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Comment by maxk42 | Hacker News Reader

Well perhaps it's mathematics that could benefit from an update to its representation. Mathematical symbols have evolved over hundreds of years and aren't really suited to modern systems of representation. When it comes to computers is it really easier to look up the unicode symbol '∩' or its LaTeX representation when you're trying to write 'A ∩ B' -- or would it be better to begin noting mathematics online in a portable way such as: (intersection A B)

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One of the reasons for infix notation in math is actually that it provides a 'visual' reminder of useful properties such as associativity, and possibly others e.g. commutativity or distributivity. If all we ever used was a strict LISP-like, function-based notation, such a reminder would be lost and understanding or manipulating non-trivial expressions would be quite a bit harder. The effort in OP is actually a way of generalizing this idea to broader settings, where one is dealing with something more complex than a single domain of number-like values, and a handful of operations on them. This is arguably how one should think of "graphical linear algebra" as well: the 'diagrams' one's dealing with there can be thought of as generalized expressions, so there's nothing overly strange in being able to manipulate those formally according to well-defined rules of some sort.

> 'visual' reminder of useful properties such as associativity, and possibly others e.g. commutativity or distributivity

These are semantic properties that most binary operators do not in fact have.

E.g. C syntax:

  A << B
  A = B
  A - B
  A / B
  A % B
  A < B

very well put!

this is exactly where the statebox project comes from, there is updated syntax for mathematics in the form of diagrams. of course not for all of it, but certainly very applicable to CS stuff

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