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Comment by susam | Hacker News Reader

> I believe inability to do arithmetic correctly is more common in folks with maths and other STEM degrees

Reminds me of a story from <https://www.ams.org/notices/200410/fea-grothendieck-part2.pd...>. Quoting it below:

One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”

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This is absolutely my personal experience. I am absolutely awful at arithmetic, but I think pretty competent at decently advanced mathematics.

It's like they say: the only numbers a mathematician needs are 0, 1, and 2 (and just because it's not 1).

In number theory, 2 is often a special case in a lot of theorems. There's something odd about the even prime.

i.e. the first information-encoding base.

I'm not sure. The Fibonacci numbering system has a smaller effective base.

(And there's always unary.)

See https://en.wikipedia.org/wiki/Fibonacci_coding

In analysis and its applications, the L^2 norm is also rather special.

My hot take is that it should be called the L^(1/2) norm. Many theorems and formulas become a lot easier to state if you redefine L^p as L^(1/p).

For instance, under this notation, the dual of L^p is just L^(1-p). And Littlewood’s interpolation inequality is a lot easier to remember, since the exponents used come directly from the coefficients in the convex combination:

If r = ap + bq, where a and b are nonnegative and sum to 1, then |f|_r <= (|f|_p)^a (|f|_q)^b

You should join the folks at the tau-not-pi club.

And going off on a tangent: in thermodynamics, we should measure coldness (coldness ~ 1 / temperature). It makes all the math come out nicer.

See https://en.wikipedia.org/wiki/Coldness

Coldness handles 'negative temperatures' much better. As Wikipedia puts it:

> Though completely equivalent in conceptual content to temperature, β [= coldness] is generally considered a more fundamental quantity than temperature owing to the phenomenon of negative temperature, in which β is continuous as it crosses zero whereas T has a singularity.[7]

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