The Blind Watchmaker (12 page)

I set about trying to ‘find’ them again. They had evolved once, so it seemed that it must be possible to evolve them again. Like the lost chord, they haunted me. I wandered through Biomorph Land, moving through an endless landscape of strange creatures and things, but I couldn’t find my insects. I knew that they must be lurking there somewhere. I knew the genes from which the original evolution had started. I had a picture of my insects’ bodies. I even had a picture of the evolutionary sequence of bodies leading up to my insects by slow degrees from a dot ancestor. But I didn’t know their genetic formula.

You might think that it would have been easy enough to reconstruct the evolutionary pathway, but it wasn’t. The reason, which I shall come back to, is the astronomical number of
possible
biomorphs that a sufficiently long evolutionary pathway can offer, even when there are only nine genes varying. Several times on my pilgrimage through Biomorph Land I seemed to come close to a precursor of my insects, but, then, in spite of my best efforts as a selecting agent, evolution went off on what proved to be a false trail. Eventually, during my evolutionary wanderings through Biomorph Land - the sense of triumph was scarcely less than on the first occasion - I finally cornered them again. I didn’t know (still don’t) if these insects were exactly the same as my original, ‘lost chords of Zarathustra’ insects, or whether they were superficially ‘convergent’ (see next chapter), but it was good enough. This time there was no mistake: I wrote down the genetic formula, and now I can ‘evolve’ insects whenever I want.

Yes I am piling on the drama a bit, but there is a serious point being made. The point of the story is that even though it was I that programmed the computer, telling it in great detail what to do, nevertheless I didn’t plan the animals that evolved, and I was totally surprised by them when I first saw their precursors. So powerless was I to control the evolution that, even when I very much wanted to retrace a particular evolutionary pathway it proved all but impossible to do so. I don’t believe I would ever have found my insects again if I hadn’t had a printed picture of the
complete set
of their evolutionary precursors, and even then it was difficult and tedious. Does the powerlessness of the programmer to control or predict the course of evolution in the computer seem paradoxical? Does it mean that something mysterious, even mystical was going on inside the computer? Of course not. Nor is there anything mystical going on in the evolution of real animals and plants. We can use the computer model to resolve the paradox, and learn something about real evolution in the process.

To anticipate, the basis of the resolution of the paradox will turn out to be as follows. There is a definite set of biomorphs, each permanently sitting in its own unique place in a mathematical space. It is permanently sitting there in the sense that, if only you knew its genetic formula, you could instantly find it; moreover, its neighbours in this special kind of space are the biomorphs that differ from it by only one gene. Now that I know the genetic formula of my insects, I can reproduce them at will, and I can tell the computer to ‘evolve’ towards them from any arbitrary starting point. When you first evolve a new creature by artificial selection in the computer model, it feels like a creative process. So it is, indeed. But what you are really doing is
finding
the creature, for it is, in a mathematical sense, already sitting in its own place in the genetic space of Biomorph Land. The reason it is a truly creative process is that finding any particular creature is extremely difficult, simply and purely because Biomorph Land is very very large, and the total number of creatures sitting there is all but infinite. It isn’t feasible just to search aimlessly and at random. You have to adopt some more efficient - creative - searching procedure.

Some people fondly believe that chess-playing computers work by internally trying out all possible combinations of chess moves. They find this belief comforting when a computer beats them, but their belief is utterly false. There are far too many possible chess moves: the search-space is billions of times too large to allow blind stumbling to succeed. The art of writing a good chess program is thinking of efficient short cuts through the search-space. Cumulative selection, whether artificial selection as in the computer model or natural selection out there in the real world, is an efficient searching procedure, and its consequences look very like creative intelligence. That, after all, is what William Paley’s Argument from Design was all about. Technically, all that we are doing, when we play the computer biomorph game, is
finding
animals that, in a mathematical sense, are waiting to be found. What it feels like is a process of artistic creation. Searching a small space, with only a few entities in it, doesn’t ordinarily feel like a creative process. A child’s game of hunt the thimble doesn’t feel creative. Turning things over at random and hoping to stumble on the sought object usually works when the space to be searched is small. As the search-space gets larger, more and more sophisticated searching procedures become necessary. Effective searching procedures become, when the search-space is
sufficiently
large, indistinguishable from true creativity.

The computer biomorph models make these points well, and they constitute an instructive bridge between human creative processes, such as planning a winning strategy at chess, and the evolutionary creativity of natural selection, the blind watchmaker. To see this, we must develop the idea of Biomorph Land as a mathematical ‘space’, an endless but orderly vista of morphological variety, but one in which every creature is sitting in its correct place, waiting to be discovered. The 17 creatures of Figure 5 are arranged in no special order on the page. But in Biomorph Land itself each occupies its own unique position, determined by its genetic formula, surrounded by its own particular neighbours. All the creatures in Biomorph Land have a definite spatial relationship one to another. What does that mean? What meaning can we attach to spatial position?

The space we are talking about is genetic space. Each animal has its own position in genetic space. Near neighbours in genetic space are animals that differ from one another by only a single mutation. In Figure 3, the basic tree in the centre is surrounded by 8 of its 18 immediate neighbours in genetic space. The 18 neighbours of an animal are the 18 different kinds of children that it can give rise to, and the 18 different kinds of parent from which it could have come, given the rules of our computer model. At one remove, each animal has 324 (18x18, ignoring back-mutations for simplicity) neighbours, the set of its possible grandchildren, grandparents, aunts or nieces. At one remove again, each animal has 5,832 (18 x 18 x 18) neighbours, the set of possible great grandchildren, great grandparents, first cousins,
etc.

What is the point of thinking in terms of genetic space? Where does it get us? The answer is that it provides us with a way to understand evolution as a gradual, cumulative process. In any one generation, according to the rules of the computer model, it is possible to move only a single step through genetic space. In 29 generations it isn’t possible to move farther than 29 steps, in genetic space, away from the starting ancestor. Every evolutionary history consists of a particular pathway, or trajectory, through genetic space. For instance, the evolutionary history recorded in Figure 4 is a particular winding trajectory through genetic space, connecting a dot to an insect, and passing through 28 intermediate stages. It is this that I mean when I talk metaphorically about ‘wandering’ through Biomorph Land.

I wanted to try to represent this genetic space in the form of a picture. The trouble is, pictures are two-dimensional. The genetic space in which the biomorphs sit is not two-dimensional space. It isn’t even threedimensional space. It is ninedimensional space! (The important thing to remember about mathematics is not to be frightened. It isn’t as difficult as the mathematical priesthood sometimes pretends. Whenever I feel intimidated, I always remember Silvanus Thompson’s dictum in
Calculus Made Easy
: ‘What one fool can do, another can’.) If only we could draw in nine dimensions we could make each dimension correspond to one of the nine genes. The position of a particular animal, say the scorpion or the bat or the insect, is fixed in genetic space by the numerical value of its nine genes. Evolutionary change consists of a step by step walk through ninedimensional space. The amount of genetic difference between one animal and another, and hence the time taken to evolve, and the difficulty of evolving from one to the other, is measured as the
distance
in ninedimensional space from one to the other.

Alas, we can’t draw in nine dimensions. I sought a way of fudging it, of drawing a two-dimensional picture that conveyed something of what it feels like to move from point to point in the ninedimensional genetic space of Biomorph Land. There are various possible ways in which this could be done, and I chose one that I call the triangle trick. Look at Figure 6. At the three corners of the triangle are three arbitrarily chosen biomorphs. The one at the top is the basic tree, the one on the left is one of ‘my’ insects, and the one on the right has no name but I thought it looked pretty. Like all biomorphs, each of these three has its own genetic formula, which determines its unique position in ninedimensional genetic space.

The triangle lies on a flat two-dimensional ‘plane’ that cuts through the ninedimensional hypervolume (what one fool can do, another can). The plane is like a flat piece of glass stuck through a jelly. On the glass is drawn the triangle, and also some of the biomorphs whose genetic formulae entitle them to sit on that particular flat plane. What is it that entitles them? This is where the three biomorphs at the corners of the triangle come in. They are called the anchor biomorphs.

Remember that the whole idea of ‘distance’ in genetic ‘space’ is that genetically similar biomorphs are near neighbours, genetically different biomorphs are distant neighbours. On this particular plane, the distances are all calculated with reference to the three anchor biomorphs. For any given point on the sheet of glass, whether inside the triangle or outside it, the appropriate genetic formula for that point is calculated as a ‘weighted average’ of the genetic formulae of the three anchor biomorphs. You will already have guessed how the weighting is done. It is done by the distances on the page, more precisely the
nearnesses
, from the point in question to the three anchor biomorphs. So, the nearer you are to the insect on the plane, the more insect-like are the local biomorphs. As you move along the glass towards the tree, the ‘insects’ gradually become less insect-like and more tree-like. If you walk into the centre of the triangle the animals that you find there, for instance the spider with a Jewish seven-branched candelabra on its head, will be various ‘genetic compromises’ between the three anchor biomorphs.

But this account gives altogether too much prominence to the three anchor biomorphs. Admittedly the computer did use them to calculate the appropriate genetic formula for every point on the picture. But actually any three anchor points on the plane would have done the trick just as well, and would have given identical results. For this reason, in Figure 7 I haven’t actually drawn the triangle. Figure 7 is exactly the same kind of picture as Figure 6. It just shows a different plane. The same insect is one of the three anchor points, this time the right-hand one. The other anchor points, in this case, are the spitfire and the bee-flower, both as seen in Figure 5. On this plane, too, you will notice that neighbouring biomorphs resemble each other more than distant biomorphs. The spitfire, for instance, is part of a squadron of similar aircraft, flying in formation. Because the insect is on both sheets of glass, you can think of the two sheets as passing, at an angle, through each other. Relative to Figure 6, the plane of Figure 7 is said to be ‘rotated about’ the insect.

The elimination of the triangle is an improvement to our method, because it was a distraction. It gave undue prominence to three particular points in the plane. We still have one further improvement to make. In Figures 6 and 7, spatial distance represents genetic distance, but the
scaling
is all distorted. One inch upwards is not necessarily equivalent to one inch across. To remedy this, we must choose our three anchor biomorphs carefully, so that their genetic distances, one from the other, are all the same. Figure 8 does just this. Again the triangle is not actually drawn. The three anchors are the scorpion from Figure 5, the insect again (we have yet another ‘rotation about’ the insect), and the rather nondescript biomorph at the top. These three biomorphs are all 30 mutations distant from each other. This means that it is equally easy to evolve from any one to any other one. In all three cases, a minimum of 30 genetic steps must be taken. The little blips along the lower margin of Figure 8 represent units of distance measured in genes. You can think of it as a genetic ruler. The ruler doesn’t only work in the horizontal direction. You can tilt it in any direction, and measure the genetic distance, and hence the minimum evolution time, between any point on the plane and any other (annoy - ingly, that is not quite true on the page, because the computer’s printer distorts proportions, but this effect is too trivial to make a fuss about, although it does mean that you will get slightly the wrong answer if you simply count blips on the scale).

These two-dimensional planes cutting through ninedimensional genetic space give some feeling for what it means to walk through Biomorph Land. To improve that feeling, you have to remember that evolution is not restricted to one flat plane. On a true evolutionary walk you could ‘drop through’, at any time, to another plane, for instance from the plane of Figure 6 to the plane of Figure 7 (in the vicinity of the insect, where the two planes come close to each other).

I said that the ‘genetic ruler’ of Figure 8 enables us to calculate the minimum time it would take to evolve from one point to another. So it does, given the restrictions of the original model, but the emphasis is on the word
minimum
. Since the insect and the scorpion are 30 genetic units distant from one another, it takes only 30 generations to evolve from one to the other
if you never take a wrong turning
, if, that is, you know exactly what genetic formula you are heading towards, and how to steer towards it. In real-life evolution there is nothing that corresponds to steering towards some distant genetic target.