From: Avshalom Elitzur <CFELI@WEIZMANN.weizmann.ac.il>
Newsgroups: bionet.info-theory
Subject: Book Reviews of Information Theory and Molecular Biology
Date: 31 Jan 1995 17:00:58 -0000
Lines: 149
Sender: lpddist@mserv1.dl.ac.uk
Distribution: bionet
Message-ID: <3glqca$pof@mserv1.dl.ac.uk>
Original-To: bio-info@dl.ac.uk
I was pleased to read the posting by Professor Hubert P. Yockey, author
of "Information Theory and Molecular Biology" (1992). He commented on
some reviews of his book, among them one by me (1994b). The passages he
quoted indicate my appreciation of his many-years work. As he has nearly
guessed, I was only one year old when his 1958 contribution was
published. However, I do not qualify for "professor" yet.
I would like to address one point of disagreement between Yockey and me,
not resolved even after our private correspondence, that constitutes the
core of the entire argument.
Yockey repeatedly argues that the HIGHER an organism is on the
evolutionary scale, the greater its ENTROPY. This was the main target of
my criticism (1994), as well as the criticism in Tom Schneider's
illuminatig posting. I argue, as most people do, that evolution produces
more and more ORDERED organisms; that man is a more ordered system than a
bacterium. Yockey dismisses this as mere confusion between unrelated
terms. For him, organisms possess only "complexity," a term that he
defines, following Chaitin, by the length of the algorithm needed to
describe the system in question. Yockey claims that a complex system
resembles a disordered system in that both require long algorithms. I
shall refer to this claim as the "complexity=entropy equation."
At first sight, Yockey seems to have a point. An ordered sequence like
1,1,1,... or 1,2,3,... can indeed be compressed into a simple algorithm,
while a completely random sequence requires an algorithm as long as the
sequence itself. Clearly, living organisms require long algorithms, and
the more advanced and "high" the organism, the longer is the respective
algorithm. This is, then, Yockey's argument: Evolution is characterized
by an increase of the organisms' complexity AS WELL AS their entropy.
However, this argument cannot stand a closer inspection. Complexity,
while not synonymous with order, is by no means its opposite. Complexity
means correlations between the system's different components, a state
that sharply deviates from randomness. You don't expect a complex system
-- i.e. a system whose various components manifest dependence or
correspondence to one another -- to be formed by chance alone. Also,
complexity has its thermodynamic cost; more energy is needed to create a
complex system than to create a disordered one. Complexity is therefore
more akin to "order" than to "entropy." Yockey fell into a sorry trap by
failing to make these distinctions.
A few observations on living organisms will make it clear why the living
state is characterized by low entropy and not, as Yockey so obstinately
insists, by high entropy. Being alive means being far from equilibrium.
An organism begins to approach equilibrium with its surroundings only
when it dies. Also, being alive is thermodynamically costly: energy is
dissipated and the environment's entropy always increases as long as the
organism is alive. These are unmistakable characteristics of order, not
of entropy.
Now let us examine the organism's complexity in terms of the above
criterion. Every organism manifests strict correlations between its
parts. If you know the sequence of the DNA residing in an organism's
single cell, you know the sequence of the DNA of all that organism's
cells. If you know the shape of a plant's single leaf, you know the
shape of all other leaves. And if you have seen an animal's right side,
you know how its left side looks like as well. All these correlations
considerably shorten the algorithm describing an organism. The basic
fault in Yockey's entropy=complexity equation is therefore this: These
correlations can be measured by probabilistic terms just as order is
measured. Just ask what is the probability for a system's component A to
have value x, given that component B has value y. Complexity thus
deviates from randomness, thereby being much more akin to order than to
entropy.
But the best argument against the complexity=entropy equation is supplied
by Yockey's very subject-matter, the DNA! Take a living organism, measure
its microstate, namely, the precise position of all its molecules. Then
take a dead, decomposed organism and measure its microstate too. Now try
to produce two systems identical in all their microstates to the living
and the decomposed organism. Which task is easier? In order to replicate
even roughly the decomposed organism you have to know the precise state
of each molecule, while it is much easier to replicate much more
accurately the living organism, just by extracting from it a single DNA
strand! Thus, the very criterion used by Yockey to define biological
complexity speaks against his complexity=entropy equation.
Lila Gatlin (1972), has written a brilliant book that Yockey (private
communication) dismisses and did not consider worthy of discussion in his
book. She referred to the increasing complexity of organisms through
evolution as an increase of information. Admittedly, introducing the
term "information" in this context might give rise to some additional
difficulties, so I shall use the better-defined term "complexity" instead
(see, however, Schneider's careful handling of the term in his reply to
Yockey). But regardless of these caveats, Gatlin's method is worth
taking up. She characterizes the increasing complexity along the
evolutionary tree by two parameters of deviation from randomness: D1
denotes deviation from equiprobability (say, the probability for each
amino-acid to be A, T, C, or G), and D2 denotes deviation from
independence (say, the probability for one amino-acid to be A, given that
the next one is C). Gatlin has shown that evolution has gradually
shifted from D1 to D2. It is this D2, pointed out above in my discussion
of correlations, that is the more fundamental characteristic of
biological order. It can be measured, objectively and precisely. It is
NOT entropy.
Yockey has never seriously addressed these arguments. Instead, he
repeatedly resorts to the same formalistic objections: "There is no
relation between Shannon entropy in information theory and
Maxwell-Boltzmann-Gibbs entropy in statistical mechanics," and "the
concept of entropy in classical thermodynamics is different from that in
statistical mechanics and from that in information theory." As Schneider
has shown in his last posting, this argument is flawed in itself. In the
present context it can hardly be a satisfactory reply to the questions
raised here. Present shortcomings of the formalism alone can never
suffice against simple physical, common-sense arguments.
Let me close by pointing out the general misgiving I have against
Yockey's book. While reach and illuminating, its bottom-line is highly
nihilistic. The impression of information theory emerging from Yockey's
book is that of a purely technical tool, hardly interesting for the
biologist. While offering detailed analyses of DNA sequences, Yockey
dismisses any attempt to go beyond that. In contrast, numerous other
authors, from Schrodinger to Eigen (see Elitzur 1994a, 1995 for reviews),
have pointed out several exciting aspects of thermodynamics and
information theory that make them relevant for biology. Especially,
evolution has been studied as a process by which organisms accumulate
more and more information about their environment. The central notion of
evolutionary theory, namely, adaptation, can thus be substantiated on the
more basic physical notions of entropy and information.
One more comment concerning another of Yockey's critics, Schneior Lifson,
to whom I am indebted for having initiated me into this fascinating
topic. Yockey refers the readers to his reply to Lifson, to be published
in BioEssays. I would like to refer the readers also to Lifson's
counter-reply, to be published in the next issue. Indeed, Yockey should
be commended for having stirred such a lively debate.
Avi Elitzur
Chemical Physics Department
The Weizmann Institute of Science
76100 Rehovot, Israel.
REFERENCES
Elitzur, A. C. (1994a) Let there be life: Thermodynamic reflections
on biogenesis and evolution. _Journal of Theoretical Biology_, 168:
429--459.
--- (1994b) The origin of life. _Contemporary Physics_, 34: 275--278.
--- (1995) Life and mind, past and future: Schrodinger's vision fifty
years later. _Perspectives in Biology and Medicine_, 38, in press.
Gatlin, L. (1972) _Information Theory and the Living System._
New York: Columbia University Press.
Yockey, H. P. (1992) _ Information Theory and Molecular Biology._
Cambridge: Cambridge University Press.
======================================================================
========================
Brian Harper |
Associate Professor | "It is not certain that all is uncertain,
Applied Mechanics | to the glory of skepticism" -- Pascal
Ohio State University |
========================