Tuesday, 7 July 2015

Numb and Number


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.

7 comments :

  1. Maths is a largely foreign language to me too.

    There was a trailer shown on TV a few years ago for a programme called "Educating Essex". I never saw the programme but I remember the lovely girl on the trail saying "What is pi? Where does it come from?" I very much identified with that young lady.

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  2. I'm sure we had that Berry Paradox in a cracker oner Christmas. May have been the Cranberry Paradox. Are you sure you haven't accidentally read The Information by Martin Amis?
    (Liz is still focussed on comestibles also I see.)

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  3. The chance of even your very best tweet being seen again by human eyes is approximately zero.
    Tweets are just bits.
    I wonder if approximately zero is a random enough number to avoid the algo-rhythm? Perhaps this is the meeting point of music and mathematics.

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  4. Liz, it's frustrating, because I'm fascinated by languages, but know I'll never understand that one.

    Rog: I haven't tried cranberry pi. I have read the Amis, and I'm pretty sure he didn't cover set theory and Boolean algebra, so not accidental, probably. (Although Probability is a big theme in Information Theory, as it happens.)

    Richard, that's very probable, given that I've only ever done about six tweets. And it's too late to ask Ornette Coleman about randomness in music, though I'm sure he'd have had a lot to tell us.

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  5. Oh, and I thought I'd made a mistake in naming 5 as the third prime, because I'd forgotten 2 (which is interesting - the only even prime number). But it turns out that 1 isn't counted, for some reason.

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  6. Living with Sir Bruin, it's inevitable that Liz should focus on pi.

    I know little about maths but I enjoy numbers. My children are bemused when I explain how I remember a long number a series of - the square root of one number followed by the square root of another number gives the year that your grandmother was born, followed by her age when I was born ... and so I ramble on. It all makes sense to me. Or anyway, it did before I wrote it down.

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  7. I had two grandmothers, and I know the years they were born. Can your algorhythm work backwards so that I can find out the number I first thought of?

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