This lowland ramp pushed on up towards the evolution of the living equivalent of the photocell, a cell specialized for capturing photons with a pigment, and translating their impact into nerve impulses. I shall continue to use the word photocell for those cells in the retina (in ourselves they are called rods and cones) which are specialized for capturing photons. The trick that they all use is to increase the number of layers of pigment available to capture photons. This is important because a photon is very likely to pass straight through any one layer of pigment and come out the other side unscathed. The more layers of pigment you have, the greater the chance of catching any one photon. Why should it matter how many photons are trapped and how many get through? Aren't there always plenty of photons to spare? No, and the point is fundamental to our understanding of the design of eyes. There is a kind of economics of photons, an economics as mean-spirited as human monetary economics and involving inescapable trade-offs.
Before we even get into the interesting economic trade-offs, there can be no doubt that in absolute terms photons are in short supply at some times. On a crisp, starry night in 1986 I woke my two-year-old daughter Juliet and carried her, wrapped in blankets, out into the garden where I pointed her sleepy face towards the published location of Halley s Comet. She didn't take in what I was saying, but I stubbornly whispered into her ear the story of the comet and the certainty that I could never see it again but that she might when she was seventy-eight. I explained that I had woken her so that she'd be able to tell her grandchildren in 2062 that she had seen the comet before, and perhaps she'd remember her father for his quixotic whim in carrying her out into the night to show it to her. (I may even have whispered the words quixotic and whim because small children like the sound of words they don't know, carefully articulated.)
Probably some photons from Halley's Comet did indeed touch Juliet's retinas that night in 1986 but, to be truthful, I had a hard time convincing myself that I could see the comet. Sometimes I seemed to conjure a faint, greyish smear at approximately the right place. At other times it melted away. The problem was that the number of photons falling on our retinas was close to zero. {143}
Photons arrive at random times, like raindrops. When it is really raining properly we are in no doubt of the fact and wish our umbrella hadn't been stolen. But when rain starts gradually, how do we decide the exact moment when it begins? We feel a single drop and look up apprehensively, unconvinced until a second or a third drop arrives. When rain is spitting infrequently like this, one person may say that it is raining while his companion denies it. The drops can fall infrequently enough to hit one person a minute before his companion registers a hit. To be really convinced that there is light, we need the photons to patter on our retinas at an appreciably high rate. When Juliet and I gazed in the general direction of Halley's Comet, photons from the comet were probably hitting individual photocells on our retinas at the fantastically slow rate of about one every forty minutes! This means that any one photocell could be saying, ‘Yes there is light there,’ while the vast majority of its neighbouring photocells were not. The only reason I received any sensation at all of a comet-shaped object was that my brain was summing up die verdicts of hundreds of photocells. Two photocells capture more photons than one. Three capture more than two, and so on up the slope of Mount Improbable. Advanced eyes like ours have millions of photocells densely packed like pile in a carpet, and each one of them is set up to capture as many photons as possible.
Figure 5.2 is a typical advanced photocell, from a human as it happens, but others are much the same. The writhing colony of apparent maggots in the middle of the picture are mitochondria. These are small bodies that live inside cells. They are originally descended from parasitic bacteria but they have made themselves indispensable for producing energy in all our cells. The nervous connecting wire of the photocell leads off at the left of the picture. The elegant rectangular array of membranes, lined up with military precision on the right, is where the photons are trapped. Each layer contains molecules of the vital, photon-trapping pigment. I count ninety-one layers of membrane in this picture. The exact number is not critical: the more the merrier as far as catching photons is concerned, though there will be overhead costs prohibiting too many layers. The point is that ninety-one membranes are more effective in stopping photons than ninety, ninety are more effective than eighty-nine, and so on back to one {144}
Figure 5.2 Photon-capturing device or ‘biological photocell’: a single retinal cell (rod) of a human.
membrane, which is more effective than zero. This is the kind of thing I mean when I say that there is a smooth gradient up Mount Improbable. We would be dealing with an abrupt precipice if, say, any number of membranes above forty-five was very effective while any number below forty-five was totally ineffective. Neither common sense nor the evidence leads us to suspect any such sudden discontinuity.
Squids, as we have seen, evolved their similar eyes independently of vertebrates. Even their photocells are very alike. 1 he main difference is that in the squid the layers, instead of being packed as a stack of discs, are rings stacked around a hollow tube. (This kind of superficial difference is common in evolution, for the same kind of inconsequential reason as, say, the fact that English light switches go down for on, American ones down for off.) All advanced animal photocells are playing different versions of the same trick of increasing the number of layers of pigment-laced membranes through which a photon must pass if it would escape untrapped. From Mount Improbable's point of view, the important point is that one more layer marginally improves the chance of trapping photons no matter how many, or how few, layers there already are. Ultimately, when most of the photons have been caught, there will be a law of diminishing returns for the increasing cost of more layers. {145}
Of course there is not much call, in the wild, for detecting Halley's Comet, returning every seventy-six years with its negligible contribution of reflected photons. But it is very useful to have eyes sensitive enough to see by moonlight and even starlight if you are an owl. On a typical night, any one of our photocells might receive photons at about one per second, admittedly a higher rate than for the comet, but still slow enough to make it vital to trap every last photon if it can be done. But when we speak of a harsh economics of photons it would be quite wrong to assume that the harshness is confined to the night. In bright sunlight the photons may drum the retina like a tropical cloudburst, but there is still a problem. The essence of seeing a patterned image is that photocells in different parts of the retina must report different intensities of light and this means distinguishing different rates of pattering in different parts of the photon rainstorm. The sorting of photons coming from different fine-grained parts of the scene can lead to local impoverishments of photons just as serious as the global impoverishment of the night. It is to this sorting that we now turn.
Photocells on their own just tell an animal whether there is light or not. The animal can tell the difference between night and day, and can tell when a shadow falls which might, for example, portend a predator. The next step of improvement must have been the acquisition of some rudimentary sensitivity to direction of light and direction of movement of, say, a menacing shadow. The minimal way of achieving this is to back the photocells with a dark screen on one side only. A transparent photocell without a dark screen receives light from all directions and cannot tell where light is coming from. An animal with only one photocell in its head can steer towards, or away from, light, provided the photocell is backed by a screen. A simple recipe for doing this is to swing the head like a pendulum from side to side; if the light intensity on the two sides is unbalanced, change direction until it is balanced. There are some maggots that follow this recipe for steering directly away from light.
But swinging your head from side to side is a rudimentary way of detecting the direction of light, fit for the lowest slopes of Mount Improbable. A better way is to have more than one photocell pointing {146} in different direc
tions, each one backed by a dark screen. Then by comparing the rates of photon rain on the two cells you can make inferences about direction of light. If you have a whole carpet of photocells, a better way is to bend the carpet, with its backing screen, into a curve, so that the photocells on different parts of the curve are pointing in systematically different directions. A convex curve can give rise, eventually, to the sort of ‘compound eye’ that insects have, and I'll return to this. A concave curve is a cup and it gives rise to the other main kind of eye, the camera eye like our own. Photocells in different parts of a cup will fire when light is coming from different directions, and the more cells there are the finer-grained will be the discrimination.
Figure 5.3 A simple cup eye can detect the direction of light.
The light rays (parallel white lines with arrows) are halted by the thick black screen at the back of the cup (Figure 5.3). By keeping track of which photocells are firing and which are not, the brain can detect the direction from which the light is coming. From the point of view of climbing Mount Improbable, what matters is that there is a continuous evolutionary gradation — a smooth incline up the {147} mountain — connecting animals with a flat carpet of photocells to animals with a cup. Cups can get gradually deeper or gradually shallower, by continuous slow degrees. The deeper the cup, the greater the ability of the eye to discriminate light coming from different directions. On the mountain, no steep precipices have to be leapt.
Cup eyes like this are common in the animal kingdom. Figure 5.4 shows the eye of a limpet, of a bristleworm, of a dam and of a
Figure 5.4 Cup eyes from around the animal kingdom: (a) flatworm; (b) bivalve mollusc; (c) polychaet worm; (d) limpet. {148}
Figure 5.5 How eyes do
not work — would that
light rays were so obliging!
flat-worm. These eyes have probably evolved their cup shape independently. This is particularly clear in the case of the flatworm eye which betrays its separate origin by keeping its photocells inside the cup. On the face of it this is an odd arrangement — the light rays have to penetrate a thicket of connecting nerves before they hit the photocells — but let's not be snobbish about it because the same apparently poor design mars our own much more sophisticated eyes. I'll return to this and show that it isn't really such a bad idea as it seems.
In any case, a cup eye on its own is far from capable of forming what we humans, with our excellent eyes, would recognize as a proper image. Our kind of image-formation, which depends upon the lens principle, needs a little explanation. We approach the problem by asking why an unaided carpet of photocells, or a shallow cup, will not see an image of, say, a dolphin, even when the dolphin is conspicuously displayed in front of it.
If light rays behaved as in Figure 5.5, everything would be easy and an image of die dolphin, the right way up, would appear on die retina. Unfortunately diey don't. To be more precise, diere are rays that do exactly what I have drawn in die picture. The trouble is diat diese are swamped by any number of rays going in every other direction at die same time. Every bit of the dolphin sends a ray to every point on die retina. And not just every bit of the dolphin, but every bit of the background and of everything else in die scene. You can diink of die result as an infinite number of dolphin images, in every possible position on the surface of die cup and every possible way up and way round. But {149}
Figure 5.6 Light rays
from everywhere go
everywhere and no image
is seen. An infinite number
of dolphin images clash
with each other, and nothing
is clear.
what this amounts to, of course, is no image at all, just a smooth spreading of light over the whole surface (Figure 5.6).
We have diagnosed the problem. The eye is seeing too much: an infinity of dolphins instead of only one. The obvious solution is to subtract: cut out every dolphin image except one. It wouldn't matter which one, but how to get rid of the rest? One way is to trudge on up the same slope of Mount Improbable as gave us the cup, steadily deepening and enclosing the cup until the aperture has narrowed to a pinhole. Now the vast majority of rays are prevented from entering the cup. The minority that remain are just those rays that form a small number of similar images — upside-down — of the dolphin (Figure 5.7). If the pinhole becomes extremely small, the blurring disappears and a single, sharp picture of the dolphin remains (actually, extremely small pinholes introduce a new kind of blurring, but we'll forget about that for a moment). You can think of the pinhole as an image filter, removing all but one of the bewildering visual cacophony of dolphins.
The pinhole effect is just an extreme version of the cup effect that we have already met as an aid to telling the direction of light. It belongs only a bit farther up the same slope of Mount Improbable and there are no sharp precipices between. There is no difficulty in a pinhole eye's evolving from a cup eye, and no difficulty in a cup eye's evolving from a flat sheet of photocells. The slope up the mountain from flat carpet to pinhole is gradual and easily dimbable all the way. Climbing it represents a progressive knocking {150}
Figure 5.7 Principle of the
pinhole eye. Most of the
competing dolphin images
are cut out. Ideally only one
(inverted) gets through the
pinhole.
out of conflicting images until, at the peak, only one is left.
Pinhole eyes in varying degrees are, indeed, scattered around the animal kingdom. The most thoroughgoing pinhole eye is that of the enigmatic mollusc Nautilus (Figure 5.8a), related to the extinct ammonites (and a more distant relative of an octopus, but with a coiled shell). Others, such as the eye of a marine snail in Figure 5.8b, are perhaps better described as deep cups than true pinholes. They illustrate the smoothness of this particular gradient up Mount Improbable.
A first thought suggests that the pinhole eye ought to work rather well, provided you make the pinhole small enough. If you make the pinhole almost infinitely small, you might think that you'd get an almost infinitely perfect image by cutting out the vast majority of competing, interfering images. But now two new snags arise. One is diffraction. I deferred talking about it just now. It is a blurring problem that results from the fact that light behaves like waves, which can interfere with each other. This blurring gets worse when the pinhole is very small. The other snag with a small pinhole recalls the hard tradeoffs of our ‘photon economy’. When the pinhole is small enough to make a sharp image, it necessarily follows that so little light gets through the hole that you can see the object well only if it is illuminated by an almost unattainably bright light. At normal lighting levels not enough photons get through the pinhole for the eye to be certain what it is seeing. With a tiny pinhole we have a version of the Halley's Comet problem. You can combat this by opening out the pinhole {151}
Figure 5.8 (opposite) A range of invertebrate eyes that illustrate approaches to the formation of crude but effective images: (a) Nautilus's pinhole eye; (b) marine snail; (c) bivalve mollusc; (d) abalone; (e) ragworm. {152}
again. But now you are back where you were with a confusion of competing ‘dolphins’. The photon economy has brought us to an impasse on this particular foothill of Mount Improbable. With the pin-hole design you can have a sharpish but dark image, or a brightish but fuzzy one. You cannot have both. Such trade-offs are meat and drink to economists, which is why I coined the notion of an economy of photons. But is there no way to achieve a bright and yet simultaneously sharp image? Fortunately there is.
First, think of the problem computationally. Imagine that we broaden the pinhole out to let in a nice lot of light. But instead of leaving it as a gaping hole, we insert a ‘magic window’, a masterpiece of electronic wizardry embedded in glass and connected to a computer (Figure 5.9). The property of this computer-controlled window is the following. Light rays, instead of passing straight through the glass, are bent through a cunning angle. This angle is carefully cal
culated by the computer so that all rays originating from a point (say the dolphins nose) are bent to converge on a corresponding point on the retina. I've drawn only the rays from the dolphin's nose, but the magic screen, of course, has no reason to favour any one point and does the same calculation for every other point as well. All rays originating at the tail of the dolphin are bent in such a way that they converge on a corresponding tail point on the retina, and so on. The
Figure 5.9 A
complicated and
ridiculously expensive
hypothetical approach to