Is Encoded Information an Essential Part of the Universe?

In a previous blog entitled "All Things", I discussed how the universe is made of the four essentials:

matter — energy — space — time

-- and how, according to the laws of physics, as best we know them, none of these can exist without the others. Now I would like to extend the discussion by talking about information.

Information is made of none of these. Information can be represented, or encoded, by arrangements of matter (ink on paper, magnetic patterns in a disk, etc.) that lie motionless in space, unchanging in time. Or information can be encoded by patterns of energy (sound, radio waves, etc.) that move through space, changing in time. Matter and energy are only containers and vehicles to store and transmit information within space-time.

When you write your thoughts in your diary, the ink and paper do not make your thoughts; they simply 'record' them: that is, they hold what you have recorded. When you record an experience, the information comes from external sources, but is filtered by your perceptions. When you record a question that you wish to have answered, or record an ambition for the future, the source of the information is more internal, originating from who you are.

Scientists have discovered much about the laws of physics that mathematically describe the behavior of matter, energy, space, and time, although there are a few things they are still hoping to discover. And in modern times, scientists have discovered laws that govern the storage and transmission of information, the application of which has revolutionized our present "information age" of computers and communication devices. So it seems that we should add information to the list of essentials that the universe is made of:

matter — energy — space — time -- information

Or should we? Recall that we argued that matter, energy, space, and time belonged together because there are "inexorably, inextricably joined". We said that "energy and mass (matter) are interchangeable" and that "time and space are different sides of the same fabric" and that matter and energy were like "wrinkles or knots in the fabric of space-time". That is, the laws of physics that we observe does not allow for an empty space-time that is not filled with matter, and that does not have energy. But do these same laws of physics allow for a universe of matter, energy, space, and time that has no information?

To be clear, the information that we are discussing is encoded information, not physical information. For example, if you print this web page, you will get a piece of paper with a certain pattern of ink on it. You can measure the height, width, thickness, and weight of the paper and get physical information about the paper. Someone that does not know English can count the words and letters, and measure the height of the letters, getting more physical information. But only by reading and understanding the English can they get the encoded information that was encoded one way in the computer, then encoded another way on the paper.

We can splatter some ink on the paper, also producing a pattern of ink on it. But there will only be physical information but no encoded information.

You may have heard stories of a crime scene where a pattern of splattered blood is analyzed by a forensic scientist, who tries to determine something about the events that caused the blood to splatter. His analysis relies on the laws of physics that govern how drops travel through the air, adhere to a surface, or bounce, skid, roll, or run on the surface, or how larger drops can break into smaller ones.

In the case of the printed page, the laws of physics can only explain the general process by which the printer works, but cannot explain the particular pattern that encodes a particular message. The science of information can explain how the pattern of keystrokes on my keyboard was encoded into bit patterns entering my computer, stored there, sent to a web server computer, and ultimately sent to your computer and then to your printer. But it can't explain what happened in my head to make my fingers do what they did to the keyboard.

Now that we have clarified the difference between encoded information and physical information, we can state (and answer) our question more clearly:

Do these same laws of physics allow for a universe of matter, energy, space, and time that has no encoded information? The answer is YES!

There is no physical law that requires encoded information to exist. And what do we observe? We observe encoded information only where there is life, and there is no physical law that requires life to exist. The universe can be full of stars and inert, lifeless planets such as we have observed elsewhere, and no physical laws would be broken.

Where there is life, we observe encoded information. First, we see animals (as well as people) communicating. Birds will make one sound that means "This territory is mine! Stay out!" And another sound that means "Watch out! Danger is close." For example, chickadees have a song that sounds like "chick-a-dee-dee-dee-dee!" Ornithologists have discovered that the number of dee's is an indication of the perceived danger level. Honeybees perform a dance on the honeycomb that reports to other bees the direction and distance from the hive to a source of nectar. Many animals use pheremones (specialized scents) to convey information to one another. Even plants use chemical communication.

This information is encoded, because there is a fundamental difference between the action of chasing another bird out of the claimed territory and a message that threatens this action in the future when needed. There is a fundamental difference between fleeing from danger or ducking out of sight, and warning another bird that one of those actions may be necessary.

We also observe encoded information in the communication of one part of a living body to another part of the same body. An obvious example is the communication within the nervous system.

There is also encoded information in the DNA and RNA of living things. This is stored information, which is communicated in three ways: (1) the construction of proteins, etc. -- ultimately, the body -- from the 'stored blueprints' of the DNA repository, (2) the replication of the information into new cells, and (3) the replication of the information (generally combining with another DNA source) to produce progeny.

There is an interesting parallel between the operation of data within a computer and the operation of DNA information within the 'hardware' of a living organism. But that is too much to explain here -- this is the subject of later blogs:
"The Digital Control of Life"
and
"The First Digitally-Controlled Designs".

Fairness Doctrine? Who are They Kidding?

If you recognize that the so-called ‘Fairness’ Doctrine isn’t fair, then you don’t need to read this. But if you think the ‘Fairness’ Doctrine is fair, then you need a lesson in logic -- read on if you are open-minded.

Basically, the ‘Fairness’ Doctrine seeks to enforce equal time for conservative and liberal views on American radio stations. But why do that and not also enforce equal time on cable and broadcast TV, equal print space in newspapers, etc.? If we really need to enforce an equal voice for conservative and liberal views, it would be ‘fair’ to do it equally for all outlets. But the liberals don’t want that, because then they would lose their advantage in the TV and newspaper outlets. Is a 'fairness' only in an area that gives an advantage to the liberals fair?

Some of the misunderstanding of the ‘Fairness’ Doctrine relates to a common misunderstanding of the freedom of speech. The free communication of ideas involves listening as well as speaking, and thus involves the freedom of listening (or not listening) to any one, as well as the freedom of speaking. For an example, even though people are free to say stupid things, the rest of us are free not to listen to stupid speeches. The natural result, fortunately, is that stupid people don’t get equal time. You can substitute other words such as ‘ranting’ instead of ‘stupid’, and the logic works the same. In an unregulated media that is funded by advertising, advertisers pay for listeners, so programs with few listeners will fail financially. The speakers on these failing programs may not be stupid or ranting, but something is causing potential listeners to tune out, which is freedom at work.

Another part of the issue is: why should conservative and liberal views get equal time? Why not conservative, centrist, and liberal getting equal thirds? Why not far right, right, centrist, left, and far left? Why not Democrat and Republican? Why not pro-life and pro-choice? Pro-amnesty and anti-amnesty? Who should decide the categories? Just to be sure we are really fair, shouldn’t we include all categories, including cat-lovers and dog-lovers? (For a bonus, all the government regulators needed to make this system work will reduce the jobless rate.) Imagine all the paperwork -- does that sound like freedom of speech to you?

I Dreamed I Met My Guardian Angel

I had a dream that I arrived in heaven and was escorted to my new living quarters -- my "mansion". I was introduced to my guardian angel, who explained to me that he would now be my personal servant -- valet, housekeeper, etc.

All kinds of questions began to flood my mind. "Does this mean that my house will get dirty and need cleaning?" I asked.

"No, there is never any dirt or dust in the houses; only dirt in the gardens where the flowers grow", he explained. "But you might, for example, not return books to their proper places in your library. I will make sure that the books are filed correctly, and will help you find books in your library."

"Wow! My house is furnished with a library!" I thought, hoping that he didn't notice the big grin that broke out across my face.

"The same goes for keeping your personal wardrobe in order", he continued.

"We don't all wear white robes?" I asked.

"Only on special occasions", he replied. "God loves variety, so He not only has made individual human bodies different -- both before and after resurrection -- but He also allows people to wear a variety of clothing colors and styles."

"Since you were my guardian angel," I began, changing the subject, "you must recall times in my life when.."

"When you nearly got into trouble", he said, laughing. "Yes, I have lots of stories about your life on earth. And I also have lots of questions. I don't understand about forgiveness and grace, for example. We angels -- I mean, the ones that sinned -- didn't get forgiveness. But we will have lots of time to talk."

I looked into his friendly face, and somehow I sensed a child-like innocence. Even a pet-dog innocence, I thought, though more intelligent and conversant than a dog. My heart suddenly discovered a love for this wonderful creature that God had created before I was born. And I began to realize that through my salvation and sanctification experience, God had taught me lessons about things that baffled this angel.

Impulsively, I reached out and hugged him, and told him that I loved him. He reacted with great surprise, even shock, it seemed.

"You love me?"

"Yes, God loves you, and He has given me a love for you, and has given me to you even as He has given you to me, so that He can love you through me." As I spoke these words, I realized that God had given them to me through His Spirit.

"Show me the library" I asked. He led me down a hallway, but before we got to the library, I passed another room that caught my attention. "What's this?" I asked.

"That's the music room." As we walked in, I could see many kinds of musical instruments arranged neatly on one side of the room.

"But I don't play any musical instruments."

"You didn't." He corrected my tense. "But you will. Haven't you always wished you could play a musical instrument?"

I picked up a stringed instrument, quite unlike anything I had ever seen before, yet it seemed simple in design. I plucked the strings, and found that I could remember the tone of each string. My angel friend started singing a song of praise that somehow seemed both new and familiar. A harmony for his song began to form in my mind, and I began to pluck the strings, discovering that my fingers were finding the strings that matched the notes in my head. "This is amazing!" I exclaimed, interrupting the song. "I really can play this thing!"

"You are surprised?" He laughed with joy at my obvious delight. "Who taught the birds to sing? And who taught the birds to fly?"

"You are so right. I remember that when I first got my resurrection body that I just started flying up towards Jesus, and it seemed as natural as walking."

"Literary Meme"

A friend passed on this concept that was titled "Literary Meme", which she got from http://www.rusticanda.blogspot.com/. This is how it works:

1. grab the book closest to you
2. open it to page 161
3. find the fifth full sentence
4. post the text of the sentence to your blog
5. don't search around for the coolest book you have, use the one that is really next to you.

My daughter Susan's new novel, "And the Violin Cried", wasn't the closest book to me, but it was the first book that came to mind, so I was curious as to what the sentence would be:

Samantha’s father pounded the last nail into the manger, while Angelica Nelson toddled over toolboxes and through sawdust to donate her baby doll to the cause.

That was from chapter 34, "Send Aaron!", describing Pinedale Bible Church's preparations for a Christmas production.

The nearest book other than my Bible was an anthology called "The Intellectuals Speak Out About God", and the sentence is:

What, for example, the ontological argument basically says is that if you understand what is meant by "God" and at the same time fail to see the necessity of the reality of that Being, then you are not really talking about God but about something else.

This was from chapter 11, "The Rationality of Belief in God", in a section where Professor John E. Smith attempts to answer the question "How best can the theistic point of view be presented to modern man?"

The reason why this book is so close by is that the reading is so deep that I can only read small portions at a time. But I don't want to give up on the book, so I keep it near as a reminder to read more later.

Equally close was my NKJ Bible, and the sentence is:

It is perversion.

That was from Leviticus 18, where God proscribes homosexuality and bestiality. A reminder that belief in God, and necessarily, acceptance of His absolute proclamations, is an inconvenience to those who would rather define morality on their own terms.

The Better Mouse Trap

When I recall my youth, I remember a number of activities that foretold my career as an engineer, including the time that I tried to make a better mouse trap.

We sometimes had mice (I remember Mom catching one with a broom and a dustpan), so we also had mousetraps. I noticed that mice could sometimes nibble the cheese gently enough to avoid getting caught, so I concluded that the triggering lever wasn’t sensitive enough. The big strong lever for catching the mouse was held by a second lever, which in turn was held by a third triggering lever that held the cheese.

I figured out that the purpose of the second lever was to reduce the force at the triggering lever. But the problem was that the triggering force was not reduced enough. So I built a mouse trap with more levers. As best as I can recall, the improved design was something like this:

A triggering lever made of a length of horse-hair held a stouter lever made of a broom-straw, which held a lever made of a tooth-pick, which held a lever made of a Popsicle stick, which held the strong capturing lever. The horse-hair didn’t need to hold the cheese, because the mouse’s whiskers would spring the trap if he just got close enough to sniff the cheese.

To test the trap, I set it up on the stairs that went from the kitchen up to the boys’ bedroom. (My three brothers and I shared one big bedroom.)

Now you must understand that one could not tip-toe up these stairs without most of the steps creaking. (This was advantageous to us boys when our parents could hear mischievous noise coming from the bedroom, and one of them tried to sneak up the stairs to find out who was doing what. But that’s another story.) But actually you could sneak up the stairs noiselessly if you knew the secret sequence: step over the first three steps, landing on the far left side of the fourth step, then go to the far right of the sixth step. etc.

Because the trap was essentially a vibration sensor, I thought that by setting it up near the top of the stairs, one of my brothers would walk up the stairs, would creak a step near the trap, and then be surprised by the trap snapping.

So I set up the mouse trap on the stairs – easy to say, but tedious to do. First, pull back the big spring lever, then get the Popsicle stick to hold it down, then set the tooth-pick to hold the Popsicle stick, then set the broom-straw to hold the tooth-pick, then set the horse-hair to hold the broom-straw. The process got more and more delicate.

That done, I next had to retreat, navigating the secret sequence in reverse. I tip-toed down nearly to the bottom when I miscalculated, a step creaked, and ten steps above me, the trap snapped shut.

That was the end of the experiment. I concluded that the trap was a bit too sensitive.

The Nine-Bite Sandwich

The Nine-Bite Sandwich was one of my early, unpatented inventions, before I entered the field of electrical engineering. It may have had its origins in some earlier, secret culinary experiments conducted in the kitchen when nobody else, especially not my mother, was in the house. Those experiments turned out rather badly — so distasteful, in fact, that I'd rather not remind myself any further about them. The Nine-Bite Sandwich, however, was successful enough that I shared it with the rest of the family. As a father, I have explained it to my children, and now I document it for further generations.

The Nine-Bite Sandwich is a Construction process followed by an Eating process, which I will explain with patent-style drawings. Since it is not patented, I hereby put it into the Public Domain.

Ingredients

The ingredients are two slices of bread and four different spreads of your choice. For the bread, use sandwich bread — the real kind, not that so-called 'Wonder bread' ("I wonder why they call it bread", I always say) that sticks to your gums and palate. For the spreads, I will illustrate with peanut butter (PB), margarine (M), blueberry jam (BB) and strawberry preserves (SB); but you can choose your own.

The Construction Process

As shown in Figure 1, lay the slices of bread (S1 and S2) down in a symmetrical position. This is needed so that the slices will fit neatly when one slice is turned over onto the other slice.

Figure 1

As shown in Figure 2, spread margarine (M) on the left half of slice S1, and spread peanut butter (PB) on the right half of slice S1. Also, spread blueberry jam (BB) on the top half of slice S2, and spread strawberry preserves (SB) on the bottom half of slice S2.

Figure 2

As shown in Figure 3, turn slice S1 (the one on the left) onto slice S2. Notice that this instantly creates four flavor combinations as shown.

Figure 3
The Eating Process

As shown in Figure 4, take the first four bites from the corners of the sandwich as shown. You can peek first, to anticipate each flavor combination, or you can surprise yourself by flipping or rotating the sandwich a few times first.

Figure 4

As shown in Figure 5, take the next four bites from the 'arms' of the cross shape left by the first four bites. Notice that these bites are three-flavor combinations — a more complex flavor experience.

Figure 5
The remaining center is the last, ninth bite. It combines the flavors of all four spreads. This sandwich is fun to make and eat because each bite is a different flavor combination. Yet the sandwich is really quite easy to make.

Susan's Novel to be Published Soon

I haven't been posting for a while, because my computer died, and I lost my Internet connection. Now I'm back.

The big news around here is that my daughter Susan has found a publisher (Publish America) for her novel (And the Violin Cried). It will be published by late February or March. You can read reviews and articles about it, and get up-to-date news about book signings, etc. at www.PublishedAuthors.net/SusanJoyClark.

I've transitioned from being her nit-picking editor to being her Publish America Publicity Agent (PA PA). (ha ha) So I set up and maintain web sites, design and print business cards and bookmarks for her. I have also done photography for her, including photos of three young friends who posed as three of the characters in the novel.

Susan, who has training in graphic design, has designed a book cover for her novel which uses these three photos. The publisher may use her cover design as is, or may modify it, or do something different (no promises). But when we saw the page proofs, we were happy to see that the photos were incorporated into the book. Various chapters tell the story from the point of view of different characters; and each photo appears at the beginning of the chapter that first takes that character's point of view. We are taking that as a sign that the publisher likes Susan's cover design as well.

We decided that the title page should feature a picture of a violin, so we found a violin shop and asked if we could take a photo of a violin. They were quite gracious in spite of the fact that they were quite busy. One wall was covered with hundreds of violins. We explained that her novel featured a Schweitzer violin that survived the Holocaust, and the lady took a violin from the wall, and handing it to me, said "This one's a Schweitzer."

"Really?", I said, and she explained that it was actually a replica. But the way it was finished, it looked like an old violin that was re-varnished.

Dawkins' Weasel Algorithm, Revisited

In a previous article, "Information From Randomness?", I discussed Dawkins' "Weasel" Algorithm, which Richard Dawkins claimed was a demonstration or proof that evolution was inevitable. Here, we discuss the algorithm further.

Each character position (or column in the list of states) of the "Weasel" Algorithm can be described as an independent Markov process.

A Markov process has a set of states, and there are fixed probabilities for all possible transitions from one state to another. Take, for example, the process of tossing a die until it comes up "5".
The diagram at left describes this as a Markov process. The states are represented by the numbered circles. The interconnecting lines with arrow-heads represent one-way transitions from one state to the next. Lines without arrow-heads represent a pair of transitions in opposite transitions. Note that the looping arrow-lines indicate that a state may sometimes transition to itself -- for example, when the die is "1" and on the next toss is "1" again. Generally, probability values are written next to the transition lines in a Markov graph, but here we will simply state that all the transitions that exit any state are equally probable.

In this case, state "5" has no exits except the transition to itself because we stop tossing the die when it comes up "5". This called an absorbing state.

Markov processes can be analyzed by means of matrix algebra and graph theory, and in the case (as here) where there is one absorbing state which is reachable (there is a path to it) from all other states, it can be proved that the process will always end in that state.

Let us return to our statement that each character position of the "Weasel" Algorithm can be described as an independent Markov process. Each of these Markov processes are similar in form to the one that we illustrated in the above transition graph, except that it has 53 states instead of 6. And the template (the target phrase) determines, for each character position (each independent Markov process) which state will be the absorbing state. So, as we said earlier, the mathematics of Markov processes can be used to prove that each independent Markov process will stop in its absorbing state. Since the template determines the absorbing states, it also determines the results before the independent processes even start.

Let us return for a moment to the process of tossing a die until it comes up "5". It should be obvious that since we mentioned "5" in the definition of the process, there is no need to do anything random to get the result "5", because "5" is selected before we even start. Likewise for Dawkins' "Weasel" Algorithm, the random events do not select the result, because we selected it when we defined the template, or target phrase.

Thus we have shown that the information of the result of Dawkins' "Weasel" Algorithm does not come from the randomness, but from the definition of the explicit form of the algorithm. That is, the information is present before the process even starts.

It is also easy to show that Dawkins' "Weasel" Algorithm does not come close to approximating an evolutionary process. This is because the processes at each character position are independent. This is equivalent to saying that each bone, each muscle, etc. of an animal evolves independently, which of course is preposterous.

---

In the future, I will discuss more serious algorithms that seek to simulate or model evolution. However, there will be a delay, because I will shortly be off on a one-week trip, and when I return, my computer will be off for some serious repair. (Right now, it doesn't do much more than a WebTV.)

Why Music Sounds Musical

I wrote a piece called "Some Musical Theory, from a Christian Perspective" that discussed some of the mathematical aspects of musical theory, and I related that theory to some of the physics of how musical sound is made and how our ears and brains are constructed to hear it. It demonstrates how God designed us to recognize and appreciate music. Much of this I learned from a wonderful book called The Science of Musical Sound by John R. Pierce.

I regret that the wonderful message of that piece is not accessible to those that are not inclined to mathematics. I sympathize with them because in my career as an engineer, I have sometimes been 'dragged kicking and screaming' as I often have said, into the intricacies of mathematics because it was necessary to get my work done.

So here I will try to extract the basic ideas of that piece, leaving behind the equations and as much math as I can, and present them in a more palatable form. Here goes ..

Making Musical Sound

Music is made by vibrations: sometimes the shaking of strings, or sometimes of surfaces, but always involving the shaking of air, because sound is a moving variation of air pressure. The notes with higher pitch involve faster shaking, so that we can measure the pitch by measuring the number of shakes per second, called the frequency.

A string pulled tightly between two anchor-points can vibrate, as in many musical instruments. The frequency (pitch) will increase with increased tension, or with less weight of the string. or with decreased length between the anchor-points. (The bass strings of a piano are wrapped with heavy wire to save making the piano larger.) For the same weight and tension, a string half as long will have twice the frequency.

Air vibrates inside a long tube or pipe in other instruments. A pipe half as long will have twice the frequency, as for the strings.

When a string is plucked or struck or bowed near one end, the energy given to the string travels down the length of the string and bounces back and forth between the two anchor-points. When the air in a tube or pipe is made to vibrate by blowing over a hole or by a vibrating reed near one end, the energy given to the air travels down the length of the tube and bounces back and forth between the two ends of the tube. So in the case of a longer string or a pipe, the energy must travel further, so the vibration is slowed down, making a lower frequency.

Modes of Vibration

In its simplest mode of vibration, a string bends back and forth between two positions represented by the solid and dotted lines in the next diagram:
But the string can also bend back and forth between these two positions:
... Or bend back and forth between these two positions:
... And so forth.

The same modes occur in the case of air vibrating in a pipe. The first mode is called the fundamental, and the others are called overtones. The first overtone, where the string vibrates in two sections, has twice the frequency of the fundamental. The second overtone has three times the frequency, etc.

An example (for musicians): If the fundamental were middle C, the first overtone is C one octave higher (twice the frequency). The second overtone is the G a fifth interval higher (3/2 the frequency) than the first overtone. The third overtone is the next C a fourth interval higher (4/3 the frequency) than the second overtone. Notice that we get a lot of frequency ratios: 2/1, 3/2, 4/3, etc.

In most cases, especially when the string is plucked, struck, or bowed near the end of the string, the string actually vibrates in all these modes at the same time. That is, the actual motion is the sum of all these simple motions, with the overtones generally weaker as they go higher.

Hearing Tones

If the tones of the fundamental and overtones were sounded by separate strings, our ears would hear a chord (a set of related notes), but when these tones come from a single vibrating string, we hear one note with a rich sound that is more interesting than hearing only the fundamental. Another way of describing it is that we hear one note having the fundamental tone, but enriched by the overtones.

We hear the chord because the separate strings normally are not perfectly tuned, and we can hear that the frequency ratios are not exact. We hear the single rich-sounding note because the tones are 'locked' by perfect ratios, and our ears can hear the difference. How can our ears do this?

Sound entering one of our ears shakes our ear-drum, which shakes the three tiniest bones in our body (all three fit on a dime), which act as an adjustable lever, or volume control. These tiny bones transfer the sound vibrations to the cochlea, a snail-shaped organ in the inner ear. The cochlea is a coiled and tapered tube, with the fattest end connected to the bones.

If the tube of the cochlea were sliced, it would look like the diagram on the left, which shows the interior of the tube divided into three regions (shown as gray) filled with fluid: the vestibular canal (top) , the tympanic canal (bottom), and the cochlear duct (middle). The inner-most bone (the stapes) is attached to the oval window at the fat end of the vestibular canal. The sound pressure travels down the vestibular canal to the small end of the cochlea, where it connects to the tympanic canal. Then the sound pressure travels back up the tympanic canal to the fat end of the cochlea, ending at the round window below the oval window.

The pressure wave travelling down the top side reacts with the pressure wave travelling up the bottom side through the vestibular membrane and basilar membrane that separate them. The result is that high frequency tones shake the basilar membrane near the fat end of the cochlea, and low frequency tones shake the basilar membrane near the small end. Hair cells connected to nerve fibers leading to the brain detect the vibration of the basilar membrane. When we are hearing a complex sound with many frequencies, we hear each frequency component at a different place along the length of the cochlea. The precision of this detection is so good that scientists are baffled to fully explain it.

Hearing Chords

Another question that needs to be answered is: Why do the combinations of notes that we call chords appeal to us as sounding 'musical'? The key to the answer is the overtones that we described earlier. Take for example, the C major 7th chord CEGB. In the chart below, we list the positions of the fundamental tones (1) and overtones (2,3,4..) of each note of the chord (row labels at left) in the musical scale (column labels at top) :
The letters X, Y, Z, etc. on the bottom of the chart mark positions where overtones of different notes of the chord nearly match in frequency. Because the notes are never perfectly tuned, the overtones match, but not perfectly, and the small difference causes an interaction called the 'beat' effect that signals our ears that these notes are 'connected' to each other. Because the lower overtones are generally louder, this kind of 'connection' is stronger for pairs of notes related by a frequency ratio that is expressed by smaller integers -- what we call 'simple ratios'.

For musicians: The fact that our musical sensibilities favor simple frequency ratios leads to the spacing of the notes in a major scale, and is the basis of chord structure and melody. Using just a few mathematical rules about these simple ratios, the frequency of all the notes of any scale, and the sharps and flats for all of the keys can be calculated.

Summary

When we examine in detail how our hearing is designed, we can see that its capabilities goes beyond what is needed for recognition and interpretation of speech -- it has 'bonus' features designed for the appreciation of music.

ALL Things

All things were made through Him, and without Him nothing was made that was made.

John 1:3 (NKJV)

Modern science provides a remarkable perspective and insight to the "all things" of this verse. As summarized by the famous formula E=mc², energy and mass (matter) are interchangeable; thus the creation must include not only material things (matter), but also all forms of energy.

matter — energy

Also, Einstein's theory of relativity, confirmed by experiments and measurements, shows that time and space are different sides of the same fabric.

space — time

More recent physics theories describe matter and energy as wrinkles or knots in the fabric of space-time. Space cannot exist empty, that is, without matter and energy.

matter — energy — space — time

So everything is inexorably, inextricably joined. Time cannot pass without space also existing, and space cannot exist empty, without matter and energy. So when "God created the heavens and the earth" (Gen. 1:1), the eternal God created a wondrous unity: matter, energy, space, and time, and all of the 'laws of physics' that make these a cohesive whole.

God must exist apart from time, because time is part of His creation. I used to think that the eternalness of God meant that He was infinitely old; but no, He can exist outside of time. And outside of space, and not made of matter or energy. And because He created all of these, that makes Him older and bigger and more powerful and massive than all that He has created.

Read it again:

All things were made through Him, and without Him nothing was made that was made.

But because of His great love and concern for His creation, He entered His own world and became one of His own creatures, that we might know Him better, and not be strangers to Him. Read verses 10 to 12 that follow soon after the above verse:

He was in the world, and the world was made by Him, and the world knew Him not.

He came unto His own, and His own received Him not.

But as many as received Him, to them gave He power to become the sons of God, even to them that believe on His name.

That name is Jesus -- which means Savior.

NOTE: Another blog considers whether information should be added to the unity of matter, energy, space, and time.