Clippings

Another member of the religious meme complex is called faith. It means blind trust, in the absence of evidence, even in the teeth of evidence. The story of Doubting Thomas is told, not so that we shall admire Thomas, but so that we can admire the other apostles in comparison. Thomas demanded evidence. Nothing is more lethal for certain kinds of meme than a tendency to look for evidence. The other apostles, whose faith was so strong that they did not need evidence, are held up to us a worthy of imitation. The meme for blind faith secures its own perpetuation by the simple unconscious expedient of discouraging rational inquiry.

Blind faith can justify anything. If a man believes in a different god, or even if he uses a different ritual for worshipping the same god, blind faith can decree that he should die — on the cross, at the stake, skewered on a Crusader’s sword, shot in a Beirut street, or blown up in a bar in Belfast. Memes for blind faith have their own ruthless ways of propagating themselves. This is true of patriotic and political as well as religious blind faith.

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Faith is such a successful brainwasher in its own favour, especially a brainwasher of children, that it is hard to break its hold. But what, after all, is faith? It is a state of mind that leads people to believe something — it doesn’t matter what — in the total absence of supporting evidence. If there were good supporting evidence then faith would be superfluous, for the evidence would compel us to believe it anyway. It is this that makes the often-parroted claim that ‘evolution itself is a matter of faith’ so silly. People believe in evolution not because they arbitrarily want to believe it but because of overwhelming, publicly available evidence.

I said ‘it doesn’t matter what’ the faithful believe, which suggests that people have faith in entirely daft, arbitrary things, like the electric monk in Douglas Adam’s delightful Dirk Gently’s Holistic Detective Agency. He was purpose-built to do your believing for you, and very successful at it. On the day that we meet him he unshakeably believes, against all the evidence, that everything in the world is pink. I don’t want to argue that the things in which a particular individual has faith are necessary daft. They may or may not be. The point is that there is no way of deciding whether they are, and no way of preferring one article of faith over another, because evidence is explicitly eschewed. Indeed the fact that true faith doesn’t need evidence is held up as its greatest virtue; this was the point of my quoting the story of Doubting Thomas, the only really admirable member of the twelve apostles.

Faith cannot move mountains (though generations of children are solemnly told the contrary and believe it). But it is capable of driving people to such dangerous folly that faith seems to me to the qualify as a kind of mental illness. It leads people to believe in whatever it is so stongly that in extreme cases they are prepared to kill and to die for it without the need for further justification. Keith Henson has coined the name ‘memeoids’ for ‘victims that have been taken over by a meme to the extent that their own survival becomes inconsequential … You see lots of these people on the evening news from such places as Belfast or Beirut.’ Faith is powerful enough to immunize people against all appeals to pity, to forgiveness, to decent human feelings. It even immunizes them against fear, if they honestly believe that a martyr’s death will send them straight to heaven. What a weapon! Religious faith deserves a chapter to itself in the annals of war technology, on an even footing with the longbow, the warhorse, the tank, and the hydrogen bomb.

What … is so special about genes? The answer is that they are replicators. The laws of physics are supposed to be true all over the accessible universe. Are there any principles of biology that are likely to have similar universal validity? When astronauts voyage to distant planets and look for life, they can expect to find creatures too strange and unearthly for us to imagine. But is there anything that must be true of all life, wherever it is found, and whatever the basis of its chemistry? If forms of life exist whose chemistry is based on silicon rather than carbon, or ammonia rather than water, if creatures are discovered that boil to death at −100 degress centigrade, if a form of life is found that is not based on chemistry at all but on electronic reverberating circuits, will there still be any general principle that is true of all life? Obviosly I do not know but, if I had to bet, I would put my money on one fundamental principle. This is the law that all life evolves by the differential survivial of replicating entities. The gene, the DNA molecule, happens to be the replicating entity that prevails on our own planet. There may be others. If there are, provided certain other conditions are met, they will almost inevitably tend to become the basis for an evolutionary process.

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I want to claim almost limitless power for slightly inaccurate self-replicating entities, once they arise anywhere in the universe. This is because they tend to become the basis for Darwinian selection which, given enough generations, cumulatively builds systems of great complexity. I believe that, given the right conditions, replicators automatically band together to create systems, or machines, that carry them around and work to favour their continued replication. The first ten chapters of The Selfish Gene had concentrated exclusively on one kind of replicator, the gene. In discussing memes in the final chapter I was trying to make the case for replicators in general, and to show that genes were not the only members of that important class. Whether the milieu of human culture really does have what it takes to get a form of Darwinism going, I am not sure. But in any case that question is subsidiary to my concern. Chapter 11 will have succeeded if the reader closes the book with the feeling that DNA molecules are not the only entities that might form the basis for Darwinian evolution.

The account of the origin of life that I shall give is necessarily speculative … At some point a particularly remarkable molecule was formed by accident. We call it the Replicator. It may not necessarily have been the biggest or the most complex molecule around, but it had the extraordinary property of being able to create copies of itself.

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The primeval soup was not capable of supporting an infinite number of replicator molecules. … There was a struggle for existence among replicator varieties. They did not know they were struggling, or worry about it; the struggle was conducted without any hard feelings, indeed without feelings of any kind. But they were struggling in the sense that any mis-copying that resulted in a new higher level of stability, or a new way of reducing the stability of rivals, was automatically preserved and multiplied. The process of improvement was cumulative. … Some of them may even have ‘discovered’ how to break up molecules of rival varieties chemically, and to use the building blocks so released to make their own copies. … Other replicators perhaps discovered how to protect themselves, either chemically, or by building a physical wall of proteins around themselves. This may have been how the first living cells appeared. Replicators began not merely to exist, but to construct for themselves containers, vehicles for their continued existence. The replicators that survived were the ones that built survival machines for themselves to live in. The first survival machines probably consisted of nothing more than a protective coat. But making a living got steadily harder as new rivals arose with better and more effective survival machines. Survival machines got bigger and more elaborate, and the process was cumulative and progressive.

Was there to be any end to the process of the gradual improvement in the techniques and artifices used by the replicators to ensure their own continuation in the world? There would be plenty of time for improvement. What weird engines of self-preservation would the millenia bring forth? Four thousand million years on, what was to be the fate of the ancient replicators? They did not die out because they are past masters of the survival arts. But do not look for them floating loose in the sea; they gave up that cavalier freedom long ago. Now they swarm in huge colonies, safe inside gigantic lumbering robots, sealed off from the outside world, communicating with it by tortuous indirect routes, manipulating it by remote control. They are in you and in me; they created us, body and mind; and their preservation is the ultimate rationale for our existence. They have come a long way, those replicators. Now they come by the name of genes, and we are their survival machines.

Category theory originated, in part, as a technique for seeing a collection of similar results from disparate parts of mathematics as instances of a more general theory of mathematical structures and the relationships between structures. To encompass a wide range of results, it was necessary to develop a quite abstract collection of conditions that apply in many instances. As a result, mathematicians sometimes refer to category theory as ‘abstract nonsense’ — especially when they are taking advantage of its power of generality! Because of this generality, category theory has had a crucial influence of the study of the semantics of programming languages, often guiding or inspiring the discovery of the right concepts, definitions, structures, and theorems. As a tool for studying the semantics of programming languages, the usefulness of category theory goes beyond its position as a well-developed, general theory of mathematical structures. In many instances, the ‘categorical viewpoint’ matches much better with basic motivations in computer science than the alternative foundational theories.

…Nicolas Bourbaki is the pseudonym of a group of mathematicians — mostly French, mostly young — who tidied up the mathematics of the mid-20th century in a lengthy series of books. Their guiding principle was never to prove a theorem if it could be deduced as a special case of a more general theorem. To study planar geometry, work in n dimensions and then let n = 2.

Fashions change, and nowadays the presentation of mathematics has veered back toward specific examples and a preference for ideas that are more concrete, more down-to-earth. Though what counts as concrete today would have astonished the mathematicians of the 19th century to whom the general polynomial over the complex numbers was the height of abstraction, to us it is a single concrete example.

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There is nothing wrong with abstraction and generality — they are still cornerstones of the mathematical enterprise. But “abstract” is a verb as well as an adjective: general ideas should be abstracted from something, not conjured from thin air. Abstraction in this sense is highly non-Bourbakiste, best summed up by the counter-slogan “let 2 = n.” To do that we have to start with case 2, and fight our way through it using anything that comes to hand, however clumsy, before refining our methods into an elegant but ethereal technique which — without such preparation — lets us prove case n without having any idea of what the proof does, how it works, or where it came from.

Cantor became aware of such antinomies in 1895, and over the next decades the mathematical community tried to find a way to patch up the logical breach they had created. The final resolution of this affair required the formal axiomatization of set theory — even as Euclid had provided his axiomatic approach to geometry — in which the carefully chosen axioms prohibited just such paradoxes as these. Logically, this was no easy matter. But, in the end, the newly created “axiomatic set theory” more carefully controlled precisely what was and what was not a “set.” Under this system, the “universal set” was not a set at all; it was exclued from the collection of objects that the axioms of set theory addressed. Thus, almost by magic, the paradox dissolved.

This resolution was, obviously, a compromise measure, an axiomatic attempt to carve away, with surgical precision, the troubling features of set theory while retaining all of the good points of Cantor’s creation. Cantor’s own, more informal approach is now called “naive set theory,” to contrast it with the logical superstructure of axiomatic set theory. The latter now stands as a satisfactory, albeit rather abstruse and technical, foundation for the theory of sets. It represents a triumph of the sentiments expressed by mathematician David Hilbert, who vowed, “No one will expel us from the paradise that Cantor has created.”

It was Leibniz who sought to develop a perfect system of formal logic, based on an “alphabet of human thought” and governed by a carefully prescribed “rational calculus.” With such logical tools, Leibniz hoped that mankind could rid everyday life of its pervasive imprecision and irrationality. Of course, he never came close to succeeding in what can only be called a grandiose plan, but his attempts constituted the first real steps toward what we today call “symbolic logic.” In particular, his use of algebraic forumlas to denote logical statements was a significant advance beyond the verbal syllogisms of Greek logical theory.