On: Tips for mathematical handwriting (2007)

[paulluuk]

Mostly unrelated, but I wish the field of math would step away from greek letter notatation and just make variable and function names readable as programmers do. I know there are historic reasons, and I'm sure that mathematicians' time is so valuable that they can't be bothered to write more than 1 character, but it's a real barrier to entry in my opinion.

  def α(β, γ):
      δ = β ** 2 + γ ** 2
      ε = δ ** 0.5
      return ε
  
  ζ = α(3, 4)
  print(ζ)

[fujinghg → paulluuk]

The use of the Greek alphabet is mostly driven by convention. You get used to it. They aren't just sprayed around randomly wherever you look.

As for your code, urgh. A mathematician would carefully define what the function and operands are and the domain of each. More, and I'm vasty simplifying here as I don't have LaTeX available. I don't know what your code does so I've invented some words.

Let f(x,y) represent the rate of change of doodads where x is the number of doodads and y is the amount of doodads per gronk.

    f(x,y) = ( x^2 + y^2 ) ^ (1/2)

That's pretty tight and clearer than the code is.

[card_zero → fujinghg]

Maybe tight is harmful.

The code is unclear because it has single-letter variables instead of names, exacerbated by being in Greek, which mathematicians reached for because they were using single-letter variables, and ran out of them, and weren't bold or imaginative enough to break from convention. Then they used up the best of the Greek letters too and moved on to things like Gothic. This is stupid.

[fujinghg → card_zero]

No they didn't use them because they ran out. You know nothing about mathematics clearly. There are conventions to keep it concise. Some definitions of simple things would be unreadable if you used longer names. Consider the quotient rule:

    k'(x)=(g(x)f'(x)-f(x)g'(x))/(g(x)^2

Or in your world apparently

    quotient'(expression)=(left_expression(expression)right_expression'(expression)-right_expression(expression)left_expression'(expression))/(left_expression(expression)^2

Yeah, no.

Surprisingly I've just gone through the last 30 pages of mathematical work I've done and there's a couple of π in ∫ there and that's it.

[BeetleB → fujinghg]

I'm sorry, but you used ' to denote differentiation.

To have it his way, you'd right:

(derivative(right_expression))(expression)

and so on.

Clear as mud!

[fujinghg → BeetleB]

Good point. Urgh.

Perhaps he's a LISP programmer and has some spare brackets floating around :-)

[xigoi → card_zero]

How would you name the variables in the code to make it clearer?

[jordigh → paulluuk]

> they can't be bothered to write more than 1 character

You try handwriting all of your code and let's see how long until you start abbreviating everything.

Mathematical notation is all abbreviations. We used to write mathematics without abbreviations. It was absolutely horrid. Try reading some 13th century mathematics, translated to your language (e.g. Fibonacci https://archive.org/details/laurence-sigler-fibonaccis-liber... ), and see how much of it you understand without the benefit of symbolic notation. We would even write aaa instead of a^3.

The point with mathematical notation is that it can all be sounded out and it's extremely general and abstract. Generally, x is not a measurement, a quantity with a unit, a meaningful anything. It's just a number, and x is a better name than front_server_count or whatever thing you're programming about.

[annzabelle → paulluuk]

A massive amount of day to day pure mathematics work is still done by hand, on paper, whiteboard, or even chalkboard (and there's a preferred brand of chalk). Of course it will all be typeset before sharing, but mathematicians typically think by writing by hand, not think by typing.

[xanderlewis → paulluuk]

It’s for the same reason that almost everything in Unix is like

ls, man, wc, ps, grep, …

instead of

list, manual, word count, process(es?), <actually, what the hell does that stand for again>, ….

You get used to it, and then it’s much quicker. And being able to write things down quickly is very important when you’re in flow.

[The_suffocated → paulluuk]

Personally I don't find greek letters problematic. In contrast, I was traumatised by upper-case Fraktur font in older abstract algebra texts.

[jks → The_suffocated]

Fraktur is still used in model theory, but I don't believe that is easier to write than A' or  or something like that.

Set theory has aleph א and beth ℶ which are refreshingly not Greek but Hebrew letters.

[jks → jks]

Heh, U+1D504 MATHEMATICAL FRAKTUR CAPITAL A seems to have been filtered out of my comment, perhaps because it's outside the BMP.

[fxwin → paulluuk]

the vast majority of mathematical equations/terms would become completely unreadable if you replaced single symbols with descriptive terms. You are going to have to internalize what the symbols refer to anyways to understand the formula, and once that is accomplished any additional description is a waste of space and cognitive bandwidth.

[card_zero → fxwin]

Nah, try it, you'll be fine.

The real problem is, everybody else will complain, because its unconventional. Then you look foolish.

[jordigh → card_zero]

We did try it. We tried it for a couple of millenia. It was much harder to understand and our collective mathematical output as a human species was much slower than it is now.

Shorthand is better.

[card_zero → jordigh]

No, I don't believe you. Mathematicians love inaccessibility.

[fujinghg → card_zero]

It's not that.

You know when you go to a foreign country, ask for a particular thing in a restaurant proudly in their language that you picked up on Duolingo the week before and the waiter starts talking to you quickly in their language and you lose it completely.

We are just that waiter. You didn't learn the language or get the prerequisite skills. So do that or don't bother. It's not easy and there are no shortcuts.

[fxwin → card_zero]

Even if i agreed with you that full words/phrases were easier to parse, any gains made here are easily offset by how much harder and laborious it is to manipulate them on paper

[xigoi → card_zero]

Consider the formula (a+b)² = a² + 2ab + b². How would you name the variables to make it more “readable”?

[jordigh → xigoi]

The square of the sum of two quantities equals the sum of the square of each quantity plus twice their product.

So much more readable! /s

[queuebert → paulluuk]

It's only a small part of the barrier to entry, though. I could write Einstein's equations out in words, and most people still wouldn't be able to do GR.

[layer8 → paulluuk]

Handwriting doesn’t have autocomplete.