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Comment by hutzlibu | Hacker News Reader

Whats wrong with long variable names?

Did you ever need to do involved mathematical manipulations using pen and paper? How would you judge the readability of the following expressions:

  zero_point equals negative prefactor divided_by two plus_or_minus square_root_of( square_of(prefactor divided_by two) minus absolute_term )

  zero_point = -prefactor/2 ± √((prefactor/2)² - absolute_term)

  x = -p/2 ± √((p/2)² - q)

I might be strange but the second seems far more readable than the third to me. The first is of course nonsense.

In my opinion, it puts too much emphasis on the variables compared to the operators and numbers and makes the expression as a whole harder to parse at a glance as I have to actually read the names.

Yeah, when doing it with hand, I surely would shorten it. But when doing math on the computer with help of autocomplete, why not? But well, I do not really know if that in pure math shape exists, I am only doing Math in the context of programming.

And for pedagogic purposes, I do would like more meaningful names at times.

It's definitely a lot harder to read and make sense of an equation that is sprawled out. In some domains, I would contend that using greek letters in code would increase readability, especially for those familiar with the underlying formula, and especially if the code is not edited frequently (e.g. implementing a scientific formula which won't change).

A good compromise might be to put the equation in the comments in symbol-heavy form, and use the spelled out names in code.

Try to solve the Schrodinger Equation for even an infinite well using long variable names.

I'm not talking about using it in code, I'm talking about someone arguing that books and articles should do it as well.

If you go watch math lectures, there's a bunch of "x means Puppy Constant" or, "let's substitute in k for the Real component", or "let's signify <CONCEPT> by collecting these terms into a variable". My argument wouldn't be to replace ALL the variables with meaningful names, just the ones with a lot of meaning that a reader might not understand. It'd also be great if constants, variables, and functions all got naming conventions. Lowercase letters are variables, all caps for constants, etc. It saves a little bit on writing to shorten the variable names, but if the goal of math is to share and spread knowledge within the community or without, better naming and less-memorization would both help. You can also rename things for the working out and use friendlier names for the final equations, just tell people how you're renaming them and everyone will follow along and the programmers will stop trying to sell you one readable code.

Most importantly the flat dismissal and horror that many express when someone brings up adjusting the symbolic traditions of Maths should be investigated. Engage with why you feel so strongly that anything other than rigid adherence to tradition is sacrilege. Based on what I've heard, in order to be a great Mathematician, you need to hold onto tradition lightly and think outside the box. Rigid adherence to tradition doesn't sound like that to me.

> Engage with why you feel so strongly that anything other than rigid adherence to tradition is sacrilege

Who’s saying that? Inventing good notation is a big part of mathematics (and that also frequently gets criticized on HN because it may introduce ambiguities)

Also, there’s nothing wrong with texts that target an audience with a certain level of understanding.

It’s not as if adding, for example, “By Hermetian matrix we mean a complex square matrix that is equal to its own conjugate transpose” will make a paper much easier to understand, just as adding a comment “this is where the program starts running” doesn’t help much in understanding your average C program, or adding a definition of “monarchy” to a history paper.

In the end, any scientific paper has to be read critically, and that means making a serious effort in understanding it. A history paper, for example, may claim that Foo wrote “bar” but implied “baz”. A critical reader will have read thousands of pages, and (especially if they disagree with the claim) then think about that for a while, and may even walk to their bookshelf or the library to consult other sources before continuing reading.

Again, try to solve the Schrodinger Equation for even an infinite well using long variable names.

Got a reference for what that looks like with current notation? The internet is basically just showing the starting equation and ending equation and skipping all the intermediaries.

You can use whatever notation you want for your own work, but documenting with, at least, formal variable definitions would be a significant boon for math literacy.

Nothing, but their use in mathematical equations will certainly conflict with the implicit multiplication in equations (i.e. `abc` in a formula means `a * b * c`, not a variable abc).

This is already a problem, sin is the sine function, not sin.

You can use a different font.

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