Comment by gjulianm | Hacker News Reader

Comment by gjulianm | Hacker News Reader

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Variable naming is important because variables are used to represent almost anything, you have autocomplete and search so longer variable names are quickly typed, and most lines of codes will have one, two or three of these names.

On the other hand, notation in mathematics is used to represent only a limited set of common concepts for the field, you don't have autocomplete and a single line can contain a lot of concepts. For example, compare two expressions of Stokes' theorem (given HN typesetting limitations):

    ∫_A dω = ∫_∂A ω

versus

   integral(A, differential(ω)) = integral(boundary(A), ω)

While the second one is easier to understand at a first glance, the problem of that equation is not the symbols but the concepts behind them. And to understand the concepts you're going to go over similar equations time and time again, and at that point the extra letters and extra space used is going to complicate both writing and reading the equations. Of course, there is always people who overuse and underuse notation, but if mathematics relies heavily on notation it's for a reason: it's useful.

Edit: Also, the second one is only "easy" if you're familiarized with function calling in programming. One could argue that to go full notation-less you should only write in proper sentences, and that would make it even more complex.

> One could argue that to go full notation-less you should only write in proper sentences, and that would make it even more complex.

Reading Newton’s principia is humbling. He does that the whole book; it takes him pages to explain concepts we now learn before university and that can be condensed in a couple of equations. Finding words to describe the maths he uses is difficult, you can almost feel the insane amount of work just to translate the concepts into sentences. It’s a wonderful example, and of course a masterpiece. But reading it is also very difficult because of all the noise around the concepts. Words are fine to give an intuitive understanding, but at some point you need equations.

Same for Maxwell’s equations, for example. You’d spend less time learning basic calculus and algebra than trying to understand what the hell he was meaning.

Or 19th-century chemists, who used fancy and complicated names for compounds that are described much more clearly and succinctly with a chemical formula. Yes, you need to learn the formalism, but it pays off.

Some counter examples are Einstein and Feynman, who could communicate complex concepts with words in an understandable way. Though even them need some abstract notation at some point (lots of it, actually).

I can search the words. I can ask people what the words mean. If don’t even know what the symbols are called then how do I begin?

I had this problem when I started higher level maths and the Greek alphabet was used. I couldn’t ask what a symbol meant when I couldn’t say what the symbol was. I couldn’t write down a symbol whose name was read out when I didn’t know what it should look like.

I tried learning the Greek alphabet but flash cards and spaced repetition didn’t work for my ADHD brain and I just had to stop doing maths, which was a shame, because up to that point I was good at it.

> I can search the words. I can ask people what the words mean. If don’t even know what the symbols are called then how do I begin?

Usually by looking at the words that surround the equation. Most math texts will introduce notation in words, and it's common to repeat something in words and notation (e.g. 'let the field extension L/k...'). I have studied math for five years and I don't think I ever had the problem of not knowing how to search for something. The only problem I had with notation was finding the LaTeX code for a specific symbol, but other than that the bigger problem were the concepts.

There are also glossaries at the end of books and in some specialized pages too (https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo...)

> I couldn’t ask what a symbol meant when I couldn’t say what the symbol was. I couldn’t write down a symbol whose name was read out when I didn’t know what it should look like.

In my classes these problems were usually solved by asking "what's that wiggly thingy" or "how do you write 'alpha'".

And the greek alphabet is not used because mathematicians like to annoy people. There are certain customs for how objects are notated. x,y,z for unknowns/variables; f,g,h for variables; α,β for angles; A,B for matrices; G, H for groups... They are used because, even though they might be harder for beginners, they aren't harder than the concepts they're describing and help a lot in reducing the cognitive load when reading things.

Great to hear you didn’t find these things a problem and that they aren’t really that hard to understand.

Not sure whether you're being sarcastic, but in case you are:

The internet, including this forum, is chock-full of people making useless comments like "well I like it" or "it works for me", just asserting their views or experiences while advancing no argument and offering no discussion.

The post you just replied to is not doing that.

The poster you replied to is taking the time to describe and explain his experiences and their implications. He's contributed a lot more to the conversation than you have, and doesn't deserve sarcasm.

You weren't sure whether I was being sarcastic, yet you /are/ sure that the post I sarcastically responded to was written in the spirit of contribution, and was not itself insincere.

Sincerity doesn't matter when the commenter is correct. I've taken plenty of math classes, and everything he describes is accurate.

There's only 24 letters in the Greek alphabet, and any given piece of math doesn't use more than a few of them at a time.

You're clearly capable of learning at least one alphabet, why was the second so much harder?

First one probably took hundreds of hours or practice and a ton of exposure, to be fair.

> First one probably took hundreds of hours or practice and a ton of exposure, to be fair.

Learning the Greek alphabet shouldn't take more than 10 hours. Not that one needs to. I never did. However, in a given discipline, practitioners tend to be consistent on which Greek letters they use for which concepts. As long as you spend time on a given topic, the Greek symbols should become ingrained - just as knowing how to write a for loop in C would become if you do it often enough.

And I would hope people studying math spend a lot more than hundreds of hours on it. If someone came and complained about the arcane syntax used in programming languages and hadn't spent, say, 100 hours programming, I don't think you would give much weight to their views.

Actually you have an example of the unexplained oddness there: what does the underscore mean?

I can't put subscript on HN (or at least I don't know how), see https://en.wikipedia.org/wiki/Generalized_Stokes_theorem (first equation) for how it should be typeset.

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