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J . theor . Biol . (1995) 176, 349–355 0022–5193/95/190349+07 $12.00/0 7 1995 Academic Press Limited Comments on ‘‘Let there be Life; Thermodynamic Reflections on Biogenesis and Evolution’’ by Avshalom C. Elitzur H P. Y 1507 Balmoral Drive Bel Air MD 21014-5638, U.S.A. (Received on 12 January 1995, Accepted in revised form on 3 May 1995) This comment is in response to a paper previously published in the Journal entitled ‘‘Let there be life’’, by A. C. Elitzur. Elitzur ascribes to Eigen the proposal that life began with the appearance of an autocatalytic (self-replicating) molecule. This was discussed by biologists and philosophers in the nineteenth century. Eigen’s proposal is moot: there never was a primeval soup. The absence of evidence is evidence of absence. Elitzur also confuses thermodynamics with statistical mechanics. The statistical equation of Boltzmann and Planck for entropy appears in discussions of statistical mechanics, not in discussions of classical thermodynamics. Elitzur calls the Second Law of Thermodynamics an explanation of evolution. On the contrary, his mentor Eigen wrote: ‘‘In physics we know of principles which cannot be reduced to any more fundamental laws. As axioms, they are abstracted from experience, their predictions being consistent with the consequences that can be subjected to experimental test. ‘‘Typical examples are the first and second law of thermodynamics. Darwin’s principle of natural selection does not fall into the category of first principles.’’ The reader is invited to compare the material in Elitzur’s paper with the discussion in Yockey’s (1992) book, Information Theory and Molecular Biology, Cambridge, Cambridge University Press. 7 1995 Academic Press Limited The purpose of this comment is to point out the more egregious errors of omission and commission in Elitzur (1994). He began his paper with the following remarks on the chirality of biomolecules and the origin of life: . . . The evolutionary explanation for this handedness is simple: It was a common ancestor that, by sheer coincidence , happened to have these molecules rather than their mirror-images (Shapiro, 1986; this issue will be returned to later). This coincidental yet universal handedness [My emphasis] of life highlights the question of common ancestry, vividly raised by Darwin: ‘‘It is often said that all the conditions for the first production of a living organism are now present, which could ever have been present. But if (and oh! what a big if!) we could conceive in some warm little pond, with all sorts of ammonia and phosphoric salts, light, heat, electricity, &c., present, that a proteine (sic) compound was chemically formed ready to undergo still more complex changes, at the present day such matter would be instantly absorbed, which would not have been the case before living creatures were found.’’ This passage (obviously not having been subjected to an editor’s blue pencil) is from a private letter Darwin wrote to his friend Joseph Hooker (1817–1911) in 1871 and appears in a footnote of F. Darwin (1898). This fragment was not indexed and remained unnoticed until 1950 (Hardin, 1950). Everyone has the right to float tentative ideas and even nonsense to his friends in his personal correspondence without responsibility being assumed by snoopers. In selecting the personal letter to Hooker rather than what Darwin published a year later in The Origin of Species , dialectical materialists are quoting selected writings to support their convictions, to seduce the unwary reader, even though they must reach rather deep for it. If Darwin had regarded the ‘‘warm little pond’’ at all seriously in 1871 he had changed his mind by 1872. What Darwin ‘‘vividly raised’’ and published as his considered opinion, and what he was prepared to take responsibility for on the question of origin of life is in Chapter XV of the 1872 edition of Origin of Species : It can hardly be supposed that a false theory would explain, in so satisfactory a manner as does the theory of natural selection, the several classes of facts above specified. It has recently been objected that this is an unsafe method of arguing; but it is a method used in judging of the common events of life, and has 349

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Page 1: Comments on “Let there be Life”; Thermodynamic Reflections on Biogenesis and Evolution” by Avshalom C. Elitzur

J. theor. Biol. (1995) 176, 349–355

0022–5193/95/190349+07 $12.00/0 7 1995 Academic Press Limited

Comments on ‘‘Let there be Life; Thermodynamic Reflections on Biogenesis

and Evolution’’ by Avshalom C. Elitzur

H P. Y

1507 Balmoral Drive Bel Air MD 21014-5638, U.S.A.

(Received on 12 January 1995, Accepted in revised form on 3 May 1995)

This comment is in response to a paper previously published in the Journal entitled ‘‘Let there be life’’,by A. C. Elitzur. Elitzur ascribes to Eigen the proposal that life began with the appearance of anautocatalytic (self-replicating) molecule. This was discussed by biologists and philosophers in thenineteenth century. Eigen’s proposal is moot: there never was a primeval soup. The absence of evidenceis evidence of absence. Elitzur also confuses thermodynamics with statistical mechanics. The statisticalequation of Boltzmann and Planck for entropy appears in discussions of statistical mechanics, not indiscussions of classical thermodynamics. Elitzur calls the Second Law of Thermodynamics an explanationof evolution. On the contrary, his mentor Eigen wrote: ‘‘In physics we know of principles which cannotbe reduced to any more fundamental laws. As axioms, they are abstracted from experience, theirpredictions being consistent with the consequences that can be subjected to experimental test. ‘‘Typicalexamples are the first and second law of thermodynamics. Darwin’s principle of natural selection doesnot fall into the category of first principles.’’ The reader is invited to compare the material in Elitzur’spaper with the discussion in Yockey’s (1992) book, Information Theory and Molecular Biology,Cambridge, Cambridge University Press.

7 1995 Academic Press Limited

The purpose of this comment is to point out the moreegregious errors of omission and commission in Elitzur(1994). He began his paper with the following remarkson the chirality of biomolecules and the origin of life:

. . . The evolutionary explanation for this handedness is simple: Itwas a common ancestor that, by sheer coincidence, happened to havethese molecules rather than their mirror-images (Shapiro, 1986; thisissue will be returned to later). This coincidental yet universalhandedness [My emphasis] of life highlights the question of commonancestry, vividly raised by Darwin:

‘‘It is often said that all the conditions for the first productionof a living organism are now present, which could ever have beenpresent. But if (and oh! what a big if!) we could conceive in somewarm little pond, with all sorts of ammonia and phosphoric salts,light, heat, electricity, &c., present, that a proteine (sic)compound was chemically formed ready to undergo still morecomplex changes, at the present day such matter would beinstantly absorbed, which would not have been the case beforeliving creatures were found.’’

This passage (obviously not having been subjectedto an editor’s blue pencil) is from a private letterDarwinwrote to his friend JosephHooker (1817–1911)in 1871 and appears in a footnote of F. Darwin (1898).

This fragment was not indexed and remainedunnoticed until 1950 (Hardin, 1950).

Everyone has the right to float tentative ideas andeven nonsense to his friends in his personalcorrespondence without responsibility being assumedby snoopers. In selecting the personal letter to Hookerrather than what Darwin published a year later in TheOrigin of Species, dialectical materialists are quotingselectedwritings to support their convictions, to seducethe unwary reader, even though they must reach ratherdeep for it.

If Darwin had regarded the ‘‘warm little pond’’ at allseriously in 1871 he had changed his mind by 1872.What Darwin ‘‘vividly raised’’ and published as hisconsidered opinion, and what he was prepared to takeresponsibility for on the question of origin of life is inChapter XV of the 1872 edition of Origin of Species:

It can hardly be supposed that a false theory would explain,in so satisfactory amanner as does the theory of natural selection,the several classes of facts above specified. It has recently beenobjected that this is an unsafe method of arguing; but it is amethod used in judging of the common events of life, and has

349

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often been used by the greatest natural philosophers. Theundulatory theory of light has been thus been arrived at; and thebelief in the revolution of the earth on its own axis was until latelysupported by hardly any direct evidence. It is no valid objection(to the theory of natural selection) that science as yet throws nolight on the far higher problem of the essence or the origin of life.Who can explain the essence of the attraction of gravity? No onenow objects to following out the results consequent on thisunknown element of attraction; notwithstanding that Leibnitzformerly accused Newton of introducing ‘‘occult qualities andmiracles’ into philosophy.

This passage makes it clear that Darwin’s publishedopinion on the nature and origin of life actuallyanticipated the position of Niels Bohr (1993) in hisfamous Light and Life lecture that, like the quantumof action that appears as an irrational element from thepoint of view of classical mechanical physics, life mustbe accepted as an axiom, rather than the dialecticalmaterialist scenario, usually attributed to Oparin andHaldane that life is a property of matter.

Darwin’s Origin of Species is, perhaps, among theten most famous and influential books of all time, yetElitzur (and many others as well), ignoring the passagequoted above, pursues his scenario: ‘‘In this paper thisbig if will be addressed in detail. Such an undertakingpromises much more than just a scenario of life’sbeginning; seeking a physical process that gave rise toevolution ought to shed new light on evolution and lifein the universe.’’ He continues later in the paper:

Addressing the problem of the origin of life, the sole assumptionthat is proposed is due mainly to Manfred Eigen: Life began withthe appearance of an autocatalytic (self-replicating) molecule.Nearly four billion years ago, in ‘‘Darwin’s pond’’ [sic], as biologistslike to call the primordial lake or sea in which life supposedlyemerged, a molecule was formed by chance, that had a peculiarcapability: it initiated a chemical reaction that produced an identicalmolecule, thereby giving rise to a long-lasting process. Thishypothesis will henceforth serve as the ‘‘Minimal Assumption’’ fromwhich the emergence of life from inanimate matter should follow asa natural consequence.

Elitzur’s ‘‘Minimal Assumption’’ and ManfredEigen’s autocatalytic scenario are neither new, nor dueto Eigen. It was discussed frequently by biologists andphilosophers in the nineteenth and early twentiethcentury. The discussion was so widespread amongthe theater-going public that Sir William SchwenckGilbert (1836–1911) had Pooh-Bah, a comic character,introduce himself as follows: ‘‘I am in point of fact, aparticularly haughty and exclusive person, of pre-Adamite ancestral descent. You will understand thiswhen I tell you that I can trace my ancestry back toa protoplasmal primordial atomic globule.’’ [TheMikado, Act 1]. Jacques Loeb (1906), a convincedmechanist, wrote:

But we see that plants and animals during their growthcontinually transform dead into living matter, and that thechemical processes in living matter do not differ in principle fromthose in deadmatter. There is, therefore, no reason to predict that

abiogenesis is impossible, and I believe that it can only helpscience if younger investigators realize that experimentalabiogenesis is the goal of biology. On the other hand, our lecturesshow clearly that we can only consider the problem ofabiogenesis solved when the artificially produced substance iscapable of development, growth, and reproduction. It is notsufficient for this purpose to make proteins synthetically, or toproduce in gelatin or other colloidal material round granules thathave an external resemblance to living cells. [My emphasis.]

About 1875 Friedrich Engels began The Dialectics ofNature, in which he discussed the nature and origin oflife:

Life is the mode of existence of protein bodies, the essentialelement of which consists in continual metabolic interchange withthe natural environment outside them, and which ceases with thecessation of this metabolism, bringing about the decompositionof the protein. If success is ever attained in preparing proteinbodies chemically, they will undoubtedly exhibit the phenomenaof life and carry out the mechanism of metabolism, howeverweak and short-lived they may be [italics in original].

Engels did not live to finish The Dialectics of Nature;nevertheless, his views reflected those of Marxistphilosophers at the time. The document was foundamong his papers and published in Moscow in 1925,from photocopies of the manuscripts, in the originalGerman and in a Russian translation.

Alexander Ivanovich Oparin’s paper, written inRussian in 1924, was reductionist-mechanist. Oparin,upon reading The Dialectics of Nature, became animmediate convert to dialectical materialism—verypolitically appropriate for his career, as it turned out.After his conversion, Oparin revised and expanded hisoriginal paper several times during his career andbecame a promoter of dialectical materialism. Hewas later the only well-known biologist to supportLysenkoism (Trofim Desinovich Lysenko, 1898–1967)(Joravsky, 1970). Gilbert’s protoplasmal primordialglobules became coacervates that Oparin got fromBungenberg de Jong (1932). Neither he nor de Jongmentioned Jacques Loeb, although Loeb hadpublished extensively on the relation of colloidalmaterials and proteins (Loeb, 1924) and was muchmore famous than either at the time. It is a travesty thatJacques Loeb’s comments are not now mentioned inthe literature.

Shapiro (1986) wrote ‘‘Oparin’s views are the solesurviving fragment of Lysenkoite biology, derivedfrom dialectical materialism.— When Oparin stated,for example, that only dialectical materialism hasfound the correct routes to the origin of life, he wascontributing dogma rather than experiment.’’

De Duve (1991) also called attention to FriedrichEngels and dialectical materialism as the source of thenotion that life is a natural emerging property ofmatter. ‘‘It is of possible historical relevance that allthree [Oparin, Haldane and Bernal] were confirmed

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Marxists, militant defenders of dialectical materialism.One may wonder to what extent ideology hadsomething to do with their desire to explain life as anaturally emerging phenomenon in the evolution ofthe Earth. It certainly had with Oparin, whose book ispeppered with references to the philosopher FriedrichEngels. Rumor even has it that he was set on theproblem by the Party.’’

The ‘‘warm little pond’’ albatross is often hungaround Charles Darwin’s neck as propaganda andpublic enlightenment to establish legitimacy for theprimeval soup scenario from one of the saints ofbiology. The standard dialectical materialist model ofthe origin of life absolutely requires a primeval soup inthe early ocean. The source of these biochemicals mustbe through non-biological processes. This soup, ifthere ever was one, may have lasted no more than 100million years. According to Stanley Miller’s ‘‘historicand seminal experiments’’ (sic) amino acids and other‘‘prebiotic’’ ‘‘building blocks’’ of life are supposed tohave been formed in the atmosphere by the action ofultraviolet light, lightning strokes and other electricspark discharges. It has long been admitted, even bythe true believers, that the atmosphere of the earlyEarth was not composed of ammonia, hydrogen,methane and water vapor (Space Studies Board, 1990).Reasonable models of the atmosphere of the earlyEarth accepted today suggest that it was composed tocarbon dioxide, nitrogen and water vapor. StanleyMiller, himself, was one of the first to show that theyield of ‘‘prebiotic chemical compounds’’ from electricdischarges, and ultraviolet light in neutral atmospheresis very small or nonexistent (Schlesinger & Miller,1983). When it transpired that the ‘‘prebioticatmosphere’’ was not reducing, comets and meteoriteswere proposed as means of supply (Chyba et al., 1990).Nevertheless, Elitzur clings as a true believer to thereducing prebiotic atmosphere:

This last requirement is fairly realistic in view of presentknowledge about the conditions on Earth prior to life’semergence: Miller’s celebrated experiments have demonstratedthe possibility of spontaneous assembly of various organiccompounds, including some amino acids like alanine, underexperimental simulations of possible ancient atmospherescomposed ofmethane, ammonia,molecular hydrogen andwater,and with the presence of electrical sparks.

Would there not be geological evidence in rocks of3.8 to 4 billion years old, if there had been such a soup?The Space Science Studies Board (1990) suggests thatthere should be: ‘‘These speculations on chemicalevolution, multiple origins of life, and models of earlyenvironmental conditions in the atmosphere andoceans can only be substantiated by the geologicalrecord.’’ I showed in Yockey (1992) that, if one looksat the geological record, one finds no evidence that a

primeval soup ever existed. Sedimentary rocks at Isuain Greenland have been dated at 3.8 billion years ago,a time near the end of the late heavy bombardment.The kerogen of the very old Isua rocks is depleted in13C (Schidlowski, 1988). De Duve (1995) has come tothe same conclusion as I (Yockey, 1992) that this is justwhat is to be expected if the kerogen had been derivedonly by enzymatic action, perhaps from cyanobacteria-like microorganisms capable of photosynthesis ofcarbon dioxide and nitrogen.

The vastly more abundant result of all ‘‘prebiotic’’experiments is an insoluble tarry mixture. After theorigin of life, this tarry mixture would have precipi-tated out of the primeval ocean and have been foundin the kerogen of sedimentary rocks. Since it wouldhave carried the 13C rejected by enzymatic action, noenhancement of 12C, would have occurred. Thesignificance of the isotopic enhancement of 12C in thevery old kerogen in the Isua rocks in Greenland is thatthere never was a primeval soup and that, nevertheless,living matter must have existed abundantly on Earthbefore 3.8 billion years ago.

Even true believers such as Stanley Miller (1992) andCarl Sagan (1992) have estimated an extremely diluteprimeval soup. Miller’s latest (1992) estimate of theconcentration of the primeval soup is 0.0003 molar.Chyba & Sagan (1992) estimated the concentration oforganic compounds in the primeval ocean as 0.1% ifthe atmosphere had been reducing (it was not) or0.0001% if it had been neutral (it was). That is as faras a true believer has gone toward admitting noprimeval soup ever existed. So much for prebioticsynthesis of organic compounds and chemicalevolution! Since there never was a primeval soup,Elitzur’s ‘‘Minimal Assumption’’ and Eigen’s hyper-cycles are moot because there were no self-organizingautocatalytic molecules to grow exponentially.

Furthermore, without getting the point, Elitzurquotes von Neumann’s (1966) requirement for aself-reproducing automaton that, ‘‘in order to give riseto an exponentially growing number of copies, mustpossess a certain degree of complexity, belowwhich theprocess would be degenerate’’. The same restrictionapplies to the RNA-world and any other speculationabout the origin of life based on dialecticalmaterialism. There is no gradual sequence of eventsfrom the primeval soup to an element that records thedegree of complexity (that is information content)fromwhich the process could grow exponentially. Thatdegree of complexity (measured in bytes) must be hadin order to begin (Yockey, 1992). By the same token,as Bohr (1933) pointed out, there is no gradual pathfrom the classical mechanics of physics to the quantumof action of quantum theory.

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One would suppose that the establishment of theexistence of the primordial soupwould have been givena first priority by workers on the origin of life. Strangeto say, this search seems to have been left for later inthe manner of an ingenious architect in the GrandAcademy of Lagado, as reported by Captain LemuelGulliver in Jonathan Swift’s Gulliver’s Travels. Thisarchitect contrived a new method for building housesby starting at the roof and working down andestablishing the foundation at the end of the project.The architect pointed out that among the obviousadvantages of this method is that once the roof was inplace the workers could toil in the shade of the hot sunand at other times be protected from rain and snow.Thus the progress of the construction would not bedelayed by inclement weather. Although this idea hadbeen approved by peer review, it was still in theresearch stage and he had not yet put in into practiceat the time of Captain Gulliver’s visit.

Elitzur, following the reasoning of the architect inthe Grand Academy of Lagado, cites the existence oflife as a justification and a proof that a primeval soupmust have existed. ‘‘The model proposed [of the originof life] here is based on a simple assumption, namely,that life began with the accidental assembly of aself-replicating molecule [in a primeval soup]. Fromthis assumption the emergence of life naturally follows,enabling a new understanding of evolution as awhole.’’ Thus Elitzur and others are not deterred intheir beliefs by the fact that the absence of evidence isindeed evidence of absence.

Elitzur peppers his paper with an astonishingmisunderstanding of the basic concepts of the moderntheory of probability, information theory, thermo-dynamics and statistical mechanics. The phrasemere coincidence and accidental assembly are nottechnical and nomenclature and are more suitableto the Sunday newspaper supplements or parlorconversation than a paper in this distinguished journal.According to modern theory of probability, onecannot speak of a probability without first establishinga probability space and setting up a probabilitydistribution appropriate to the problem.The axioms ofprobability theory must be satisfied in order to avoida ‘‘Dutch book’’ (Press, 1989) and to be sure that weare not using knowledge we do not have (Yockey,1992: 20–33).

Elitzur is totally at odds with current concepts of‘‘entropy’’, or ‘‘order’’ and ‘‘information’’:

We will start with three thermodynamic concepts that willprove highly fruitful for our goals: ‘‘entropy’’, ‘‘order’’, and‘‘information’’. What we need is some concise definitions,presented with the minimum of necessary mathematics, in orderto efficiently apply them later to the problems awaiting us.

The curious phrase ‘‘with the minimum of necessarymathematics’’ may belong in a piece directed to thegeneral public but not in this Journal.

Throughout his paper, Elitzur confuses thermo-dynamics with statistical mechanics. The concept ofentropy in the continuous matter considerations ofclassical thermodynamics, which was developed byengineers to understand the design of heat engines, isdifferent from the statistical concepts based on theinteraction of atoms. Classical thermodynamics wasdeveloped in the nineteenth century when even theexistence of atoms was controversial. Indeed, it was aslate as 1909 that Wilhelm Ostwald, a distinguishedchemist and the last hold-out for the continuousmattertheory, finally acknowledged their existence in thefourth edition of his text book. The statistical equationof Boltzmann and Planck for entropy appears indiscussions of statistical mechanics, not in discussionsof classical thermodynamics.

As Elitzur admits, I (Yockey, 1992) warnedrepeatedly against the careless use of such words as‘‘information’’, ‘‘order’’ and ‘‘complexity’’. I pointedout that ‘‘order’’ and ‘‘complexity’’, for example, taketheir meaning from mathematical formalism. Themeaning of words, in technical discussions, comesfrom the mathematics, not the other way around(Yockey, 1990). Ignoring that, Elitzur produces thefollowing bloopers in which, like Humpty-Dumpty,words mean exactly what he wants them to mean:‘‘Entropy means equilibrium; Entropy is disorder.Entropy is a state of higher probability. Entropy is amacrostate compatible with more microstates thanorder.’’ ‘‘Information is an ordered relation betweena message and a certain reality. Mere order, wherethe system’s constituents display correspondence onlywith one another, regardless of the environment, isinsufficient for the evolution of life.’’ ‘‘Life is a highlyordered phenomenon.’’ ‘‘The organism must haveorder, but not the barren, self-correlated order of acrystal; it must be an order in relation to theenvironment, namely, information.’’ ‘‘Having definedentropy and order, one can see how the concept ofinformation is closely related. Information is asequence of symbols that is highly correlated with acertain reality. [It is well known that the more‘correlated’ the sequence of symbols is the lessinformation it can contain (Yockey, 1992).] The realityand the information describing it form an orderedrelation, a state that is unlikely to be created by chance.Information is therefore the opposite of entropy.Indeed, the generation of information is subject to allthe thermodynamic constraints imposed by the SecondLaw, as the information is bound to degenerate intorandom ‘noise’, like other forms of order.’’ Communi-

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cation engineers will be astonished to learn that:‘‘Notice, however, that ‘signal’ and ‘noise’ aresomewhat relative terms.’’

Geneticists will be startled to learn that: ‘‘TheDarwinian prohibition on inheritance of acquiredtraits is a simple biological manifestation of the SecondLaw.’’ The ‘‘prohibition of inheritance of acquiredtraits’’ is not due to Darwin but rather to AugustWeismann who in 1884 separated the organism intogerm plasm and somatoplasm thus establishing abarrier to information transfer between the two.Darwin and most of his contemporaries accepted theblending theory of Fleeming Jenkin (1867). It was notuntil 1930 that Fisher (1930) showed that the blendingtheory was incorrect and that natural selectionproceeds according to the particulate laws of GregorMendel.

Elitzur tosses the word ‘‘random’’ about like a foot-ball totally unaware of its mathematical significance:‘‘The sequence 5177274740 is random, taken from atable of random numbers. Yet 51772747405177274740is far from random, for it consists of two identicalrandom sequences. The amount of order in each of thesequences in itself was zero, but the joint order iscertainly not’’. It is impossible to prove that a givensequence was generated by a random process.Sequences of digits taken from a table of randomnumbers are at best pseudo-random. Elitzur isunaware of the work of Solomonoff, Kolmogorov,Chaitin and Martin-Lof. I have explained this point ina note to Nature (Yockey, 1990) and in Yockey (1992)where references may be found.

Elitzur misquotes Shannon’s expression for entropyin information theory as:

i=−kSpi ln pi (1)

where i is the information entropy or averageinformation per letter of a single symbol of probabilitypi and, as usual, k is the Boltzmann constant. Theexpression for information entropy that appears inShannon (1948) is:

H=−KSipi log pi . (2)

Shannon is quick to explain that K is a positiveconstant that ‘‘merely amounts to a choice of a unit ofmeasure’’. K appears from the mathematical argumentthat justifies eqn (2). It has no physical dimensions andwhen the logarithm is taken to base 2 and K=1, H ismeasured in bits.

As I explained in Yockey (1992), entropy is a generalterm and must be defined as a function of theprobability space and the probability distribution towhich it refers. Every probability distribution has an

entropy. For example, the probability space instatistical mechanics, called phase space by theoreticalphysicists, is six-dimensional and is defined by theposition and momentum vectors of the particles in theensemble. The statistical function for entropy instatistical mechanics has the dimensions of theBoltzmann constant k and has to do with energy, notinformation. Entropy in information theory andprobability theory has no mechanical dimensions.There are no counterparts in communication theory totemperature, energy, pressure, work or volume. Thereis, furthermore, no counterpart to the First Law ofThermodynamics, namely, the conservation of theenergy of a system.

On the other hand, information theory is concernedwith messages expressed in sequences of letters selectedfrom a finite alphabet of a Markov process. Theprobability space is constructed of the letters of thealphabet under consideration and the pi are definedaccordingly. As Hamming (1986) wrote: ‘‘For usentropy is simply a function of a probability distri-bution pi . . . .The confusion at this point has been verygreat for outsiders who glance at information theory.’’

To illustrate this point further, one may consider theprobability space of a dice game that consists of thenumbers 2 through 12 and calculate the correspondingentropy (Yockey, 1992: 88). Clearly, the entropy of adice game has nothing whatever to do with statisticalmechanics or thermodynamics. It may have somethingto do with information theory since a sequence ofsymbols selected from the alphabet is generated as astochastic Markov process by a series of tosses of thedice. Such a sequence of letters forms a message inwhich some gamblers find meaning or knowledge bywhich they make their bets.

Note also that like the genetic code the dice game isa many-to-one code and for that reason has a CentralDogma. The source alphabet has 36 members, namely,all pairs of the numbers 1 through 6. These pairs ofnumbers are analogous to codons in the genetic code.The receiver alphabet is formed by adding the twonumbers and has only 11 members, the numbers 2through 12. These numbers are analogous to the aminoacids in protein sequences. Except for 2 and 12, alltotals can be made by more than one combination ofnumbers read from the dice. Thus there is a loss ofinformation (and knowledge) when the numbers areadded because the logic operation lacks a single-valuedinverse. This is known as a logic OR gate and isirreversible. Thus the Central Dogma is a theorem incoding theory and the logic of the genetic communi-cation system. It does not come from biochemistry. Inthe full glory of its mathematical generality it appliesto all codes where the information entropy of the

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source alphabet is larger than that of the receiveralphabet (Yockey, 1992).

Elitzur is confused on this point for, after quotingmy explanation of the Central Dogma he writes:‘‘While this argument is a step in the right direction, itmust be generalized; the Central Dogma must holdeven if the ‘‘source alphabet’’ has the same number ofsymbols as the ‘‘receiving alphabet’.’’ This is just whatI had written and required no generalization. It isobvious that if the source and receiver alphabets havethe same number of symbols, the logic operation hasa single valued inverse and information may be passed,without loss, in either direction. Thus, since RNA andDNA both have a four letter alphabet, geneticmessages may be passed from RNA to DNA. Thepassage of information from protein to RNA or DNAis prohibited for two reasons, (i) the logic OR gate isirreversible and (ii) there is not enough information inthe protein sequence to determine the mRNA sequencefrom which it is translated.

There are a number of other mistakes and blundersin Elitzur’s paper that I shall deal with briefly:

‘‘They all possess the same genetic code.’’ Themitochondrial genetic codes that differ from thestandard genetic code are well known (Yockey, 1992;Osawa et al., 1992). ‘‘For most scientists, as has beennoted, the preference exhibited by all living forms forL-amino acids and D-sugars is due to a merecoincidence in the appearance of the ancestor of allorganisms (Eigen, 1992; Shapiro, 1986).’’ Elitzur isunaware of the fact that the genetic information systemis capable of forming D amino acids and placing themin specified locations in antibiotics. This can hardly be‘‘due to a mere coincidence’’.

Elitzur is at odds with his mentor Manfred Eigenwhen he says (p. 430): ‘‘As this paper intends to show,it is the Second Law of Thermodynamics itself thatenables that most satisfactory explanation of evol-ution.’’ On the contrary, Eigen and Schuster (1977)wrote: ‘‘In physics we know of principles which cannotbe reduced to any more fundamental laws. As axioms,they are abstracted from experience, their predictionsbeing consistent with the consequences that can besubjected to experimental test. Typical examples arethe first and second law of thermodynamics. Darwin’sprinciple of natural selection does not fall into thecategory of first principles.’’ (p. 546).

This letter does not exhaust the errors andmisstatements in Elitzur’s paper, those in his review(Elitzur, 1993) or the review by Lifson (1994) ofYockey (1992). Some of these comments are publishedin BioEssays (1995) in reply to a review by Lifson(1994). I suggest the reader compare the material

in Elitzur’s paper, those in his review and that of Lifsonwith the correct discussion in Yockey (1992).

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