Luci for Chai Tea
I don’t want to be too disruptive
but I want you to try to imagine what maths could be like if we had a notation designed in a way in which running out of unique symbols just isn’t a problem
in a similar way that representing very large numbers doesn’t require an endless supply of new symbols in a positional number system; like a roman numeral style system would
Luci for Chai Tea
@apophis well, UUIDs would be a little bit hard to write I think
🐛
cathos
@zens making me think about lambda calculus again...
Luci for Chai Tea
@VolatileDream still only 26 letters in an alphabet minus e, i, r, and in many contexts t-z are taken up by 7 dimensions of coordinate system
VolatileDream
@zens Can't we do this relatively trivially by requiring folks to explicitly multiply rather than it being implicit? We already do this for numbers, so why not symbols too?
eg: `xy != x*y`, just like `12 != 1*2`
Luci for Chai Tea
@VolatileDream we cwn start numbering things like x_1 x_2 etc but then that’s ultimately a bandaid especially if you run into problems that have a *lot* of free variables
which can be fine if they can be reasoned about as a tensor like thing, but heterogeneous problems… not so much
Luci for Chai Tea
@VolatileDream it’s fine for software but keep in mind that part of the premise here is optimising for writing, and thus ensuring that symbols are not ambiguous. so at a minimum our * multiplicator must be clearly distinct from 𝑥
VolatileDream
@zens I think that if you explicitly state you're using "long symbol names" or "explicit multiplication" (name tbd), then only the single symbols are taken (and possibly only in limited contexts), and the system allows for longer strings of symbols as a unique identifier.
So even if e is taken, "ee" is a different identifier, and doesn't represent "e*e".
Eg, some physics: "speed = distance / time" involves 3 unique identifiers.
This seems similar to math & variables in software to me.
Luci for Chai Tea
@VolatileDream but also a lot of maths notation is the way it is to make writing and reading as easy as possible. but what is easy to write and read has changed since its original design
Luci for Chai Tea
@VolatileDream i find the same thing, which is what started my rant. i am just noting the historical reason for the terseness and opaqueness’s
VolatileDream
@zens I think we might have different experiences with math & how easy the status quo is to read or write.
I find a lot of math notation needlessly terse to the point of being opaque. Maybe it's fine on a chalk board for yourself or during a lecture, but on slides or in a paper you should optimize for time spent reading and use more descriptive names.
I've seen so much abbreviated "f(x) = ..." when that function and variable would benefit from more descriptive names.
Luci for Chai Tea
@VolatileDream there’s a lot of things. the point of OP is to prompt people to come up with their own schemes; which you have done, even if i find taking inspiration from programming languages a little boring
VolatileDream
@zens my bad, text is a lossy medium.
Do you know of any math journals that have proposed notation changes? It seems like something that must have happened before, at least to standardize on specific things.
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