In their computer models, Nilsson and Pelger made no attempt to simulate the internal workings of cells. They started their story after the invention of a single light-sensitive cell – it does no harm to call it a photocell. It would be nice, in the future, to do another computer model, this time at the level of the inside of the cell, to show how the first living {80} photocell came into being by step-by-step modification of an earlier, more general-purpose cell. But you have to start somewhere, and Nilsson and Pelger started after the invention of the photocell. They worked at the level of tissues: the level of stuff made of cells rather than the level of individual cells. Skin is a tissue, so is the lining of the intestine, so is muscle and liver. Tissues can change in various ways under the influence of random mutation. Sheets of tissue can become larger or smaller in area. They can become thicker or thinner. In the special case of transparent tissues like lens tissue, they can change the refractive index (the light-bending power) of local parts of the tissue.

The beauty of simulating an eye, as distinct from, say, the leg of a running cheetah, is that its efficiency can be easily measured, using the laws of elementary optics. The eye is represented as a two-dimensional cross section, and the computer can easily calculate its visual acuity, or spatial resolution, as a single real number. It would be much harder to come up with an equivalent numerical expression for the efficacy of a cheetah's leg or backbone. Nilsson and Pelger began with a flat retina atop a flat pigment layer and surmounted by a flat, protective transparent layer. The transparent layer was allowed to undergo localized random mutations of its refractive index. They then let the model deform itself at random, constrained only by the requirement that any change must be small and must be an improvement on what went before.

The results were swift and decisive. A trajectory of steadily mounting acuity led unhesitatingly from the flat beginning through a shallow indentation to a steadily deepening cup, as the shape of the model eye deformed itself on the computer screen. The transparent layer thickened to fill {81} the cup and smoothly bulged its outer surface in a curve. And then, almost like a conjuring trick, a portion of this transparent filling condensed into a local, spherical subre-gion of higher refractive index. Not uniformly higher, but a gradient of refractive index such that the spherical region functioned as an excellent graded-index lens. Graded-index lenses are unfamiliar to human lensmakers but they are common in living eyes. Humans make lenses by grinding glass to a particular shape. We make a compound lens, like the expensive violet-tinted lenses of modern cameras, by mounting several lenses together, but each one of those individual lenses is made of uniform glass through its whole thickness. A graded-index lens, by contrast, has a continuously varying refractive index within its own substance. Typically, it has a high refractive index near the center of the lens. Fish eyes have graded-index lenses. Now it has long been known that, for a graded-index lens, the most aberration-free results are obtained when you achieve a particular theoretical optimum value for the ratio between the focal length of the lens and the radius. This ratio is called Mattiessen's ratio. Nilsson and Pelger's computer model homed in unerringly on Mattiessen's ratio.

And so to the question of how long all this evolutionary change might have taken. In order to answer this, Nilsson and Pelger had to make some assumptions about genetics in natural populations. They needed to feed their model plausible values of quantities such as “heritability.” Heritability is a measure of how far variation is governed by heredity. The favored way of measuring it is to see how much monozygotic (that is, “identical”) twins resemble each other compared with ordinary twins. One study found the heritability of leg {82} length in male humans to be 77 percent. A heritability of 100 percent would mean that you could measure one identical twin's leg to obtain perfect knowledge of the other twin's leg length, even if the twins were reared apart. A heritability of 0 percent would mean that the legs of monozygotic twins are no more similar to each other than to the legs of random members of a specified population in a given environment. Some other heritabilities measured for humans are 95 percent for head breadth, 85 percent for sitting height, 80 percent for arm length and 79 percent for stature.

Heritabilities are frequently more than 50 percent, and Nilsson and Pelger therefore felt safe in plugging a heritability of 50 percent into their eye model. This was a conservative, or “pessimistic,” assumption. Compared with a more realistic assumption of, say, 70 percent, a pessimistic assumption tends to increase their final estimate of the time taken for the eye to evolve. They wanted to err on the side of overestima-tion because we are intuitively skeptical of short estimates of the time taken to evolve something as complicated as an eye.

For the same reason, they chose pessimistic values for the coefficient of variation (that is, for how much variation there typically is in the population) and the intensity of selection (the amount of survival advantage improved eyesight confers). They even went so far as to assume that any new generation differed in only one part of the eye at a time: simultaneous changes in different parts of the eye, which would have greatly speeded up evolution, were outlawed. But even with these conservative assumptions, the time taken to evolve a fish eye from flat skin was minuscule: fewer than four hundred thousand generations. For the kinds of small animals we are talking about, we can assume one generation per year, so {83} it seems that it would take less, than half a million years to evolve a good camera eye.

In the light of Nilsson and Pelger's results, it is no wonder “the” eye has evolved at least forty times independently around the animal kingdom. There has been enough time for it to evolve from scratch fifteen hundred times in succession within any one lineage. Assuming typical generation lengths for small animals, the time needed for the evolution of the eye, far from stretching credulity with its vastness, turns out to be too short for geologists to measure! It is a geological blink.

Do good by stealth. A key feature of evolution is its gradu-alness. This is a matter of principle rather than fact. It may or may not be the case that some episodes of evolution take a sudden turn. There may be punctuations of rapid evolution, or even abrupt macromutations – major changes dividing a child from both its parents. There certainly are sudden extinctions – perhaps caused by great natural catastrophes such as comets striking the earth – and these leave vacuums to be filled by rapidly improving understudies, as the mammals replaced the dinosaurs. Evolution is very possibly not, in actual fact, always gradual. But it must be gradual when it is being used to explain the coming into existence of complicated, apparently designed objects, like eyes. For if it is not gradual in these cases, it ceases to have any explanatory power at all. Without gradualness in these cases, we are back to miracle, which is simply a synonym for the total absence of explanation.

The reason eyes and wasp-pollinated orchids impress us so is that they are improbable. The odds against their spontaneously assembling by luck are odds too great to be borne in {84} the real world. Gradual evolution by small steps, each step being lucky but not too lucky, is the solution to the riddle. But if it is not gradual, it is no solution to the riddle: it is just a restatement of the riddle.

There will be times when it is hard to think of what the gradual intermediates may have been. These will be challenges to our ingenuity, but if our ingenuity fails, so much the worse for our ingenuity. It does not constitute evidence that there were no gradual intermediates. One of the most difficult challenges to our ingenuity in thinking of gradual intermediates is provided by the celebrated “dance language” of the bees, discovered in the classic work for which Karl von Frisch is best known. Here the end product of the evolution seems so complicated, so ingenious and far removed from anything we would ordinarily expect an insect to do, that it is hard to imagine the intermediates.