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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 s

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).

eru 3y ago
In number theory, 2 is often a special case in a lot of theorems. There's something odd about the even prime.
- xeonmc 3y ago
  i.e. the first information-encoding base.
  - eru 3y ago
    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 https://en.wikipedia.org/wiki/Fibonacci_coding
- 1propionyl 3y ago
  In analysis and its applications, the L^2 norm is also rather special.
  - daynthelife 3y ago
    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
    - eru 3y ago
      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 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]

eru 3y ago

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

xeonmc 3y ago
i.e. the first information-encoding base.
- eru 3y ago
  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 https://en.wikipedia.org/wiki/Fibonacci_coding
1propionyl 3y ago
In analysis and its applications, the L^2 norm is also rather special.
- daynthelife 3y ago
  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
  - eru 3y ago
    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 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]