What Role Does Entropy Play In
Destiny?
THE NEXT TWO chapters deal with some heavy material. They are concerned with an unseen quality that all physical things possess, called entropy. Although perhaps unfamiliar, the word is over one hundred years old. This chapter has been included to explain what it is — and what it is not.1 Understanding its meaning will prove valuable to all readers, both technical and nontechnical alike.
The word entropy is used to describe a certain mathematical quantity 2 that is quite important in any discourse on origins; 3 as such, it is mentioned in later chapters as well. Hopefully, presenting it here will give most readers a clear and accurate picture of its meaning, along with insight into changes that occur in our world. Although this chapter may require some effort, it is worthwhile in our quest for knowledge about origins.
As scientists learned more about the universe the meaning of the word entropy underwent change in our century. Today it is widely misunderstood, even among technical people. Although it is my purpose to clarify the misunderstanding as we proceed, the changes in meaning are discussed in a later chapter.
Entropy is a mathematical quantity that allows scientists to measure the way physical systems change. It doesn't matter whether we're talking about a tennis ball or the sun, a galaxy or a razor blade. Everything possesses entropy which changes with the passage of time. As we have seen, the First Law teaches that mass and energy are conserved.4 The Second Law teaches that, on average, the entropy of any physical system increases with the passage of time.5 But what is entropy?
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Some Old Ideas
Entropy was recognized when Nicolaus Carnot pioneered fictitious engine cycles in 1824.6 Rudolf Clausius stated the earliest version of the Second Law in 1850, and in 1865 he coined the word entropy 7 to describe an unusual mathematical quantity that he had discovered. (The mathematical function discovered by Clausius was a "differential" whose integral vanished around a closed path.)
In 1896 Ludwig Boltzman recognized the close relationship between this quantity and the way gas molecules move at differing speeds. He showed that the molecular velocity distribution had all of the observable properties of Clausius's "entropy." However, Boltzman identified it with spontaneous heat change.8 This concept underwent further refinement in the early decades of the twentieth century, leading to the notion of entropy in terms of heat exchange.
However, widespread confusion persisted concerning entropy's real meaning, and this led to the misuse of the term by a number of authors, even in recent times.9 But despite the confusion, scientists agreed that it was important, and showed a growing awareness of its utility in expressing the way physical things change with the passing of time.10
How Do We Know That Entropy Always Increases?
Entropy is simply the name of a mathematical expression that measures the degree to which energy becomes less available for useful work with the passage of time. In this sense, entropy is a measure of the deterioration of the energy that an observer deems useful — and it is the observer who gives meaning to the term "useful." Entropy always increases because as time passes, the kinds of energy that do useful work continue to change into a form that is less available for such work.
For example, air that is released from a balloon exhibits pressure that could be channeled to do useful work, such as turning a windmill connected to an electric generator. But air randomly distributed throughout a room cannot do useful work because it is as likely to move in one direction as the other; each movement is canceled by an equal but opposite movement, giving zero net pressure, on average, in any one direction.
Early in the twentieth century there was scientific consensus that nature moved in one direction — entropy always increased during any physical change. But here an error developed: Entropy began to be identified with disorder. The reason was that nature was observed to change from states that were well defined to those that were confused and in disarray. This seemed particularly true when, for example, water changed into steam. But to see why nature moved in this one-way direction, we need to look at things on a much smaller scale.
Scientists are convinced that everything in the physical world is composed
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of tiny elements called atoms. We believe that there are ninety-two useful kinds, and that different combinations are organized into "building blocks" called molecules. This picture allows us to understand the materials that we see and touch, such as glass or wood. For example, water is made from molecules that contain hydrogen and oxygen atoms. A glass of water contains many billions of these molecules, which are always moving around and bumping into each other. The hotter the water, the more collisions among the molecules and, therefore the greater the confusion in this tiny molecular world. Water molecules that are used to make a hot cup of tea are, therefore, in greater disarray than those used to make iced tea.
In the case of iced tea, the water is colder so that the water molecules move more slowly and collide less; this means they are more ordered. If they are made cold enough, the water changes to ice and they almost stop moving altogether. In this case, each water molecule remains more or less in place, a picture very different from when the water is hot and the molecules are colliding helter-skelter. Thus, unlike ice, the molecules in hot water are very disordered.
Many people wrongly identify the word entropy with the disordered state 11 (e.g., colliding water molecules in hot tea). Since the Second Law teaches that entropy increases with the passage of time, 12 they conclude that disorder must do likewise and the result is a wrong understanding of the Second Law — namely, the erroneous idea that entropy and disorder are the same, and that since entropy always increases, disorder must do likewise.13 Let's illustrate this with an example.
In your mind's eye, picture an ice cube slowly melting from heat flowing into it. As water forms and as more and more heat raises the water temperature, its molecules move faster and faster. Since heat flows from hot to cold, the colder parts of any system become more disordered as they heat up. But what about the hot parts that supply the heat? They, of course, cool down. This means that their molecules are moving slower and are therefore becoming more ordered, whereas the colder parts that heat up from gain of heat become more disordered.
The Second Law requires that, on average, the total entropy must increase. However, if the entropy increase required a net increase in disorder, it would force us to believe that the increase in disorder as the colder parts heat up exceeds the decrease in disorder as the hotter parts cool down. Many people believe that the Second Law teaches this. But they are wrongly identifying entropy with disorder, and they wrongly understand the Second Law to require that the total disorder in both the cold and the hot parts (the total system) must increase.
A Popular Yet Naive Fantasy
What has entropy to do with disorder? The truth is, practically nothing. Yet a common belief is that the two are one and the same. Entropy can be
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correlated with disorder, but not identified with it. For example, think of entropy as rain and disorder as your umbrella. Each time it rains your umbrella gets wet, thus rain and wet umbrellas correlate; they both appear at the same time. But although they are correlated, they are not related; i.e., there is no direct connection between your umbrella and rain clouds. Should you decide to stay home when it rains, your umbrella won't get wet.
Entropy can be correlated with disorder in the same way rain can be correlated with your umbrella — but even that correlation is valid only in three special cases: ideal gases, isotope mixtures, and crystals near zero degrees Kelvin.14
Not only is entropy wrongly identified with disorder; the error has caused some people to introduce a nonsensical thing called "negentropy."15 This idea assumes that negative entropy exists, and that it can be identified with order. It says that the onset of life was accompanied by a change in negentropy that just balanced the increase in entropy, and that this change explains the order found in life.
However, the idea of negentropy is quite wrong because it is defective in several basic ways.16 Nevertheless, over the past twenty years a number of people have used this erroneous concept in an attempt to justify the creation of life by natural processes.17 To understand how they do this, picture water in an ice cube tray in a refrigerator. Let the tray represent the earth, the refrigerator represent the sun, and the transition of water into ice, the creation of life. The order that arises when water becomes ice is said to be balanced by the disorder that occurs when the liquid refrigerant changes into a gas (molecules are in greater disarray in a gas than a liquid). The spontaneous creation of life is then justified by saying that the increased order in life corresponds to negentropy that is offset by the greater increase in entropy (disorder).
But life is complex, nor ordered; and the basic natural process that changes water into ice is counterproductive to the creation of life because it results in a loss of complexity. The reason that ice is ordered and not complex is that ice is made up of millions of tiny atomic units that are identical to each other. This means that if we describe one of them, we will have described all of them. When water changes into ice, we actually need less information to describe the ice because its molecules no longer behave in an independent manner. It is less complex because we need less information to describe it. But unlike ice, life is vastly complex because we require staggering quantities of information to describe even the simplest of cells. Negentropy is thus an erroneous concept.
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When something becomes ordered, it becomes less complex. On the other hand, a living cell is a highly complicated structure whose description requires a vast amount of information. To explain life's origin we must explain the source of the information that resides in each cell. Whatever brought life into being involved an act which, rather than losing information, created it.
Notwithstanding the confused analogies between "life" and "crystals" that are sometimes found in books on origins,21 the fact is that the latter are ordered whereas the former is complex. Therefore, to explain life's origin one must identify the source of the information (algorithms) embodied in the complexity along DNA. Yockey is particularly lucid on this point.22 However, some writers, in their zeal to dissociate entropy from disorder, have inadvertently contributed to the confusion they sought to eradicate by also dissociating entropy from the concept of "information."23 This latter error is very widespread25 and is the reason why so many intelligent people mistakenly believe that nature can create life. The entropy that is germane to life concerns the distribution of nucleotides along DNA — and not the distribution in the levels of energy.26
The important truth for our discussion is that life isn't ordered; it is complex. We saw that clearly in chapter 4 in our consideration of the materialistic world view. An increase in organization of a structure — from simple dust particles to the oriental rug to the vacuum cleaner to the house (to repeat an earlier metaphor) — requires the systematic increase of information, but information is not produced by natural processes in the magnitude necessary to explain the origin of life.
Let's summarize what's been said thus far:
1. The Second Law requires entropy to increase.2. Entropy cannot be identified with disorder.
3. Negentropy cannot be identified with order.
4. Ordered molecules (ice) present less information.
5. Living cells are not ordered — they are complex.
The Meaning of Entropy
If entropy isn't disorder, then what is it?
We said earlier that it's the name of a mathematical expression that measures how the form of energy changes with the passage of time. However, we can gain greater insight into the nature of this change by considering
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the most modern sense of the word's meaning. Picture in your mind a nurse operating a slide projector displaying an eye chart on a large wall screen as in an eye examination. At the top is a very large letter, followed by two somewhat smaller letters below. Each subsequent line on the chart contains greater numbers of letters, but of diminishing size.
Now suppose that while viewing this white chart with its black letters, you are asked by the nurse operating the slide projector to take an eye exam. You agree to take the test and after doing so the nurse reports your score as 20:20.
Distrustful of so perfect a result, she asks you to retake the eye exam. Again you agree, and your score is 23:23, a result almost the same as the first. Certain that your eyes have not deteriorated over the short span of several minutes, you request a third exam and are given one. This time your score is 27:27.
Perplexed, you discuss the matter with the nurse. You wonder whether her telling you the score affected the result of the test. Although skeptical, she agrees to withhold future scores until four additional tests are completed. Now you score, in sequence, 30:30, 34:34, 39:39, and 45:45. Despite the larger numbers, these scores convince you that your eyes have not deteriorated, for why should both eyes change in exactly the same way? Also, how could so large a deterioration in eyesight occur in the short span of time over which the tests were administered? Yet the scores also convince you that each time you take a test, you do more poorly than the time before. Something is changing, but what?
The answer, of course, is that the eye chart is changing. Looking over at the projector, you see smoke rising above the lamp. Heat from the bulb was ever-so-slightly warping the slide, causing it to gradually go out of focus so that the image on the wall screen was losing its sharpness and becoming progressively defocused.
This is precisely the concept of entropy. With the passage of time, the physical world undergoes gradual "defocusing" to an observer. The way this deterioration manifests itself is that energy becomes less available for useful work with the passage of time.
Useful work is accomplished when physical objects undergo directed motion in space. An observer's act of describing the motion of the objects produces information — information that is true about the movement of the objects at the time the observation is made. However, with the passage of time, the motion continues, now unobserved, rendering the observer less able to direct the objects in the way desired — and thus accomplish useful work — because of his growing uncertainty of the object's whereabouts.
In the words of the New Generalized Second Law, an observer functioning within a closed system will lose, but never gain, information.27 In essence, this result follows from the fact that all measurements yield incomplete information; an observer's uncertainty increases with the passage of time (your
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scores on the eye test). Entropy is this uncertainty. These simple words come from some rather deep physics, parts of which are outlined in simplified ways in other chapters. (For further discussion of the more technical aspects of entropy and its relationship to the Second Law, see Appendix 2.)
In summary, entropy is a mathematical expression that allows scientists to assign numbers measuring the degree to which energy deteriorates into less useful forms with the passage of time. This decay corresponds to the progressive decline of an observer's ability to extract useful work from the system due to his growing uncertainty of the whereabouts of the physical objects described by him at an earlier time.
When rigorously formulated with all of the "bells and whistles" the observer must be included as part of the system that is described. The mathematical expression that assigns numbers is found to measure also the observer's uncertainty of the location and velocity of every object within the system, and at each instant of time. The New Generalized Second Law is a formal mathematical statement showing that the decline on average of an observer's information is an inevitable result of the passing of time, and that the total information available to an observer cannot exceed what exists in the system's overall description.
These considerations impose important constraints on the theory of the chemical origin of life, and the commonly held belief that natural laws can energize biological structures into increasing levels of complexity. Virtually all attempts to justify these ideas have focused upon the thermodynamic flow of energy in an organism, rather than on the genetic blueprint by which the flow is controlled. This unfortunate confusion has created the false impression that living organisms sprang from dead chemicals, and that their progeny prospered under processes which, under any other circumstance, would be regarded as the inspired product of intellect.
Chapter Seven || Table of Contents
1. Popper K. Brit Jour. for Phil Sci. (1957) 8:151.
2. Levine R. & Tribus M. ed. The Maximum Entropy Formalism (1979) MIT Conference (May 2, 1978) MIT Press.
3. Prigogine I. & Stengers I. Order Out of Chaos (1984) Bantam B.
4. Zemansky M. & Dittman R. Heat & Thermodyna (1981) McGraw Hill.
5. Jaynes E. The Maximum Entropy Formalism (1978 MIT Conf. May 2) Levine R. & Tribus M. ed. (1981) McGraw Hill.
6. Cardwell D. From Watt to Clausius (1971) Heinemann (London).
7. Clausius R. Ann. Phys. (1865) 125:353.
8. Boltzmann L. Vorlesungen uber Gastheorie (1896/1898) Brush S. (translator) (1964) Univ. Calif. Berkley.
9. Kitcher P. Abusing Science (1982) MIT Press (4:89).
10. Davydov B. Jour. Phys. Moscow (1947) 11:33.
11. Morris H. The Biblical Basis For Modern Science (1984) Baker (7:204); Futuyama D. Science On Trial (1983) Pantheon (10:183); Kitcher P. (1982) ibid. (4:91); Asimov I. In the Beginning (1981) Crown (1:17); Coppedge J. Evolution: Possible or Impossible (1973) Zondervan (14:238); and Gatlin L. Information Theory and the Living System (1972) Columbia Univ. Press (2:29).
12. Yourgrau W. et al. (1982) ibid. Ch. 2 (1:10).
13. Guggenheim E. Research (1949) 2:450.
14. McGlashan M. Jour. Chem. Ed. (1966) 43:226.
15. Schroedinger E. What Is Life (1955) Cambridge Univ. Press; Brillouin L. Science and Information Theory (1962) Academic P.
16. (1) It is conceptually flawed — order and disorder are not identified with entropy.17
(2) It is physically flawed — it violates one-sided conservation laws.18
(3) It is mathematically flawed — the function describing our intuitive notion of disorder is unique when positive.19
17. Dingle H. Bull. Inst. Phys. (1959) 10:218.
18. Yockey H. Jour. Theor. Biol. (1974) 46:369.
19. Khinchin A. Math. Founda. of Information Theory (1957) Dover.
20. Schuster P. Biophysics (1983) Hoppe W. et al. ed. Springer-Verlag (8:346).
21. Bernal J. The Origin of Life (1967) World Publishing.
22. Yockey H. (1974) ibid.
23. Although this latter term is commonly understood in the general sense of knowledge, the word is used in science to mean the logarithim of the probability of the corresponding state of a physical system.24 (old 23)
24. Prigogine I. & Stengers I. (1984) ibid. Ch. 4. Asimov I. Asimov's New Guide to Science (1984) Basic Books (13:641); Futuyma D. (1983) ibid. (4:95); Kitcher P. (1982) ibid. (4:89); Eigen M. et al. Scientific American (1981) 244:88 Apr; Sagan C. (1980) ibid. Ch. 4 2:31); Gatlin L. Sixth Berkley Symp. Proc. Math. Stat. (1972) Cal. U.; and Calvin M. Chemical Evolution (1969) Oxford Univ. Press.
25. Margenau H. The Nature of Physical Reality (1950) New York.
26. All natural distributions exhibit entropy, but the entropy of one distribution has nothing whatever to do with that of another. Thermodynamic and genetic entropy respectively describe the energy path and plan of an organism. They've been confused for decades.
27. Hobson A. (1971) ibid. (5:142).
