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Math is easier to understand with symbols if you've been trained in what all the symbols and syntax means, and virtually impossible to understand if you haven't

Math is easier to understand with symbols if you've been trained in what all the symbols and syntax means, and virtually impossible to understand if you haven't. This is easy to miss because for the most part we have one unified syntax taught in most the world. Words may not be the optimal format to express equations, but are the lowest denominator that would allow everyone to understand if they knew the concepts. That should illuminate why your opinion and other people's opinion of this differ. You likely each have different relative opinions and skills reading syntaxes like this.

avmich 5y ago
I think you're too categorical. We don't only use words in written communication - there are pictures and symbols too, so restricting ourselves to spoken words in largely symbolic activity seems a disadvantage. For both math and programming it makes sense to invest into training of symbols and then get to the matter with expanded toolset, rather than keep using something more similar to COBOL. Tools are important for the progress. It's not a random event that digits - essentially symbols for numbers - were invented millennia ago.
- kbenson 5y ago
  I wasn't making a case that words are better than symbols, only that there's always a trade off between representing something using existing known syntax and a somewhat less known but more concise and exact syntax, and that tradeoff is largely defined by how familiar your target audience is with that syntax. C-like syntaxes are more popular than lisp syntax(for example) not because it's inherently better but because most people have some exposure to it at this point through other languages they have been exposed to. Interestingly, that actually does make it inherently better in some aspects when choosing a syntax to adopt, such as learnability. For the person that only knows C and the person that only knows Lisp, which might have an easier time with the average rust program? What about someone that only knows Prolog? The issue is not about only using words, the issue is about using things your audience already knows. People use numbers in letters not just because words are less convenient, but because words are less convenient and they know the people on the other end know Arabic numerals so that's a valid medium to rely on. For programming languages it's less that words are better and more that there are either different or conflicting meanings for many symbols leading to confusion for those that deal with multiple languages or are new to the current language, so time needs to be taken to internalize what they mean in this new context. That doesn't make them bad or worse than words, but often they necessarily are less obvious in meaning to those new to the language to benefit those that are more familiar or experts.
void_mint 5y ago
> Math is easier to understand with symbols if you've been trained in what all the symbols and syntax means, and virtually impossible to understand if you haven't. I haven't and it continues to be a massive source of shame. Maybe today's the day I do something about it.

avmich 5y ago

I think you're too categorical. We don't only use words in written communication - there are pictures and symbols too, so restricting ourselves to spoken words in largely symbolic activity seems a disadvantage. For both math and programming it makes sense to invest into training of symbols and then get to the matter with expanded toolset, rather than keep using something more similar to COBOL. Tools are important for the progress. It's not a random event that digits - essentially symbols for numbers - were invented millennia ago.

kbenson 5y ago
I wasn't making a case that words are better than symbols, only that there's always a trade off between representing something using existing known syntax and a somewhat less known but more concise and exact syntax, and that tradeoff is largely defined by how familiar your target audience is with that syntax. C-like syntaxes are more popular than lisp syntax(for example) not because it's inherently better but because most people have some exposure to it at this point through other languages they have been exposed to. Interestingly, that actually does make it inherently better in some aspects when choosing a syntax to adopt, such as learnability. For the person that only knows C and the person that only knows Lisp, which might have an easier time with the average rust program? What about someone that only knows Prolog? The issue is not about only using words, the issue is about using things your audience already knows. People use numbers in letters not just because words are less convenient, but because words are less convenient and they know the people on the other end know Arabic numerals so that's a valid medium to rely on. For programming languages it's less that words are better and more that there are either different or conflicting meanings for many symbols leading to confusion for those that deal with multiple languages or are new to the current language, so time needs to be taken to internalize what they mean in this new context. That doesn't make them bad or worse than words, but often they necessarily are less obvious in meaning to those new to the language to benefit those that are more familiar or experts.

void_mint 5y ago

> Math is easier to understand with symbols if you've been trained in what all the symbols and syntax means, and virtually impossible to understand if you haven't. I haven't and it continues to be a massive source of shame. Maybe today's the day I do something about it.