NILSSON AND Pelger's work is a critic's smorgasbord.Questions are free and
there are second helpings.Every scientific paper must begin somewhere.
Nilsson andPelger begin with their assumption that, with respect to the eye,
morphologicalchange comes about by invagination, aperture constriction, and
lens formation.Specialists may wish to know where those light-sensitive cells
came from and whythere are no other biological structures coordinated with or
contained withinthe interior of the initial patch-for example, blood vessels,
nerves, or bones.But these issues may be sensibly deferred.Not so the issues
that remain. Nilsson and Pelger treat abiological organ as a physical system,
one that is subject to the laws oftheoretical optics. There is nothing amiss
in that. But while theoretical opticsjustifies a qualitative relationship
between visual acuity on the one hand andinvagination, aperture constriction,
and lens formation on the other, therelationships that Nilsson and Pelger
specify are tightly quantitative. Numbersmake an appearance in each of their
graphs: the result, it is claimed, ofcertain elaborate calculations. But no
details are given either in their paperor in its bibliography. The
calculations to which they allude remain out ofsight, if not out of mind.The
1-percent steps: in what units are they expressed? Andhow much biological
change is represented by each step? Nilsson and Pelger donot say. Nor do they
coordinate morphological change, which they treat assimple, with biochemical
change, which in the case of light sensitivity is knownto be monstrously
complex.Does invagination represent a process in which the patchchanges as a
whole, like a balloon being dimpled, or is it the result of variouslocal
processes going off independently as light-sensitive cells jostle with
oneanother and change their position? Are the original light-sensitive cells
thecomplete package, or are new light-sensitive cells added to the ensemble
as timeproceeds? Do some cells lose their sensitivity and get out of the
light-sensingbusiness altogether? We do not know, because Nilsson and Pelger
do not say.Biologists commenting on Darwin's theory have almost alwaysassumed
that evolution reflects what the French biologist Francois Jacob
calledbricolage-a process of tinkering. Biological structures are put
together out ofpieces; they adapt their function to changes in their
circumstances; they getby. This suggests that in the case of eye formation,
morphological change mightwell purchases less visual acuity than Nilsson and
Pelger assume, the eye beingtinkered into existence instead of flogged up an
adaptive peak. But if, say,only half as much visual acuity is purchased for
each of Nilsson and Pelger's1-percent steps, twice as many steps will be
needed to achieve the effect theyclaim. What is their justification for the
remarkably strong assertion thatmorphological transformations purchase an
optimal amount of visual acuity ateach step?Again we do not know, because
they do not say.More questions-and we have not even finished the
horsd'oeuvres. The plausibility of Nilsson and Pelger's paper rests on a
singlenumber: 1,829. But without knowing precisely how the number 1,829 has
beenderived, the reader has no way of determining whether it is reasonable or
evenmeaningful.If nothing else, the number 1,829 represents the maximumpoint
of a curve juxtaposing visual acuity against morphological
transformation.Now, a respect for the ordinary mathematical decencies would
suggest that thecurve is derived from the number, and the number from various
calculations. Butall such calculations are missing from Nilsson and Pelger's
paper. And if thecalculations are not given, neither are any data. Have
Nilsson and Pelger, forexample, verified their estimate, either by showing
that 1,829 1-percent stepsdo suffice to transform a patch into an eye, or by
showing that such an eye may,in 1,829 1-percent steps, be resolved backward
into an initial light-sensitivepatch? Once again, we do not know because they
do not say.Still other questions suggest themselves. Although
naturalselection is mentioned by Nilsson and Pelger, it is a force that plays
no rolein their reasoning. Beyond saying that it "constantly favors an
increase inthe amount of detectable spatial information," they say nothing at
all.This is an ignominious omission in a paper defending Darwinian
principles. Animprovement in visual acuity is no doubt a fine thing for an
organism; but noform of biological change is without cost.Let us agree that
in the development of an eye, an initiallight-sensitive patch in a given
organism becomes invaginated over time. Such achange requires a corresponding
structural change to the organism's anatomy. Ifnothing else, the development
of an eye requires the formation of an eyesocket-- hardly a minor matter in
biological terms. Is it really the case thatan organism otherwise adapted to
its environment would discover that the costsinvolved in the reconstruction
of its skull are nicely balanced by what wouldinitially be a very modest
improvement in sensitivity to light? I can imaginethe argument going either
way, but surely an argument is needed.Then there is Nilsson and Pelger's
data-free way withstatistics. What is the basis of the mathematical values
chosen for the numbersthey use in assessing how rapidly transformation
spreads in a population of eyepatches? The coefficient of variation is the
ratio of the standard deviation tothe mean. The standard deviation, one might
ask, of what? No population figuresare given; there are no quantitative
estimates of any relevant numericalparameter. Why is selection pressure held
constant over the course of 300,000years or so, when plainly the advantages
to an organism of increasing lightsensitivity will change at every step up
the adaptive slope? Why do they calltheir estimates pessimistic (that is,
conservative) rather than wildlyoptimistic?Finally, Nilsson and Pelger offer
an estimate of the numberof steps, computed in 1-percent (actually,
1.00005-percent) intervals, that arerequired to transform their initial
patch. At one point, they convert the stepsinto generations. But a step is
not a temporal unit, and, for all anyone knows,each step could well require
half again or twice the number of generations theysuggest. Why do Nilsson and
Pelger match steps to generations in the way theydo? I have no idea, and they
do not say.WE ARE at last at the main course. Curiously enough, it isthe
intellectual demands imposed by Darwin's theory of evolution that serve
toempty Nilsson and Pelger's claims of their remaining plausibility.Nilsson
and Pelger assert that only 363,992 generations arerequired to generate an
eye from an initial light-sensitive patch. As I havealready observed, the
number 363,992 is derived from the number 80,129,540,which is derived from
the number 1,829-which in turn is derived from nothing atall. Never mind. Let
us accept 1,829 pour le sport. If Nilsson and Pelger intendtheir model to be
a vindication of Darwin's theory, then changes from one stepto another must
be governed by random changes in the model's geometry, followedby some
mechanism standing in for natural selection. These are, after all, thecrucial
features of any Darwinian theory. But in their paper there is no
mentionwhatsoever of randomly occurring changes, and natural selection plays
only aceremonial role in their deliberations.At the beginning of their paper,
Nilsson and Pelger write oftheir initial light-sensitive patch that "we
expose this structure toselection pressure favoring spatial resolution"
(emphasis added), and laterthat "[a]s the lens approaches focused conditions,
selection pressuregradually appears to ... adjust its size to agree with
Mattiesen's ratio"(emphasis added). But whatever Nilsson and Pelger may have
been doing to theirpatch, they have not been exposing it to "selection
pressure." Thepatch does only what they have told it to do. By the same
token, selectionpressures play no role in adjusting the size of their lenses
to agree withMattiesen's ratio. That agreement is guaranteed, since it is
Nilsson and Pelgerwho bring it about, drawing the curve and establishing the
relevant results.What Nilsson and Pelger assume is that natural selection
would track theirresults; but this assumption is never defended in their
paper, nor does it playthe slightest role in their theory.And for an obvious
reason: if there are no random variationsoccurring in their initial
light-sensitive patch, then natural selection hasnothing to do. And there are
no random variations in that patch, their modelsucceeding as a defense of
Darwin's theory only by first emptying the theory ofits content.An example
may make clearer both the point and itsimportance. Only two steps are
required to change the English word"at" to the English word "do": "at" to
"ao"and "ao" to "do." The changes are obvious: they have beendesigned to
achieve the specified effect. But such design is forbidden inDarwinian
theory. So let us say instead, as Darwin must, that letters are
chosenrandomly, for instance by being fished from an urn. In that case, it
will take,on average, 676 changes (26 letters times 26) to bring about the
same two steps.Similarly, depending on assessments of probability, thenumber
of changes required to bring about a single step in Nilsson and
Pelger'stheory may range widely. It may, in fact, be anything at all. How
long would ittake to transform a light-sensitive patch into a fully
functioning eye? It alldepends. It all depends on how likely each
morphological change happens to be.If cells in their initial light-sensitive
patch must discover their appointedrole by chance, all estimates of the time
required to bring about just thetransformations their theory
demands-invagination, aperture construction, andlens formation-- will
increase by orders of magnitude.If Darwin were restored to pride of place in
Nilsson andPelger's work, the brief moment involved in their story would
stretch on and onand on.FINALLY, THERE is the matter of Nilsson and Pelger's
computersimulation, in many ways the gravamen of my complaints and the
dessert of thisdiscussion.A computer simulation of an evolutionary process is
not amysterious matter. A theory is given, most often in ordinary
mathematicallanguage. The theory's elements are then mapped to elements that
a computer canrecognize, and its dynamical laws, or laws of change, are
replicated at adistance by a program. When the computer has run the program,
it has simulatedthe theory.Although easy to grasp as a concept, a computer
simulationmust meet certain nontrivial requirements. The computer is a harsh
taskmaster,and programming demands a degree of specificity not ordinarily
required of amathematical theory. The great virtue of a computer simulation
is that if theset of objects is large, and the probability distribution and
fitness functioncomplicated, the computer is capable of illustrating the
implications of thetheory in a way that would be impossible using ordinary
methods of calculation."Hand calculations may be sufficient for very simple
models," asRobert E. Keen and James Spain write in their standard text,
Computer Simulationin Biology (1992), "but computer simulation is almost
essential forunderstanding multi-component models and their complex
interrelationships."Whatever the merits of computer simulation, however, they
arebeside the point in assessing Nilsson and Pelger's work. In its six pages,
theirpaper contains no mention of the words "computer" or"simulation." There
are no footnotes indicating that a computersimulation of their work exists,
and their bibliography makes no reference toany work containing such a
simulation.Curious about this point, I wrote to Dan-Erik Nilsson in thelate
summer of 2001. "Dear David," he wrote back courteously and atonce,You are
right that my article with Pelger is not based oncomputer simulation of eye
evolution. I do not know of anyone else who [has]successfully tried to make
such a simulation either. But we are currentlyworking on it. To make it
behave like real evolution is not a simple task. Atpresent our model does
produce eyes gradually on the screen, but it does notlook pretty, and the
genetic algorithms need a fair amount of work before themodel will be useful.
But we are working on it, and it looks both promising andexciting.These are
explicit words, and they are the words of thepaper's senior author. I urge
readers to keep them in mind as we return to theluckless physicist Matt
Young. In my COMMENTARY essay of last December, I quotedthese remarks by Mr.
Young:Creationists used to argue that ... there was not enough timefor an eye
to develop. A computer simulation by Dan-Erik Nilsson and SusannePelger gave
the lie to that claim.These, too, are forthright words, but as I have just
shown,they are false: Nilsson and Pelger's paper contains no computer
simulation, andno computer simulation has been forthcoming from them in all
the years since itsinitial publication. Sheer carelessness, perhaps? But now,
in responding to myCOMMENTARY article, Matt Young has redoubled his
misreading and proportionatelyaugmented his indignation. The full text of his
remarks appears in last month'sCOMMENTARY; here are the relevant passages:In
describing the paper by Nilsson and Pelger..., I wrotethat they had performed
a computer simulation of the development of the eye. Idid not write, as Mr.
Berlinski suggests, that they used nothing more thanrandom variation and
natural selection, and I know of no reference that saysthey did....The paper
by Nilsson and Pelger is a sophisticatedsimulation that even includes quantum
noise; it is not, contrary to Mr.Berlinski's assertion, a
back-of-the-envelope calculation. It begins with aflat, light-sensitive
patch, which they allow to become concave in increments of1 percent,
calculating the visual acuity along the way. When some othermechanism will
improve acuity faster, they allow, at various stages, theformation of a
graded-index lens and an iris, and then optimize the focus.Unless Nilsson and
Pelger performed the calculations in closed form or by hand,theirs was, as I
wrote, a "computer simulation." Computer-aidedsimulation might have been a
slightly better description, but not enough tojustify Mr. Berlinski's sarcasm
at my expense....And here is my familiar refrain: there is no
simulation,"sophisticated" or otherwise, in Nilsson and Pelger's paper, and
theirwork rests on no such simulation; on this point, Nilsson and I are in
completeagreement. Moreover, Nilsson and Pelger do not calculate the visual
acuity ofany structure, and certainly not over the full 1,829 steps of their
sequence.They suggest that various calculations have been made, but they do
not show howthey were made or tell us where they might be found. At the very
best, they havemade such calculations for a handful of data points, and then
joined thosepoints by a continuous curve.There are two equations in Nilsson
and Pelger's paper, andneither requires a computer for its solution; and
there are no others. Usingprocedures very much like Nilsson and Pelger's own,
Mr. Young has neverthelessdeduced the existence of a missing computer
simulation on theoretical grounds:"Unless Nilsson and Pelger performed the
calculations in closed form or byhand, theirs was, as I wrote, a computer
simulation." But anotherpossibility at once suggests itself: that Nilsson and
Pelger did not require acomputer simulation to undertake their calculations
because they made no suchcalculations, their figure of 1,829 steps
representing an overall guess based onthe known optical characteristics of
existing aquatic eyes.Whatever the truth-and I do not know it-Mr. Young's
inferenceis pointless. One judges a paper by what it contains and one trusts
an author bywhat he says. No doubt Matt Young is correct to observe
that"computer-aided simulation might have been a better description"
ofNilsson and Pelger's work. I suppose one could say that had Dan-- Erik
Nilssonand Susanne Pelger rested their heads on a computer console while
trying toguess at the number of steps involved in transforming a
lightsensitive patchinto a fully functioning eyeball, their work could also
be represented ascomputer-- aided.MATT YOUNG is hardly alone in his lavish
misreadings. Themathematician Ian Stewart, who should certainly know better,
has made virtuallythe same patently false claims in Nature's Numbers (1995).
So have many otherprominent figures.3 But misreadings are one thing,
misrepresentations another.More than anyone else, it has been Richard Dawkins
who has been responsible foractively misrepresenting Nilsson and Pelger's
work, and for disseminatingworldwide the notion that it offers a triumphant
vindication of Darwinianprinciples.In a chapter of his 1995 book, River Out
of Eden, Dawkinswrites warmly and at length about Nilsson and Pelger's
research.4 Here is whathe says (emphasis added throughout):[Their] task was
to set up computer models of evolving eyesto answer two questions ... [:] is
there a smooth gradient of change, from flatskin to full camera eye, such
that every intermediate is an improvement? ...[and] how long would the
necessary quantity of evolutionary change take?In their computer models,
Nilsson and Pelger made no attemptto simulate the internal workings of
cells.... Nilsson and Pelger began with a flat retina atop a flatpigment
layer and surmounted by a flat, protective transparent layer. Thetransparent
layer was allowed to undergo localized random mutations of itsrefractive
index. They then let the model tramform itself at random, constrainedonly by
the requirement that any change must be small and must be an improvementon
what went before.The results were swift and decisive. A trajectory of
steadilymounting acuity led unhesitatingly from the flat beginning through a
shallowindentation to a steadily deepening cup, as the shape of the model eye
deformeditself on the computer screen.... And then, almost like a conjuring
trick, aportion of this transparent filling condensed into a local, spherical
region ofhigher refractive index.... This ratio is called Mattiessen's ratio.
Nilsson andPelger's computer-simulation model homed in unerringly on
Mattiessen's ratio.How very remarkable all this is-inasmuch as there are
nocomputer models mentioned, cited, or contained in Nilsson and Pelger's
paper;inasmuch as Dan-Erik Nilsson denies having based his work on any
computersimulations; inasmuch as Nilsson and Pelger never state that their
task was to"set up computer models of evolving eyes" for any reason
whatsoever;inasmuch as Nilsson and Pelger assume but do not prove the
existence of "asmooth gradient of change, from flat skin to full camera eye,
such that everyintermediate is an improvement"; and inasmuch as the
originallight-sensitive patch in Nilsson and Pelger's paper was never allowed
to undergo"localized random mutations of its refractive index."And how very
remarkable again-inasmuch as there are nocomputer "screens" mentioned or
cited by Nilsson and Pelger, noindication that their illustrations were
computer-generated, and no evidencethat they ever provided anyone with a
real-time simulation of their paper whereone could observe, "almost like a
conjuring trick," the "swiftand decisive" results of a process that they also
happen to have designed.And yet again how very remarkable-inasmuch as Nilsson
andPelger's "computer-simulation model" did not home in unerringly
onMattiessen's ratio, Nilsson and Pelger having done all the homing
themselves andthus sparing their model the trouble.Each and every one of
these very remarkable asseverations canbe explained as the result of
carelessness only if one first indicts theirauthor for gross
incompetence.FINAL QUESTIONS. Why, in the nine years since their
workappeared, have Nilsson and Pelger never dissociated themselves from
claims abouttheir work that they know are unfounded? This may not exactly be
dishonest, butit hardly elicits admiration. More seriously, what of the
various masters ofindignation, those who are usually so quick to denounce
critics of Darwin'stheory as carrying out the devil's work? Eugenie Scott,
Barbara Forrest,Lawrence Krauss, Robert T. Pennock, Philip Kitcher, Kelly
Smith, Daniel Dennett,Paul Gross, Ken Miller, Steven Pinker-they are all warm
from combat. Why havethey never found reason to bring up the matter of the
mammalian eye and thecomputer simulation that does not exist?And what should
we call such a state of affairs? I suggestthat scientific fraud will do as
well as any other term.[Footnote]
1 "A Pessimistic Estimate of the Time Required for an Eye to Evolve,"
Proceedings of the Royal Society, London B (1994) 256, 53-- 58. In my essay I
twice misspelled Susanne Pelger's name, for which I apologize.

2 A graded-index lens is a lens that is not optically homogeneous; the figure
of 1.52 is "the value close to the upper limit for biological material."

3 Among those who, by contrast, have raised (on the Internet) points similar
to my own, I would single out especially Brian Harper, a professor of
mechanical engineering at Ohio State University.
 4 A version of the same material by Dawkins, "Where D'you Get Those
Peepers," was published in the New Statesman (July 16, 1995).

[Author note]
DAVID BERLINSKI is the author of A Tour of the Calculus, The Advent of the
Algorithm, and Newton's Gift. His new book, Secrets of the Vaulted Sky, is
forthcoming from Harcourt later this year.

John Landon
Website for
World History and the Eonic Effect