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Comment by ndriscoll | Hacker News Reader

Incidentally this is why people miss the mark when they get mad about mathematicians using single letter variable names. Short names let you focus on the structure of equations and relationships, which lets you more easily pattern match and say "wait, this is structurally the same as X other thing I already know but with different names". It's not about saving paper or making it easier to write (it is not easier to write Greek letters with super/subscripts in LaTeX using an English keyboard than it would be to use words). It is about transmitting a certain type of information to the reader that is otherwise very difficult to transmit.

While it uses letters so it looks vaguely like writing, math notation is very pictorial in nature. Long words would obscure the pictures.

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I disagree. Single letter variables are meaningless. In order to get the big picture, you have to remember what all those meaningless letters stand for. Using meaningful variables would make this easier.

If you work with them long enough it becomes second nature to read them, and then it is easier to manipulate and compose them. The rest of the context is the background knowledge to understand the pithy core equations. Papers are for explaining concepts, equations are for symbolic manipulation. Meaningful variable names would be middle ground and not good at either, except to help someone not familiar with the subject to understand the equation, but a lot of the symbols are so abstract that they really need to be explained in more detail elsewhere or would be arbitrarily named.

If you're in an abstract/general mathematical function, then sure: single letters. If you're doing more business logic kind of stuff (iterating through a list of db/orm objects or processing a request body) then the names should be longer

Mathematics doesn't usually deal with databases or http requests

IMO your comment seems not to be addressing the point made in its parent comment. To make the point again with different words:

- Using long descriptive variable names would give them meaning, and make the particular equation/expression easier to understand or apply.

- Using short single-letter variable names allows you to forget the meaning of the variables and see the underlying structure, thus making the expression easier to connect to other situations (with completely unrelated meanings) that happen to have the same underlying structure. (The letters being meaningless, or at least not carrying their meaning so strongly, is a feature, not a bug.)

(See the highest-voted answer to https://math.stackexchange.com/questions/24241/why-do-mathem... for example.)

(Another way of seeing the distinction is whether you consider the equation to be the final result, to be used and applied, or as a starting point, to be manipulated further.)

Ok, that makes sense. Then maybe use single-letter variables for when working on something, and meaningful variable names for when publishing.

Edit: I realise, like someone mentioned in another comment, that sometimes you also want to make the pattern visible to readers.

Often the actual meaning of the symbols is subordinate to the point you're trying to convey. e.g. I can tell you that `integrate(boundary(Region), form) = integrate(Region, differentiate(form))`, which is great and all, but I might write `<∂M|w> = <M|dw>` because what I'm trying to tell you is that you should think of these things as a dual-pairing of vector spaces (via integration) and that ∂ and d are somehow adjoint. They're both Stokes' theorem, but the emphasis is different, and in either case the hard part is the mountain of work it takes to define what the words even mean (limits, and integrals, and derivatives, and vectors, and covectors, and manifolds, and tangent spaces, and vector fields, and covector fields, and partitions of unity, and symmetric and alternating forms, and exterior derivatives, etc. etc. all so you can finally write one equation, which really just says that all the swirlies inside a region cancel out so if you want to add them all up, you can just add up the outer swirly).

The thing about math is you need to be comfortable viewing the same concept through a bunch of different lenses, and various notations are meant to help you do that by emphasizing different aspects of "the picture" you're looking at.

Ok, I can accept that. At the same time, my impression is that mathematicians always use single-letter variables.

It's like either they're not clear who their audience is or they're afraid to get off the beaten path. If they're explaining a classic algorithm, they use the common, single-letter variables instead of replacing them with meaningful names.

yeah, that is why no one should use "i" and "j" in their loops. but instead choose "outerLoopIterator" and "innerLoopIterator" /s

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