You will all be immensely relieved, I'm sure, when I tell you this is my final post on the subject of Darwinism, well, until the next time, of course! Anyway, at this point I would like to introduce you all to my e-pal, Richard J. Bird, well, he's not really 'a pal' because all I did was exchange a couple of e-mails with him a few years back. What I did do, however, is to read his fascinating book Chaos and Life. Now Prof. Bird is Supernumerary Fellow of Computation at Lincoln College, Oxford, or, an A1 maths swot of the first order!
I have already expressed my doubts concerning traditional Darwinian evolution as a process of tiny mutations which eventually lead to new species. Prof. Bird puts it this way:
If we assume that mutations are the agents of evolutionary change, the question becomes how to account for mutations of an adequate number and variety to bring about the observed rate of evolution. The difficulty is that, if mutations are unsystematic, how can they have resulted in such a well-patterned outcome? The legendary monkeys at their word processors could not write the works of Shakespeare just by chance. In the history of the world they would not complete even a single line.
If you consider even for a minute the prolific range of proficient and operative life forms that exist, a truly huge number, then, if mutation is indeed random, you have to consider the equally great or even greater number of mutations that were not successful.
Mutation rates would have to be directed in some way in order to produce creatures like those presently observed. On the face of it there are far too many possibilities that might arise in unpatterned mutation. [S.W.] Ulam [another maths swot] has calculated that, if achieving a significant advantage, such as the human visual system, requires 106 changes, then it will take 1013 generations in a population of 1011 individuals for the change to become established. If there is one generation per day, this means several billion years.
All that is merely the tip of the iceberg on which the good ship Darwin might well founder. So what is the solution? Well, at this point it is necessary to remind you that my knowledge of mathematics reaches no further than the twelve times table - and I'm not too sure about all of them! So, when I raise the subject of 'iterated algorithms' you will understand the thinness of the ice upon which I am skating. Happily, rescue is at hand in the form of Prof. Gove Effinger, a maths swot at an American college. He (like me!) was entranced by Tom Stoppard's wonderful play, Arcadia, in which a very young teenage girl, Thomasina Coverly, living in the early 19th century has an incredible insight which, due to her untimely death, would not be rediscovered until the 20th century. Here is an extract which shows her working with her young tutor, Septimus Hodge:
- Thomasina: . . . Each week I plot your equations dot for dot, xs against ys in all manner of algebraical relation, and every week they draw themselves as commonplace geometry, as if the world of forms were nothing but arcs and angles. God's truth, Septimus, if there is an equation for a curve like a bell, there must be an equation for one like a bluebell, and if a bluebell, why not a rose? Do we believe nature is written in numbers?
- Septimus: We do.
- Thomasina: Then why do your equations only describe the shapes of manufacture?
- Septimus: I do not know.
- Thomasina: Armed thus, God could only make a cabinet.
- Septimus: He has mastery of equations which lead into infinities where we cannot follow.
- Thomasina: What a faint-heart! We must work outward from the middle of the maze. We will start with something simple. (She picks up the apple leaf.) I will plot this leaf and deduce its equation. You will be famous for being my tutor when Lord Byron is dead and forgotten.
Happily, Prof. Effinger explains:
The idea which Thomasina discovers, as we find out later from the present day discussions of Hannah and Valentine [in the play], is that of iterated algorithms, that is: the idea of starting with a number (or point), processing it somehow to obtain a new number or point (which you record), and then feeding that new number or point back into the process. You do this "feedback mechanism" again and again, and after a long time you see the pattern which emerges.
It is in these iterated algorithms that the mystery of evolution may be found because when you carry them out - well, actually an individual armed with paper and pencil couldn't do so at a sufficiently high rate if you lived for a hundred years! So, a computer is required and when that is used a zillion times over with the result of each algorithm being fed back into the next algorithm - nothing much happens! Which is what you might expect but then, if you keep going, suddenly, out of the blue, you get an extraordinarily different result. Don't ask me how, and certainly don't ask me why, it just happens.
And here - at last - are you still with me? - we come to the point. Procreation is, in effect, an iterated algorithm. In animal procreation, long strings of DNA from two separate donors are joined together, in time the resulting new creature will pass its DNA to join with another to form a new being. You might call the process a 'sexy iterated algorithm'! This can happen a zillion times over but every so often that dreaded exception will occur when something totally unexpected suddenly appears. Here is an example of an iterated algorithm that went wrong (or perhaps right, who knows?) in the pig world where a piglet was born with a very strange face:
So there you have it, well, for the time being because all theories are subject to correction over time as poor old Darwin found out the hard way! In the meantime, what can one say? Well, I suppose you can always trot out a bit of Shakespeare, the bloody man has a phrase for every occasion:
There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.