4 ms·

Variable naming is important because variables are used to represent almost anything, you have autocomplete and search so longer variable names are quickly type

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.

Izkata 5y ago
Actually you have an example of the unexplained oddness there: what does the underscore mean?
- gjulianm 5y ago
  I can't put subscript on HN (or at least I don't know how), see https://en.wikipedia.org/wiki/Generalized_Stokes_theorem https://en.wikipedia.org/wiki/Generalized_Stokes_theorem (first equation) for how it should be typeset.
tokamak-teapot 5y ago
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.
- gjulianm 5y ago
  > 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_symbols 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.
  - tokamak-teapot 5y ago
    Great to hear you didn’t find these things a problem and that they aren’t really that hard to understand.
    - zazen 5y ago
      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.
kergonath 5y ago
> 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).

Izkata 5y ago

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

gjulianm 5y ago
I can't put subscript on HN (or at least I don't know how), see https://en.wikipedia.org/wiki/Generalized_Stokes_theorem https://en.wikipedia.org/wiki/Generalized_Stokes_theorem (first equation) for how it should be typeset.

tokamak-teapot 5y ago

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.

gjulianm 5y ago
> 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_symbols 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.
- tokamak-teapot 5y ago
  Great to hear you didn’t find these things a problem and that they aren’t really that hard to understand.
  - zazen 5y ago
    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.

kergonath 5y ago

> 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).