Tuesday, January 27, 2009

An apeal for clarity

Dear Fellow Mathematicians

Letters make Lousy Names For Theories! I mean, no-one goes around talking about "H-theory", it's Homology and Homological Algebra; analysis isn't "ε-δ-theory" even if within analysis "ε-δ-arguments" are a hugely fundamental skill to develop.

So, then, why have we got "q-deformation", "K-theory", or "π-categories", or "L-series"? (Unless π is some special value of n?) For one thing, when you hear it, how do you know that "q-deformation" isn't Q-deformation? Sure, "λ-calculus" is pretty special, but---accepting the Church-Turing [hypo]thesis---you might also call it "recursion".

On the one hand, "q" "K" "π" "L" and "λ" don't actually convey anything about what they signify. Within the cultures that give rise to these names, "q" is a number which might be prime, or might be close to zero, or close to 1; K is a functor to graded modules; "λ" is a piece of syntax, and could formally be replaced by "[" without loss of legibility. I don't even know what "L" and "π" are; though I do know many things that get called "L-series", and have my own ideas about what common ground they inhabit. And that brings up another thing: when the name for a province of research is an "in"-joke or otherwise obscure reference, it makes it intimidating for neighbors to take an interest in what you're really studying, and it's not clear to me that this helps you write grant proposals. Short, cultural nicknames are suitable for those intimately familiar with the subject; there should be better language for talking with foreigners.

On the other hand, there just AREN'T enough letters to reserve them for broad concepts at whim or out of laziness. So, if you're on the cusp of formalizing a grand new scheme of gadgets or tying together some ring of concepts, try to at least give them a decent, pronounceable, memorable name? It'll be very confusing when we have to re-name half of our things four decades from now, so be considerate.

From a crowded address space


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