I can't find exactly what you're talking about, but here's some websites with the info. Some of the links from the 2nd site have diagrams:
There is a science called population genetics, and it has mathematical formulae for how quickly favorable genetic changes can spread throughout a population of sexually reproducing creatures. From these formulae, Nilsson and Pelger concluded that the 1829 steps could happen in about 350,000 generations.
In real life, an eye could evolve a little more quickly than that, or more slowly. It would depend on how much the specific creatures were being pressured to change, and on whether vision was relevant to their lifestyle.
If one year equals one generation, then a fairly good eye could evolve in maybe a third of a million years. It is thought that animal life has been on earth for at least 600 million years. That is certainly enough time for eyes to have evolved many times over.
In fact, taxonomists say that eyes have evolved at least 40 different times, and and possibly as many as 65 times. There are 9 different optical principles that have been used in the design of eyes and all 9 are represented more than once in the animal kingdom. Why so many? Well, because there was time.
This is for all those creos who claim there is not enough time for evolution to have occurred.
"To suppose that the eye with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest degree.
Yet reason tells me, that if numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor, can be shown to exist; if further, the eye does vary ever so slightly, and the variations be inherited, which is certainly the case; and if any variation or modification in the organ be ever useful to an animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real. How a nerve comes to be sensitive to light, hardly concerns us more than how life itself first originated; but I may remark that several facts make me suspect that any sensitive nerve may be rendered sensitive to light, and likewise to those coarser vibrations of the air which produce sound."
The impossibility of the evolution of the eye (according to Michael Behe):
What is needed to make a light sensitive spot? What happens when a photon of light impinges on the retina?
When a photon first hits the retina, it interacts with a small organic molecule called II-cis-retinal. The shape of retinal is rather bent, but when retinal interacts with the photon, it straightens out, isomerizing into trans-retinal. This is the signal that sets in motion a whole cascade of events resulting in vision. When retinal changes shape, it forces a change in the shape of the protein rhodopsin, which is bound to it. Now part of the transducin complex dissociates and interacts with a protein called phosphodiesterase, When that happens, the phosphodiesterase acquires the ability chemically to cut a small organic molecule called cyclic-GMP, turning it into 5'-GMP. There is a lot of cyclic-GMP in the cell, and some of it sticks to another protein called an ion channel. Normally the ion channel allows sodium ions into the cell. When the concentration of cyclic-GMP decreases because of the action of the phosphodiesterase, however, the cyclic-GMP bound to the ion channel eventually falls off, causing a change in shape that shuts the channel. As a result, sodium ions can no longer enter the cell, the concentration of sodium in the cell decreases, and the voltage accross the cell membrane changes. That in turn causes a wave of electrical polarization to be sent down the optic nerve to the brain. And when interpreted by the brain, that is vision. So this is what modern science has discovered about how Darwin's 'simple' light sensitive spot functions.
From: Michael Behe, 'Design at the Foundation of Life".
Now which one of the two is science and which one is not?????
The complete quote by Darwin is from The Origin of the Species(Chapter 6 under the heading "Organs of extreme perfection"). The ... second paragraph [below] is the part [creationists] omit.
"Yet reason tells me, that if (SPECULATION) numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor (IMMENSE SPECULATION), can be shown to exist; if further, (SPECULATION) the eye does vary ever so slightly, and (COMPOUND SPECULATION) the variations be inherited, which is certainly the case; (ASSUMED, NOT SHOWN) and if (MORE SPECULATION) any variation or modification in the organ be ever useful to an animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real. (WHOLLY UNWARRANTED CONCLUSION BASED WHOLLY UPON SPECULATION). How a nerve comes to be sensitive to light, hardly concerns us more than how life itself first originated; but I may remark that several facts make me suspect that any sensitive nerve may be rendered sensitive to light, and likewise to those coarser vibrations of the air which produce sound."
This supposedly stunning "proof" of the evolution of the eye, so stunning that "creationists" would pointedly omit it, has been (ANALYSED) by me and it establishes only that Darwin was a Sophist, not that the eye evolved.
But we know this already, don't we?
There follows an except from Gertrude Himmelfarb's Darwin and the Darwinian Revolution, Copyright 1959, Doubleday. The Times Literary Supplement had this to say about the work:
A thorough and masterly book punctuated with a delicate sense of humor ... Until he has read, marked, learnt and inwardly digested this authoritative volume, no one should presume henceforth to speak on Darwin and Darwinism.
We begin at page 333 of the Elephant Paperback edition published in 1996:
"...For his essential method was neither observing nor the more prosaic mode of scientific reasoning, but a peculiarly imaginative, inventive mode of argument.
"In was this that Whewell objected to in the Origin:
For it is assumed that the mere possibility of imagining a series of steps of transition from one condition of organs to another, is to be accepted as a reason for believing that such transition has taken place. And next, that such a possibility being thus imagined, we may assume an unlimited number of generations for the transition to take place in, and that this indefinite time may extinguish all doubt that the transitions really have taken place.
"What Darwin was doing, in effect, was creating a 'logic of possibility'. Unlike conventional logic, where the compound of possibilities results not in a greater possibility, or probability, but in a lesser one, the logic of the Origin was one in which possibilities were assumed to add up to probability.
"Like many revolutionaries, Darwin embarked upon this revolutionary enterprise in the most innocent and reasonable spirit. He started out by granting the hypothetical nature of the theory and went on to defend the use of hypotheses in science, such hypotheses being justified if they explained a sufficiently large number of facts. His own theory, he continued, was 'rendered in some degree probable' by one set of facts and could be tested and confirmed by another -- among which he included the geological succession of organic beings. It was because it 'explained' both of these bodies of facts that it was removed from the status of mere hypothesis and elevated to the rank of 'well-grounded theory'. This procedure, by which one of the major difficulties of the theory was made to bear witness in its favor, can only be accounted for by a confusion in the meaning of 'explain' -- between the sense in which facts are 'explained' by a theory and the sense in which difficulties may be 'explained away'. It is the difference between compliant facts which lend themselves to the theory and refractory ones which do not and can only be brought into submission by a more or less plausible excuse. By confounding the two, both orders of explanation, both orders of fact, were entered on the same side of the ledger, the credit side. Thus the 'difficulties' he had so candidly confessed to were converted into assets.
"This technique for the conversion of possibilities into probabilities and liabilities into assets was the more effective the longer the process went on. In the chapter entitled 'Difficulties on Theory' the solution of each difficulty in turn came more easily to Darwin as he triumphed over -- not simply disposed of -- the preceding one. The reader was put under a constantly mounting obligation; if he accepted one explanation, he was committed to accept the next. Having first agreed to the theory in cases where only some of the transitional stages were missing, the reader was expected to acquiesce in those cases where most of the stages were missing, and finally in those where there was no evidence of stages at all. Thus, by the time of the problem of the eye was under consideration, Darwin was insisting that anyone who had come with him so far could not rightly hesitate to go further. In the same spirit, he rebuked those naturalists who held that while some reputed species were varieties rather than real species, other species were real. Only the 'blindness of preconceived opinion', he held, could make them balk at going the whole way -- as if it was not precisely the propriety of going the whole way that was at issue.
"As possibilities were promoted into probabilities, and the probabilities into certainty, so ignorance itself was raised to a position only once removed from certain knowledge. When imagination exhausted itself and Darwin could devise no hypothesis to explain away a difficulty, he resorted to the blanket assurance that we were too ignorant of the ways of nature to know why one event occurred rathar than another, and hence ignorant of the explanation that would reconcile the facts to his theory..." And so on ...
Darwin was a masterly Sophist and Evolution was gleam in his eye, but that is all.