> there's a reason math is so much easier to understand when it's expressed with symbols than with words
Had to do a double-take to make sure this wasn't /s
It's my opinion that the use of random symbols is the primary reason math is so inaccessible. It is for me, and anecdotally I've heard dozens of others say the same thing. The only imaginable benefit I can see to using symbols is that they're easier to write quickly on a chalkboard.
As an educator, I think about this a lot. One approach I'm prototyping for a (hopefully freely available) course on reinforcement learning is to translate dense math expressions into English sentences, and then link each piece of text<=>math with a corresponding color. (Quick example I just uploaded: https://gfycat.com/favorablemintyharrier ).
By doing this consistently, I can highlight the link between math symbol and corresponding concept, and help the student learn how to read and interpret dense constructions as we go.
(Note that this approach is intended to be used as part of a larger explanatory strategy, so please assume the example is embedded in an appropriate context.)
Amazing! I had a similar idea a long time ago, but never put effort into it. Tools like this help fill the gap between the formality and "humanity" when expressing and presenting such concepts to receptors (students).
I completely agree. For me it's less readable. I also think math is less accessible due to its use of random symbols that are context-dependent.
"Readability" is a highly, highly subjective matter, and depends on one's education, background, knowledge, experience etc. People seem to use it as a shorthand for "math-like shorthand", but that's not what I mean when I say readable, it's like we speak in a different language.
Personally I find the adjective "readable" a major trigger, it seems to be thrown around by people who are either trolling or who seem to live in a kind of a social (online) bubble and don't know anyone else with a even a slightly different background. This is always slightly shocking to me.
I remember sitting in the hallway of the building with the math department waiting for a class to start and picking up a booklet on a table with a style guide for writing mathematics and it specifically advised using words in place of symbols, e.g., preferring “for all x in the integers” over “∀x ∊ ℝ.”
Does this mean you prefer Ada or COBOL to C or JavaScript? All symbols (and words!) are “random” if you haven’t learned what they mean. I remember when I transitioned from BASIC to C (this was a while ago) it seemed ridiculously terse and full of crazy punctuation, but C-like syntax is now considered “accessible”.
The other huge benefit to symbols is that they are compact, and recognising patterns or performing symbolic manipulation is much easier when everything is shorter and closer together. Mathematics also uses a two-dimensional layout in some places (integrals, fractions), with very well-chosen and suggestive notation, which would be lost completely going to words.
Right. It's not just that they are random symbols. They are also inherently obscure symbols.
But just bad as or maybe worse are the variable names which are random, short, and completely non-descriptive. If you compare it to source-code, it's like the worst code ever written.
Had to do a double-take to make sure this wasn't /s
It's my opinion that the use of random symbols is the primary reason math is so inaccessible. It is for me, and anecdotally I've heard dozens of others say the same thing. The only imaginable benefit I can see to using symbols is that they're easier to write quickly on a chalkboard.