2013-01-20

Towards less opaque mathematics

Language, too often, thou art dirty.

I say it too often because I feel it too often. Conventional mathematical language overcomplicates math. I was relearning the language of exponentiation and logarithms today. These are merely inverse ("opposite") functions. Here's a teardown.

\[\begin{bmatrix}aˆb = c\end{bmatrix}\]Where
  • a \(\equiv\) "base"
  • b \(\equiv\) "index" or "power"
  • c \(\equiv\) "a to the b-th power"

... versus...

\[\begin{bmatrix}\log_a c = b\end{bmatrix}\]Where
  • a \(\equiv\) "base"
  • b \(\equiv\) "logarithm-of-c to base-a"
  • c \(\equiv\) "a to the b-th power"

I mean, look, the verbal description (as read aloud) is clearly asymmetric, let alone the graphic morphemes of the notation.

Big sigh. So much friction in the language layer.

I want a mathematical morphology that is Pythonesque, one way to write anything, and it makes the most sense. Can we have such a revolution? It might make math a lot more popular. I'm almost sure it would increase the acceleration of quantitative literacy in the human race.

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