xHsqXJCgC51dYrRUAUyHUUWZkNsZ_dmPd8CAtrXGYOtovSA/s200/P3251607.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606756325352843314" /></a>< P19. Fold up on either side of the cut, from the edge of each nearby 'arrow-head' sink fold straight to the center. <br /><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhE_FL_Sf3pEcqdl_FIiheEj5Wikw8YW-nk6JfqE4-NSYYDkfiAewnV1Gq3hLduqMgDibD86K35UWUdbB8Dl6FPHNBysy81CW5lbfGhRTVoUCS-xXonnxhObDdbYdMQAyuB_tTwpw/s1600/P3251608.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhE_FL_Sf3pEcqdl_FIiheEj5Wikw8YW-nk6JfqE4-NSYYDkfiAewnV1Gq3hLduqMgDibD86K35UWUdbB8Dl6FPHNBysy81CW5lbfGhRTVoUCS-xXonnxhObDdbYdMQAyuB_tTwpw/s200/P3251608.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606756574949057138" /></a>P20. > Turn over, and reverse the folds made in step P19 <br /><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCY212lZoOtfMPDuPRQpn7wLnnwmxb4qhTYVE3B30LhTPo5uHUafwTjxqkZRGG9guAhAnCmrHjeGYzDeeE2n4QDqh4RDgJOa1mBzLH0vxzAo1uhaKb3JnuRE9s2W2O_tSlS_h1YQ/s1600/P3251609.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCY212lZoOtfMPDuPRQpn7wLnnwmxb4qhTYVE3B30LhTPo5uHUafwTjxqkZRGG9guAhAnCmrHjeGYzDeeE2n4QDqh4RDgJOa1mBzLH0vxzAo1uhaKb3JnuRE9s2W2O_tSlS_h1YQ/s200/P3251609.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606756880960185986" /></a>< P21. Open up one side of the cut, and fold the paper inward on the recently made creases, like this. Notice the point at the right where the 2 new folds meet.<br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX7jr_-X0xlmDjD5btk-dPM6uD1YE7MmWbi-7Pf-7NkqsZ6MZDnhidLQpLzMuEASAqzvYUh2sZDxWqLez-BTG9GD8giUokfQ4jQW03aNOI6yOLIgDI98iQwuG8wpxJ-Bq9cQseKw/s1600/P3251610.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX7jr_-X0xlmDjD5btk-dPM6uD1YE7MmWbi-7Pf-7NkqsZ6MZDnhidLQpLzMuEASAqzvYUh2sZDxWqLez-BTG9GD8giUokfQ4jQW03aNOI6yOLIgDI98iQwuG8wpxJ-Bq9cQseKw/s200/P3251610.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606757121277667842" /></a>P22. > Step P21 seen from another viewpoint. Notice 2 small triangular surfaces next to the 'arrow-head' sink. Push this area toward the center of the model. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLvDGwyOKgTezlHsbquESEsBc7Auq3FNS-O5M3QOGGs9kAal4jOzuw8sClI_VdOETQzNHVAGbM2RVCSsRB07lUj8XRlCoPZJkvTJ1i-PNPbbw8o08TrrEpy6D7KkJmcyj2xx4s5A/s1600/P3251611.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLvDGwyOKgTezlHsbquESEsBc7Auq3FNS-O5M3QOGGs9kAal4jOzuw8sClI_VdOETQzNHVAGbM2RVCSsRB07lUj8XRlCoPZJkvTJ1i-PNPbbw8o08TrrEpy6D7KkJmcyj2xx4s5A/s200/P3251611.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606757471155785746" /></a>< P23. Seen from another viewpoint, the new point is swinging toward the center and will fit between the top and bottom layers. <br /><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTiUQrN11cmoogCsofO_Xmv9Af_4Guw3Ufssp8oi5pfqIfoO-mpHOafgAnS5-heecG9v1l7nVEwSY7wkrnafXiw5r_ct7m_keJ1VAjpn5vovKY1puUUR_Zp95tb_2tQcuHHHIsbw/s1600/P3251612.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTiUQrN11cmoogCsofO_Xmv9Af_4Guw3Ufssp8oi5pfqIfoO-mpHOafgAnS5-heecG9v1l7nVEwSY7wkrnafXiw5r_ct7m_keJ1VAjpn5vovKY1puUUR_Zp95tb_2tQcuHHHIsbw/s200/P3251612.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606757786318900898" /></a>P24. > Seen from this viewpoint, the new point has swung nearly inside, between the top and bottom layers. (It needs to be pushed a little more to the left.)<br /><br />Repeat steps P21-P24 on the other side of the cut. <br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvXW1-6qpleBuPjFQXBo62KiIhUgK3-gGUsqYlqvSYBePXSUPeP_okMfnir4BS0vtNPgyOTK9OYZ1RPbRXmE195OkR4fg1LVunO01VEkGKuNPYwvB988XXc7LdfxLHpIrI7URVaQ/s1600/P3251613.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvXW1-6qpleBuPjFQXBo62KiIhUgK3-gGUsqYlqvSYBePXSUPeP_okMfnir4BS0vtNPgyOTK9OYZ1RPbRXmE195OkR4fg1LVunO01VEkGKuNPYwvB988XXc7LdfxLHpIrI7URVaQ/s200/P3251613.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606758170731265650" /></a>< P25. These white circles (from a paper punch) mark the locations where a SMALL drop of glue is needed -- not on top, but inside between the top and bottom layers. First check that the folds on either side of the cut are neatly tucked in. Do the glue spots near the center first.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8UrBlB8M0ijSAkQOQqXh3sTAJtgKSAPzMQhmj1-m6VqqcTAlljkQtjvt4nQ34ZsVkorVdxzTuLLBq3wgGsMjcPs7ax9KuLnl8zqQbFKihtPg4-8uzC3346aL0OM3Ln0lBTPl3Fg/s1600/P3251614.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8UrBlB8M0ijSAkQOQqXh3sTAJtgKSAPzMQhmj1-m6VqqcTAlljkQtjvt4nQ34ZsVkorVdxzTuLLBq3wgGsMjcPs7ax9KuLnl8zqQbFKihtPg4-8uzC3346aL0OM3Ln0lBTPl3Fg/s200/P3251614.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606758507253267154" /></a>P26. > Bottom-side view. <br /><br><br><br><br><br><br><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwjakGYczFuSOUR-bkVJheIZ9QnJPaoEuR4-MO4FzpiVa6d-RX4P3CebJk8eDBK7Vu2MCV5D_IJhSj0-HU1uX_9wrKSmlPY77oZ-5M_YXf9h73uvVuT20_Ca9rMCOZcKlGIVuWWw/s1600/P3251620.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 200px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwjakGYczFuSOUR-bkVJheIZ9QnJPaoEuR4-MO4FzpiVa6d-RX4P3CebJk8eDBK7Vu2MCV5D_IJhSj0-HU1uX_9wrKSmlPY77oZ-5M_YXf9h73uvVuT20_Ca9rMCOZcKlGIVuWWw/s200/P3251620.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5606758906880710290" /></a>< P27. Top-side view. Water lilly pads usually have a waxy surface texture. To imitate this look, you can rub the finished lilly pad with a white or green candle.<br /><br>JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-48350570744916169682011-05-06T17:03:00.024-04:002011-05-09T01:47:51.909-04:00'Rhombicized' Classic Origami<em>This article is written for folders that are familiar with the basics of origami and the classic models such as the Crane and the Masu box -- and especially for folders that like to experiment.</em><br /><br /><strong>Overview</strong><br /><br />I have recently experimented with some simple modifications of classic origami bases. First, I was developing a modular Water Lily design using bird bases, and I wanted more slender petals. So I modified the classic bird base to make what I call the "skinny bird base" (photo below). <br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIQBrh-yWyXT93xSK-jBmugr6x2IHSTxXJgKoedS8W20QxSo8aCdxpqThvlD2ZFYl6zlnKGrhnreCQdhtkgswO1rhXVov4t3f3eUwoP49mmAlV9SxXUNuOGtrien-GBV9cRyyO9w/s1600/P3221534.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIQBrh-yWyXT93xSK-jBmugr6x2IHSTxXJgKoedS8W20QxSo8aCdxpqThvlD2ZFYl6zlnKGrhnreCQdhtkgswO1rhXVov4t3f3eUwoP49mmAlV9SxXUNuOGtrien-GBV9cRyyO9w/s320/P3221534.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603725222333532514" /></a>Later, I was contemplating the classic Masu box, wondering if there was a way to make it rectangular. So I envisioned a rectangular Masu box, unfolded it in my mind, and found that I got a rhombus rather than a rectangle. I then verified the mental exercise with a physical experiment: I started with a rhombus and did all the same folds as I would use on a square to get a Masu box. The result was a rectangular tray, with a few surprises that I did not anticipate. The photo below shows two trays and a rhombus of the size and shape used for the trays.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvXKpPft6NgHqajox15l5sCC21ly3gmdw670qjlZ1wU0xNh6en9FORAuaWxBK2_9EgdeVaMDLQlEffD1b9x0m6_0S3_XADf2QJbNdSCezmbS1Xh8bvScpypCDQygT42sxcLik5vg/s1600/P4291666.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvXKpPft6NgHqajox15l5sCC21ly3gmdw670qjlZ1wU0xNh6en9FORAuaWxBK2_9EgdeVaMDLQlEffD1b9x0m6_0S3_XADf2QJbNdSCezmbS1Xh8bvScpypCDQygT42sxcLik5vg/s320/P4291666.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603726550843317970" /></a>This encouraged me to try folding other classic bases and designs using a rhombus instead of a square: <br /><br />preliminary and water-bomb bases<br />blintz fold<br />fish base<br />bird base<br />classic crane<br />classic flapping bird<br />petal-topped container<br /><br />I'm calling these "Rhombicized Classic Origami", and I am reporting my findings here. But first, let's return to the "skinny bird base".<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzciw9MuwzIaTD8BEq8_RkImflZc2a2rAGdAg2qArrvGUTsZnQIHubiqtwN4wa0YYX6GX_1AAm3OrTMgVZ9jDh_FeKSTYQmpdwJZtOr9LPFxNnXvBO91kwjEYjudGTgV2IXe4uqw/s1600/P5080003.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzciw9MuwzIaTD8BEq8_RkImflZc2a2rAGdAg2qArrvGUTsZnQIHubiqtwN4wa0YYX6GX_1AAm3OrTMgVZ9jDh_FeKSTYQmpdwJZtOr9LPFxNnXvBO91kwjEYjudGTgV2IXe4uqw/s320/P5080003.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5604587164766465874" /></a><strong>The Skinny Bird Base</strong><br /><br />When making a bird base, one starts with a preliminary base and folds each 'wing' angularly in half. Two wings are shown folded in the photo at the right. <br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdc_aJIIL8ptKb7BrPP-WZmid4yLY0fdiuEvjH8L01DI3MdbaOrWj8P9lzEsuMg_tSDW3JJKUnuFKzf8kKeKnZzAFm6V0HzZV4YArjaZtI5_U99FrNVt-WmjF-aHiTmRb7vccoIA/s1600/P5080002.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdc_aJIIL8ptKb7BrPP-WZmid4yLY0fdiuEvjH8L01DI3MdbaOrWj8P9lzEsuMg_tSDW3JJKUnuFKzf8kKeKnZzAFm6V0HzZV4YArjaZtI5_U99FrNVt-WmjF-aHiTmRb7vccoIA/s320/P5080002.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5604587798628614962" /></a><br />For the skinny version, each 'wing' is angularly folded in thirds. The first step is to fold a pair of wings over each other so that they divide the 90 degrees of the bottom corner in thirds, making three 30-degree angles, as shown in the photo at the left. <br /><br />Then each wing is folded again at the center line, so that the 45 degrees of each wing is divided in thirds, making three 15-degree angles (stacked) for each wing, as shown in the photo below right.<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvL1sKNO6mTWkEjfUMQYFpL6AhAtXJH3b3HBzau59i7ZkX7cIJH46mkTaolZ9jLNyZVa_sO7YSjnE4nJNxLKBN8Zelp-2pWyBdVahtUnGGzM2ACSy7LqKQ2HHzsfpQYpNRGP7YZQ/s1600/P3221519.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvL1sKNO6mTWkEjfUMQYFpL6AhAtXJH3b3HBzau59i7ZkX7cIJH46mkTaolZ9jLNyZVa_sO7YSjnE4nJNxLKBN8Zelp-2pWyBdVahtUnGGzM2ACSy7LqKQ2HHzsfpQYpNRGP7YZQ/s320/P3221519.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603735167013466434" /></a><br />As for the classic bird base, these folds are repeated behind, and all folds are converted to reverse folds, to obtain the skinny bird base (below left). <br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJdlOQnup77wpEuQvKuzknVwkJSEO4qbwFkHlb-gZChuPwer2G7QNvACxmpXX8TOWpDWBEzV0pX96OVQWYLtovitclJKgKrGj3pU1ABvCvHT6JDS8qaye2AqIB7W4p8jBGpeYXCQ/s1600/P3221534.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJdlOQnup77wpEuQvKuzknVwkJSEO4qbwFkHlb-gZChuPwer2G7QNvACxmpXX8TOWpDWBEzV0pX96OVQWYLtovitclJKgKrGj3pU1ABvCvHT6JDS8qaye2AqIB7W4p8jBGpeYXCQ/s320/P3221534.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603736354036721538" /></a><br />Notice that there are two corners instead of one on either side of each wing. The 'top' corner is easily seen on the outer layers, but the 'bottom' corner is below it on the inner layers. If a wing needs to be hinged upward, it cannot fold along a horizontal line joining the two outer top corners without tearing the paper. Instead the fold line must be between the two inner bottom corners. We will call this the 'hinge line'.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiff_NBPwuclwEE0JDvWu3s95e27KirvQ0u0K85eemv7AeEpOdXswQF5-xmpfzzk9CpVOGBPtxvCI2faWMhfxTaNhBM7yGOghGDT4yqv2LuvoVzEV30Lw848hCl0qY7g2X2gX5fLQ/s1600/P3231538.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiff_NBPwuclwEE0JDvWu3s95e27KirvQ0u0K85eemv7AeEpOdXswQF5-xmpfzzk9CpVOGBPtxvCI2faWMhfxTaNhBM7yGOghGDT4yqv2LuvoVzEV30Lw848hCl0qY7g2X2gX5fLQ/s320/P3231538.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603739275257332354" /></a>If a sink fold is needed at the top of the bird base (sometimes leading to a twist fold), the preparation for this sink fold should be to fold the top corner (central point) down to the center of the 'hinge line' as shown in the photo at the right. (The wing in front is hinged toward the viewer, and the wing behind is hinged to the right.)<br /><br /><strong>Making a Rhombus</strong><br /><br />Like a square, a rhombus has four equal sides; but instead of having four corners with equal (90 degree) angles, two opposite corners have equal angles less than 90 degrees, and the other two corners have equal angles greater than 90 degrees. We will call these the 'sharp' corners and the 'blunt' corners.<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinmWpjVax9zYU1zjTvaKXCBbOr28cSoZ-s-ClRvdJfTSw6qICDUE6DjjboDWgaHVmRCMq_-PllVr_PO78bW3rnAQqCYdTjP76BGc2i5XXSeFbulQ-h9vGFsBdbbbCwb1hGEy78hg/s1600/P5060001.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinmWpjVax9zYU1zjTvaKXCBbOr28cSoZ-s-ClRvdJfTSw6qICDUE6DjjboDWgaHVmRCMq_-PllVr_PO78bW3rnAQqCYdTjP76BGc2i5XXSeFbulQ-h9vGFsBdbbbCwb1hGEy78hg/s320/P5060001.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603792122496876994" /></a><br />To make a rhombus from a rectangle such as an 8.5 by 11 inch sheet of letter paper, fold the rectangle in half by bringing two opposite corners of the rectangle together, as shown in the photo at right. Then cut off the two triangular areas that are only one layer thick. Unfold the remaining two-layer-thick area, and you have a rhombus, already creased on the diagonal between its blunt corners. You can crease the other diagonal by bringing together the two blunt corners and bisecting the angles of the two sharp corners.<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqTCHgwA5rjJEnNS6kAjxOEW_NCM2C5HpgPeEbsmqSo2GWClmheMLZcHMB6rpPXpOH-fe0iVbHf5hQuEfw-DhaDregVu40gpBWFNKQAtvAsUFnrJHeegZwa9iFY_Xuej9KzrsApA/s1600/P5051693.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqTCHgwA5rjJEnNS6kAjxOEW_NCM2C5HpgPeEbsmqSo2GWClmheMLZcHMB6rpPXpOH-fe0iVbHf5hQuEfw-DhaDregVu40gpBWFNKQAtvAsUFnrJHeegZwa9iFY_Xuej9KzrsApA/s320/P5051693.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603793726601410898" /></a><br /><strong>Folding the Rhombus</strong><br /><br />There are two different ways of adding two more creases after creasing the two diagonals:<br /><br />On the left of the photo, the angles between the diagonals are bisected by bringing two half-diagonals together and creasing the paper between them. This folding method is appropriate when making a rhombicized bird base.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO2OaVxeG5vhOXIG8sjk3-afFHpI9jhsGgLnrfxZdBIM_9RX1WitRNiGCONMAcgET-cK4WJddBWQnf2wmF9Oj4VMURZdOjZLmMMmuwd8hFX6pCE_EMprE1W0HDMivBmss1o6cPWw/s1600/P4291668.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO2OaVxeG5vhOXIG8sjk3-afFHpI9jhsGgLnrfxZdBIM_9RX1WitRNiGCONMAcgET-cK4WJddBWQnf2wmF9Oj4VMURZdOjZLmMMmuwd8hFX6pCE_EMprE1W0HDMivBmss1o6cPWw/s320/P4291668.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603796907332198530" /></a>On the right of the above photo, each new crease is made by bringing one side of the rhombus over to align with the opposite side as shown in the photo at left. (See how the corners don't meet.) Each of these creases is parallel to two sides of the rhombus, and intersects the mid-points of the other two sides. This folding method is appropriate when making a rhombicized blintz fold, and also for dividing a rhombus into four similar rhombuses.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzo43xTM56IeKvyIYyYgNFaFbTrrRQJ1Fqte089RA3TNC2qE9fH8F7NiedZOSbI7S3Qmy1gT1SWdeet4Fm68Kkh0aKrrQ5EHkJihwO0jg3ODH650nn2CH6pYbFavbyv9IyXvFmQw/s1600/P4291670.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzo43xTM56IeKvyIYyYgNFaFbTrrRQJ1Fqte089RA3TNC2qE9fH8F7NiedZOSbI7S3Qmy1gT1SWdeet4Fm68Kkh0aKrrQ5EHkJihwO0jg3ODH650nn2CH6pYbFavbyv9IyXvFmQw/s320/P4291670.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603798690122434082" /></a>To make the blintz fold, fold each short edge of the top layer over to the folded edge, as shown in the photo at right, being careful not to go past the folded edge.<br /><br />Turn over and repeat, then unfold the first (longest) fold.<br /><br /><strong>Some Results</strong><br /><br />Here are the rhombicized bird base, blintz fold, and windmill base:<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpTzUkvu9RI-GkoZBkGu6ASU2LuO8FPPcUFNApv9q2MkZIi-aVt47FXT-L4nDei8YUTz1hyphenhyphenXSfWSQo_wvswXRR0HmUGvx4u3DdrUp6-cyWjnxXp4D-ziO9z2vGes-mBpcTcCniSw/s1600/P5051694.JPG"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 299px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpTzUkvu9RI-GkoZBkGu6ASU2LuO8FPPcUFNApv9q2MkZIi-aVt47FXT-L4nDei8YUTz1hyphenhyphenXSfWSQo_wvswXRR0HmUGvx4u3DdrUp6-cyWjnxXp4D-ziO9z2vGes-mBpcTcCniSw/s400/P5051694.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603800028986852482" /></a><br />Notice that two wings of the rhombicized bird base are longer than the other two wings. Notice that the rhombicized blintz fold is rectangular. Notice that the rhombicized windmill base is shaped like a rhombus.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnRAtq8OiC_TFes6lMmtiTEcSKwMB36oB5UNkhTFlYDu-L_g7okU6upj27W9f8g6xHaSNobo-BCyqHs2ywQdOH2MAXgh8g6BbW2syCDvrn4LHpZWxuX-HAKbwaozk3rW6qRBlIMA/s1600/P5051690.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnRAtq8OiC_TFes6lMmtiTEcSKwMB36oB5UNkhTFlYDu-L_g7okU6upj27W9f8g6xHaSNobo-BCyqHs2ywQdOH2MAXgh8g6BbW2syCDvrn4LHpZWxuX-HAKbwaozk3rW6qRBlIMA/s320/P5051690.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603801129110264562" /></a>Here on the left are two fish bases, both folded from identical rhombuses.<br /><br />The difference between these two fish bases is which diagonal of the rhombus is used as the central axis of the fish base. The 'tail' angle of one version is exactly half the 'head' angle of the other version.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlIKfYnEqq5tZOCKl5A-jaOvHOv0GQWDTYlrk-qRnvhHN1y49moGMV_0f1nlioCZpq3kKj58vhOkRsdnFHXXsSPH2jSSwEUozorKFA-yYaO_I7I0uWFYkHR6ixpWRC7EIZHmAe7Q/s1600/P5051687.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlIKfYnEqq5tZOCKl5A-jaOvHOv0GQWDTYlrk-qRnvhHN1y49moGMV_0f1nlioCZpq3kKj58vhOkRsdnFHXXsSPH2jSSwEUozorKFA-yYaO_I7I0uWFYkHR6ixpWRC7EIZHmAe7Q/s320/P5051687.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603801712737936098" /></a><br />Here on the right is the classic Masu box (left) and the rhombicized Masu box (right).<br /><br />When making the rhombicized Masu box, the short sides must be closed last, because they are taller. The result of using existing creases to close the box is that the long sides lean outward.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOywho5-hWo7zpM54gT_C3sawMgmcnzf95qpUEUv_QZaMQHIPh2UWvMa8N8BLNZdSPHHakhJiSqz7srfJqzwlQr-jsaHyX6y77STxbuYfpbWZJM5tO9D8D_p4TBBbWy63khaxVvw/s1600/P5051688.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOywho5-hWo7zpM54gT_C3sawMgmcnzf95qpUEUv_QZaMQHIPh2UWvMa8N8BLNZdSPHHakhJiSqz7srfJqzwlQr-jsaHyX6y77STxbuYfpbWZJM5tO9D8D_p4TBBbWy63khaxVvw/s320/P5051688.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603802749033873794" /></a><br />Here on the left are two Cranes, both folded from identical rhombicized bird bases.<br /><br />Recall that two of the wings of the rhombicized bird base are longer than the other two wings. The difference between the two cranes is which pair of wings of the bird base were used for the head and tail of the crane.<br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFWB3YjlXPQhOxzqaHMA1MtrsSiVe2p2_558ChrjeSkppGgyO90fDvH4kQL4jIEnHRua5uzNVZ06NLXMM7uBjH7YeSW-swkuK_6pDvA-uohYuSCa9-CBPjhNwpqBoqpZzf9cEbTA/s1600/P5051692.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFWB3YjlXPQhOxzqaHMA1MtrsSiVe2p2_558ChrjeSkppGgyO90fDvH4kQL4jIEnHRua5uzNVZ06NLXMM7uBjH7YeSW-swkuK_6pDvA-uohYuSCa9-CBPjhNwpqBoqpZzf9cEbTA/s320/P5051692.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603803994720038194" /></a><br />Here on the right is a rhombicized Flapping Bird. <br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLoWp8MtgeJ0_eo5SkaOWePJ-PW7bvB-vRBAUhbWGh6fbyweIpdN0Epc1awwmyX6imd3_3y6Uhg9PhULxpdT2vwXB8mAcIDhZzL0vFuqmLaqCDlaKpXt_XYiqAg3EkIM6O_YD00w/s1600/P5051691.JPG"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLoWp8MtgeJ0_eo5SkaOWePJ-PW7bvB-vRBAUhbWGh6fbyweIpdN0Epc1awwmyX6imd3_3y6Uhg9PhULxpdT2vwXB8mAcIDhZzL0vFuqmLaqCDlaKpXt_XYiqAg3EkIM6O_YD00w/s320/P5051691.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5603804784290352178" /></a><br />The <a href="http://home.comcast.net/~JamesMClark5/Origami/PETALTOP.pdf">Petal-Topped Container</a> can be made from any regular polygon. An easy polygon to use is an octagon, made by modifying a square. For the rhombicized version, we modify a rhombus in a similar way, getting an octagon that appears to inscribe an ellipse. The Petal-Topped Container is then folded from this 'elliptical' octagon. In the photo on the left, the rhombus for one container was made from an 8.5 x 11 inch rectangle, and the other from an 8.5 x 10 inch rectangle.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-46853488658572912482011-04-08T16:37:00.007-04:002011-04-08T17:26:34.448-04:00Advice for DIY Irreducible ComplexityThis is an addendum to the previous blog, <a href="http://jamesmclark.blogspot.com/2011/04/do-it-yourself-irreducible-complexity.html">"Do-It-Yourself Irreducible Complexity".</a> Here I give advice to anyone who wants to construct, demonstrate, or experiment with the 4-stick weaving illustrated in the previous blog.<br /><br />(1) To construct the 4-stick weaving, begin by holding a V in each hand, with the left-leaning stick on top for each V, as shown in the next photo. Keep your index fingers free, because you will need them later. That is, use the thumb and the lower three fingers to hold each V.<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjumxAIFLZEYCoOVDxOTkskSSDmNlixOn1-iQo7NFnlPnrH-Cqnr5zcqRQnip20tbrbpKhCb9c3hMth71hzXI1mc1uDiLiWe7UDmkV1Tr4f-fh-R_uQdkLMASqLXpTdpNykCEg0_A/s1600/P4081641.JPG"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjumxAIFLZEYCoOVDxOTkskSSDmNlixOn1-iQo7NFnlPnrH-Cqnr5zcqRQnip20tbrbpKhCb9c3hMth71hzXI1mc1uDiLiWe7UDmkV1Tr4f-fh-R_uQdkLMASqLXpTdpNykCEg0_A/s320/P4081641.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5593316180938308530" /></a><br />(2) Next, make a W by overlapping the two V's a bit, with the left side of the right V underneath the right side of the left V, as shown in the next photo.<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ4ObEWkYhC145lHY0_7e9IT5QwaGu6YLRNpNnezVcrRcI6tftcCPe0q0j9pBTCzgjFBHZknThsl9Bn1tD37ShQa3O243AmFc_EZgsvJLJFrJUnRrhzDGqON4t1zBa13YtQfgYdw/s1600/P4081642.JPG"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ4ObEWkYhC145lHY0_7e9IT5QwaGu6YLRNpNnezVcrRcI6tftcCPe0q0j9pBTCzgjFBHZknThsl9Bn1tD37ShQa3O243AmFc_EZgsvJLJFrJUnRrhzDGqON4t1zBa13YtQfgYdw/s320/P4081642.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5593316615792936322" /></a><br />(3) Next, pivot the V's, bringing the tip of the left side of the right V over the left side of the left V, and the left side of the right V over the right side of the left V, as shown in the next photo. The basic principle is that each stick will have an alternating over-under-over or under-over-under pattern.<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgyb78i-LR0Li64a9KqpI3mNy30qOwhZv-7F1Hp59sfDaRy2FANfGbCse9orUQkDD-YbAqBsmuqwHXYYQ_5_Rqz9FayZaCmhSYGZ14Xmvc2w7hLpjKqsQ-rEfH5I5Z-Mho3ALMug/s1600/P4081643.JPG"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgyb78i-LR0Li64a9KqpI3mNy30qOwhZv-7F1Hp59sfDaRy2FANfGbCse9orUQkDD-YbAqBsmuqwHXYYQ_5_Rqz9FayZaCmhSYGZ14Xmvc2w7hLpjKqsQ-rEfH5I5Z-Mho3ALMug/s320/P4081643.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5593316893906542002" /></a><br />(4a) Next, pivot the V's some more, bringing the two tips at the top of the configuration closer together. The tip coming from the right will naturally be on top, but you will need to reverse this. Here is where you need your index fingers. With your left index finger, push up on the middle of the left-most stick, and with your right index finger, push down on the middle of the right-most stick. Now, as you pivot the V's, the tip coming from the right can go under the tip coming from the left, as shown in the next photo.<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5be9JDzK0eTxmRa2mMEt5G4k52g9UX3ikwKrPpPSQEh6Bz3fBv6GCHPEFc2v9u6yoSth4QT50j-ChO3uNDcQJI5KEE_DIzaZRX86VQh2X9_2TnMpuJkE9P5TponitFvkB8MYatg/s1600/P4081644.JPG"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5be9JDzK0eTxmRa2mMEt5G4k52g9UX3ikwKrPpPSQEh6Bz3fBv6GCHPEFc2v9u6yoSth4QT50j-ChO3uNDcQJI5KEE_DIzaZRX86VQh2X9_2TnMpuJkE9P5TponitFvkB8MYatg/s320/P4081644.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5593317334099512482" /></a><br />(4b) BUT BEFORE letting go or putting it down, check that all six overlap 'joints' are secure and equally spaced. Because you can't let go yet, you need to use whatever fingers are closest to the joint that needs adjusting.<br /><br /><strong>Extra Challenge</strong><br /> <br />Those practiced with crafts such as origami will feel more comfortable using all fingers individually like this. If you have this kind of dexterity, you may want to accept the challenge of 'evolving' the design into the 5-stick weaving shown in the next photo. Or you can get a partner so that four hands can be used together. To truly emulate evolution, you must add the fifth stick without the configuration 'dying' (coming apart). And strictly speaking, you must do this without a plan (so I'm not giving you one), because evolution is supposed to be mindless and without even a goal, no less a plan. (So partners are not allowed to talk.)<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhISbUrOrfY-CqJSxXWyHFdRMIjdOJ30lJsdNznJ6Zy2YZps7oSzGRoQfkmHsf_84acj9DjfL4VcBVedmI9Que2vyNmXVnUkWGqNixemrm0ba5dZ7cnonW6N9N6LW1Qg1MWKmWVRw/s1600/P4081645.JPG"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 239px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhISbUrOrfY-CqJSxXWyHFdRMIjdOJ30lJsdNznJ6Zy2YZps7oSzGRoQfkmHsf_84acj9DjfL4VcBVedmI9Que2vyNmXVnUkWGqNixemrm0ba5dZ7cnonW6N9N6LW1Qg1MWKmWVRw/s320/P4081645.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5593317685890893746" /></a><br />If you succeed in assembling the 4-stick weaving, and especially if you could assemble the 5-stick weaving, you will have noticed that there is absolutely no way for the sticks to fall together this way. In fact, many simultaneous forces at very specific positions and directions and sequence were needed -- in other words, INFORMATION was needed.<br /><br /><strong>An Abstract Analogy</strong><br /><br />This exercise also provides a rather abstract analogy of a problem encountered in biology. Proteins are made of peptide chains that are folded in specific ways, and often multiple folded chains are assembled into a working unit. Often, proteins cannot fold correctly without the help of a tool to guide or to correct the folding. Also, tools are often needed to assemble multiple-chain protein units. These tools are called chaperone proteins; and they are also used to disassemble and unfold proteins (for digestion, for example). So the DNA information defines not only the 'parts' but also the 'tools', with built-in 'assembly instructions'. When constructing a stick weaving, your hands are acting (abstractly) 'like' chaperone proteins, but the details are very different, of course.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com1tag:blogger.com,1999:blog-13817057.post-382269901034049622011-04-06T22:56:00.007-04:002011-04-08T17:19:18.765-04:00Do-It-Yourself Irreducible ComplexityThis weaving of four sticks is <em>irreducibly complex</em>. You can't do it with less than four sticks. (By "it" I mean a construction that holds together: that if you pick up one stick, the others come with it.) Therefore you can't construct it one stick at a time. <p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSfmDZ4j_JSFkFePK0L1TpwmMkVwJbes6a12reBOoWVg-woFTlePv7sJmKol2yf6PVyuizz1WSC5r66akdIk64BmHzWKOhS1OQIQpdD6mIxNCWvRcRqIM8dpP3QDi-4r93AtgcBQ/s1600/P4061629.JPG"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 320px; DISPLAY: block; HEIGHT: 239px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5592671209938288578" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSfmDZ4j_JSFkFePK0L1TpwmMkVwJbes6a12reBOoWVg-woFTlePv7sJmKol2yf6PVyuizz1WSC5r66akdIk64BmHzWKOhS1OQIQpdD6mIxNCWvRcRqIM8dpP3QDi-4r93AtgcBQ/s320/P4061629.JPG" /></a> <br />It is held together by six overlapping 'joints'. ALL six are needed, because if you undo the overlap at ANY one of the six locations, the WHOLE thing falls apart. Therefore you can't construct it one joint at a time. You have to hold all four sticks in the right positions and force the last overlap WHILE also forcefully maintaining all other overlaps, thus applying forces in the right directions on ALL overlaps at once.<br /><br />Try it yourself, and you will surely be convinced that shaking a bunch of sticks will NEVER make this, the simplest possible weaving of sticks. If you are still not convinced, try 'evolving' the 4-stick weaving into a 5-stick weaving without it 'dying' (coming apart). Better yet, try doing it without a plan in mind. For fun, invite your friends to watch or even help you do it, because it will be hilarious! (Did you guess that I have tried it?) <br /><br />God's biological designs have LOTS of irreducibly complex components, often MORE complex than this. Evolutionary theory has NO WAY of explaining this. (But they are great story-tellers, and will PRETEND to explain it.) <br /><br /><strong>More about Irreducible Complexity</strong> <br /><br />The complexity of many designs can be reduced with the result that the design remains useful and functional, although the usefulness and functionality are reduced. For example, automatic adjustment features can usually be removed. A temperature control on a heater can be removed, for example, and it will still provide heat. It may be a nuisance to manually turn it off when there is too much heat and to turn it on later when more heat is needed, but it's better than no heater at all. <br /><br />But there comes a point when removing parts does not simplify a design, but rather destroys it. If we remove the heating element from the heater, we might as well discard the entire heater. When we can find no way of reducing the complexity of a design without making it no longer suited for its fundamental purpose, the design has āirreducible complexityā. The concept was introduced in 1994 by Michael J, Behe and later (1996) in his book āDarwin's Black Boxā. Actually, we have simplified the concept by talking only about parts, but things like shape and position of the parts are also important, as should be obvious in our first example. In general terms, 'critical characteristics' are counted rather than, or in addition to, just parts. <br /><br /><strong>Example: The Knee Joint</strong> <br /><br />An example of a biological design exhibiting irreducible complexity is the knee joint. The knee cap is an example of a part that can be eliminated, although this reduces safety and durability. It has been estimated that the knee joint has at least 16 critical characteristics, and these cannot tolerate much variation without destroying the design. Because of this, evolutionists have not been able to describe a step-by-step process whereby the simpler ball-and-socket joint can be converted to the more sophisticated knee joint. For more details, see <a href="http://www.yodelingfrog.com/objects/CHRISTIAN%20DOCUMENTATION/(pdf)%20Ken%20Ham%20-%20Intelligent%20Design%203.pdf">ā<em>Is the āirreducible complexity argument still valid? (Critical characteristics and the irreducible knee joint)ā</em> by Stuart Burgess.</a> <br /><br /><strong>Example: A Molecular Motor/Generator</strong> <br /><br />A much smaller example of a biological design exhibiting irreducible complexity is ATP Synthase, which is needed for all cells, plant or animal. ATP Synthase is a tiny 'motor/generator' that uses the energy of fuel to recharge tiny 'batteries' called ATP molecules, which transport the energy to wherever it is needed in the cell. <br /><br />One scientist said āThe enzyme is composed of 8 distinct peptide chains. If any one of the chains is missing, the enzyme does not function. So ATP synthase is an irreducibly complex system.ā Another scientist considers the enzyme F1-ATPase, a subunit of ATP synthase, to be the essential motor. The F1-ATPase motor has nine components, (using five different proteins, two of which are used three times each). This motor is so tiny that 100,000,000,000,000,000 of them would be the size of a pinhead. <br /><br />Another scientist said: āI am a biologist. Irreducible Complexity is actually a very sound argument against Darwin's theory of macroevolution. There's not a man alive that can demonstrate convincingly how, for example, the ATPase enzyme could have possibly evolved into its present form. If you can, you're up for the next Nobel prize.ā <br /><br /><strong>A Failed Evolutionist Argument</strong> <br /><br />I recall debating an evolutionist on Facebook about whether the irreducible complexity argument proved that ATP Synthase was designed. He argued that ATP Synthase could be broken into two parts, each of which were already used elsewhere for other functions. I didn't question his premises about other functions. I answered that if his line of argument were valid, then an automobile isn't designed either, because the first automobile combined an engine design that previously was used in a factory with a buggy design that previously was pulled by a horse. I never heard from him again. <br /><br />Even if he was correct about the two parts, at least one of the parts would be irreducibly complex, so he didn't dodge the problem like he thought he did. <br /><br />If it was that easy to construct ATP Synthase, or even ATPase from two parts, then you could put those parts in a beaker and do an experiment and get a Nobel prize like the quoted biologist said. Why not? What is overlooked is that DNA provides the assembly instructions and tools for the construction of ATP Synthase (and all other biological designs). These complex protein subsystems do not assemble themselves without DNA instructions. <br /><br />But here's another problem for which evolutionists have no solution. Evolutionists admit that ATP Synthase is needed for all cells, plant or animal. So how did plants and animals survive before ATP Synthase evolved? (Details, please. Don't tell me it just had to happen SOMEHOW because we just KNOW that evolution is true. I've heard that backward logic before.) <br /><br /><strong>Another Failed Evolutionist Argument</strong> <br /><br />As I said earlier, evolutionists are great story-tellers (but poor system engineers). Another evolutionist argument is that Hermann Joseph MĆ¼ller had previously devised a scheme whereby complex system could evolve two steps at a time. The two steps are: <br /><br />Step 1: Add a component; <br /><br />Step 2: Make it necessary. <br /><br />This simple description says nothing about the 'critical characteristics', which presumably are handled by modifying the proteins.) But if this is a valid explanation, this two-step cycle should work <u>in practice</u>, not just in a story made to sound like a theory. So let's try to use this method to make our simple 4-stick weaving, starting with one stick: <br /><br />Step a1: Add a component. (Add 2nd stick) <br /><br />Step a2: Make it necessary. Well, it's only one of three more necessary sticks, but it's not <u>sufficient</u> for the weaving. You could claim that you now have a pair of chopsticks, but a hand is needed for this 'system', because they won't feed you all by themselves. <br /><br />Step b1: Add a component. (Add 3rd stick) <br /><br />Step b2: Make it necessary. We really need to use our imaginations here. Make a triangle? Use it for what? Is it really a system? -- because they aren't connected, and can't stay together and hold any shape. <br /><br />Step c1: Add a component. (Add 4th stick) Actually, we can't add the 4th stick without first arranging the first 3 sticks, which can't hold themselves together. And as explained earlier, or perhaps experimentally confirmed by the reader, we need to apply a specific set of forces on all sticks at the same time. These forces are totally unrelated to using two sticks as chopsticks or other hypothetical intermediate functions. <br /><br />Step c2: Make it necessary. The completed design can fulfill a number of purposes. It can be used as a fence to prevent small animals from entering a pipe or hole. It can provide insulation between a hot mug of coffee and a table, etc. <br /><br /><strong>Summary:</strong> We had a lot of problems and needed a lot of imagination trying to apply this method to one actual, SIMPLE design. Explain step by step how it works for a knee joint. Try for a Nobel prize ā I dare you.<br /><br />For advice on constructing, demonstrating, or experimenting with the 4-stick weaving, see <a href="http://jamesmclark.blogspot.com/2011/04/advice-for-diy-irreducible-complexity.html">Advice for DIY Irreducible Complexity</a>.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-7668165094158883002010-09-05T21:27:00.004-04:002010-09-05T21:54:15.284-04:00Can Artificial Intelligence be Evolved?Now and then we see a claim that an evolutionary program has advanced the pursuit of artificial intelligence (AI). Because the degree of 'intelligence' is invariably minuscule compared to advances in AI using non-evolutionary methods, the report will typically use words such as "..evolved to produce basic intelligence" and "it is hoped that the discovery may in future.." That is, even though the 'intelligence' could be demonstrated by a pre-schooler, there is great hope of super-human intelligence down the road.<br /><br />Usually the reports lack the detail required for critical review. Partly, this is justified because there is so much detail involved that it is not practical to publish everything. But usually there is not even complete disclosure at a functional level.<br /><br />For example, suppose it is claimed that the 'artificial life-form' developed the use of memory. It could be that the simulated system was simply given the opportunity to do a task with or without memory, and it found that using memory led to greater success. Well, you don't need an evolutionary algorithm to do that. But without disclosing a functional description, the reader can be left with the impression that a memory mechanism was 'evolved'.<br /><br />For many readers, AI is a great mystery, and the reader has no way to judge whether such reports are overly optimistic or not. So here I will try to remove much of the mystery by providing an overview without getting too deeply into the math and logic.<br /><br /><strong><span style="font-size:130%;">An Overview of AI</span></strong><br /><br />AI is a broad field of study, and not all researchers or developers have the same goals, nor use the same methods.<br /><br />The process of intelligent thinking is generally described as having two parts: analysis (taking apart) and synthesis (putting together). Closely related to these, the terms induction (logically proceeding from the specific to the generic) and deduction (from generic to specific) are also used. Some AI efforts focus on analysis, some on synthesis, and some on both.<br /><br />For example, one project focused on using highly abstract formal language to build a data base of 'expert knowledge' garnered from doctors (who did most of the analysis) to synthesize an 'artificial expert' to diagnose diseases, thus simulating a team of medical experts.<br /><br />Fields of practical science generally have two sub-fields of endeavor: research and development. Research seeks to discover new principles and methods, and development seeks to find effective ways to use the new principles and methods to accomplish practical purposes. Some AI efforts focus on research, some on development, and some on both.<br /><br />There is a wide variety of methods used to try to create artificial intelligence. Usually an AI project focuses on one method, but sometimes methods are combined. Some methods are attempts to mimic natural patterns or structures.<br /><br />The 'evolutionary' (selective adaptation) algorithms are in this category. Some model biological selective adaptation closely, and some more loosely, using the 'evolution' concept more as inspiration. It seems to depend on the motive. The motive may be theoretical -- to prove evolution -- and they may talk of "intelligent agents". Or the motive may be practical -- to provide better computing -- and they may talk of "intelligent machines" instead.<br /><br />Another AI method that mimics nature is neural networks. I remember that the early research in this area focused closely on modelling the operation of actual neurons, trying to understand how they worked. Some used software models, and others built circuits that mimicked neurons. But these early models were very complex, so they chose simpler models so that they could build larger networks.<br /><br />Other AI methods seek to borrow and adapt the mental methods that people use to reason and solve problems. These AI systems are primarily rule-based -- instead of just handling data that represent facts, they use lists of rules, including rules for choosing rules, or making new rules from other rules, etc. They use category theory, means-end analysis, and planning strategies to try to construct a logical network connecting known facts to a target question. These rule-based systems depend heavily on very abstract formal languages to describe relationships, categories, and attributes of objects.<br /><br />As an engineer and programmer who has seen up close the development of computing from the days when transistors were first used, I see the rule-based AI methods as a natural extension of the development of computing.<br /><br />For example, suppose the solution of a problem requires us to determine the length H of the hypotenuse (longest side) of a right triangle when we know the lengths A and B of the shorter sides. To find the answer for a particular case, all we need to do is arithmetic. (I'm including finding square roots as arithmetic.) A machine that can do arithmetic for us is called a calculator.<br />But to express how to solve all such problems, we use an algebraic expression to say that H is the square root of the sum of A squared and B squared. We have gone to a higher level of abstraction -- from describing the solution of one problem to describing the solution of a class of similar problems. A machine that can do arithmetic for us, guided by an algebraic expression (a formula) is called a programmable calculator.<br /><br />Now suppose that we need to know how to compute length B when we know length H and length A. This requires a different algebraic expression, which can be derived from the expression that we described earlier. A programmer that knows algebra can manipulate the first expression to derive the second expression, then write another program to solve this new kind of problem. But suppose that we require that the computer should do this algebraic manipulation? This is a different matter. Instead of merely writing software that can interpret an algebraic expression to do the correct arithmetic procedure, the programmer must write software that "knows how to do algebra", that is, to manipulate algebraic expressions. Now we have stepped up to an even higher level of abstraction.<br /><br />Years ago, I bought a program called MathCad (from Mathsoft) that "knows how to do algebra" -- and calculus, statistics, matrix algebra, graphs, and many other mathematical techniques. It is so good at this that the program taught me math that I hadn't learned in college. There is a similar program named Mathematica produced by Wolfram Research, which is more powerful (and expensive).<br /><br />Now, Wolfram Research is developing an even 'smarter' program, making the current <a href="http://www.wolframalpha.com/">"Wolfram Alpha"</a> available on the Internet. It has access to a wide variety of scientific data. For example, you can enter "amino acids" and it will list the 20 kinds. Enter "weights of amino acids", and it will assume you meant atomic weights, and tell you the highest, lowest and median values. Better yet, it knows how to interpret these facts. Enter "distance from Venus to Mars", and it will consult its data about the planetary system, and report that right NOW, the distance is 148.7 million miles (and in other units) and that it takes 13 minutes for light to travel that distance in empty space. It's an even higher level of abstraction, without evolution, just more abstract rules.<br /><br /><strong><span style="font-size:130%;">Conclusion<br /></span></strong><br />In summary, the rule-based style of AI has been far more successful in a practical way (accomplishing smarter computing than ever before) than the neural networks and evolutionary algorithms. The neural and evolutionary strategies are pursued not for near-term practical benefit, but on theoretical grounds.<br /><br />The neural networks are pursued to try to demonstrate that brain-like structures can produce artificial 'thought', in contrast to philosophers who see the brain as not the producer of thought, but more like the soul's keyboard. After decades of research, progress has been painstakingly slow, and results very limited.<br /><br />The evolutionary strategies are pursued to try to demonstrate that evolution can produce design. But so far, the results only demonstrate what selective adaptation does in the biological world -- namely, to adjust and adapt a design within the confines of the resources already provided within the design.<br /><br />To designers, such as myself, the reason why the rule-based systems are far more successful is obvious: they are compatible with the top-down principles of design, which works from well-defined purposes toward increasingly more-detailed design. The other methods attempt to achieve design bottom-up, starting with the details and working toward a goal that is not defined, with no strategy as to how to get there. It's implicitly based on the myth that randomness magically produces information, or on the concept of a 'learning machine'. When a design IS 'found', AND the researchers allow you to look at their software, it becomes evident that the result was actually designed into the software. When you hide Easter eggs and search randomly, you might actually find Easter eggs.<br /><br />But 'learning machines' are inherently complex, and must themselves be designed. Also a 'learning machine' is just an optimizer that finds the 'best' within some domain that is limited by the design. And the principle of irreducible complexity is a huge hurdle that blocks the bottom-up approach. When probabilities are computed for achieving complex designs by random methods, they invariably turn out to be practically zero.<br /><br />What is "practically zero"? I will define it as 1 divided by a very large number. So what is "a very large number"? In the physical world, it is hard to get numbers larger than about 100 digits. For example, if you estimate the ratio of the mass of the observable universe to the mass of the electron, you get only an 84-digit number. But when you compute the probability of getting some irreducibly complex design by a random method, and express it as 1 divided by X, then X is typically thousands of digits long.<br /><br />That generally means that the universe doesn't have enough material and enough time for the random experiment to succeed. <strong>That's</strong> practically zero.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-61983752965578622932010-06-26T18:29:00.000-04:002014-07-30T09:21:04.260-04:00The Digital Control of LifeIn other blog articles such as <i><a href="http://jamesmclark.blogspot.com/2008/09/life-is-more-than-chemistry.html">Life is More Than Chemistry</a></i> and <i><a href="http://jamesmclark.blogspot.com/2008/02/can-chemical-evolution-work.html">Can Chemical Evolution Work?</a></i> I point out how living things fundamentally differ from nonliving things. Both are controlled by the laws of chemistry, but in living things, the <span class="blsp-spelling-corrected" id="SPELLING_ERROR_0">chemistry</span> is guided by information from the DNA data source. That explains why organic molecules are generally much larger than inorganic molecules. To make such large molecules, the limitations of pure chemistry are overcome by 'helper' molecules such as <span class="blsp-spelling-error" id="SPELLING_ERROR_1">chaperone</span> molecules made according to the DNA design plan. If the DNA data source is cut off, the organic molecules decompose as the laws of pure chemistry take over.<br />
<br />
In a recent blog article, <i><a href="http://jamesmclark.blogspot.com/2010/03/first-digitally-controlled-designs.html">The First Digitally Controlled Designs</a></i>, I point out that each living organism is a digitally-controlled design, using the same design paradigm now commonly used in most household appliances, where an embedded controller uses symbolic digital codes (software) to control the functions of the appliance. Because the 'software' in these cases is stored in read-only memory (ROM), it is technically called 'firmware'.<br />
<br />
The DNA is also firmware, because:<br />
<br />
(1) It is <b>digital</b>: the digits are Adenine, Cytosine, Thymine, and Guanine, equivalent to a 2-bit code. The fact that genetic control uses 4-valued digits, and man-made controllers use 2-valued digits (bits) is a mere design detail.<br />
<br />
(2) It is <b>symbolic</b>: Each <span class="blsp-spelling-error" id="SPELLING_ERROR_2">codon</span>, a sequence of three DNA digits, equivalent to a 6-bit code, is NOT an amino acid, but a symbol that represents an amino acid (or in one case, a stop signal). The fact that genetic control uses 6-bit <span class="blsp-spelling-error" id="SPELLING_ERROR_3">codons</span>, and man-made controllers use 8-bit bytes is a mere design detail.<br />
<br />
(3) It is <b>stored in read-only memory</b>. There is no information flow from polypeptides to <span class="blsp-spelling-error" id="SPELLING_ERROR_4">mRNA</span> to DNA, or any writing process.<br />
<br />
(4) In the reading process, <b>selected information</b> from the DNA is copied to <span class="blsp-spelling-error" id="SPELLING_ERROR_5">mRNA</span> (temporary copies) and then <b>interpreted</b>: that is, translated to polypeptides (the basic form of proteins). In man-made digital <span class="blsp-spelling-corrected" id="SPELLING_ERROR_6">controllers</span>, selected information from the read-only memory is copied to temporary memory and then interpreted: that is, translated to signals that produce desired actions.<br />
<br />
In addition to the temporary (<span class="blsp-spelling-error" id="SPELLING_ERROR_7">mRNA</span>) copying, in cells there are two other copying processes. There is a copying process that occurs during cell mitosis for growth and repair, and a rearrangement/copying process that occurs during cell meiosis for sexual reproduction. Neither process creates new information. Man-made digital <span class="blsp-spelling-corrected" id="SPELLING_ERROR_8">controllers</span> are not designed to grow and reproduce by themselves, so similar copying is not provided. Instead, there is copying in the manufacturing process.<br />
<br />
(5) There is a <b>higher structure</b> typical of <b>digital</b> <b>control languages.</b> These specialized languages have data units that operate somewhat like the verbs, nouns, and modifiers of 'natural' (human) languages. Some, like a noun, specify an object or subject; some, like a verb, specify an action; and others (modifiers) specify a condition or selection or limitation, etc. The DNA information is used not only to create the basic structures (nouns) of life, but also specialized molecules (modifiers) that control the operations (verbs) of these structures.<br />
<br />
If you want to appreciate the complexity of life designs at the cellular level, consider the process of extracting energy from food molecules like glucose. Simply put, the process is a "controlled burn" of the food-fuel, producing energy, carbon dioxide and water. The released energy is transported by ATP molecules (like rechargeable batteries) to the sites of all the energy-consuming activities of the cell.<br />
<br />
This process, called <a href="http://www.ptbeach.com/cms/lib02/NJ01000839/Centricity/Domain/113/Cellularrespiration.JPG" target="_blank">Cellular Respiration</a>, involves 4 stages:<br />
<br />
<br />
<li><a href="http://biochem.co/wp-content/uploads/2010/02/glycolysis-simple.png" target="_blank">Glycolysis</a> (10 steps), </li>
<li>the <a href="http://creationwiki.org/pool/images/thumb/1/1a/Citric_acid_cycle.png/350px-Citric_acid_cycle.png" target="_blank">Citric Acid Cycle</a> (8 stages), </li>
<li>the <a href="http://media.npr.org/assets/img/2011/09/13/krebs_cycle-46b152fcf30abdad1e42cce4ded6e2d99d00f458-s6-c30.jpg" target="_blank">Kreb's Cycle</a> (8 stages), and </li>
<li>the <a href="http://www.tutorsglobe.com/CMSImages/2434_electron%20transport%20chain.jpg" target="_blank">Electron Transport Chain</a> (4 steps). </li>
<br />
If you click on each of the above links, you will see what organic chemists call a "simplified" or "summary" diagram of each part of the process. Unless you are an organic chemist or a student of organic chemistry, you will not understand these diagrams, but one glance will give you a good idea of the level of complexity of so-called 'primitive' life. These diagrams represent only <b>some</b> of the cell processes, and they are only <b>summaries</b>! There are diagrams for other complex processes, such as <a href="http://content.answers.com/main/content/img/oxford/Oxford_Chemistry/0192801015.photosynthesis.1.jpg" target="_blank">Photosynthesis</a>, which captures the energy of sunlight and stores it by making glucose (food-fuel).<br />
<br />
The process of reading and interpreting the DNA information creates all the chemical 'machinery' (such as <a href="http://waynesword.palomar.edu/images/enzyme5.gif" target="_blank">enzymes</a>) and chemical 'factories' (such as <a href="http://jcarpentercell.weebly.com/uploads/1/9/3/9/1939921/9297470.gif?434x310" target="_blank">mitochondria</a>) for these and many other complex processes of living things.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-76047074279118612192010-05-05T21:49:00.009-04:002010-05-09T21:49:37.675-04:00Update on Dave McKean's 'Luna' FilmHere is an update on Dave <span id="SPELLING_ERROR_0" class="blsp-spelling-error">McKean's</span> upcoming film <em>Luna</em> for which I folded two origami crabs in 2007. If you haven't read my previous blogs about this, they are <a href="http://jamesmclark.blogspot.com/2007/11/origami-emergency.html">Origami Emergency</a> and <a href="http://jamesmclark.blogspot.com/2007/11/more-about-origami-crabs.html">More About the Origami Crabs</a>.<br /><br /><strong><span style="font-size:130%;">First, some additional details about the crabs.</span></strong><br /><br />Luna filming began in early November of 2007. The request for t<span id="SPELLING_ERROR_1" class="blsp-spelling-error">he</span> origami crabs was sent on 10-30-07 and the crabs arrived on the set 11-08-07.<br /><br />Through my friend Mark Kennedy and Nick Robinson, word reached Dennis Walker, the articles editor of the British Origami Society (<span id="SPELLING_ERROR_2" class="blsp-spelling-error">BOS</span>), who asked me for permission to put my blog article in the <span id="SPELLING_ERROR_3" class="blsp-spelling-error">BOS</span> magazine. Dennis also told me that he was "VERY jealous" and "pretty chuffed that it was through the Origami Database". I think he figured that a British filmmaker should have asked the British Origami Society first.<br /><br />After completing the live action shooting, and starting some editing, financing for the film collapsed at the end of 2007. About two years later, new financing allowed post production of Luna to resume in March of 2010.<br /><br /><span style="font-size:130%;"><strong>Twitter Info</strong><br /></span><br />I extracted the following information from Dave <span id="SPELLING_ERROR_4" class="blsp-spelling-error">McKean's</span> Twitter page:<br /><br />"Answering request for Luna stills, here's a few, from the live action shoot only. As we progress I'll post more: <a href="http://bundl.it/MjY2Mjk">http://bundl.it/MjY2Mjk</a> "<br /><br />A "90% version of Luna" has been shown to producers. "Four people have now seen my film all the way through." "... the crab performed beautifully."<br /><br />"Several small animated scenes + <span id="SPELLING_ERROR_5" class="blsp-spelling-error">fx</span>, music, sound etc." need to be done. Many 'small' details, but "a long process". Anticipate completion by the end of 2010. Listing in the Internet Movie Data Base (<span id="SPELLING_ERROR_6" class="blsp-spelling-error">IMDB</span>) by July 2010, perhaps.<br /><br />"It's nothing like <span id="SPELLING_ERROR_7" class="blsp-spelling-error">MirrorMask</span> to be honest, although it does have Stephanie Leonidas in it, and some dreamlike scenes. It's an adult drama."<br /><br />While looking for details on Luna progress, I came across this delightful bit of banter which I'll include for your enjoyment:<br /><blockquote><strong>Ken</strong> <strong>Fries:</strong> Steve probably already has a copy of Luna...<br /><br /><strong>Dave <span id="SPELLING_ERROR_8" class="blsp-spelling-error">McKean</span>:</strong> Great! Can I see it? Then I'll know if it's worth finishing...<br /><br /><strong>Ken Fries:</strong> Nah, u shouldn't see it, I don't want to spoil the ending for you.</blockquote><br /><strong><span style="font-size:130%;">Photos:</span></strong><br /><a href="http://picasaweb.google.com/lh/photo/jLRBBvrb4ecYDVQx0RzNAPoj45_-2C5w2k5PnCSwGXk?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3IuPK5gkbGNLCayvsPMj8NAQalw9ZcBo8tEnXD9Bf5O6O7ITtbYyPaKUktX2PQ5T9cXXgM_KfpnryWWj5Lj1Me2ng0X_2XlGYnObeskFYFBJ7ZwsC_soFZMX72Pv1Irmp_cUFFA/s400/crab_origami1.jpg" /></a><br /><br />Dave <span id="SPELLING_ERROR_9" class="blsp-spelling-error">McKean</span> sent me the following still shots from the film, in addition to the above photo of the crab "that will be in the book of the film." "The stills show Grant (Ben Daniels) folding the crab, with his wife Christine (<span id="SPELLING_ERROR_10" class="blsp-spelling-error">Dervla</span> <span id="SPELLING_ERROR_11" class="blsp-spelling-error">Kirwan</span>), which he symbolically buries in the sand. They hide behind a rock and watch a real crab emerge from the same place."<br /><br />Folding the crab, wide shot and close-up:<br /><a href="http://picasaweb.google.com/lh/photo/peP4J1rdR2jUALASO4nyefoj45_-2C5w2k5PnCSwGXk?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHIvWgIT0vU1WiDzARgzcpAKsZ3l71TZBE08h3n3uFrE4vK3y0_Pj2ddEeoe_ZIThTVcGcJ_uM0Lk5CMGMzYs792B-RbpOG_UpMrNS5K1xWPKPln697gvh16UnRYmQJK8d6hgASw/s400/Grant_folds_crab.jpg" /></a><br /><br /><a href="http://picasaweb.google.com/lh/photo/F0prkjAezSIwyf-vrPJcQPoj45_-2C5w2k5PnCSwGXk?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXY3mXzX4-M4iZ5qANHhIX-RtdQYFzzJJ6JLN9ERPhUM1onsH1JFF_5FWHuSvfsVvsdEWngJ5nj7T1YIxVnpSf6un9-0S8Vs1hVyQQ5qWj7iwKED1a7u-WcYVbGLfAD9jS1R_7tw/s400/Grant_folds_crab_close.jpg" /></a><br /><br />The crab, on hand:<br /><a href="http://picasaweb.google.com/lh/photo/u8MnyCAFKm3Ei-wYY_hhV_oj45_-2C5w2k5PnCSwGXk?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj6e1MVC0ukhBOLGt0rltVC_snA5ZDBHsM9WOKsDG980vuoEierjuuyFEXqOHsvVnOwQMEhKPLldMvXH_5-jlUssPhi9-NRRRJzH3blI6imKKsfmGiYD0grFXN7KaPPEVpPXiqug/s400/crab_on_hand.jpg" /></a><br /><br />The crab burial:<br /><a href="http://picasaweb.google.com/lh/photo/Kvd5NhnYMJrO3w944akHbfoj45_-2C5w2k5PnCSwGXk?feat=embedwebsite"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisd_lQXdpsyIwE3GzgPzno1U_D7Ha9MXtkq0oYh-TcFJ6_X-7r_yZi2nidLblEyIGu6iQ5h20nb7ExwRDpKKeeqpgFubvHuomSJgIKquhWv1S5-EIy0UnAhPZIeXaEx6PTL-DI7A/s400/crab_burial.jpg" /></a><br /><br /><span style="font-size:130%;"><strong>Some <span id="SPELLING_ERROR_12" class="blsp-spelling-corrected">contributors</span> to the Luna film:</strong><br /></span><br /><ul><li><strong>Dave <span id="SPELLING_ERROR_13" class="blsp-spelling-error">McKean</span></strong> (writer, director, designer, editor)</li><br /><li><strong>Keith Griffiths</strong>, producer (produced 78 films, directed 16 films)</li><br /><li><strong>Simon <span id="SPELLING_ERROR_14" class="blsp-spelling-error">Moorhead</span></strong> (produced all <span id="SPELLING_ERROR_15" class="blsp-spelling-error">Mckean's</span> films, including <span id="SPELLING_ERROR_16" class="blsp-spelling-error">MirrorMask</span>)</li><br /><li><strong>Antony <span id="SPELLING_ERROR_17" class="blsp-spelling-error">Shearn</span></strong> (director of photography)</li><br /><li><strong>Tessa <span id="SPELLING_ERROR_18" class="blsp-spelling-error">Beazley</span></strong>, production manager (production manager for about a dozen films, and other production)</li><br /><li><strong><span id="SPELLING_ERROR_19" class="blsp-spelling-error">Darkside</span> Animation</strong> of London, animation support (graphics and special effects for 3 films)</li><br /><li><strong>Ashley Slater</strong>, music (actor, music writer, performer, and producer; music producer, mixer, programmer, and performer for "<span id="SPELLING_ERROR_20" class="blsp-spelling-error">MirrorMask</span>" soundtrack)</li><br /><li><strong>Iain <span id="SPELLING_ERROR_21" class="blsp-spelling-error">Ballamy</span></strong> (jazz player and composer, composed the score for <span id="SPELLING_ERROR_22" class="blsp-spelling-error">MirrorMask</span>)</li><br /><li><strong><span id="SPELLING_ERROR_23" class="blsp-spelling-error">Dervla</span> <span id="SPELLING_ERROR_24" class="blsp-spelling-error">Kirwan</span></strong>, actress (<span id="SPELLING_ERROR_25" class="blsp-spelling-error">Ballykissangel</span>, Casanova, Dr. Who, <span id="SPELLING_ERROR_26" class="blsp-spelling-error">Ondine</span>)</li><br /><li><strong>Stephanie Leonidas</strong>, actress (<span id="SPELLING_ERROR_27" class="blsp-spelling-error">MirrorMask</span>, Yes, Feast of the Goat, Crusade in Jeans, Dracula)</li><br /><li><strong>Michael <span id="SPELLING_ERROR_28" class="blsp-spelling-error">Maloney</span></strong> (In the Bleak Midwinter, Babel, Notes on a Scandal, Truly Madly Deeply)</li><br /><li><strong>Ben Daniels</strong> (Spooks, Doom, The State Within, Fogbound, I Want You)</li><br /><li><strong>Maurice <span id="SPELLING_ERROR_29" class="blsp-spelling-error">Roƫves</span></strong> (The Damned United, <span id="SPELLING_ERROR_30" class="blsp-spelling-error">Hallam</span> Foe, Tutti <span id="SPELLING_ERROR_31" class="blsp-spelling-error">Frutti</span>, Beautiful Creatures) </li><br /></ul>JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com2tag:blogger.com,1999:blog-13817057.post-47835833489215761492010-03-18T19:55:00.017-04:002010-06-26T17:51:35.218-04:00The First Digitally-Controlled DesignsSince the discovery of DNA and RNA and the Genetic Code, it is indisputably clear to biologists that the structure and function of all living things is determined by the information stored in the DNA. The interpretation of the DNA information according to the Genetic Code creates a enormous set of specific proteins and other complex organic molecules that implement the structure and function of a particular organism. (See <a href="http://jamesmclark.blogspot.com/2009/02/genetic-code-how-to-read-dna-record.html"><em>The Genetic Code - how to read the DNA record</em></a> and <a href="http://jamesmclark.blogspot.com/2010/03/more-about-genetic-code.html"><em>More About the Genetic Code</em></a>.) Some of these complex molecules are building blocks of the living structure; some are the tools or 'workmen' that build the structure; other organic molecules function more like supervisors that control when and where and how this work of construction is done. Still others supervise various functions of the living structure, such as digestion, breathing. sight, growth, etc. All of these complex functions are guided not exclusively by chemical laws, but also by the information from the DNA. (See <em><a href="http://jamesmclark.blogspot.com/2008/09/life-is-more-than-chemistry.html">Life is more than chemistry</a></em> and <em><a href="http://jamesmclark.blogspot.com/2008/02/can-chemical-evolution-work.html">Can Chemical Evolution Work?</a></em>) This is true of all living things, whether a single-celled organism or a much larger plant or animal such as an oak tree or an elephant. <strong>Such a complex, coordinated interplay of material and function at multiple levels is clearly DESIGN.</strong><br /><br />I ought to explain that I understand and appreciate this from experience. I worked for 43 years as a designer and inventor of computers and other digital systems, acquiring 45 patents in that time; and in my retirement years, I have been studying organic chemistry. When I started my career, a typical computer was a roomful of refrigerator-sized cabinets. but less powerful than today's pocket calculator; and I have seen the technology grow functionally and shrink physically since then. In between then and now, the <span id="SPELLING_ERROR_0" class="blsp-spelling-error">Quintrel</span> computer that I designed, one of the first to do speech processing (like speech recognition) in real time (that is, as fast as you can talk) was the size of a cookie baking pan. Inside all GPS satellites, the computer system that controls all the signals is my design. <strong>So I know a design when I see one.</strong><br /><br />I especially appreciate the advantages of a <em>digitally-controlled design</em> over a design that is just digital. The old-fashioned mechanical adding machines did digital calculation, but the control was manual; that is, the operator had to select the sequence of operations as well as the input data. I remember the company used to have one with a typewriter-like shifting carriage so that it could do multiplication and division; but it was still manually controlled.<br /><br />In human history, digitally controlled designs started with things like the 'player piano', where the keyboard was controlled by a roll of paper with punched holes to specify the sequence and timing of the notes, and the Jacquard loom, where punched holes caused threads to be raised or lowered to create intricate designs such as brocade and damask. Herman Hollerith adapted the punched cards of the weaving industry for data input for his Tabulating Machines, and Charles Babbage planned to use punched cards for his Analytical Engine, which began the age of computers. (See <em><a href="http://jamesmclark.blogspot.com/2005/07/development-of-information-processing.html">The Development of Information Processing</a></em>.)<br /><br /><em><strong>Let me tell a story that illustrates how "I especially appreciate the advantages of a digitally-controlled design" as I said earlier.<br /></strong></em><br />There was a period in my career when we designed digital devices for communication of digital messages. No calculation in the ordinary sense of the word was needed, but the digital logic needed to be 'smart'. For example, before sending a piece of a message (called a <em>packet</em>), an error-checking code needed to be generated and attached to the message, along with a packet number. When receiving a packet, the error-checking code needed to be checked to see if the packet had any errors. (Most errors were <span id="SPELLING_ERROR_1" class="blsp-spelling-corrected">detectable</span>.) If the packet had no errors, an <em>'<span id="SPELLING_ERROR_2" class="blsp-spelling-error">ack</span>'</em> (acknowledgement) message was returned to the sender; but if errors were detected, a <em>'<span id="SPELLING_ERROR_3" class="blsp-spelling-error">nak</span>'</em> (no-acknowledgement) message was returned. Both <span id="SPELLING_ERROR_4" class="blsp-spelling-error">ack</span> and <span id="SPELLING_ERROR_5" class="blsp-spelling-error">nak</span> messages included the number of the good or bad packet that had been checked. A <em><span id="SPELLING_ERROR_6" class="blsp-spelling-error">nak</span></em> message was a request to resend the packet (hoping to get it right on the next try), and an <em><span id="SPELLING_ERROR_7" class="blsp-spelling-error">ack</span></em> message told the sender that it no longer needed to keep a copy of the packet. A communication protocol like this was controlled by logic hardware similar to that used to construct a computer, but there was no computer and no software involved. The designs were digital, but not digitally-controlled as computers are controlled by software.<br /><br />A major problem with this style of design was that if a design error needed to be corrected, or a new design feature added, new parts would need to be added, and the layout and wiring of the parts modified. The parts might not fit, so even the mechanical design might need to be redone.<br /><br />An obvious solution to this problem is to include an '<em>embedded</em>' computer in the design, so that software can define the functions of the design, because software is far more easily changed than the hardware. Once the software is thoroughly tested and no longer needs to be changed, it is typically embedded in read-only memory (ROM) and is called '<em>firmware</em>'. This tactic is commonplace today, with embedded computers in automobiles and in nearly every electrical household appliance. That's easy today, because electronic circuits have shrunk enough for small computers, including all memory and other supporting logic, to be placed in one small, low-cost chip. But back then, electronics had shrunk only enough for simple circuits such a counter to fit in one chip. An embedded computer would require at least several chips.<br /><br />We couldn't buy a general-purpose computer chip (they didn't exist then), but had to design a computer made of several chips. But this gave us the freedom to design a smaller 'custom' computer with only the functions actually needed. For example, we didn't need to add, subtract, multiply or divide; the only 'arithmetic' needed was to count the bits of a packet. Mostly, the computer needed to make decisions based on a specialized set of conditions. If such a design primarily controlled not a sequence of calculations, but a sequence of other operations (such as those needed for a communications protocol), it was usually called a <em>'controller'</em> rather than a computer. Often, such a simplified computer / controller could be made with only a half-dozen parts. This 'custom' controller would thus have a 'custom' set of instructions that it could execute. (Each instruction is a group of binary codes and data that tell the computer / controller what to do for each step of its actions.)<br /><br />Theoretically, a programmer (software writer) could write out the sequence of instructions (the software, or program) in the form of the ones and zeros that the hardware actually reads. But this would be very error-prone, because it is hard for people to memorize these codes, or even to copy them from a list without making mistakes. So, instead, equivalent codes that look more like English are invented, thus creating a special language that is much easier to learn and understand. Then a program called an <em>'assembler'</em> is used to translate the semi-English to the ones and zeros that the hardware uses. (Also, decimal numbers are translated to binary numbers.)<br /><br />Thus, almost every computer / controller design would have a different<em> instruction set</em>, and a correspondingly different <em>'assembly language'</em>, and a different <em>assembler program</em>. The assembler is what connected the software design to the hardware design.<br /><br />Mostly, there were two kinds of designers: <em>hardware logic designers</em> that knew at least how to design parts of the computer hardware, and <em>software designers</em> that knew how to write software. A third kind of designer was a relative minority: the <em>'system designer'</em>, who understood both hardware and software -- the whole system, or the 'big picture'. (See <em><a href="http://jamesmclark.blogspot.com/2005/07/start-of-system-engineering.html">The Start of System Engineering</a></em>.) A few of these, who also knew the theory of formal languages, were able to write assembler programs, and even 'compilers', which can translate more abstract software languages. With my insatiable curiosity and willingness to self-educate myself in related fields on my own time, I became part of that minority.<br /><br />The engineering supervisors resisted the idea of embedding computers in a design. Their reasoning was that we had hardware designers and software designers, but nobody that knew how to make a custom assembler. We would have to give such a job to outside specialists, which would be too expensive and troublesome.<br /><br />It irked me that this judgement was hindering us from making compact and flexible designs. So, on my own time, I designed what I called the "General-Purpose Assembler". It was a step beyond a custom assembler, because before assembling a program, it first read a "language table", which defined the custom assembly language. So, the next time that a supervisor tried to veto a proposal for a design with an embedded computer / controller, I explained that I "happened to have" an assembler that could do the job. I did the extra work on my own time because I knew that digital control of a design was an <strong>optimum design paradigm</strong>.<br /><br />I wrote an instruction manual for how to construct a "language table" and how to use the "General-Purpose Assembler", and soon other departments and projects were using it. A few years later, I estimated that about two dozen language tables had been written, creating that many custom assemblers for that many different embedded controllers. The "General-Purpose Assembler" also became a component of the assembler for the <span id="SPELLING_ERROR_8" class="blsp-spelling-error">Quintrel</span> processor that I mentioned earlier. These were all digitally-controlled designs.<br /><br /><strong><em>Now, this story may seem like an utter digression from my initial discussion of DNA and RNA and the Genetic Code, but it was all to underscore and emphasize the following point:<br /></em></strong><br />I used to think of digitally-controlled designs as a modern phenomena -- but this is true only if you are limited to <strong>designs made by humans</strong>. But when I started to study organic chemistry and the workings of the Genetic Code, I soon realized that the greatest Engineer of all, <strong>God, got there first.</strong> For indeed, <strong>all living things of all kinds are digitally-controlled designs</strong>. The DNA is the read-only memory (ROM) that holds the genome, which is the software (firmware) that controls the chemistry that plays the role of 'hardware'. Each unit of DNA (<em><span id="SPELLING_ERROR_9" class="blsp-spelling-corrected">nucleotide</span></em>) is equivalent to two bits, having one of four values, and each <em><span id="SPELLING_ERROR_10" class="blsp-spelling-error">codon</span></em> (three DNA units) is equivalent to six bits, with one of 64 values. It compels one to ask "Where did all that DNA-software come from?" (See <a href="http://jamesmclark.blogspot.com/2005/07/in-beginning-was-information.html"><em>In The Beginning Was Information</em> </a>.) The reason why there is only one universal genetic code, and why so many life-forms share common design structures is not because all descended from a single common ancestor (unlikely if evolution is inevitable, as Richard <span id="SPELLING_ERROR_11" class="blsp-spelling-error">Dawkins</span> claims), but because all have a single Creator.<br /><br />I know that some readers will dismiss my comparison of life designs to man-made designs as mere analogy. But my argument rests on more than analogy. It involves what in <em>category theory</em> is called <em>isomorphisms</em>. Rather than getting too technical, I will illustrate the principles involved by a simple example:<br /><br />If two species have sufficient similarities (putting them in the same category), we can expect them to have similar locomotion. For example, cats and dogs both have four legs of nearly equal lengths, and the knees bend in the same directions; so we can expect them to walk and run in similar ways. Frogs, kangaroos, and apes also have four legs, but not all four of equal length, so the locomotion is different. There is greater similarity of function when there is greater similarity of structure.<br /><br />With similar logic methods, we can show that DNA-controlled life forms are more similar to embedded controllers than personal computers. For example, in both, the completed design has no capability of loading new software (not true for PCs). In both computers and controllers, the same hardware with completely different software will have completely different functionality. In life, the same chemical laws, chemical resources (food, air, water, etc) and same genetic code with a completely different genome will have completely different functionality.<br /><br />As an experienced designer, I not only know a design when I see one, <strong>I know a digitally-controlled design when I see one;</strong> and I appreciate that it is an <strong>optimum design paradigm</strong>. No wonder that people are using the term "<em>Intelligent Design</em>" to describe living things.<br /><br />For more on this subject, see <em><a href="http://jamesmclark.blogspot.com/2010/03/digital-control-of-life.html">The Digital Control of Life</a></em>.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com2tag:blogger.com,1999:blog-13817057.post-61413967829392305162010-03-08T00:56:00.004-05:002010-03-08T10:02:36.233-05:00God's Unilateral AgreementThe Bible is divided into two major parts called the Old Testament and the New Testament. "Testament" and "Covenant" are two English words that are used to translate the Hebrew "<span id="SPELLING_ERROR_0" class="blsp-spelling-error">beriyth</span>" and the Greek "<span id="SPELLING_ERROR_1" class="blsp-spelling-error">diatheke</span>" as used in the Bible. Both words are used to refer to a solemn or legally binding contract or treaty.<br /><br />In the time of Abraham, a covenant between men was often solemnized by a ceremony whereby an animal was cut in half and both parties walked between the pieces of flesh, signifying "so let it be done to me if I do not keep this covenant". But when God made a covenant with Abraham (in Genesis 15:7-21) to give to his descendants the "Promised Land" (called "The Land of Israel" until the Romans renamed it "Palestine"), the ceremony was remarkably changed. After "a deep sleep fell upon Abram" (verse 12), "there appeared a smoking oven and a burning torch that passed between those pieces" (verse 17), signifying the <span id="SPELLING_ERROR_2" class="blsp-spelling-corrected">presence</span> of God certifying the contract. Since sleeping Abraham (then called Abram) did not also walk between the pieces, this signified that the covenant was unilateral -- God took full responsibility for keeping His promise to Abraham and his descendants.<br /><br />However, God's covenant through Moses with His chosen people concerning the Law, repeated in the books of Exodus, Leviticus, Numbers, and Deuteronomy, was a bi-lateral covenant, because the people promised "All that the LORD has said we will do, and be obedient" (Exodus 24:7 and elsewhere), and because curses were promised if His people broke the covenant, and blessings promised if they kept it.<br /><br />Central to the Old Testament covenants was the sacrifice of animals, signifying the debt of mankind toward God for his sin, which was only symbolically paid by the animal sacrifices. The most solemn of these sacrifices occurred each year at Passover, which foretold the true sacrifice, the actual payment, to come.<br /><br />In the New Testament, we read of a day when Jesus celebrated a modified Passover ceremony with His disciples. It was modified because He ended the ceremony before the third cup, and because the ceremony was given new meaning while fulfilling the old meaning. Jesus Himself was the Passover Lamb that the cup signified; and hours later, He was sacrificed on a cross. Jesus gave the first cup (Luke 22:17) to His disciples, saying "Take this and divide it among yourselves", but didn't partake Himself, saying "I will not drink of the fruit of the vine until the kingdom of God comes." At the second cup (Luke 22:20), Jesus said "This cup is the new covenant in My blood, which is shed for you." Since then, Christians repeat an <span id="SPELLING_ERROR_3" class="blsp-spelling-corrected">abbreviated</span> form of that Passover ceremony that we now call Communion or The Lord's Supper.<br /><br />The sacrifice of Christ on the cross fulfilled the old covenants and introduced a new covenant because His actual and effective sacrifice ended the need for symbolic sacrifices. The apostle Paul called it the 'covenant confirmed by God in Christ' (Galatians 3:17), and 'a better covenant' (Hebrews 7:22, 8:6, 9:15, and 12:24). Paul also explains that when the prophesy of Jeremiah (31:31-34) is fulfilled, this covenant will be embraced by a rejuvenated nation of Israel.<br /><br />The new covenant is also unilateral, because Jesus Christ has paid the price in full, and we bring nothing. God says that "...all our <span id="SPELLING_ERROR_4" class="blsp-spelling-error">righteousnesses</span> are like filthy rags". (Isa 64:6) There are many Bible passages that make it clear that our righteous obedience of God's laws contributes nothing to the salvation that Christ freely offers to us. A few verses are:<br /><br />Gal 2:16<br />...a man is not justified by the works of the law but by faith in Jesus Christ, even we have believed in Christ Jesus, that we might be justified by faith in Christ and not by the works of the law; for by the works of the law no flesh shall be justified.<br /><br />Rom 4:4-5<br />4 Now to him who works, the wages are not counted as grace but as debt.<br />5 But to him who does not work but believes on Him who justifies the ungodly, his faith is accounted for righteousness<br /><br />Rom 11:6<br />...if by grace, then it is no longer of works; otherwise grace is no longer grace...<br /><br /><span id="SPELLING_ERROR_5" class="blsp-spelling-error">Eph</span> 2:8-9<br />8 For by grace you have been saved through faith, and that not of yourselves; it is the gift of God,<br />9 not of works, lest anyone should boast.<br /><br />If our righteousness is insufficient, then how can we settle our debt of sin with God, and escape condemnation? We need to "declare bankruptcy", by confessing our sin and accepting the free gift of Christ's sacrifice, His payment for our sin:<br /><br />1 John 1:9-10<br />9 If we confess our sins, He is faithful and just to forgive us our sins and to cleanse us from all unrighteousness.<br />10 If we say that we have not sinned, we make Him a liar, and His word is not in us.<br /><br />John 3:16-19<br />16 For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life.<br />17 For God did not send His Son into the world to condemn the world, but that the world through Him might be saved.<br />18 He who believes in Him is not condemned; but he who does not believe is condemned already, because he has not believed in the name of the only begotten Son of God.<br /><br />(The name "Jesus" means "Savior", so believing in His name means that you trust His ability to save you.) There is no other way:<br /><br />Acts 4:12<br />Nor is there salvation in any other, for there is no other name under heaven given among men by which we must be saved.<br /><br />John 14:6<br />Jesus said to him, "I am the way, the truth, and the life. No one comes to the Father except through Me."<br /><br />It doesn't take a lot of faith; a genuine faith is sufficient to begin, and God will cause your faith to grow. A man once told Jesus "Lord, I believe", and then, doubting <span id="SPELLING_ERROR_6" class="blsp-spelling-corrected">himself</span>, added "help my unbelief". (Mark 9:24) Ephesians 2:8, quoted above, indicates that even faith is a gift of God.<br /><br />Rather than righteousness saving us, it is God's saving of us that leads to righteousness, because God's Spirit works in us to change us, and God's love motivates us to please Him:<br /><br />Titus 3:5<br />not by works of righteousness which we have done, but according to His mercy He saved us, through the washing of regeneration and renewing of the Holy Spirit<br /><br /><span id="SPELLING_ERROR_7" class="blsp-spelling-error">Eph</span> 2:10<br />For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand that we should walk in them.<br /><br />Phil 2:13<br />for it is God who works in you both to will and to do for His good pleasure.<br /><br />There are also many verses that indicate that 'works' that result from God's work of renewal in us, demonstrate to others that we truly know God, such as:<br /><br />Titus 1:16<br />They profess to know God, but in works they deny Him<br /><br />(All verses quoted from the New King James version)<br /><br />So, we start by confessing our sins, which implies a desire to stop sinning; but God, while He helps us to stop sinning, does not make our success at not sinning part of His covenant. He knows we are unable to keep such a requirement. Our righteousness, however much it was, was insufficient in the first place, and it makes no sense to add it afterward. Any righteousness we <span id="SPELLING_ERROR_8" class="blsp-spelling-corrected">achieve</span> afterward is by availing ourselves of His help, so how can we claim any credit for that?<br /><br />It is truly comforting to know that our right standing with God rests securely on His unilateral agreement and promise to us, motivated by His unconditional love for us.<br /><br />When in trouble, we may reach up as a child to grasp His hand; but His hand is too big for us. Instead, He reaches down and holds us -- and that is far more secure.<br /><br /><a href="http://jamesmclark.blogspot.com/2005/06/faith-and-sin-are-opposites.html">For more on trusting God, click here.</a>JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com0tag:blogger.com,1999:blog-13817057.post-13795124107305723632010-03-06T09:53:00.006-05:002010-03-06T12:24:55.282-05:00More About the Genetic CodeSometimes I will go back to one of my blog articles to correct minor errors; and a few times I have made major additions. But a disadvantage of this is that people that have already read the original article will probably not go back to read it again.<br /><br />A little more than a year ago, I wrote <a href="http://jamesmclark.blogspot.com/2009/02/genetic-code-how-to-read-dna-record.html">The Genetic Code - how to read the DNA record</a>, and recently added some details to a paragraph and expanded the conclusion of the article. So here is the <span id="SPELLING_ERROR_0" class="blsp-spelling-corrected">amended</span> paragraph and the expanded conclusion.<br /><br />The original article gave the impression that only the transfer RNA (<span id="SPELLING_ERROR_1" class="blsp-spelling-error">tRNA</span>) molecules define the genetic code. Actually, other, larger, molecules are also involved. So the <span id="SPELLING_ERROR_2" class="blsp-spelling-corrected">amended</span> paragraph clarifies this:<br /><br /><strong>===</strong><br />The key elements of translation are small transfer RNA (<span id="SPELLING_ERROR_3" class="blsp-spelling-error">tRNA</span>) molecules. Each kind of <span id="SPELLING_ERROR_4" class="blsp-spelling-error">tRNA</span> molecule has a region called the <span id="SPELLING_ERROR_5" class="blsp-spelling-error">anticodon</span> that can recognize and attach to a particular <span id="SPELLING_ERROR_6" class="blsp-spelling-error">codon</span> of a messenger RNA (<span id="SPELLING_ERROR_7" class="blsp-spelling-error">mRNA</span>) molecule. The <span id="SPELLING_ERROR_8" class="blsp-spelling-error">tRNA</span> molecule has another region called the "3' terminal" that attaches to a particular amino acid. This attachment is aided by molecules called <span id="SPELLING_ERROR_9" class="blsp-spelling-error">aminoacyl</span>-<span id="SPELLING_ERROR_10" class="blsp-spelling-error">tRNA</span> <span id="SPELLING_ERROR_11" class="blsp-spelling-error">synthetases</span>, of which there is generally one kind for each kind of amino acid. There are even helper molecules that provide a proofreading function to detect and correct any translation errors.<br /><strong>===</strong><br /><br />(Actually, there are some variations of this, but discussing these would be distracting. There are also many other types of complex molecules that control the code-translation process but do not define the genetic code -- another subject.)<br /><br />Then I expanded the conclusion:<br /><br /><strong>===</strong><br />Where does the genetic code come from? It is not the result of chemistry or any laws of physics. It is determined by the set of <span id="SPELLING_ERROR_12" class="blsp-spelling-error">tRNA</span> molecule types, and <span id="SPELLING_ERROR_13" class="blsp-spelling-error">aminoacyl</span>-<span id="SPELLING_ERROR_14" class="blsp-spelling-error">tRNA</span> <span id="SPELLING_ERROR_15" class="blsp-spelling-error">synthetase</span> types, which are constructed according to DNA information, which encodes not only the building materials and the building plans, but also the building tools and the building methods. In other words, the genetic code is just information that has always been there since life began.<br /><br />The number of possible genetic codes is a huge number, 85 digits long:<br /><br />1,510,109,515,792,918,244,116,781,339,315,785,081,841,294, 607,960,614,956,302,330,123,544,242,628,820,336,640,000<br /><br />and all of these many codes would work equally well. But all of life uses just one genetic code, about 280 bits of information, the one that scientists Watson and Crick discovered in 1953, but was there since creation. The theory of evolution has no explanation for how the genetic code began, because it can't explain how information can arise from no information. Nor can it explain why there is only one genetic code (out of such a huge number of equally workable codes), even though there is extreme variation of everything else. The mechanism of the present genetic code is very complex; and evolutionary theory supposes that it randomly evolved from a simpler, smaller code. But because there are so many equally viable genetic codes, random evolution should have produced species with many different codes. The evolutionary explanation is far more unlikely than dumping a bucketful of dice on the floor and expecting them to all land with the same number up.<br /><br />The creationist explanation is that the universal genetic code is like a signature of the creator, who chose a uniform code for all of the designs of life. A short story will illustrate the principle:<br /><br />During the Cold War, Russia was suspected of stealing American technology. Proof came when some Russian war equipment given to a third country was captured and examined. It contained an integrated circuit that was identical to an American design. It is theoretically possible that the Russians had the same design concept, leading to a similar design. But digital circuits have thousands of component parts connected by thousands of wires. There trillions of ways to position the parts on the chip and trillions of ways to route the connecting wires that work equally well. It would be impossible for the Russians to <span id="SPELLING_ERROR_16" class="blsp-spelling-corrected">independently</span> produce the same positions and <span id="SPELLING_ERROR_17" class="blsp-spelling-error">routings</span> even if the logical design were identical. But examination showed the details were identical, even details left over from correcting wiring errors. In effect, there was an American 'signature' in the copied design.<br /><strong>===</strong><br /><br />For the Math fans, I'll add a footnote on how that 85-digit number was calculated:<br /><br />That big number counts the number of ways that the 64 <span id="SPELLING_ERROR_18" class="blsp-spelling-error">codons</span> can be mapped to 21 interpretations, or interpreted as 21 'messages'. One message is to start with a Methionine (or add a Methionine if already started); one is to stop, and the other 19 messages are to add one of the other 19 amino acids [to the peptide chain that will fold into a protein molecule]. This 64-to-21 mapping can be enumerated in two steps:<br /><br />First, we count the number of partitions of a set of 64 items into 21 non-empty, pair-wise disjoint subsets. In plain language, this means that:<br /><ul><li>Together, the 21 subsets must contain all of the 64 <span id="SPELLING_ERROR_19" class="blsp-spelling-error">codons</span>.</li><li>Each <span id="SPELLING_ERROR_20" class="blsp-spelling-error">codon</span> must be assigned to only one subset.</li><li>None of the subsets can be empty; each must contain at least one <span id="SPELLING_ERROR_21" class="blsp-spelling-error">codon</span>.</li></ul>This count is calculated by a mathematical function called the <a href="http://mathforum.org/advanced/robertd/stirling2.html">Sterling number of the second kind</a>, which is S(64, 21) in this case.<br /><br />Second, we need to count the number of ways that the 21 subsets can be mapped to the 21 messages. This the number of permutations of 21 things, which is 21 factorial, written 21!<br /><br />So the desired number is S(64, 21) times 21! But typical computer hardware cannot directly compute numbers that large. Special software that partitions a big number into slices small enough for the hardware is needed. When I was designing special hardware for very large integers (for public key cryptography; I have two patents, #4,658,094 and #5,289,397, for that), I wrote such software so that I could test and verify my designs. So I used my '<span id="SPELLING_ERROR_22" class="blsp-spelling-error">BigInt</span>' software to do the arithmetic.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com1tag:blogger.com,1999:blog-13817057.post-33385392010885245782010-01-25T10:08:00.015-05:002010-01-29T23:03:49.633-05:00Dawkins' ConfessionI found this video showing Gary <span id="SPELLING_ERROR_0" class="blsp-spelling-error">DeMar</span> of <a href="http://www.americanvision.org/">The American Vision</a> discussing Richard <span id="SPELLING_ERROR_1" class="blsp-spelling-error">Dawkins</span>' new book, <em>The Greatest Show on Earth</em>:<br /><br /><object width="450" height="279"><param name="movie" value="http://www.youtube.com/v/a5o3kQljyM8&hl=en_US&fs=1&rel=0&color1=0x2b405b&color2=0x6b8ab6&border=1"><param name="allowFullScreen" value="true"><param name="allowscriptaccess" value="always"><embed src="http://www.youtube.com/v/a5o3kQljyM8&hl=en_US&fs=1&rel=0&color1=0x2b405b&color2=0x6b8ab6&border=1" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="450" height="279"></embed></object><br /><br /><span id="SPELLING_ERROR_2" class="blsp-spelling-error">DeMar</span> points out some interesting quotes from <span id="SPELLING_ERROR_3" class="blsp-spelling-error">Dawkins</span>' book which I have reproduced below, and will comment on each.<br /><br />Many churches, and even <span id="SPELLING_ERROR_4" class="blsp-spelling-error">parachurch</span> organizations, each have a 'statement of faith', or 'confession of faith' whereby they define their core beliefs. It seems that in the beginning of his book, <span id="SPELLING_ERROR_5" class="blsp-spelling-error">Dawkins</span> gives his 'confession of faith', beginning with:<br /><blockquote>"It is the plain truth that we are cousins of chimpanzees, somewhat more distant cousins of monkeys, more distant cousins still of aardvarks and manatees, yet more distant cousins of bananas and turnips..."</blockquote>Notice that he speaks of cousins, not brothers, because brothers, mothers, and fathers are not to be found. He continues: <blockquote>"Evolution is a fact, and [my book <em>The Greatest Show on Earth</em>] will demonstrate it. No reputable scientist disputes it..." </blockquote>Speaking of evolution as a fact doesn't sound, at first, like a statement of faith, but given his admission of lack of evidence (quoted later), it seems that what he really means by this is that he believes so fervently in evolution that it seems like a fact to him. Thinking of my own faith, I know the feeling.<br /><br />He also promises that his book will demonstrate the 'fact' of evolution, but no real demonstration of this is possible. There is <em>experimental</em> demonstration, where one sets up <span id="SPELLING_ERROR_6" class="blsp-spelling-error">initial</span> conditions, controls, and measurements on real physical objects, living or not. But the evolution that relates man to turnips is an interpretation of the past, and no part of it has been experimentally demonstrated in modern times. Parenthetically -- <blockquote>We perhaps may need, at this point, to explain to some readers the distinction between macro-evolution, also called goo-to-you evolution, and micro-evolution, the kind that when guided by man breeds cats to get more kinds of cats, but never dogs, and breeds dogs to get more kinds of dogs, but never cats. Creationists believe in micro-evolution, and that's not debated here. The relevance here is that experimental demonstrations have been applied to micro-evolution, but not macro-evolution, which remains in the realm of story-telling.</blockquote>There is also <em>logical</em> demonstration, which in its most reliable form is a formal proof. But the lack of evidence, which <span id="SPELLING_ERROR_7" class="blsp-spelling-error">Dawkins</span> admits to, <span id="SPELLING_ERROR_8" class="blsp-spelling-corrected">precludes</span> logical demonstration of macro-evolution.<br /><br />His statement "No reputable scientist disputes it" is a tautology in disguise. There are many reputable scientists that dispute evolution, but to evolutionists like <span id="SPELLING_ERROR_9" class="blsp-spelling-error">Dawkins</span>, that <em>defines</em> them as not reputable.<br /><br />As though to illustrate the fervency of <span id="SPELLING_ERROR_10" class="blsp-spelling-error">Dawkins</span>' faith, the next quote sounds like an enthusiastic description of a miracle: <blockquote>"The universe could so easily have remained lifeless and simple -- just physics and chemistry, just the scattered dust of the cosmic explosion that gave birth to time and space. The fact that it did not -- the fact that life evolved literally out of nothing -- is a fact so staggering that I would be mad to attempt words to do it justice. And even that is not the end of the matter. Not only did evolution happen: it eventually led to beings capable of comprehending the process by which they comprehend it." </blockquote>His phrase "lifeless and simple" is similar to <span id="SPELLING_ERROR_11" class="blsp-spelling-corrected">Genesis</span> 1:2, where the earth is described as "formless and empty" before God gives it form and fills it with life; but in <span id="SPELLING_ERROR_12" class="blsp-spelling-error">Dawkins</span>' account, God gets no credit.<br /><br />His description of dust giving "birth to time and space" contradicts physics as we now know it. According to modern physics, matter cannot exists separately from time and space, and vice <span id="SPELLING_ERROR_13" class="blsp-spelling-error">versa</span>.<br /><br />Again he uses the word 'fact' to refer to his interpretation of facts. But I would agree that the idea that "life evolved literally out of nothing" is staggering -- so much so that one would be mad to believe it.<br /><br />If you still doubt that <span id="SPELLING_ERROR_14" class="blsp-spelling-error">Dawkins</span>' words are a 'confession of faith', read this quote:<br /><blockquote>"We have no evidence about what the first step on making life was, but we do know the kind of step it must have been. It must have been whatever it took to get natural selection started." </blockquote>In other words, <span id="SPELLING_ERROR_15" class="blsp-spelling-error">Dawkins</span> knows that there must have been an event when life began, there must have a 'first cause' that caused it to begin, and he knows that he has no evidence of how it began. He is unwilling to believe that God was that cause, so he resorts to a tautology: "It must have been whatever it took".<br /><br />Given the huge amount of information and artful design that we now observe in all living things, requiring enormous intelligence, I'd say it must have been God -- it took God to get natural selection started. And by God's account, He created various kinds of living things, so natural selection started on some collection of kinds, rather than one kind of life. And the experimental evidence is that even when we give natural selection an extra push, and the advantage of our intelligence, we can't change cats into dogs, or vice <span id="SPELLING_ERROR_16" class="blsp-spelling-error">versa</span>, let alone turning turnips into chimpanzees.<br /><br />I think my faith fits the evidence better.JChttp://www.blogger.com/profile/12753309808254573131noreply@blogger.com1