13/01/2013

the mathematical food chain

 
"Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum,
And the great fleas themselves, in turn, have greater fleas to go on,
While these again have greater still, and greater still, and so on
."
- Augustus De Morgan
 

I do maths these days. But, even studying the elementary things I am, I get vertigo off the scale of the differences in mathematical ability. It's super-logarithmic. Let's torture a metaphor:

  • God: Euler. Cos of his thousand instinctive transformations, foundation of the modern manner, and being 200 years ahead of his time. Hear us testify!
    "I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was... expelled from the Cantorian paradise." - Alexander Stepanov

    "Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence." - Keith Devlin
    'Physicists and mathematicians sometimes jest that, in an effort to avoid naming everything after Euler, discoveries and theorems are named after the "first person after Euler to discover it".'

  • Prophet: Ramanujan. Riemann.

  • Theologian: Hilbert, Frege. (Probing the roots.) Perelman. 

  • Anchorite: The likes of James Reid and his mere million current and historical peers.

  • Missionary: Johnny, and all the other Applied users.

  • Lay preacher: Me

  • Congregation: everyone.


(Alternative metaphor: God > Stars > Primary producer > Secondary producer > Reproducer > Consumer > Coprophage. Yes, I did just put plants closer to god than humans.)

I'm not in general enamoured of hierarchies. To do the above (list the BEST EVER) in art terms, or philosophy terms, or even science terms would be tasteless, misleading and sensationalist. (And it should be emphasised that almost anyone with the time and inclination can get themselves up to Missionary grade.) What makes maths different? There is after all certainly still loads of room for disagreement, human factors, and politicisation in it. But it maybe isn't so mysterious, since consensus and the appreciation of fixed measures are in the essence of maths, and since with a good fixed measure (and only with that measure) one can appreciate magnitude.

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