Story-telling pieces of maths

When I was wee and being taught maths in the bad standard manner, I instinctively came up with little characterisations of various mathematical objects, to protect myself from boredom:

• The positive and negative numbers are mortally opposed armies; the modulus denotes the size of each army; each unit can handle one unit of the enemy before dying (evaporating together, in fact). Addition and subtraction are fair fights upon the field; multiplication and division are espionage and political overthrow. The negatives hate each other as much as they hate positives (-10 x -10 = 100). The positives are very simple and can be easily tricked into fighting for the other side (-1 x 1,000,000 = -1,000,000).


• Differentiation is desecration and zoom. Integration is reconsecration and overview. Going by the basic fairy-tale story arc, then, differdesecration is never the real end-point; a calculation isn't complete until it is brought back to the initial function... (Here we see the beginning of a perverse side to telling maths stories; it brings arbitrary constraints on operations.)


• Humans have no right to be using the infinite summation symbol so casually. It is a tense and crackling thing, like the Demon core.


• I also had a distinct emotional bias against discrete mathematics. 'Discrete entities are fake human constructs; your units are suspended over deep blackness. The awkward, smooth, tricky, crackling continuous is the real.' (Despite appearances, quantum physics doesn't weigh against this metaphysics.)


• The confusion matrix. Just get a deep sense of security and importance off it. Very glad we worked this out.

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Why is this so twee? Among laypeople (who, like feudal peasants listening to a Latin Mass, are forced to put up with a lot of maths despite incomprehension) it is strange because maths is represented as inhuman and boring and not the kind of thing that takes or needs creativity. Among the cognoscenti it's a strange thing to do, because the above is undignified, and one of the big reasons to do Higher mathematics is that it lets you take on the fearsome and transcendent silence of (the lay conception of) maths; difficult, unnarrated mystery is very high status. (This makes Ben Orlin wonderful in yet another way.) Of course one of the things about humans is that they will find meaning, project meaning, anywhere.