Doctor Who_ The Algebra of Ice - Lloyd Rose [84]
‘What’s that mean?’
‘I mess around. Try to turn maths into music.’
She frowned. ‘And what’s that mean?’
‘You really don’t want to hear about it.’
‘Stop telling me what I won’t like!’
‘Seriously. It’ll bore the hell out of you, Ace. It bores most people.’
She plunked stubbornly down on the bench beside him. ‘Try me.’
‘OK, then.’ Ethan made a mental bet with himself as to how long it would be before her eyes glazed over. Less than three minutes or more than three Chapter Twenty
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minutes? There was always something dispiriting about watching the interest drain from a listener’s face. ‘By plucking a string, Pythagoras worked out that a note’s relation to its overtones was always a fraction: 1/2, 1/4, 1/3, 1/5. For reasons having to do with the human ear and brain, we find the correspondence between any given note and its third and fifth harmonics the most pleasing. I’m losing you, aren’t I?’
‘No,’ Ace said bravely.
‘Here. I’ll show you on the piano.’ He picked out the keys. ‘Our main note, its third, and its fifth. Now I’ll do the same thing in D. Already, you see, we have a whole and its fractions turned into music.’
‘Wicked!’
He glanced sideways to see whether she were having him on, but she was grinning, happy at learning something new. Well, that was why the Doctor travelled with her. One reason, anyway.
‘Well, you remember that a prime number –’
‘– is divisible only by itself and one.’
‘Right. The only even prime number is two, for obvious reasons.’ She nodded encouragingly, but he could tell she wasn’t quite following. He really wasn’t much of a teacher; it was difficult to work out how to get past his own knowledge and explain something to a novice. ‘Well, never mind about two. Not important. What matters is that as far along the number line as we go – and it goes on forever since the number of integers. . . Forget about that. The number line is infinite. Now, most numbers or combinations of numbers form a pattern along the line. The simplest example is the odd or even numbers, which follow one another, odd, even, odd, even, and so on, forever. The primes are a consistently definable entity, in the same way, for example, even numbers are always multiples of two. But where even numbers occur regularly, the primes appear to be randomly scattered. The question is, why something that is such a building block of maths – all numbers can be reduced to multiples of two primes – has a disorderly sequence of appearances in the number line.’
‘So what does this have to do with music?’
‘Stay with me a minute. The Riemann hypothesis – that we talked about that time on the street. . . ?’ She nodded. ‘The Riemann hypothesis, if proved, would mean that there is in fact an organisation of the primes on the number line. But no one’s ever been able to work out a mathematical proof for it.’
‘That’s why everyone’s so excited about working it out.’
‘Exactly. It was listed at the beginning of the twentieth century as one of the greatest unsolved problems in mathematics. Well, it’s the twenty-first century, 174
The Algebra of Ice
and we’re no nearer than we were a hundred years ago.’
She grinned. ‘Well mysterious.’
‘Yes,’ he said. ‘A beautiful, tantalising mystery. The mathematician’s Grail.
Only it’s more like the Questing Beast, running away from you up the number line. This all has to do with music,’ he went on, cutting off her question,
‘because. . . ’ He paused, very tempted to say, ‘Because it does’. This was harder than he’d thought. ‘Erm, the thing is if you restate the occurrence of the primes in the number line as a graph, the results indicate they might have an order.
And each prime point on the graph has a specific vibration. Fundamentally, at the subatomic level, everything is vibrations – let’s drop that. The point is, you can restate those vibrations as musical notes.’
Ace appeared to be trying to suppress any indications that she thought he was mental. ‘You know that makes no bloody sense at all.’
‘Well, no,’ he conceded. ‘But it is true.’
She smiled.