Going Beyond Syntax

Concerning Information Theory, and Entropy

Paul V. Hartman

Entropy. The word embodies the Second Law of Thermodynamics, which states simply that all order tends to chaos, a more general way of acknowledging that at equilibrium, randomness in a system is maximal. We learned the concept and the formula (S=k log W) in our courses in physics, after which, with no practical application, it went back on the shelf, never to be called upon again.

It is the current wisdom that the universe continues to expand, and entropy would require that the expansion be accompanied by increasing randomness. So, complexity should give way to simplicity, entropy forcing reduction to more primitive states. Is there evidence to the contrary? It abounds. Certainly life forms existing in the present age are more "complex" than those present 2 billion years ago.

The current theory of the steady expansion of the universe assaults comprehension. Ask a physicist what the universe is expanding "into", he will tell you: "nothing." Bear in mind that in his lexicon the word "something" describes empty space (a vacuum) which illustrates the soft sand upon which wisdom on the order of the universe is currently based. There is nothing simple about the concept that one cannot stand on the edge of the universe and look beyond it, since although expanding, it has no edge.

The human condition has always been to seek a unified dynamic for the order of the cosmos, and we must be prepared to accept that once/if revealed, such order may contain "laws" foreign to contemporary scientific insights. The big question: is there a master plan?

And of phylogeny, is there again a plan, or even a message? One thing that has disturbed Darwinian scholars for so very long is the difficulty in explaining natural evolution within the constraints of the time available to it. Here and there, gradual evolutionary change appears to give way to great leaps - the sudden appearance of new characters quite removed. How so? What purpose did the primitive eye serve, presuming it existed prior to becoming an organ of vision? If all order should reduce to chaos, why do simple things evolve into complex entities? Why expand the elements beyond hydrogen? Why expand life beyond bacteria?

For a possible answer, we turn to the study of Languages. What we know about each human language is that there is a lexicon - the words and phrases - and then there is grammar and syntax: rules for use, and exceptions to the rules. All languages are complex in the use of rules, and difficult to describe in the subtleties. Clearly, to know fully all the words without knowledge of the rules results in strings of nonsense. Now to say that a sentence should have a noun and a verb is a very shallow study of the rules. By "rules" is meant (for English) that the language will contain more "e's" than "t's", more "t's" than "z's". By rules is meant that if the word starts out with a "t" followed by an "h", the probability is very high that the next letter will be a vowel, and low to the point of zero that it will be a "q". By rules is meant that a root word which has both a noun and an adjectival form will have different spellings and probably take a different position in the sentence. These are just some examples of the language rules in English, which were handed down to us. You might say, we inherited them.

This probability thing relates to entropy, for which chance is much of the scheme. But there is more in language to interest the scientist: to perform as reliable communication, all languages include deliberate "redundancy" to reduce transmission error in countering unwanted "noise", which is ubiquitous in nature. Consider this sentence:

"Large colonial, four bedrooms, two baths, with fireplace, modern eat-in kitchen, finished basement."

Transmission is clear, though this sentence lacks a verb, and redundancy helps to make transmission clearer. You don't see redundancy? Then let's remove it:

"Lge col. 4 BR, 2B, Frlp, MEIK, fin bsmt."

This sentence is still intelligible and qualifies as a classified ad as typically used in the real estate columns of your local newspaper. Now let's restore redundancy, and add "noise":

"Large rqssa colonial, fkk four btwonnre bedrooms, dxrn two baths, ibh with fireplace crdav finished kr basement dfnvla pgo."

Why do you understand this sentence? Because the eye leaps over the "noise" and pulls in the appropriate words. Redundancy works. Now keep the noise, remove the redundancy, and we have:

"Lge ibh col rqssa fkk 4 btwonnre br dxrn 2 b ibh frlp crdav fin kr bsmt dfnvla pgo."

Unintelligible. Entropic. Chaos reigns. The kind of thing a monkey would print if he sat down to a keyboard. (FLASH! Suppose a monkey's typing represents messages with noise and no redundancy? Okay, just teasing.)

So what does this have to do with the universe and the descent of man? The position of the exponents of "Information Theory" is that the rules of "grammar" permeate all nature. The theory is about eighty years old. It has much to do with probabilities, and received a major impetus when, in 1941, with computers inchoate, the task was to figure out how to shoot down German bombers over England whose pilots flew deliberately erratic courses. Now while pilots may attempt chaotic flight patterns, not all paths are possible, such as flying in reverse, or at peculiar angles. In life, as in gunnery, probabilities can predict what is seemingly impossible, what is improbable, and what is likely.

To say that DNA is language is to go far beyond the metaphor: a string of symbols, certainly, with the appearance of an alphabet. Our derived impression is that DNA acts by coding for proteins. Correct, but not the whole story. The DNA "lexicon" is small, only four "words": adenine, guanine, cytosine, thymine. But - this is not as restrictive as it appears: modern computers have a two word lexicon, "zero" and "one." ("On" and "Off") with which they do everything that computers are famous for. Like language, DNA appears to contain both redundancy (for error reduction) and noise, the noise appearing for uncertain reasons (presumably unwanted), but certainly phylogenetically useful. (vide infra.)

But while the code is universal (all life forms use the same four words) the lexicon is insufficient to explain the level of complexity observed within the time allocated to its development, as we currently understand it. There is evidently more within the code. That which is not seen is the "grammar": the way the rules define the way the words are to be strung together; how the rules switch on, switch off, and why.

How does one part of DNA tell another part to start making a particular protein one year after birth, and not before? Twelve years after birth, and not before? How is it that a short length of DNA can, on the one hand, produce a fruit fly, and on the other, an Einstein? How is it that a human and a chimpanzee can be 99% identical in structural genes and differ so in phenotype, or the ability to formulate complex speech, or work mathematical mosaics?

The answer may be discovered in Information Theory. Mutations of DNA symbols that code for proteins (which may be common) may produce change with slow evolutionary result (on which natural selection acts) while changes in the symbols that code for interpretation ("syntax") may result in dramatic departures from Darwinian sequence. In other words, a point mutation at one locus in a DNA strand may change eye color from green to blue, but a point mutation at a locus destined to decide the ORDER in which other loci are to be "read" from the strand may, oh, let's take a leap: change an ape into a hairy biped with a vocabulary larger than two types of grunts.

Why such a departure? Because the mutated "interpretive segment" reads off a strand of "noise" contained in the DNA that the unmutated interpretive segment would have ignored. The resultant Words are unintended, and we can even say that redundancy failed within the mutated segment, but the Rules have not been broken. The product of this error in interpretation may be a monster (if too bizarre, unlikely to compete successfully for survival) or something entirely desirable.

If entropy increases with the arrow of time, then large scale information decays to small scale information, information fragments increase, and variety increases due to the ability of small scale information to re-combine into new arrangements. Entropy, seeming to force reduction to simplicity, produces, in the genetic alphabet, the opposite. Complexity increases, which is in harmony with what we observe in the world - more than just bacteria.

Some critics of Information Theory say its proponents search for explanations which proscribe the existence of a Supreme Being. Not so. Scientists (and other people who think) seek to discover the discoverable. If what is discovered has divine origin, so much the more interesting, while, by the same token, if it is not "meant" to be discovered, it will not be. We possess a brain which we suppose to be operating at a high level, and if it reveals to us that mankind stood upright 5 million years ago and not 40,000 years ago, how is the existence of God disproved? If there is no God, than, yes, Information Theory may explain why we are all here, chance alone operating within a long time continuum. But - the theory is insufficient to explain its own unity, its "why", even if it does print true. The Law of Nature does not INITIATE anything. Rather, the Law of Nature defines a ritual which an event must obey (provided there is no INTERFERENCE from without.) If ball B is struck by ball A, it will receive momentum, rebounding in a predictable fashion, but the Law of Nature only defines the movement of ball B; it does not start ball A moving.

Life is filled with discovered ironies: we began with the idea that the universe revolved around the earth, dropped the idea in favor of the sun as the center, dropped that to accommodate the Milky Way and millions of other galaxies, and concluded that the earth was, in relation to the rest of the universe, off to the side somewhere. Until now. Along came Big Bang, with its attendant isotropic "signature" of microwave, the signature suggesting that all points in the universe have equal claim to being at the center. We are thus come full circle: the earth IS at the center of the universe! (Or, until proven otherwise, has equal claim to the distinction!)

The problem, for the Christian, is to square what emerges from science with what is contained in scripture, ancient precepts and reason carrying only so far, after which there must be a leap of faith. The problem, for the Humanist, is to square the missing pieces (the beginning of the universe, the existence of soul, etc.) with what emerges from science, experiment and rational debate carrying only so far, after which there must be a leap of faith. What should not be lost is any truth that finds its way to the surface, including that which increases our agony over the origin of man, because of our initial bias.

The laws of the cosmos are not, all, yet discovered, and Information Theory more fully explored, may help unlock nature's most complex mysteries, and give us a better understanding of the essence of life, and the direction we are heading.

This essay was composed in 1985.

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