Origami Water Lilly and Lilly-Pad

Overview

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.

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.

(Click on any photo here to see a larger copy.)

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.

In the instructions, I provide recommended sizes and colors, but you can vary these as you like after you learn the design.

The Water Lilly   (Skip to Lilly Pad)

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).

< 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.

Four-Petal Unit ('A' and 'B' Petal Designs)

AB1. Valley-fold the two diagonals, and mountain-fold in half (twice) parallel to the sides, like this >




< 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.)


'A' Petal Design

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.

< A4. Repeat A3 on the other side. There should be a small gap at the center.





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.



< A6. Push the model into this shape.






A7. > Fold the top and bottom edges inward on existing creases.






< A8. Push the left and right sides together, like this.






A9. > Hold the 2 wings that were folded narrower and pull apart to get this.





< 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.




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'.

< 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.




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.

< 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.

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.)

< 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.


A17. > Flatten the sink fold, like this.






< A18. Raise 2 opposite 'legs' as in step A12, and fold each raised leg in half, to get this position.





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'.

< 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'.

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.

< 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.)


A23. > Align side 4 with side 3 in a similar way. (The sink fold in the center will open more.)





< 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.



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.



< 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.

A27. > Lift the side of the square button and slip the new fold under the button, like this.





< 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.



A29. > The bottom side looks like this.






< 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.

A31. > Repeat step A30 on the remaining 3 petals to get this (bottom view).





< 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.


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). Skip to step AB35.

'B' Petal Design

< 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.

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.

< B5. Fold the raw edge of each wing back to the previous crease. There should be a small gap at the center.




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.



< B7. Push the model into this shape.






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).


< B9. Repeat B8 on the bottom.







B10. > Push the left and right sides together, like this.






< B11. Hold the 2 wings that were folded narrower and pull apart to get this.





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.

< 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'.

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.

< 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.

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.

< 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.)

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.


< B19. Flatten the sink fold, like this.






B20. > Raise 2 opposite 'legs' as in step B14, and fold each raised leg in half, to get this position.





< 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'.

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'.

< B23. For EACH of the FOUR 'V' creases, continue one side of the V over to a 'shoulder' point by creasing like this.




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.

< 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.)

B26. > Align side 4 with side 3 in a similar way. (The sink fold in the center will open more.)





< 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.



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.



< B29. Lift the side of the button and fold the shoulder point under the button, like this.





B30. > Repeat steps B28 and B29 on the remaining 3 'shoulder' points to get this. These are four petals.




< B31. The bottom side looks like this.






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.

< B33. Repeat step B32 on the remaining 3 petals to get this (bottom view).





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.

Petal Assembly

AB35. Stack the 4-petal units, starting with the smallest (on top) and proceeding to the largest, using glue on the central square between units.

< 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.)

Lilly Center

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.)

< 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.

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).

< C4. Bend all the slivers toward the side with the smaller unit, and pinch the circular edge all around to get a good crease.




C5. > Holding the center with one hand, stir the slivers (stamens) into random positions by pushing them up and down and sideways repeatedly.



< C6. Form a cup shape. Some water lillies have a noticable hole in the middle of the stamens, like this.




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.

Lilly Pad

< 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.



P2. > Fold in half parallel to an edge, like this. If green on one side only, the green should be inside here.




< 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.

P4. > Turn over and repeat step P3 on the other side.






< P5. Unfold the first fold, and you have a blintz base. (Named after the Jewish pastry that is folded this way.)




P6. > Mountain-crease as shown here, by twice folding one side over to the opposite side and unfolding.




< P7. Make a valley crease by bringing two mountain creases together. Do on opposite sides, as shown here.




P8. > Rotate the model 90 degrees and repeat step P7 to get a total of 4 valley creases equally spaced around the center.



< 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.

P10. > Turn the previous corner folds inside-out as shown here progressing clockwise:
9-o'clock - the original position;
12-o'clock - opened up;
3-o'clock - corner pushed in;
6-o'clock - closed (all folds on existing creases).

< P11. Do the process P10 on all 4 corners, like this. This side, with the 4 'cracks', is the bottom of the lilly-pad.




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.



< 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.)

P14. > Top side up. We now have a polygon of 16 sides, which nearly looks like a circle.





< 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.

P16. > The 2 sink folds seen edge-on. Do 3 more pairs of 2 sink folds, for a total of 8 sink folds.




< P17. Bottom-side view when all 8 sink folds are done.






P18. > Along one of the 4 'cracks' on the bottom, cut the top layer from the outside to the center.




< P19. Fold up on either side of the cut, from the edge of each nearby 'arrow-head' sink fold straight to the center.




P20. > Turn over, and reverse the folds made in step P19






< 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.



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.



< P23. Seen from another viewpoint, the new point is swinging toward the center and will fit between the top and bottom layers.



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.)

Repeat steps P21-P24 on the other side of the cut.

< 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.

P26. > Bottom-side view.







< 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.

'Rhombicized' Classic Origami

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.

Overview

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).

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.

This encouraged me to try folding other classic bases and designs using a rhombus instead of a square:

preliminary and water-bomb bases
blintz fold
fish base
bird base
classic crane
classic flapping bird
petal-topped container

I'm calling these "Rhombicized Classic Origami", and I am reporting my findings here. But first, let's return to the "skinny bird base".

The Skinny Bird Base

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.

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.

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.

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).

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'.

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.)

Making a Rhombus

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.

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.

Folding the Rhombus

There are two different ways of adding two more creases after creasing the two diagonals:

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.

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.

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.

Turn over and repeat, then unfold the first (longest) fold.

Some Results

Here are the rhombicized bird base, blintz fold, and windmill base:

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.

Here on the left are two fish bases, both folded from identical rhombuses.

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.


Here on the right is the classic Masu box (left) and the rhombicized Masu box (right).

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.


Here on the left are two Cranes, both folded from identical rhombicized bird bases.

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.


Here on the right is a rhombicized Flapping Bird.

The Petal-Topped Container 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.

Advice for DIY Irreducible Complexity

This is an addendum to the previous blog, "Do-It-Yourself Irreducible Complexity". Here I give advice to anyone who wants to construct, demonstrate, or experiment with the 4-stick weaving illustrated in the previous blog.

(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.

(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.

(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.

(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.

(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.

Extra Challenge

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.)

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.

An Abstract Analogy

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.

Do-It-Yourself Irreducible Complexity

This weaving of four sticks is irreducibly complex. 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.

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.

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?)

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.)

More about Irreducible Complexity

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.

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 “irreducible complexity”. The concept was introduced in 1994 by Michael J, Behe and later (1996) in his book “Darwin's Black Box”. 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.

Example: The Knee Joint

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 “Is the ‘irreducible complexity argument still valid? (Critical characteristics and the irreducible knee joint)” by Stuart Burgess.

Example: A Molecular Motor/Generator

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.

One scientist said “The 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.” 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.

Another scientist said: “I 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.”

A Failed Evolutionist Argument

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.

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.

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.

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.)

Another Failed Evolutionist Argument

As I said earlier, evolutionists are great story-tellers (but poor system engineers). Another evolutionist argument is that Hermann Joseph Müller had previously devised a scheme whereby complex system could evolve two steps at a time. The two steps are:

Step 1: Add a component;

Step 2: Make it necessary.

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 in practice, 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:

Step a1: Add a component. (Add 2nd stick)

Step a2: Make it necessary. Well, it's only one of three more necessary sticks, but it's not sufficient 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.

Step b1: Add a component. (Add 3rd stick)

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.

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.

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.

Summary: 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 – I dare you.

For advice on constructing, demonstrating, or experimenting with the 4-stick weaving, see Advice for DIY Irreducible Complexity.

Can 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.

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.

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'.

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.

An Overview of AI

AI is a broad field of study, and not all researchers or developers have the same goals, nor use the same methods.

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.

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.

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.

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.

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.

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.

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.

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.

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.
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.

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.

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).

Now, Wolfram Research is developing an even 'smarter' program, making the current "Wolfram Alpha" 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.

Conclusion

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.

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.

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.

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.

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.

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.

That generally means that the universe doesn't have enough material and enough time for the random experiment to succeed. That's practically zero.

The Digital Control of Life

In other blog articles such as Life is More Than Chemistry and Can Chemical Evolution Work? I point out how living things fundamentally differ from nonliving things. Both are controlled by the laws of chemistry, but in living things, the chemistry 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 chaperone 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.

In a recent blog article, The First Digitally Controlled Designs, 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'.

The DNA is also firmware, because:

(1) It is digital: 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.

(2) It is symbolic: Each codon, 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 codons, and man-made controllers use 8-bit bytes is a mere design detail.

(3) It is stored in read-only memory. There is no information flow from polypeptides to mRNA to DNA, or any writing process.

(4) In the reading process, selected information from the DNA is copied to mRNA (temporary copies) and then interpreted: that is, translated to polypeptides (the basic form of proteins). In man-made digital controllers, selected information from the read-only memory is copied to temporary memory and then interpreted: that is, translated to signals that produce desired actions.

In addition to the temporary (mRNA) 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 controllers are not designed to grow and reproduce by themselves, so similar copying is not provided. Instead, there is copying in the manufacturing process.

(5) There is a higher structure typical of digital control languages. 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.

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.

This process, called Cellular Respiration, involves 4 stages:

Glycolysis (10 steps), 

the Citric Acid Cycle (8 stages), 

the Kreb's Cycle (8 stages), and 

the Electron Transport Chain (4 steps).  

 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 some of the cell processes, and they are only summaries!  There are diagrams for other complex processes, such as Photosynthesis, which captures the energy of sunlight and stores it by making glucose (food-fuel).

The process of reading and interpreting the DNA information creates all the chemical 'machinery' (such as enzymes) and chemical 'factories' (such as mitochondria) for these and many other complex processes of living things.

Update on Dave McKean's 'Luna' Film

Here is an update on Dave McKean's upcoming film Luna for which I folded two origami crabs in 2007. If you haven't read my previous blogs about this, they are Origami Emergency and More About the Origami Crabs.

First, some additional details about the crabs.

Luna filming began in early November of 2007. The request for the origami crabs was sent on 10-30-07 and the crabs arrived on the set 11-08-07.

Through my friend Mark Kennedy and Nick Robinson, word reached Dennis Walker, the articles editor of the British Origami Society (BOS), who asked me for permission to put my blog article in the BOS 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.

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.

Twitter Info

I extracted the following information from Dave McKean's Twitter page:

"Answering request for Luna stills, here's a few, from the live action shoot only. As we progress I'll post more: http://bundl.it/MjY2Mjk "

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."

"Several small animated scenes + fx, 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 (IMDB) by July 2010, perhaps.

"It's nothing like MirrorMask to be honest, although it does have Stephanie Leonidas in it, and some dreamlike scenes. It's an adult drama."

While looking for details on Luna progress, I came across this delightful bit of banter which I'll include for your enjoyment:

Ken Fries: Steve probably already has a copy of Luna...

Dave McKean: Great! Can I see it? Then I'll know if it's worth finishing...

Ken Fries: Nah, u shouldn't see it, I don't want to spoil the ending for you.

Photos:


Dave McKean 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 (Dervla Kirwan), which he symbolically buries in the sand. They hide behind a rock and watch a real crab emerge from the same place."

Folding the crab, wide shot and close-up:




The crab, on hand:


The crab burial:


Some contributors to the Luna film:

• Dave McKean (writer, director, designer, editor)


• Keith Griffiths, producer (produced 78 films, directed 16 films)


• Simon Moorhead (produced all Mckean's films, including MirrorMask)


• Antony Shearn (director of photography)


• Tessa Beazley, production manager (production manager for about a dozen films, and other production)


• Darkside Animation of London, animation support (graphics and special effects for 3 films)


• Ashley Slater, music (actor, music writer, performer, and producer; music producer, mixer, programmer, and performer for "MirrorMask" soundtrack)


• Iain Ballamy (jazz player and composer, composed the score for MirrorMask)


• Dervla Kirwan, actress (Ballykissangel, Casanova, Dr. Who, Ondine)


• Stephanie Leonidas, actress (MirrorMask, Yes, Feast of the Goat, Crusade in Jeans, Dracula)


• Michael Maloney (In the Bleak Midwinter, Babel, Notes on a Scandal, Truly Madly Deeply)


• Ben Daniels (Spooks, Doom, The State Within, Fogbound, I Want You)


• Maurice Roëves (The Damned United, Hallam Foe, Tutti Frutti, Beautiful Creatures)