I wish mathematicians would take a page out of computer science/software engineering, where we’ve collectively decided that single-character variable names are bad practice.
I do understand the value and beauty of a terse notation, especially when hand-writing it, but I can also appreciate similar beauty of well-structured and self-documenting code, especially within an code editor that uses a language server that can provide context for any symbol. White space hints at structure and comments clarify the more difficult to parse sections of code
I’m constantly algebraicly manipulating symbols. We generally call it refactoring, but it’s the same thing up to an isomorphism. I aim to write my code in such a way to minimize the cognitive load on the reader. Using single-character symbols adds a whole layer of cognitive load where the reader needs to keep a mental map of what each symbol represents, especially when the convention chooses an arbitrary symbol, rather than at least using abbreviations. This feels especially onerous for students who are trying to learn the concepts behind the symbols, while trying to keep track of what each symbol represents
This is really is just a general rant. You did a good job with your explanation. It balances technical nuance with approachability. That really is why I even had this thought to begin with.
This will make sense when mathematicians stop using pen and paper. Or maybe only for presenting the final equation. Otherwise solving an equation would take ten pages full of prose—and the terse notation was historically invented to prevent exactly this.
I wish mathematicians would take a page out of computer science/software engineering, where we’ve collectively decided that single-character variable names are bad practice.
I do understand the value and beauty of a terse notation, especially when hand-writing it, but I can also appreciate similar beauty of well-structured and self-documenting code, especially within an code editor that uses a language server that can provide context for any symbol. White space hints at structure and comments clarify the more difficult to parse sections of code
I’m constantly algebraicly manipulating symbols. We generally call it refactoring, but it’s the same thing up to an isomorphism. I aim to write my code in such a way to minimize the cognitive load on the reader. Using single-character symbols adds a whole layer of cognitive load where the reader needs to keep a mental map of what each symbol represents, especially when the convention chooses an arbitrary symbol, rather than at least using abbreviations. This feels especially onerous for students who are trying to learn the concepts behind the symbols, while trying to keep track of what each symbol represents
This is really is just a general rant. You did a good job with your explanation. It balances technical nuance with approachability. That really is why I even had this thought to begin with.
Thanks for sharing!
This will make sense when mathematicians stop using pen and paper. Or maybe only for presenting the final equation. Otherwise solving an equation would take ten pages full of prose—and the terse notation was historically invented to prevent exactly this.