The Unclear Impact

[2 -2] is a 1x2 matrix containing the square roots of 4
(2 -2) is 0
[2 - 2] is a 1x1 matrix containing 0
(2 + - 2) is 0

I think I'm getting the hang of it.

@pigworker i thought javascript has horrifying semantics – but this thing has horrifying syntax

if we set
A = [1 3 5]
B = [A(2)]
C = [A (2)]
D = A (2)
we find
B = 3
C = [1 3 5 2]
D = 3

@pigworker and what about (2 + / - 2)?

@BobOHara Thank Christ that's a syntax error!

The people who wrote this system have also written copious documentation with many examples but not precision whatsoever about what the rules are. We're reverse-engineering them.

Proof assistant folks, take note. When the mathematicians ask to be in charge of the notation, give them the death-stare.

@pigworker I'm pretty sure the near-universal reaction of mathematicians to MATLAB's syntax and semantics is "ewwwwww". #NotAllMathematicians

@gjm Good. I don't imagine that the criminals responsible consider themselves non-mathematicians, so there is a nontrivial internal discipline problem. Meanwhile, yikes to the variable binding discipline in calculus, for example. Intimidation doesn't work on machines; clarity does.

@pigworker Yeah. Pure mathematicians are generally better about this than applied, but definitely not as careful about notation as computer scientists.

But. A thing isn't clear or unclear, it's clear or unclear _to a given audience_, and humans are better at some things and worse at others than machines. That ambiguous notation may e.g. be terser and let us fit more in our horrifyingly small working memories, and the tradeoff might be worth it.

@gjm Two things. 1) Minding context is massive: every bit I need to carry to figure out how to read makes me sad, but I can. 2) I'm in the human business of making machines put up with humans, and the magical thinking is unbearable.

@pigworker Concrete example: Sussman & Wisdom's "Structure & interpretation of classical mechanics". Usual notation for Lagrangian mechanics is full of potentially confusing and ambiguous partial derivatives. They instead say L is (not "an expression", bleh, but) a function, conventionally passed (time, coordinates, time-derivatives of coordinates), so write ∂₀L, ∂₁L, ∂₂L for the partial derivatives.

[1/2?]

@pigworker Unambiguous and definitely not nonsensical, unlike the usual notation. But now every time I read one of their formulae I have to think about which arguments to L are in which numerical position, and it's not clear that the loss doesn't outweigh the gain. Maybe it does, maybe not. But the tradeoff for humans isn't the same as for computers: for computers their notation is _obviously_ better, for humans not so much.

[2/2]

@gjm It is certainly the case that the conventional notation is full of confusing partial derivatives, for which scope is terrifying. Inevitably, I have been forced to figure out ways to facilitate accuracy.

@pigworker If you care about that stuff at all and aren't already familiar with SICM, you might want to take a look. Classical mechanics done in a mixture of semiconventional mathematical notation, cleaned up with a computer scientist's sensibilities, and Scheme. (Yes, same Sussman. Yes, the name of the book is deliberate.)

@gjm I got that. I might indeed want to take a look. I hang out with a lot of physicists these days.