The doughnut theorem

15Jan10

Some simple maths – let’s see how much we can remember from school.

Let this be our opening hypothesis:

If 1 x a = b then 5 x a = 5b.

With me so far? Yes, of course you are. Because it’s obvious, straightforward and logical. About a year ago I watched a telly programme about maths and why it’s an academic-yet-fun-type thing to do. I ain’t no mathematician so I settled into the sofa, folded my arms and set my expression to yeah, right. But by heavens, by the end of the programme I was a convert. Not that they splained much actual maths – just as well because I lose track easily – more that they described what it could do and how.

For example, they told me in a way that I could grasp, what an algorithm is. I have never, ever known that before. And yes, once I knew what an algorithm was, I could at least dimly perceive why mathematics is like music, and just as beautiful. But. On the other hand, some strains (and I use the term advisedly) of maths are just pointless, and never applicable to real life. I shall prove it.

Let’s return to our simple equation above: If 1 x a = b then 5 x a = 5b. It must do. It can’t help it.

Now let’s substitute the letters with something everyday. Let’s try a = pint and b = great. We’ve all tried it, especially, say, during a hair-of-the-dog therapy session. You have one pint; you feel great (or at least better than you did before). Not only that, but suddenly you’re a maths genius and the whole equation vibe is blindingly obvious. Within minutes – you can’t help yourself – you’re extrapolating: multiple pints will result in an equivalent improvement in greatitude/genius because it stands to bloody reason. And that’s where this form of algebra – beerlgebra (copyright VH, my friends, and don’t you forget it) – falls down. Because it ain’t simple maths any more; somewhere between bar and whose round is it, it’s turned into complex bio-chemistry.

But the point of academic enquiry is not to accept a conclusion and leave it there. A roving intellect like mine rages without cease, driving me to interrogate the problem further, try something else, test the limits, throw in some variables.

So I tried a = doughnut, b = great (see entry below, for my early, faltering steps towards brilliance).

Two jammy delights had made me feel handsomely disposed towards the world. Therefore five would surely have a more-than-doubly-enhanced effect. Would it be exponential, or just compound? I thought I’d better find out quicksmart, so I ate three on the trot.

Now, as I bet happened with Newton, Faraday and Curie, things went a bit wrong a couple of hours later. I was pushing the boundaries of knowledge during a 15-hour-long double shift during which I barely move from my computer. To compensate for the long hours, the company hires in a caterer who chose that day to provide a (delicious) dinner of stew, dumplings and potato gratin, followed by warm chocolate and custard panettone pudding that was basically duvet covered in Bourneville.

Findings: It’s possible that the stew, dumplings, potatoes and pudding compromised the scientific rigor of the experiment, but I certainly woke up the next day feeling somewhere between -6 and -8great. By 4 o’clock I’d pushed it back to about -1. It’s my own fault, I know, but I’m buggered if I’m going to try it again.

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