You would think, considering my background, that had I ever so slight a chance to drag fantasy into any serious discussion of science, I would at once do so by neon lights flashing and fireworks blasting.
And yet, in the previous chapter on entropy, I completely ignored the most famous single bit of fantasy in the history of science. Yet that was only that I might devote another entire chapter to it.
When a hot body comes into contact with a cold body, heat flows spontaneously from the hot one to the cold one and the two bodies finally come to temperature equilibrium at some intermediate level. This is one aspect of the inevitable increase of entropy in all spontaneous processes involving a closed system.
In the early nineteenth century, the popular view was to consider heat a fluid that moved from hot to cold as a stone would fall from high to low. Once a stone was at the valley bottom, it moved no more. In the same way, once the two bodies reached temperature equilibrium, there could be no further heat flow under any circumstances.
In the mid-nineteenth century, however, the Scottish mathematician James Clerk Maxwell adopted the view that temperature was the measure of the average kinetic energy of the particles of a system. The particles of a hot body moved (on the average) more rapidly than did the particles of a cold body. When such bodies were in contact, the energies were redistributed. On the whole, the most probable redistribution was for the fast particles to lose velocity (and, therefore, kinetic energy) and the slow particles to gain it. In the end, the average velocity would be the same in both bodies and would be at some intermediate level.
In the case of this particle-in-motion theory, it was conceivable for heat flow to continue after equilibrium had been reached.
Imagine, for instance, two containers of gas connected by a narrow passage. The entire system is at a temperature equilibrium. That is, the average energy of the molecules in any one sizable portion of it (a portion large enough to be visible in an ordinary microscope) is the same as that in any other sizable portion.
This doesn't mean that the energies of all individual molecules are equal. There are some fast ones, some very fast ones, some very very fast ones. There are also some slow ones, some very slow ones and some very very slow ones. However, they all move about higgledy-piggledy and keep themselves well scrambled. Moreover, they are also colliding among themselves millions of times a second so that the velocities and t energies of any one molecule are constantly changing. Therefore, any sizable portion of the gas has its fair share of both fast and slow molecules and ends with the same temperature as any other sizable portion.
However, what if—just as a matter of chance—a number of high-energy molecules happened to move through the connecting passageway from right to left while a number of low-energy molecules happened to move through from left to right? The left container would then grow hot and the right container cold (though the average temperature overall would remain the same). A heat-flow would be set up despite equilibrium, and entropy would decrease.
Now, there is a certain infinitesimal chance, unimaginably close to zero, that this would happen through the mere random motion of molecules. The difference between "zero" and "almost-almost-almost-zero" is negligible in practice, but tremendous from the standpoint of theory; for the chance of heat-flow at equilibrium is zero in the fluid theory and almost-almost-almost-zero in the particle-in-motion theory.
Maxwell had to find some dramatic way to emphasize this difference to the general public.
Imagine, said Maxwell, that a tiny demon sat near the passage connecting the two containers of gas. Suppose he let fast molecules pass through from right the left but not vice versa. And suppose he let slow molecules through from left to right but not vice versa. In this way, fast molecules would accumulate in the left and slow ones in the right. The left half would grow hot and the right cold. Entropy would be reversed.
The demon, however, would be helpless if heat were a continuous fluid—and in this way Maxwell successfully dramatized the difference in theories.
Maxwell's demon also dramatized the possibility of escaping from the dreadful inevitability of entropy increase. As I explained in the previous chapter, increasing entropy implies increasing disorder, a running down, a using up.
If entropy must constantly and continuously increase, then the universe is remorselessly running down, thus setting a limit (a long one, to be sure) on the existence of humanity. To Some human beings, this ultimate end poses itself almost as a threat to their personal immortality, or as a denial of the omnipotence of God. There is, therefore, a strong emotional urge to deny that entropy must increase.
And in Maxwell's demon, they find substance for their denial. To be sure, the demon does not exist, but his essential attribute is his capacity to pick and choose among the moving molecules. Mankind's scientific ability is constantly increasing, and the day may come when he will be able, by some device, to duplicate the demon's function. Would he then not be able to decease entropy?
Alas, there is a flaw in the argument. I hate to say this, but Maxwell cheated. The gas cannot be treated as an isolated system in the presence of the demon. The whole system would then consist of the gas plus the demon. In the process of selecting between fast and slow molecules, the demon's entropy would have to increase by an amount that more than made up for the decrease in entropy that he brings about in the gas.
Of course, I know that you suspect I have never really studied demons of any type, let alone one of the Maxwell variety. Nevertheless, I am confident of the truth of my statement, for the whole structure of scientific knowledge requires that the demon's entropy behave in this fashion.
And if man ever invents a device that will duplicate the activity of the demon, then you can bet that that device will undergo an entropy increase greater than the entropy decrease it will bring about. You will be perfectly safe to grant any odds at all.
The cold fact is that entropy increase cannot be beaten. No one has ever measured or demonstrated an overall entropy decrease anywhere in the universe under any circumstances.
But entropy is strictly applicable only to questions of energy flow. It can be defined in precise mathematical form in relation to heat and temperature and is capable of precise measurement where heat and temperature are concerned. What, then, if we depart from the field where entropy is applicable and carry the concept elsewhere? Entropy will then lose its rigorous nature and become a rather vague measure of orderliness or a rough indicator of the general nature of spontaneous change.
If we do that, can we work up an argument to demonstrate anything we can call an entropy decrease in the broad sense of the term?
Here's an example brought up by a friend of mine during an excellently heated evening of discourse. He said:
"As soon as we leave the world of energy, it is perfectly possible to decrease entropy. Men do it all the time. Here is Webster's New International Dictionary. It contains every word in Hamlet and King Lear in a particular order. Shakespeare took those words, placed them in a different order and created the plays. Obviously, the words in the plays represent a much higher and more significant degree of order than do the words in the dictionary. Thus they represent, in a sense, a decrease in entropy. Where is the corresponding increase in entropy in Shakespeare? He ate no more, expanded no more energy, than if he had spent the entire interval boozing at the Mermaid Tavern."
He had me there, I'm afraid, and I fell back upon a shrewd device I once invented as a particularly ingenious way out of such a dead end. I changed the subject.
But I returned to it in my thoughts at periodic intervals ever since. Since I feel (intuitively) that entropy increase is a universal necessity, it seemed to me I ought to be able to think up a line of argument that would make Shakespeare's creations of his plays an example of it.
And here's the way the matter now seems to me.
If we concentrate on the words themselves, then let's remember that Shakespeare's words make sense to us only because we understand English. If we knew only Polish, a passage of Shakespeare and a passage of the dictionary would be equally meaningless. Since Polish makes use of the Latin alphabet just as English does and since the letters are in the same order, it follows, however, that a Polish-speaking individual could find any English word in the dictionary without difficulty (even if he didn't know its meaning) and could find the same word in Shakespeare only by good fortune.
Therefore the words, considered only as words, are in more orderly form in the dictionary, and if the word order in Shakespeare is compared with the word order in the dictionary, the construction of the plays represents an increase in entropy.
But in concentrating on the words as literal objects (a subtle pun, by the way), I am, of course, missing the point. I do that only to remove the words themselves from the argument.
The glory of Shakespeare is not the physical form of the symbols he uses but the ideas and concepts behind those symbols. Let Shakespeare be translated into Polish and our Polish-speaking friend would far rather read Shakespeare than a Polish dictionary.
So let us forget words and pass on to ideas. If we do that, then it is foolish to compare Shakespeare to the dictionary. Shakespeare's profound grasp of the essence of humanity came not from any dictionary but from his observation and understanding of human beings.
If we are to try to detect direction of entropy change, then, let us not compare Shakespeare's words to those in the dictionary, but Shakespeare's view of life to life itself.
Granted that no one in the history of human literature has so well interpreted the thoughts and emotions of mankind as well as Shakespeare has, it does not necessarily follow that he has improved on life itself.
It is simply impossible, in any cast of characters fewer than all men who have ever existed, in any set of passions weaker of less complex and intertangled than all that have ever existed, completely to duplicate life. Shakespeare has had to epitomize, and has done that superlatively well. In a cast of twenty and in the space of three hours, he exhibits more emotion and a more sensitive portrayal of various facets of humanity than any group of twenty real people could possible manage in the interval of three real hours. In that respect he has produced what we might call a local decrease in entropy.
But if we take the entire system, and compare all of Shakespeare to all of life, surely it must be clear that Shakespeare has inevitably missed a vast amount of the complexity and profundity of the human mass and that his plays represent an overall increase in entropy.
And what is true of Shakespeare is true for all mankind's intellectual activity, it seems to me.
How I can best put this I am not certain, but I feel that nothing the mind of man can create is truly created out of nothing. all possible mathematical relationships; natural laws; combinations of words, lines, colors, sounds; all—everything—exists at least in potentiality. A particular man discovers one or another of these but does not create them in the ultimate sense of the word.
In seizing the potentiality and putting it into the concrete, there is always the possibility that something is lost in the translation, so to speak, and that represents an entropy increase.
Perhaps very little is lost, as for instance in mathematics. The relationship expressed by the Pythagorean theorem existed before Pythagoras, mankind, and the earth. Once grasped, it was grasped as it was. I don't see what can have been significantly lost in the translation. The energy increase is virtually zero.
In the theories of the physical sciences, there is clearly less perfection and therefore a perceptible entropy increase. And in literature and the fine arts, intended to move our emotions and display us to ourselves, the entropy increase—even in the case of transcendent geniuses such as Sophocles and Beethoven—must be vast.
And certainly there is never an improvement on the potentiality; there is never a creation of that which has no potential existence. Which is a way of saying there is never a decrease in entropy.
I could almost wish, at this point, that I were in the habit of expressing myself in theological terms, for if I were, I might be able to compress my entire thesis into a sentence.
All knowledge of every variety (I might say) is in the mind of God—and the human intellect, even the best, in trying to pluck it forth can but "see through a glass, darkly."
Another example of what appears to be steadily decreasing entropy on a grand scale lies in the evolution of living organisms.
I don't mean by this the fact that organisms build up complex compounds from simple ones or that they grow and proliferate. This is done at the expense of solar energy, and it is no trick at all to show that an overall entropy increase is involved.
There is a somewhat more subtle point to be made. The specific characteristics of living cells (and therefore of living multicellular organisms, too, by way of the sex cells) are passed on from generation to generation by duplication of genes. The genes are immensely complicated compounds and, ideally, the duplication should be perfect.
But where are ideals fulfilled in this imperfect universe of ours? Errors will slip in, and these departures from perfection in duplication are called mutations. Since the errors are random and since there are many more ways in which a very complex chemical can lose complexity rather than gain it, the large majority of mutations are for the worse, in the sense that the cell or organism loses a capacity that its parent possessed.
(By analogy, there are many more ways in which a hard jar is likely to damage the workings of a delicate watch than to improve them. For that reason do not hit a stopped watch with a hammer and expect it to start again.)
This mutation-for-the-worse is in accord with the notion of increasing entropy. From generation to generation, the original gene pattern fuzzes out. There is an increase of disorder, each new organism loses something in the translation, and life degenerates to death. This should inevitable happen if only mutations are involved.
Yet this does not happen.
Not only does it not happen, but the reverse does happen. On the whole, living organisms have grown more complex and more specialized over the aeons. Out of unicellular creatures came multicellular ones. Out of two germ layers came three. Out of a two-chambered heart came a four-chambered one.
This form of apparent entropy-decrease cannot be explained by bringing in solar energy. To be sure, an input of energy in reasonable amounts (short of the lethal level, that is) will increase the mutation rate. But it will not change the ratio of unfavorable to favorable changes. Energy input would simply drive life into genetic chaos all the faster.
The only possible way out is to have recourse to a demon (after the fashion of Maxwell) which is capable of picking and choosing among mutations, allowing some to pass and others not.
There is such a demon in actual fact, though, as far as I know, I am the only one who has called it that and drawn the analogy with Maxwell's demon. The English naturalist Charles Robert Darwin discovered the demon, so we can call it "Darwin's demon" even though Darwin himself called it "natural selection."
Those mutations which render a creature less fit to compete with other organisms for food, for mating or for self-defense, are likely to cause that creature to come to an untimely end. Those mutations which improve the creature's competing ability are likely to cause that creature to flourish. And, to be sure, fitness or lack of it relates only to the particular environment in which the creature finds itself. The best fins in the world would do a camel no good.
The effect of mutation in the presence of natural selection, then, is to improve continually the adjustment of a particular creature to its particular environment; and that is the direction of increasing entropy.
This may sound like arbitrarily defining entropy increase as the opposite of what it is usually taken to be—allowing entropy increase to signify increased order rather than increased disorder. This, however, is not so. I will explain by analogy.
Suppose you had a number of small figurines of various shapes and sizes lined up in orderly rank and file in the center of a large tray. If you shake the tray, the figurines will move out of place and become steadily more disordered.
This is analogous to the process of mutation without natural selection. Entropy obviously increases.
But suppose that the bottom of the tray possessed depressions into which the various figurines would just fit. If the figurines were placed higgledy-piggledy on the tray with not one figurine within a matching depression, then shaking the tray would allow each figurine to find its own niche and settle down into it.
Once a figurine found its niche through random motion, it would take a hard shake to throw it out.
This is analogous to the process of mutation with natural selection. Here entropy increases, for each figurine would have found a position where its center of gravity is lower than it would be in any other nearby position. And lowering the center of gravity is a common method of increasing entropy as, for instance, when a stone rolls downhill.
The organism with which we are best acquainted have improved their fit to their environment by an increase in complexity in certain particularly noticeable respects. Consequently, we commonly think of evolution as necessarily proceeding from the simple to the complex.
This is an illusion. Where a simplifying change improves the fit of an organism to its environment, there the direction of evolution is from the complex to the simple. Cave creatures who live in utter darkness usually lose their eyes, although allied species living in the open retain theirs.
The reptiles went to a lot of trouble (so to speak) to develop two pairs of legs strong enough to lift the body clear of the ground. The snakes gave up those legs, slither on abdominal scales, and are the most successful of the contemporary reptiles.
Parasites undergo particularly great simplifications. A tapeworm suits itself perfectly to its environment by giving up the digestive system it no longer needs, the locomotor functions it doesn't use. It becomes merely an absorbing surface with a hooked proboscis with which to catch hold of the intestinal lining of its host, and the capacity to produce eggs and eggs and eggs and...
Such changes are usually called (with more than a faint air of disapproval) "degenerative." That, however, is only our prejudice. Why should we approve of some adjustments and disapprove of others? To the cold and random of evolution, an adjustment is an adjustment.
If we sink to the biochemical level, then the human being has lost a great many synthetic abilities possessed by other species and, in particular, by plants and microorganisms. Our loss of ability to manufacture a variety of vitamins makes us dependent on our diet and, therefore, on the greater synthetic versatility of other creatures. This is as much a "degenerative" change as the tapeworm's abandonment of a stomach it no longer needs, but since we are prejudiced in our own favor, we don't mention it.
And, of course, no adjustment is final. If the environment changes; if the planetary climate becomes markedly colder, warmer, drier or damper; if a predator improves its efficiency or a new predator comes upon the scene; if a parasitic organism increases its infectivity or virulence; if the food supply dwindles for any reason—then an adjustment that was a satisfactory one before becomes an unsatisfactory one now and the species dies out.
The better the fit to a particular environment, the smaller the change in environment required to bring about extinction. Long-lived species are therefore those which pick a particularly stable environment; or those that remain somewhat generalized, being fitted well enough to one environment to compete successfully within it, but not so well as to be unable to shift to an allied environment if the first fails them.
In the case of Darwin's demon (as in that of Maxwell's demon), the question as to the role of human intelligence arises. Here it is not a matter of imitating the demon, but, rather, of stultifying it.
Many feel that the advance of human technology hampers the working of natural selection. It allows people with bad eyes to get along by means of glasses, diabetics to get along by means of insulin injections, the feeble-minded to get along by means of welfare agencies, and so on.
Some people call this "degenerative mutation pressure" and, as you can see from the very expression used, are concerned about it. Everyone without exception, as far as I know, considers this a danger to humanity, even though practically nobody proposes any non-humane solutions.
And yet is it necessarily a danger to humanity?
Let's turn degenerative mutation pressure upside down and see if it can't be viewed as something other than a danger.
In the first place, we can't really stultify Darwin's demon, for natural selection must work at all times, by definition. Man is part of nature and his influence is as much a natural one as is that of wind and water.
So let us assume that natural selection is working and ask what it is doing. Since it is fitting man to his environment (the only thing Darwin's demon can or does do), we must inquire as to what man's environment is. In a sense, it is all the world, from steaming rain jungle to frozen glacier, and the reason for that is that all contemporary men, however primitive, band together into societies that can more or less change the environment to suit their needs even if only by building a campfire or chipping a rock or tearing off a tree branch.
Consequently, it seems clear that the most important part of a man's environment is other men; or, if prefer, human society. The vast majority of mankind, in fact, live as part of very complex societies that penetrate every facet of their lives.
If nearsightedness is not the handicap in New York that it would have been in a primitive hunting society, or if diabetes is not the handicap in Moscow that it would have been in a non-biochemical society, then why should there be any evolutionary pressure in favor of keeping unnecessarily good eyes and functional pancreases?
Man is to an increasing extent a parasite on human society; perhaps what we call "degenerative mutation pressure" is simply better fitting him to his new role, just as it better fir the tapeworm to its role. We may not like it, but it is a reasonable evolutionary change.
There are many among us who chafe at the restrictions of the crowded anthills we call cities, at the slavery to the clock hand, at the pressures and tensions. Some revolt by turning to delinquency, to "antisocial behavior." Others search out the dwindling areas where man can carry on a pioneer existence.
But if our anthills are to survive, we need those who will bend to its needs, who will avoid walking on grass, beating red lights and littering sidewalks. It is just the metabolically handicapped that can be relied on to do this, for they cannot afford to fight a society on which they depend, very literally, for life. A diabetic won't long for the great outdoors if it means his insulin supply will vanish.
If this is so, then Darwin's demon is only doing what comes naturally.
But of all environments, that produced by man's complex technology is perhaps the most unstable and rickety. In its present form, our society is not two centuries old, and a few nuclear bombs will do it in.
To be sure, evolution works over long periods of time and two centuries is far from sufficient to breed Homo technikos.
The closer this is approached, however, the more dangerous would become any shaking of our social structure. The destruction of our technological society in a fit of nuclear peevishness would become disastrous even if there were many millions of immediate survivors.
The environment toward which they were fitted would be gone, and Darwin's demon would wipe them out remorselessly and without a backward glance.