The relationship between me and mathematics has been like that between a stalker and their victim – aware of each other, but hoping never to meet face to face. (In this simile, which will not be pursued further, maths is the stalker.) The concept of the stuff fascinates me, but I don’t understand a bit* of it.
I’ve just almost finished a marvellous book which massively reinforces the fascination, and even, possibly, an itsy smidgeon of the understanding. (Well, it couldn’t reduce it, could it?) It’s called ‘The Information’, by James Gleick (Fourth Estate, 2011), and is basically a history of, well, information – its nature, how it is (or isn’t) communicated (from African talking drums to quantum computing) and, most importantly, how mathematics and information are essentially the same thing.
That’s all I’m going to say about this book, except that once or twice (all right, 150ish times), after surf-navigating a particularly turbulent stretch, my neurons and synapses (they’re in there!) felt distinctly numb.
Just a couple of snippets that particularly grabbed me:
A guy called G. G. Berry, with Bertrand Russell, cheekily constructed the Berry paradox, which goes something like this. Q: Is it possible to name the least integer not nameable in fewer than nineteen syllables? A: Yes: you’ve just done that. But ‘the least integer not nameable in fewer than nineteen syllables’ actually contains eighteen syllables. So the least integer not nameable in fewer than nineteen syllables has just been named in fewer than nineteen syllables.
That was obviously a philosophers’ in-joke, but ‘interesting’ and ‘uninteresting’ numbers are more, um, interesting. An ‘interesting’ number, in the jargon, boils down to being one that can be expressed by an algorithm. Hence ‘5’ is ‘the third prime number’, ‘121’ is ‘112’. The really interesting ones come when the algorithm is shorter than the number, thus facilitating data compression with all its essential benefits for information exchange. But the really really interesting numbers are the ‘uninteresting’ ones, because they are random. There’s no algorithm from which you can derive the number. ‘Random’ numbers are a building block of modern internet security. But the really really really interesting question is: how do you know they’re random? Couldn’t it be that you just haven’t found the algorithm yet? Vast resources at NSA and GCHQ are being devoted to cracking that one.
And finally, a quote: “What might not be gathered some day in the twenty-first century from a record of the correspondence of an entire people?” Andrew Wynter, ‘The Electric Telegraph’, 1845.
Sorry, that’s three snippets. Three is more than a couple. Like I said, numbers and me, duh.
*Carefully chosen word.