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.Let us think ofmathematics as a tool.(Language would serve equally well, here, butmathematics is a less familiar example and deserves attention in its ownright.) Children learn a lot of mathematics at school, far more than, say,early Homo erectus did 200,000 years ago.We have a much bigger brain285 WHAT DOES A MARTIAN LOOK LIKE?than they had, of course.But what were the selective forces on ourancestors, that led to the development of a brain that could domathematics if pressed?The usual answers are very diverse, but they all fall into one category:we needed our big brains (and ever bigger brains as time went on) forlanguage, or for gossip about our social group, or for planning the hunt,or for recognising different roots and learning which to plant when, orfor learning to lie to our colleagues, or for all of the above.The commonthread is this: we started with specific problems, and solving those gaveus a bigger brain.As a side effect, we can now use that clever big brainto attack much more abstract problems like those of mathematics and get real-life solutions.We can see this kind of thing happening with computers: com-petition between PC manufacturers has driven companies to inventfaster systems with much more memory, and with more user-friendlyinterfaces that exploit the speed and memory.So PCs can now do tasksthat only the largest computers could do twenty years ago.And theassumption is that these tasks were sitting there in some ethereal space,waiting like mathematics for the big-brained primate till thecomputers were clever enough to tackle them.There is a hidden assumption in that kind of thinking, and it s asubtle one that relates to the universal/parochial distinction.Are eyes,or wings, discovered or invented? Is mathematics discovered orinvented? Are swords discovered or invented?Try the middle question as a lever to pry open the other two.We areused to the idea that when we meet aliens, we can start to communicateby using the hydrogen atom, the periodic table of chemical elements,or the solar system and Newtonian geometry, or the series of primenumbers and more advanced number theory, or logical rules andRussell/Whitehead paradoxes.(Bertrand Russell and Alfred NorthWhitehead attempted to codify a perfectly logical mathematical system,resolving all its paradoxes by the use of systematic argument.Suchattempts were shown to be in vain by Kurt Godel in the 1930s, and thissuggested our logic might be parochial.) This is a useful trick forauthors, anyway.We used it to introduce the alien Zarathustrans inThe Collapse of Chaos.Sagan used the sequence of primes in Contact.And NASA put a plaque on its Pioneer space probe along just these286 THE UNIVERSALITY OF EXTELLIGENCElines.It s a pleasant image, but far too naive.It assumes that aliens willhave mathematics, chemistry, and physics that are similar enough toours for meaningful comparisons to be made.Unfortunately, theywon t, so communication with aliens can t really be initiated like this.Plaques on space-probes are based on the assumption that evolvingalien brains will carve up the universe in the same way that ours do, andorder what they find into the same patterns and logical schemes that weuse.Most people seem to think that there is only one way to carve upthe universe, and that our brains have homed in on the One TruePicture.This belief is probably false.The question of how our brains became capable of doing tasks thatare so much more general than the capabilities that honed them duringevolution is phrased the wrong way round.Where does mathematicscome from? The pragmatic view is that we make it all up as we go along;the mystical one is that mathematics is already in existence, waiting forus to discover it.The second philosophy is generally called Platonism,after the ancient Greek philosopher Plato who had some rather way-outideas about ideal forms ; the first lacks a snappy name.Platonism in itsmost extreme form holds that mathematical concepts actually exist insome weird kind of ideal reality just off the edge of the universe that weall know and love.A circle is not just an idea: it is an ideal.Weimperfect creatures may aspire to that ideal, but we can never achieveit, if only because pencil points are too thick.But our imperfectattempts are approximations to a perfect circle that really exists,somewhere out there.Though no Platonist ever says where.It s very tempting indeed to see our everyday world as a pale shadowof a more perfect, ordered, mathematically exact one, and to assumethat alien intelligences would therefore mirror the same ideal in asimilar manner to our intelligences.The evidence for this viewpoint, atfirst, seems compelling.The more deeply physicists delve into the fundamental nature of the universe, the more mathematical every-thing seems to get.The ghostly world of the quantum cannot even beexpressed without mathematics: if you try to describe it in everydaylanguage, it makes no sense.It is tempting to conclude that the universeis in some sense built from tiny bits of mathematics, and many people,philosophers and scientists, have seen mathematics as the basis of the287 WHAT DOES A MARTIAN LOOK LIKE?universe.Plato wrote that god ever geometrises.The physicist JamesJeans declared that God was a mathematician.Paul Dirac, one of theinventors of quantum mechanics, went further, opining that He was apure mathematician [ Pobierz całość w formacie PDF ]