A Second Look at the Second Law
Mathematics Dept.
In the current debate over "Intelligent Design," the strongest argument
offered by opponents of design is this: we have scientific explanations
for most everything else in Nature, what is special about evolution?
The layman understands quite well that explaining the appearance of
human brains is a very different sort of problem from finding the
causes of earthquakes; however, to express this difference in terms a
scientist can understand requires a discussion of the second law of
thermodynamics.
The first formulations of the second law were all about heat: a quantity
called thermal "entropy" was defined to measure the randomness, or disorder,
associated with a temperature distribution, and it was shown that in an isolated
system this entropy always increases, or at least never decreases, as the temperature
becomes more and more randomly (more uniformly) distributed. If we define
thermal "order" to be the opposite (negative) of thermal entropy, we can say that
the thermal order can never increase in a closed (isolated) system. However, it
was soon realized that other types of order can be defined which also never
increase in a closed system, for example, we can define a "carbon order"
associated with the distribution of carbon diffusing in a solid, using the
same equations, and through an identical analysis show that this order also
continually decreases, in a closed system. With time, the second law came to
be interpreted more and more generally, and today most discussions of the
second law in physics textbooks offer examples of entropy increases (or order
decreases, since we are defining order to be the opposite of entropy) which
have nothing to do with heat conduction or diffusion, such as the shattering
of a wine glass or the demolition of a building. For example, in
Basic Physics [Blaisdell Publishing Co., 1968] Kenneth Ford writes:
Imagine a motion picture of any scene of ordinary life run backward. You might
watch...a pair of mangled automobiles undergoing instantaneous repair
as they back apart. Or a dead rabbit rising to scamper backward into
the woods as a crushed bullet re-forms and flies backward into a rifle while
some gunpowder is miraculously manufactured out of hot gas. Or something
as simple as a cup of coffee on a table gradually becoming warmer as it
draws heat from its cooler surroundings. All of these backward-in-time
views and a myriad more that you can quickly think of are ludicrous and
impossible for one reason only--they violate the second law of thermodynamics.
In the actual scene of events, entropy is increasing. In the time reversed
view, entropy is decreasing.
It is a well-known prediction of the second law that, in a closed system,
every type of order is unstable and must eventually decrease, as everything
tends toward more probable states. Natural forces, such as corrosion,
erosion, fire and explosions, do not create order, they destroy it.
S. Angrist and L. Hepler, in Order and Chaos [Basic Books, 1967],
write, "An arsonist working on a big library is merely
speeding up the inevitable result demanded by the second law."
The second law is all about probability, it uses probability at the
microscopic level to predict macroscopic change: carbon distributes
itself more and more uniformly in an insulated solid because this is
what the laws of probability predict, when diffusion alone is operative.
The reason natural forces may turn a spaceship, or a TV set, or a
computer into a pile of rubble but not vice-versa is also probability:
of all the possible arrangements atoms could take, only a very small
percentage could fly to the moon and back, or receive pictures and
sound from the other side of the Earth, or add, subtract, multiply and
divide real numbers with high accuracy. The second law of thermodynamics
is the reason that computers will degenerate into scrap metal over time,
and, in the absence of intelligence, the reverse process will not occur;
and it is also the reason that animals, when they die, decay into simple
organic and inorganic compounds, and, in the absence of intelligence, the
reverse process will not occur.
The discovery that life on Earth developed through evolutionary
"steps," coupled with the observation that mutations and natural
selection -- like other natural forces -- can cause (minor) change, is
widely accepted in the scientific world as proof that natural selection
-- alone among all natural forces -- can create order out of disorder,
and even design human brains, with human consciousness. Only the layman
seems to see the problem with this logic. And where is the overwhelming
evidence that justifies not only believing that natural selection can
design human brains, but justifies branding as "anti-science" anyone
who doubts that it can? In his new book, The Edge of Evolution ,
[Free Press, 2007], Lehigh University biochemist Michael Behe looks in
considerable detail at the struggle for survival between humans and the
malaria parasite where, in the last 100 years, the evolution of more
organisms, and not many fewer generations, can be studied than were
involved in the entire natural history of mammals. He finds that natural
selection can be credited with some very minor change, but "Far and away
the most extensive relevant data we have on the subject of evolution's
effects on competing organisms is that accumulated on interactions between
humans and our parasites. As with the example of malaria, the data show
trench warfare, with acts of desperate destruction, not arms races, with
mutual improvements. The thrust and parry of human malaria evolution did
not build anything--it only destroyed things."
In a recent Mathematical Intelligencer article
["A Mathematician's View of Evolution,"
The Mathematical Intelligencer 22, number 4, 5-7, 2000]
I asserted that the idea that the four fundamental forces of physics
alone could rearrange the fundamental particles of Nature into
spaceships, nuclear power plants, and computers, connected to laser
printers, CRTs, keyboards and the Internet, appears to violate the second
law of thermodynamics in a spectacular way.1 Anyone
who has made such an argument is familiar with the standard reply:
the Earth is an open system, it receives energy from the sun, and order can
increase in an open system, as long as it is "compensated" somehow by a
comparable or greater decrease outside the system. S. Angrist and L. Hepler,
for example (again in Order and Chaos ) write, "In a certain sense the
development of civilization may appear contradictory to the second law....
Even though society can effect local reductions in entropy, the general and
universal trend of entropy increase easily swamps the anomalous but
important efforts of civilized man. Each localized, man-made or
machine-made entropy decrease is accompanied by a greater increase in
entropy of the surroundings, thereby maintaining the required increase
in total entropy."
According to this reasoning, then, the second law does not prevent
scrap metal from reorganizing itself into a computer in one room, as
long as two computers in the next room are rusting into scrap metal --
and the door is open. (Or the thermal entropy in the next room is
increasing--though I'm not sure what the conversion rate is between computers
and thermal entropy.) This strange argument of "compensation" makes
no sense logically: an extremely improbable event is not rendered
less improbable by the occurrence of other events which are more
probable. To understand where this argument of compensation comes
from, one needs to understand that of the example applications
mentioned in the Ford text above, the coffee cup example is special:
the application to heat conduction is special not only because it was
the first application, but because it is quantifiable. It is commonly
used as the "model" problem on which our thinking about the other, less
quantifiable, applications is based. The fact that thermal order cannot
increase in a closed system, but can increase in an open system, was
used to conclude that, in other applications, anything can happen in
an open system as long as it is compensated by order decreases outside
this system, so that the total "order" in the universe (or any closed
system containing the open system) still decreases.
In Appendix D of my new book The Numerical Solution of Ordinary and
Partial Differential Equations, Second Edition [John Wiley & Sons,
2005], I take a closer look at the equations for entropy change, which apply
not only to thermal entropy but also to the entropy associated with anything
else that diffuses, and show that they do not simply say that
order cannot increase in a closed system, they also say that in an
open system, order cannot increase faster than it is imported through
the boundary. According to these equations, the thermal order in an
open system can decrease in two different ways -- it can be converted
to disorder, or it can be exported through the boundary. It can
increase in only one way: by importation through the boundary.
Similarly, the increase in "carbon order" in an open system cannot
be greater than the carbon order imported through the boundary,
and the increase in "chromium order" cannot be greater than the
chromium order imported through the boundary, and so on.
The "compensation" argument was produced by people who generalized
the model equation for closed systems, but forgot to generalize
the equation for open systems. Both equations are only valid for
our simple models, where it is assumed that only heat conduction or
diffusion is going on; naturally in more complex situations, the
laws of probability do not make such simple predictions. Nevertheless,
in "Can ANYTHING Happen in an Open System?,"
[ The Mathematical Intelligencer 23, number 4, 8-10, 2001]
I generalized the equation for open systems to the following tautology,
which is valid in all situations: "If an increase in order is extremely
improbable when a system is closed, it is still extremely improbable
when the system is open, unless something is entering which makes it
not extremely improbable." The fact that
order is disappearing in the next room does not make it
any easier for computers to appear in our room -- unless this order is
disappearing into our room, and then only if it is a type of
order that makes the appearance of computers not extremely improbable,
for example, computers. Importing thermal order will make the
temperature distribution less random, and importing carbon order will
make the carbon distribution less random, but neither makes the
formation of computers more probable.
What happens in a closed system depends on the initial conditions; what
happens in an open system depends on the boundary conditions as well.
As I wrote in "Can ANYTHING Happen in an Open System?",
"order can increase in an open system, not because the laws of probability
are suspended when the door is open, but simply because order may
walk in through the door.... If we found evidence that DNA, auto parts,
computer chips, and books entered through the Earth's atmosphere at
some time in the past, then perhaps the appearance of humans, cars,
computers, and encyclopedias on a previously barren planet could be
explained without postulating a violation of the second law here
(it would have been violated somewhere else!). But if all we see
entering is radiation and meteorite fragments, it seems clear that
what is entering through the boundary cannot explain the increase
in order observed here." Evolution is a movie running backward, that
is what makes it special.
THE EVOLUTIONIST, therefore, cannot avoid the question of probability
by saying that anything can happen in an open system, he is finally
forced to argue that it only seems extremely improbable, but really
isn't, that atoms would rearrange themselves into spaceships and
computers and TV sets.
Darwinists believe they have already discovered the source of all this
order, so let us look more closely at their theory. The traditional
argument against Darwinism is that natural selection cannot guide the
development of new organs and new systems of organs -- i.e., the
development of new orders, classes and phyla -- through their initial
useless stages, during which they provide no selective advantage. Natural
selection may be able to darken the wings of a moth (even this is disputed),
but that does not mean it can design anything complex. French biologist
Jean Rostand [ A Biologist's View, Wm. Heinemann Ltd., 1956],
writes "I believe firmly in the evolution of organic Nature," yet says
It does not seem strictly impossible that mutations should
have introduced into the animal kingdom the differences which
exist between one species and the next...hence it is very
tempting to lay also at their door the differences between
classes, families and orders, and, in short, the whole of
evolution. But it is obvious that such an extrapolation
involves the gratuitous attribution to the mutations of the
past of a magnitude and power of innovation much greater
than is shown by those of today.
Consider, for example, the aquatic bladderwort, described in
Plants and Environment [Daubenmire, John Wiley & Sons, 1947]:
The aquatic bladderworts are delicate herbs that bear bladder-like traps
5mm or less in diameter. These traps have trigger hairs attached to a
valve-like door which normally keeps the trap tightly closed. The sides
of the trap are compressed under tension, but when a small form of
animal life touches one of the trigger hairs the valve opens, the
bladder suddenly expands, and the animal is sucked into the trap. The
door closes at once, and in about 20 minutes the trap is set ready for
another victim.
In a Nature Encyclopedia of Life Sciences [Nature
Publishing Group, 2004] article on Carnivorous Plants, authors
Wolf-Ekkehard Lonnig and Heinz-Albert Becker acknowledge that "it
appears to be hard to even imagine a clearcut selective advantage for
all the thousands of postulated intermediate steps in a gradual
scenario...for the origin of the complex carnivorous plant structures
examined above."
The development of any major new feature presents similar problems, and
according to Lehigh University biochemist Michael Behe, who describes
several spectacular examples in detail in Darwin's Black Box
[Free Press, 1996], the world of microbiology is especially loaded
with such examples of "irreducible complexity."
It seems that until the trigger hair, the door, and the pressurized
chamber were all in place, and the ability to digest small animals, and to
reset the trap to be able to catch more than one animal, had been
developed, none of the individual components of this carnivorous trap
would have been of any use. What is the selective advantage of an
incomplete pressure chamber? To the casual observer, it might seem
that none of the components of this trap would have been of any use
whatever until the trap was almost perfect, but of course a good
Darwinist will imagine two or three far-fetched intermediate useful
stages, and consider the problem solved. I believe you would need
to find thousands of intermediate stages before this example of
irreducible complexity has been reduced to steps small enough to
be bridged by single random mutations -- a lot of things have to
happen behind the scenes and at the microscopic level before this
trap could catch and digest animals. But I don't know how to prove
this. (Lest anyone imagine a lot can be accomplished by single
random mutations, note that if a billion animals each typed one random
character per second throughout the Earth's 4.5 billion year history,
there is virtually no chance any one of them would duplicate a given
20-character string.)
I am furthermore sure that even if you could imagine a long chain of
useful intermediate stages, each would present such a negligible
selective advantage that nothing as clever as this carnivorous trap could
ever be produced, but I can't prove that either. Finally, that natural
selection seems even remotely plausible depends on the fact that while
species are awaiting further improvements, their current complex
structure is "locked in," and passed on perfectly through many generations
(in fact, errors are constantly corrected and damage is constantly
repaired). This phenomenon is observed, but inexplicable -- I don't
see any reason why all living organisms do not constantly decay into
simpler components -- as, in fact, they do as soon as they die.
When you look at the individual steps in the development of life,
Darwin's explanation is difficult to disprove, because some selective
advantage can be imagined in almost anything. Like every other scheme
designed to violate the second law, it is only when you look at the net
result that it becomes obvious it won't work.
A National Geographic article from November 2004 proclaims
that the evidence is "overwhelming" that Darwin was right about
evolution. Since there is no proof that natural selection has ever done
anything more spectacular than cause bacteria to develop drug-resistant
strains, where is the overwhelming evidence that justifies assigning to
it an ability we do not attribute to any other natural force in the
universe: the ability to create order out of disorder?
Three types of evidence are cited: first, the fact that species are so
well suited to their environments is offered as evidence that they have
"adapted" to them. Of course, if they were not well-adapted, they would
be extinct, and that would be offered as even stronger evidence against
design. Second, they point to changes due to artificial selection,
where intelligent humans select features already present in the gene
pool, as evidence of what can be accomplished when natural forces
select among genetic accidents. But, as always, the main evidence
offered is the "evolutionary tree" of similarities connecting all
species, fossil and living. These similarities were of course noticed
long before Darwin (many animals have four legs, one head, two eyes and
a tail!); all modern science has done is to show that the similarities
go much deeper than those noticed by ancient man.
Although these similarities may suggest natural causes, they do not
really tell us anything about what those causes might be. In fact,
the fossil record does not even support the idea that new organs and
new systems of organs arose gradually: new orders, classes and phyla
consistently appear suddenly. For example, Harvard paleontologist
George Gaylord Simpson in "The History of Life" [in Volume I of
Evolution after Darwin, University of Chicago Press, 1960]
writes:
It is a feature of the known fossil record that most taxa appear abruptly.
They are not, as a rule, led up to by a sequence of almost
imperceptibly changing forerunners such as Darwin believed should be
usual in evolution...This phenomenon becomes more universal and more
intense as the hierarchy of categories is ascended. Gaps among known
species are sporadic and often small. Gaps among known orders, classes
and phyla are systematic and almost always large. These peculiarities
of the record pose one of the most important theoretical problems in
the whole history of life: Is the sudden appearance of higher
categories a phenomenon of evolution or of the record only, due to
sampling bias and other inadequacies?
An analogy may be useful here. If some future paleontologist were to
unearth two species of Fords, he might find it plausible that one evolved
gradually from the other through natural causes. He might find the lack
of gradual transitions between automobile families more problematic, for
example, in the transition from mechanical to hydraulic brake systems, or from
manual to automatic transmissions, or from steam engines to internal combustion
engines. He would be even more puzzled by the huge differences between the
bicycle and motor vehicle phyla, or between the boat and airplane phyla. But
if he is a Darwinist, heaven help us when he discovers motorcycles and
Hovercraft, that will constitute spectacular confirmation of his theory
that all forms of transportation arose gradually from a common ancestor,
without design.
Since I am well aware that logic and evidence are powerless against
the popular perception, nurtured by prestigious journals such as
National Geographic and Nature, that no serious scientists
harbor any doubts about Darwinism, I want to offer here a portion of
a November 5, 1980 New York Times News Service report:
Biology's understanding of how evolution works, which has long
postulated a gradual process of Darwinian natural selection acting
on genetic mutations, is undergoing its broadest and deepest
revolution in nearly 50 years.
At the heart of the revolution is something that might seem a paradox.
Recent discoveries have only strengthened Darwin's epochal conclusion that
all forms of life evolved from a common ancestor. Genetic analysis, for
example, has shown that every organism is governed by the same
genetic code controlling the same biochemical processes.
At the same time, however, many studies suggest that the origin of
species was not the way Darwin suggested or even the way most evolutionists
thought after the 1930s and 1940s, when Darwin's ideas were fused with the
rediscovered genetics of Gregor Mendel.
Exactly how evolution happened is now a matter of great controversy among
biologists. Although the debate has been under way for several years, it
reached a crescendo last month, as some 150 scientists specializing in
evolutionary studies met for four days in Chicago's Field Museum
of Natural History to thrash out a variety of new hypotheses that
are challenging older ideas.
The meeting, which was closed to all but a few observers, included nearly
all the leading evolutionists in paleontology, population genetics,
taxonomy and related fields.
No clear resolution of the controversies was in sight. This fact
has often been exploited by religious fundamentalists who misunderstood
it to suggest weakness in the fact of evolution rather than the
perceived mechanism. Actually, it reflects significant progress
toward a much deeper understanding of the history of life on Earth.
At issue during the Chicago meeting was macroevolution, a term that
is itself a matter of debate but which generally refers to the
evolution of major differences, such as those separating species or
larger classifications. Most agree macroevolution is, for example, what
made crustaceans different from mollusks. It is the process by which
birds and mammals evolved out of reptiles. It is also what gave rise to
major evolutionary innovations shared by many groups such as the flower
in higher plants or the eye in vertebrates.
Darwin suggested that such major products of evolution were the results of
very long periods of gradual natural selection, the mechanism that is
widely accepted today as accounting for minor adaptations. These small
variations, considered products of microevolution, account for such things
as the different varieties of finches Darwin found in the Galapagos Islands.
Under human control, or "artificial selection," microevolution has produced
all the varieties of domestic dog, all of which remain members of a
single species.
Darwin, however, knew he was on shaky ground in extending natural selection
to account for differences between major groups of organisms. The fossil
record of his day showed no gradual transitions between such groups, but he
suggested that further fossil discoveries would fill the missing links.
'The pattern that we were told to find for the last 120 years does not exist,'
declared Niles Eldridge, a paleontologist from the American Museum of Natural
History in New York.
Eldridge reminded the meeting of what many fossil hunters have recognized as
they trace the history of a species through successive layers of ancient
sediments. Species simply appear at a given point in geologic time, persist
largely unchanged for a few million years and then disappear. There are very
few examples--some say none--of one species shading gradually into another.
TO FULLY APPRECIATE why such an easily discredited theory is still so widely
accepted today, we need to go back to an old 1888 book Evolution
[D.Appleton & Co., 1888] by Joseph Le Conte, professor of Geology and Natural
History at the University of California,who writes:
Intermediate links may be wanting now, but they must, of course, have existed
once--i.e., in previous geological times, and therefore ought to be found
fossil. In distribution in space or geographically, organic kinds may be
marked off by hard-and-fast lines but, if their derivative origin be true, in
their distribution in time or geologically, there ought to be many examples
of insensible shadings between them. In fact, if we only had all the extinct
forms, the organic kingdom, taken as a whole and throughout all time, ought
to consist not of species at all, but simply of individual forms, shading
insensibly into each other...But this is not the fact. On the contrary, the
law of distribution in time is apparently similar in this respect to the law
of distribution in space, already given. As in the case of contiguous
geographical faunas, the change is apparently by substitution of one species
for another, and not by transmutation of one species into another. So also
in successive geological faunas, the change seems rather by substitution than
by transmutation. In both cases species seem to come in suddenly, with all
their specific characters perfect, remain substantially unchanged as long as
they last, and then die out and are replaced by others. Certainly this looks
much like immutability of specific forms, and supernaturalism of specific
origin...The reason for this, given by Darwin and other evolutionists, is the
extremely fragmentary character of the geological record...While it is true
that there are many and wide gaps in the record...yet there are some cases
where the record is not only continuous for hundreds of feet in thickness,
but the abundance of life was very great, and the conditions necessary for
preservation exceptionally good...and yet, although the species change
greatly, and perhaps many times, in passing from the lowest to the highest
strata, we do not usually, it must be acknowledged, find the gradual
transitions we would naturally expect if the changes were effected by gradual
transformations.
Le Conte also acknowledges that natural selection cannot explain the
appearance of new features:
...neither can it [natural selection] explain the first steps of advance
toward usefulness. An organ must be already useful before natural selection
can take hold of it to improve on it.
After acknowledging that the only direct evidence, the fossil record, does
not support the idea of gradual change, and that the only theory ever taken
seriously as to the causes of these changes cannot explain anything new, Le
Conte nevertheless concludes:
We are confident that evolution is absolutely certain--not evolution as a
special theory--Lamarckian, Darwinian, Spencerian...but evolution as a law
of derivation of forms from previous forms. In this sense it is not only
certain, it is axiomatic ...The origins of new phenomena are often
obscure, even inexplicable, but we never think to doubt that they have a
natural cause; for so to doubt is to doubt the validity of reason, and the
rational constitution of Nature.
SCIENCE HAS BEEN SO SUCCESSFUL in explaining natural phenomena that the
modern scientist is convinced that it can explain everything, and anything
that doesn't fit into this model is simply ignored. It doesn't matter that
there were no natural causes before Nature came into existence, so he cannot
hope to ever explain the sudden creation of time, space, matter and energy and
our universe in the Big Bang. It doesn't matter that quantum mechanics is
based on a "principle of indeterminacy", that tells us that every "natural"
phenomenon has a component that is forever beyond the ability of science to
explain or predict, he still insists nothing is beyond the reach of his
science. When he discovers that all of the basic constants of physics,
such as the speed of light, the charge and mass of the electron, Planck's
constant, etc., had to have almost exactly the values that they do have in
order for any conceivable form of life to survive in our universe, he proposes
the "anthropic principle" [eg, A.J.Leggett, The Problems of Physics,
Oxford University Press, 1987] and says that there must be
many other universes with the same laws, but random values for the basic
constants, and one was bound to get the values right. When you ask him
how a mechanical process such as natural selection could cause human
consciousness to arise out of inanimate matter, he says, "human
consciousness -- what's that?" And he talks about human evolution as if
he were an outside observer, and never seems to wonder how he got
inside one of the animals he is studying. And when you ask how the four
fundamental forces of Nature could rearrange the basic particles of
Nature into libraries full of encyclopedias, science texts and novels,
and computers, connected to laser printers, CRTs and keyboards and the
Internet, he says, well, order can increase in an open system.
The development of life may have only violated one law of science, but
that was the one Sir Arthur Eddington called the "supreme"
law of Nature, and it has violated that in a most spectacular way. At least
that is my opinion, but perhaps I am wrong. Perhaps it only seems
extremely improbable, but really isn't, that, under the right
conditions, the influx of stellar energy into a planet could cause
atoms to rearrange themselves into nuclear power plants and spaceships
and computers. But one would think that at least this would be
considered an open question, and those who argue that it really is
extremely improbable, and thus contrary to the basic principle
underlying the second law, would be given a measure of respect, and
taken seriously by their colleagues, but we aren't.
footnote
1In the original Mathematical Intelligencer article I made the
assertion that the underlying principle behind the second law is that natural
forces do not do extremely improbable things. The journal and I received
several replies arguing that everything Nature does can be considered extremely
improbable---the exact arrangement of atoms at any time at any place is
extremely unlikely to be repeated, noted one e-mail. In another published
reply [Tom Davis, "The Credibility of Evolution," The Mathematical
Intelligencer 23, number 3, 4-5, 2001], the author made an
analogy with coin flipping and argued that any particular sequence of heads
and tails is extremely improbable, so something extremely improbable happens
every time we flip a long series of coins. If a coin were flipped 1000 times,
he would apparently be no more surprised by a string of all heads than by
any other sequence, because any string is as improbable as another. This
critic concedes that it is extremely unlikely that humans and computers would
arise again if history were repeated, "but something would".
Obviously, I should have been more careful with my wording in the first
article: I should have said that the underlying principle behind the second
law is that natural forces do not do macroscopically describable
things which are extremely improbable from the microscopic point of
view. A "macroscopically describable" event is just any event which can be
described without resorting to an atom-by-atom (or coin-by-coin) accounting.
Carbon distributes itself more and more uniformly in an insulated solid
because there are many more arrangements of carbon atoms which produce
nearly uniform distributions than produce highly nonuniform distributions.
Natural forces may turn a spaceship into a pile of rubble, but not
vice-versa---not because the exact arrangement of atoms in a given
spaceship is more improbable than the exact arrangement of atoms in a
given pile of rubble, but because (whether the Earth receives energy
from the Sun or not) there are very few arrangements of atoms which would
be able to fly to the moon and return safely, and very many which could not.
The reader familiar with William Dembski's "specified complexity" concept
[ "The Design Inference," Cambridge Studies in Probability, Induction
and Decision Theory, 2006], will recognize similarities to the argument here:
natural forces do not do things which are "specified" (macroscopically
describable) and "complex" (extremely improbable). Both are just attempts
to state in more "scientific" terms what is already obvious to the layman,
that unintelligent forces cannot do intelligent things.
If we toss a billion coins, it is true that any sequence is as improbable
as any other, but most of us would still be surprised, and suspect that
something other than chance is going on, if the result were "all heads",
or "alternating heads and tails", or even "all tails except for coins
3i+5 , for integer i ". When we produce simply describable
results like these, we have done something "macroscopically" describable
which is extremely improbable. There are so many simply describable results
possible that it is tempting to think that all or most outcomes could be
simply described in some way, but in fact, there are only about
230000 different 1000-word paragraphs, so the odds are about
2999970000 to 1 that a given result will not be that highly
ordered---so our surprise would be quite justified. And if it can't be
described in 1000 English words and symbols, it isn't very simply
describable.
In the real world it is sometimes much harder to say what the laws of
probability predict than in a coin-flipping experiment; thus here it may be
even harder to define and measure order, but sometimes it is easy. In any
case, with 1023 molecules in a mole of anything, we can be confident
that the laws of probability at the microscopic level will be obeyed (at least
on planets without life) as they apply to all macroscopic phenomena;
this is precisely the assumption---the only common thread---behind all
applications of the second law. Everything the second law predicts, it
predicts with such high probability that it is as reliable as any other
law of science---tossing a billion heads in a row is child's play compared
to appreciably violating the second law in any application. One critic
[Jason Rosenhouse, "How Anti-Evolutionists Abuse Mathematics," The
Mathematical Intelligencer 23 , number 4, 3-8, 2001] wrote "His
claim that 'natural forces do not cause extremely improbable things to happen'
is pure gibberish. Does Sewell invoke supernatural forces to explain the
winning numbers in last night's lottery?" But getting the right number on 5 or
6 balls is not extremely improbable, in thermodynamics "extremely improbable"
events involve getting the "right number" on 100,000,000,000,000,000,000,000
or so balls! If every atom on Earth bought one ticket every second since
the big bang (about 1070 tickets) there is virtually no chance
than any would ever win even a 100-ball lottery, much less this one. And
since the second law derives its authority from logic alone, and thus cannot
be overturned by future discoveries, Sir Arthur Eddington called it the
"supreme" law of Nature [The Nature of the Physical World,
McMillan, 1929].
Although it is true that we sometimes are not sure what the second
law predicts, it is not true that there are so many macroscopically
describable phenomena that the second law cannot be expected to hold when
applied to all of them---there are relatively few macroscopically
describable phenomena. It is not true, as the new argument asserts, that
there are so many types of order that computers and TV sets need no
explanation.
A Mathematician's View of Evolution
"Can ANYTHING Happen in an Open System?" -- Appendix D in
"The Numerical Solution of Ordinary and Partial Differential Equations,
Second Edition," John Wiley & Sons, 2005
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