Order and Disorder in Nature.
Random thoughts on randomness and order.
The "Game of Life" shows that order can arise from disorderly arrangements of objects if there are some rules of interaction in place. Those rules can be chosen without forethought as to the outcome. The kind of order that results certainly exhibits the kind of structure, pattern and lawfulness we find in nature, but it arose without purposeful design.
Creationists and ID advocates like to choose "loaded" words to suggest the kind of conclusion they wish to draw from them. So instead of the neutral words "pattern, structure, complexity and lawfulness", they speak of these as "design", which suggests that some intelligence intended this result.
They use the word "disorder" to mean total absence of order, and then invoke the slogan "order cannot arise from disorder" as if it were a law of nature. It isn't, for the order of an open system can increase if there's energy input, and complete disorder is not to be found anywhere in nature So the question of whether disorder can arise from total disorder is moot.
Another word sometimes misused is "random" to describe chaos or disorder. The word "random" has a perfectly good mathematical definition, and it does indeed describe a state in which there's not the slightest suggestion of pattern or orderliness. But as we've observed before, mathematics is an idealized logical structure that does not by itself tell us anything about nature, and even when used as a model for nature, it isn't a perfect model. Or perhaps it's more appropriate to say that the mathematics can be perfect, but the part of nature it models never comes up to the perfection of the mathematics.
Does nature have anything that exhibits perfect randomness? It does not. Any jumble of things, no matter how carelessly they are scrambled, will show some aspects of order. The smaller the number of things, the more likely there's some order. Only when you have an infinite number of things is it possible to arrange them so that there's no order, i.e. perfect randomness. But notice that I said "You'd have to arrange them." If you just toss beans onto a table, you won't ever get the maximum randomness (the least order) that this number of beans could exhibit.
Part of the reason is physics. The beans knock against each other as they fall, and momentum conservation applies to the collision. Also they roll, with each one having only two orientations where it can come to rest in stable equilibrium. So the likelihood of two of them ending up touching is smaller than if you just calculated random positions of points with a computer, ignoring physics.
A physicist isn't surprised that it's unlikely for two beans to touch. Except when in contact, the beans exert no forces on each other. As they bounce around before coming to rest, some may head toward others and will likely bounce apart. To get two to end up touching, you'd have to have the unlikely situation of one headed slowly toward another (which is perhaps already at rest), being slowed still more by frictional drag and coming to a stop exactly when touching the other one. Consider also that the bean might be wobbling as it moves. So touching beans is a rather unlikely result. It's unlikely because of the laws of physics. A simplistic calculation that ignored the physics of forces and momentum would conclude that touching beans would be quite likely. 
This example shows that you cannot ignore the laws of physics when calculating probabilities of things happening in nature. Yet creationists are guilty of doing exactly that, especially in examples they give in public lectures (and books) that are aimed at non-scientists.
A truncated value of the fundamental physical constant p = 3.1415927... comes up when I press the π button on my calculator. Mathematicians know that π has an unending number of digits, an infinite number of them. If considered as a string of the digit symbols 0 through 9 are these digits random? Certain tests must be done to determine this. There would have to be equal occurences of each digit, just as many 7s as there are 8s, for example. No digit must predominate. There shouldn't be too many (or too few) pairings of identical digits, and the number of identical-digit strings must be tested for all digits, as well as the number of repetitions of particular strings of digits, compared to other equal length strings. It's an interesting math problem, and a difficult one. The last I heard, the question of whether p has perfect randomness in its digits is still up in the air. Whatever the outcome of this question, it would not tell us anything useful about the "real world".
Computer-scientists have written algorithms for computer-generated "pseudo-random" numbers. It's very difficult to write an algorithm that produces number strings meeting all the tests of randomness. It can't be done perfectly for finite strings of numbers. But nature can't do it either.
In nature we can only talk about degrees of randomness (or, conversely, degrees of orderliness). We can assign numeric value to order for simple systems, where we know all the operative laws and have well specified geometric constraints. It gets fiendishly difficult to quantize order for things as complex as living things. But perfect randomness (zero order) is just not found in nature.
I have avoided technical terms such as "entropy" here, for my purpose is limited to pointing out certain dangers of loose language about terms that we think we understand from experience, but which may be inadequate for scientific discourse. If I were to use more technical terms, I'd have to define them, and this document could easily expand to book length.
In any case, the slogan "order cannot arise from disorder" (in which disorder is taken to mean "total disorder or perfect randomness") is seen to be flawed because we never have perfect disorder in nature. The reason it can't happen is twofold (1) the finiteness of everything in the universe, and (2) the constraints of geometry and physical laws of interaction.
Nature exhibits many examples of systems of very small order developing greater order when they are part of an open system with energy input from outside. This comes about because of geometry and physical laws of interaction between parts of the system. The "Game of Life" shows the same process of evolution.
Nature provides many examples of stable ordered structures arising from disordered materials: snowflakes forming from liquid water, crystals of many kinds forming from solutions, or from application of heat and pressure. This isn't simply a "chance getting-together" of pieces. The geometric properties of the molecules limit what kind of ordering can happen, physical laws of attraction and bonding help assemble the crystal, forming a structure that it is strong and stable.
We have said that nature never exhibits anything with complete disorder. Sometimes a bit of disorder can encourage natural processes that result in greater order. So it is that crystals begin formation more readily if there's some disorder or imperfection in the starting materials. Very pure liquids can be cooled below their normal freezing point, and still not form crystals. But if even a tiny speck of impurity is introduced, formation of crystals proceeds quickly. Meteorologists used to encourage rain by "seeding" clouds with sodium iodide crystal "dust", though the mechanism and the reliability of the process is in some dispute.
What do we mean by "order" and "design"?
We look at snowflakes through a microscope, and admire the variety and beauty of their shapes. Some would call it "design". The trouble with the word "design" is twofold. (1) Design, like beauty, is in the eye of the beholder, and (2) the word suggests the kind of design made purposefully by some intelligent being. But when we see a complex, intricate or pleasing pattern, how can we tell whether it was intentionally or accidentally produced? 
An ink blot is just an ink blot. Yet some seem to invoke images in our mind, and once invoked, we think that the blot has more significance because of that mental association. On one hand, it is an unimaginative individual who cannot "see" something in any inkblot. And there are those of us who refuse to play that game, and declare them all "just accidental patterns in ink" even if they happen to have a shape resembling a squashed beetle.
We humans look for patterns in nature. Natural "laws" are nothing but statements or descriptions of patterns in space and time. Recognizing such patterns had evolutionary value for humans. To see the difference between a goat and a lion, and to predict their potential behavior, were certainly useful to primitive man. Knowing the shapes of leaves of nutritious or poisonous plants was also.
We have an unfortunate propensity to place undue significance on accidental patterns. Primitive man named certain patterns of stars in the skythe constellations. We now know that these patterns are quite accidental and the stars in them may be at vastly different distances from each other. Early man went further by ascribing astrological significance to these patterns and to the apparent motion of planets through the sky, even supposing that these motions influenced the fate of nations, kings, and later, even individuals. The result, astrology, is still taken seriously by some people, but its scientific content is zero. This is just one of many ancient ideas that assumed a mysterious "cosmic synchronicity" between the heavenly and earthly realms. Then there are those who claim they can see one's fate in the patterns of tea-leaves, or the arrangement of Tarot cards.
If you are dealt five cards from a fully shuffled deck in an honest deal, your chances of getting any possible set of five cards are the same. You chance of getting a royal flush in hearts is the same as getting any particular set of five cards, even a "worthless" set. What's special about the royal flush? It just happens to be one of the high scoring hands in one particular game. It is significant only because we impart significance to it, related to the pictures and numbers printed upon the cards, and arbitrarily give it a particular score based on those symbols. The physics of the shuffle and the deal are not at all affected by what's printed on the cards, and not at all affected by the symbolic significance we have granted to those patterns and numbers. Yet we have wired in our brains the unfortunate propensity to imbue symbols with physical significance, even to assume that those symbols can influence natural processes.
We should recognize that some patterns seen in nature are accidental and of no significance. But even significant patterns, like the snowflakes, clouds, tornado funnels, and even atoms, molecules, and living things, may arise from natural processes without intelligent input and without purposeful design. Yes, I'm talking about evolution here. The emergence of life on earth, and the gradual evolution of more and varied kinds of living things is a fact supported by abundant and diverse evidence. The processes that took place during this long period of time are collectively called "evolution" but there is no single "law of evolution" one can point to. To call anything a "theory of evolution" may be misleading and unhelpful. Perhaps this is due to my background as a physicist, but I find little in common in the nature of Newton's theory of mechanics, and any "theory of evolution".
Some say we shouldn't use the word "theory" in science, for the scientific use and the colloquial uses of the word are entirely different. I have mixed feelings about this. I bristle at those who deliberately refuse to acknowledge the correct scientific meaning of "theory", and then use this willful ignorance to attack science. Why should scientists change their technical language just because some non-scientists deliberately refuse to use it correctly? The scientific use of the word has a long and honorable history.
Words are just labels. We could have called it something else. Perhaps "unifying principle" or "process of evolution" would be sufficiently descriptive. That's what a good theory is: a well-tested and well-confirmed set of statements (usually mathematical, at least in physics) that logically unify a broad collection of well-established laws. A theory unifies diverse laws, showing that they are logically related and connected.
Someone may fault me for seeming to be critical of evolution in the last paragraphs. Far from it. I consider evolution of life to be an established fact, and recognize that we have very good knowledge of the natural processes that are responsible for it. But if you ask someone to summarize the basic laws that make up the "theory of evolution", you might get a list of all the laws of physics and chemistry, for they are all part of the process. It isn't a neat, small package of equations such as the equations that make up Newton's mechanics.
Evolution is our word to describe a series of connected events or things taking place over time. Generally the word is used to describe things proceeding from simple to complex, from disordered to ordered. There is no "force" of evolution. There is no "purpose" driving evolution and no "intelligence". Evolution does not guarantee a perfectly adapted result, but only a "good enough" result to ensure at least temporary survival of a particular organism. Results of evolution are not always "beneficial" but sometimes are benign and unimportant to survival. Of course the process often produces results that jeopardize survival. Too often the language of popular science books and TV programs, and even textbooks, suggests purpose, and that's misleading. Even the language of TV nature documentaries speaks of animal behavior as if the animal acts a certain way because it "knows" that that behavior will bring about a desired result.
Astrophysicists speak of the early history of the universe as a process of evolution. But the biological evolution of life on earth (or anywhere else) is a completely different set of processes. [Of course, both depend on laws of physics.] Yet critics of evolution tar both with the same feather, seeing both as something abhorrent that they refuse to "believe". What exactly is the common feature of the two that they are denying? I'm not sure they could give a coherent answer, for they don't really understand either process.
The perceptive reader may have noticed that we have stressed that there are certain conditions of the universe that make it possible to do science. One is the fact that processes in the universe show regular and predictable behavior, which we express as laws of nature. Also, in the early universe, we suppose that certain laws must have been in placefrom the very earliest time. Laws of the early universe may have been different from those that dominate nature today, but we recognize that a universe with pattern and order is a consequence of reliable laws of interaction between material objects.
Are these fundamental laws just another form of order and pattern that gives rise to other more obvious patterns and laws, or are they something fundamentally different from the laws with which we describe nature; those that we put in physics textbooks?
From the point of view of the practical scientist, it doesn't matter. So long as the laws we devise to describe nature give correct predictions, we assume they are "right". We know that they are only an approximation to nature, good enough to match the precision of our measuring instruments, and we should not delude ourselves by treating them as "discovered truths".
So long as nature has consistently reliable orderliness and lawfulness, we can do science. Science is at the mercy of this feature of nature, for without reliable order and lawfulness there's no way we could even describe nature, much less "understand" it. In fact, the whole idea of a universe without any order is incomprehensible to our minds, for we have no way to imagine how creatures such as us could exist in a totally disordered universe. This has led some (even some scientists, I hate to admit) to speculate that the very fact that we exist, and that we can comprehend the universe, is telling us something philosophically profound about the universe. Several "anthropic principles" are of this type. They can be parodied thusly: "The universe must have exactly the kind of laws that would lead to intelligent life, otherwise no intelligent being would know of the universe. If a universe had no one to observe it, how could it be said to exist?" Clearly this is a parody of the old paradox "If a tree falls in the forest and no one is there to hear it, did it make a sound?" More economically stated: "If the universe had taken any form other than the form it has, then we couldn't have arisen within it." Logically and scientifically this proposition is as unsupportable as the intelligent design hypothesis. Why? Because it tries to use logic, and experience from within our universe to try to assert something about "all possible" universes. It is only philosophical speculation, not science. If you find this sort of thing amusing, do a web search for "anthropic principles" and see what nonsense you find.
At this point someone is sure to wonder "So, if the laws of nature are responsible for the order and lawfulness we observe all around us, then who or what designed or invented the laws of nature?" Again, we bump against the "infinite regression" problem of the arguments for a deity. However, if theists wanted to assume that their god devised the laws of nature, and then left everything to proceed "naturally", this theistic view would not impact science at all, nor conflict with science. I recommend it to creationists.
I've tried to avoid unnecessary technical language in these documents, but have also tried to avoid misleading language. Sometimes that requires avoidance of certain colloquial terms that most people take for granted; words people use without thinking. Here are some examples.
When speaking of something beyond experimental verification, it's inappropriate to use the words "likely", "probably", "chance", or any other term indicating statistical "likelihood". In fact, we should avoid such words when speaking of the universe as a whole. It's the one and only universe we know, so how can we say it's an "unlikely" thing, or that its evolution involved any "unlikely" or "improbable" process or event? Compared to what? All sorts of foolish utterances are of this kind:
Consider this sentence, taken (out of context) from New Scientist, 23 July 2011, p. 34. The most likely explanation of fine-tuning is that our universe is merely one of many. The context is a discussion of the question "Why is the universe just right?" Some make a "big deal" out of the fact that the laws and the universal constants of the universe seem to be uniquely fitted to allowing life, like us to exist; they call it "fine tuning". Never mind that this assertion falls apart when examined. But even if the arguments for or against this are subtle and technical, note the absurdity of using the term "likely" when we have only one universe in our data sample. Then we postulate (without independent evidence) that there might be many other universes with different laws and constants. This creates a conceptual "sample" collection of universes, and only with many in our sample can we even speak of what's "likely". But knowing nothing of those imagined other universes, how can we say that ours is unique in being a suitable habitat for life, any more likely than the others? This is circular reasoning of the worst kind. Even the first dictionary definition of "likely" is "having a high probability of being true", clearly a statistical inference from a sufficiently large sample.
This sort of foolishness is common in the mass media and in "gee-whiz" books about science. Other examples:
Such assertions are simply unjustified for several reasons.
We simply have no tools of analysis to even talk about certain questions of a philosophical nature that many people think are of utmost importance. Much of the debate about intelligent design (on both sides of the issue) is no more than blowing hot air by people who naively imagine they know what they are talking about, and flatter themselves into thinking that what they say is profound. They are shoveling feathers and juggling eels, using words, logic, and methods of thinking entirely inappropriate and inadequate for the purpose. As we will try to show, as these chapters unfold, there are no ways to answer these questions, so we might as well quit wasting everyone's time and get on with dealing with questions for which we can find useful answers.
Endnotes. Of course this analogy, like any analogy, is crude and can be misleading. The outcome very much depends on how many beans are in a particular area. If they are dumped in a pile, then of course many beans will end up touching. But if there are few enough beans so that they never pile up the analogy serves well enough.
 The picture (from a psychology textbook) is actually biased. It was formed by putting an ink blot on paper and then folding over the paper to produce this symmetric pattern. The very fact that we deliberately did this introduces a form of order. The fact that the ink is within a bounded area surrounded by white space is also a form of symmetry and order. The universe abounds in various kinds of symmetry, one might even say that laws expressing symmetry are the fundamental laws of nature. Order and symmetry are symbiotic.
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