Ask HN: How did you learn math notation? • Hacker News Board

Re: Ask HN: How did you learn math notation?

#221

Post by webmaven » Fri, Nov 26, 2021, 2:34 AM UTC

Jensson wrote: post #150

webmaven wrote: post #135

Earlier quoted context omitted.

> Every math paper is its own DSL in this context with its own small explanations for how it does things. That's really the point though: not every piece of software defines it's own DSL, nor does it necessarily incorporate a DSL from some library or framework (which in turn may or may not borrow from other DSLs, etc.). It is also impossible to incorporate something from other software without actually referencing it…

> It is also impossible to incorporate something from other software without actually referencing it explicitly. No, some programming languages just injects symbols based on context. You'd have to compile it with the right dependencies for it to work, so it is impossible to know what it is supposed to be. And even if they reference some other file, that file might not even be present in the codebase, instead some fra…

> some programming languages just injects symbols based on context

Well, okay, yes, not all software projects deliver reproducible builds of their software. Some software is, in fact, complete garbage.

I'm also not using Gene Ray's TimeCube theory[0] as an example of a mathematical paper.

> This sort of time variance is non-existent in math

Not... entirely. You could cite a preprint that then changes in the final version.

> And you have probably seen a programming tutorial or similar which uses library functions that no longer exists in modern versions

Sure. And cited papers can be retracted entirely.

[0] https://web.archive.org/web/20070718050305/http://www.timecu...

Re: Ask HN: How did you learn math notation?

#222

Post by derekjdanserl » Fri, Nov 26, 2021, 3:08 AM UTC

ColinWright wrote: post #69

throwaway31338 wrote: post #54

Earlier quoted context omitted.

Came here to say the same thing harshly and laced with profanity. I guess I can back off a bit from that now. I was filled with crushing disappointment when I learned mathematical notation is "shorthand" and there isn't a formal grammar. Same goes for learning writers take "shortcuts" with the expectation the reader will "fill in the gaps". Ostensibly this is so the writer can do "less writing" and the reader can do…

You seem to be complaining that math isn't programming, that it's something different, and you've discovered that you don't like how mathematicians do math. Math notation is the way it is because it's what mathematicians have found useful for the purpose of doing and communicating math. If you are upset and disappointed that that's how it is then there's not a lot we can do about it. If there was a better way of doin…

This is a pretty good defense. Well done.

Re: Ask HN: How did you learn math notation?

#223

Post by klibertp » Fri, Nov 26, 2021, 5:43 AM UTC

JohnHaugeland wrote: post #213

Jensson wrote: post #206

Earlier quoted context omitted.

> Surely you must realize that you're protesting this because it has this reputation, though? I've never heard anyone make this accusation until I read it here on HN today. The reputation doesn't seem to be widespread. > Programmers work really really hard on learnability and understandability. This is a big deal to us. That's why we can't understand why it's not a big deal to you. How to better teach math is like on…

> > Surely you must realize that you're protesting this because it has this reputation, though? > > I've never heard anyone make this accusation until I read it here on HN today. The reputation doesn't seem to be widespread. blinks really? It's kind of a famous thing. Teachers are taught how to cope with math phobia; other subjects (with the exception of dissection) generally do not create this effect. . > How to bet…

> What was actually requested was a simple two page PDF.

But this is impossible, because, as I learned today, "math is a small field without money for things like this".

Thanks to my discussion here I was able to shift my perspective. Instead of thinking about an abstract thing, like "improving readability of math papers to non-mathematicians", I understood that I have to focus on people! In other words, on a bunch of guys frustrated that other STEM guys earn multiples of what they earn, even though their fields are so much "easier". Why would they help those various others use their work? They worked so hard to create the papers, living in a (shared with a philosopher) one bedroom apartment, writing their revolutionary insights on tissues stolen from McDonalds with a piece of charcoal - while those others can afford to buy computers (and even paper) easily, even though they don't work as hard as mathematicians at all!

It's just so unfair, and of course it's not like mathematicians are jealous or anything (not at all! really! honest!), it's just genuinely so much "harder" to do math, that most of those others won't be able to understand no matter what! Even if they actually listened to the masses and did as requested, the mathematicians already know that it would be useless, so there's no point in trying. Also, this is obvious, but worth noting: saying that most people are simply too dumb to ever understand the intricacies of math is not a prejudiced bias, ok, that's simply a conclusion of centuries of research into math education!

I honestly stopped expecting they'll do anything sensible ever, unless they really have no other choice. You might win against some people, but you won't ever defeat human nature.

Re: Ask HN: How did you learn math notation?

#224

Post by andreskytt » Fri, Nov 26, 2021, 6:42 AM UTC

I learned it the hard way at college. The prof just blasting off in a flurry of greek and us trying to keep up. Eventually he resorted to using the gothic alphabet and at that point I gave up. Every single field of math appears to have their own conventions and even these are but guidelines smart people often bend for perceived benefit. So I can’t really recommend anything other than learning the notation with the field. If you find yourself at loss, chances are you have missed some of the context and should backtrack.

Re: Ask HN: How did you learn math notation?

#225

Post by Jensson » Fri, Nov 26, 2021, 7:12 AM UTC

webmaven wrote: post #221

Jensson wrote: post #150

Earlier quoted context omitted.

> It is also impossible to incorporate something from other software without actually referencing it explicitly. No, some programming languages just injects symbols based on context. You'd have to compile it with the right dependencies for it to work, so it is impossible to know what it is supposed to be. And even if they reference some other file, that file might not even be present in the codebase, instead some fra…

> some programming languages just injects symbols based on context Well, okay, yes, not all software projects deliver reproducible builds of their software. Some software is, in fact, complete garbage. I'm also not using Gene Ray's TimeCube theory[0] as an example of a mathematical paper. > This sort of time variance is non-existent in math Not... entirely. You could cite a preprint that then changes in the final ver…

> Well, okay, yes, not all software projects deliver reproducible builds of their software. Some software is, in fact, complete garbage.

And not all math papers are properly documented either. Some math papers are in fact complete garbage. Why are you complaining about an entire field just because some of it is garbage.

Re: Ask HN: How did you learn math notation?

#226

Post by Jensson » Fri, Nov 26, 2021, 7:20 AM UTC

layer8 wrote: post #218

Jensson wrote: post #211

Earlier quoted context omitted.

But why are you reading research papers with math without having studied math? If you want to understand them fully then you need to do the relevant courses, people spend years learning these things. You don't have to read them all, just the branch relevant to the paper.

We are talking about nonstandard notation that is often specific to the author or to a limited research subfield, for which there are no standard courses or books that would explain the notation. You’d need to take a specific course by someone in the respective research community. Or sometimes, as noted above, it’s possible to follow back a dozen or more papers to retrace the idiosyncrasies in an almost archaeologica…

> We are talking about nonstandard notation that is often specific to the author or to a limited research subfield

Most people here talk about stuff you learn in undergrad, not some esoteric beyond grad math here.

Re: Ask HN: How did you learn math notation?

#227

Post by Jensson » Fri, Nov 26, 2021, 7:21 AM UTC

kazinator wrote: post #217

Jensson wrote: post #211

Earlier quoted context omitted.

But why are you reading research papers with math without having studied math? If you want to understand them fully then you need to do the relevant courses, people spend years learning these things. You don't have to read them all, just the branch relevant to the paper.

> But why are you reading research papers with math without having studied math? I.e. why are you knocking on this gate, if you're not worthy of passage?

If I try to read a program written by you without having learned the language, would you expect me to understand everything? Why aren't you explaining the symbols? That is the same thing. Learn the fundamentals of a paper before reading the paper, that is just common sense.

Re: Ask HN: How did you learn math notation?

#228

Post by Jensson » Fri, Nov 26, 2021, 7:36 AM UTC

klibertp wrote: post #223

JohnHaugeland wrote: post #213

Earlier quoted context omitted.

> > Surely you must realize that you're protesting this because it has this reputation, though? > > I've never heard anyone make this accusation until I read it here on HN today. The reputation doesn't seem to be widespread. blinks really? It's kind of a famous thing. Teachers are taught how to cope with math phobia; other subjects (with the exception of dissection) generally do not create this effect. . > How to bet…

> What was actually requested was a simple two page PDF. But this is impossible, because, as I learned today, "math is a small field without money for things like this". Thanks to my discussion here I was able to shift my perspective. Instead of thinking about an abstract thing, like "improving readability of math papers to non-mathematicians", I understood that I have to focus on people! In other words, on a bunch o…

The fact that the teaching material is so horrible is probably the biggest reason learning programming is so easy, because if the teaching material would be any good then the CS grads would actually know difficult things and it would be harder for me to compete. But as is it is trivial to learn what they did, because they don't learn much. For programming it didn't take me long to learn programming well enough to get into Google and work on services with a million QPS or distributed machine learning training, because programming is really really simple. Not because you are good at teaching, no, I just sat and learned on my own just writing programs, all program tutorials and helps were horrible.

> But this is impossible, because, as I learned today, "math is a small field without money for things like this".

Of course it isn't impossible, that was never the problem here. Mathematicians have written plenty of such cheat sheets, you can find them everywhere just by Googling. Here is one for physics:

https://en.wikipedia.org/wiki/List_of_common_physics_notatio...

Here is one for math:

https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo...

Can you please understand that you are complaining that nobody created something that many many people have created many times over? I found those by googling "physics notation" and "math notation". Was that really too hard for you? If you want a cheat sheet specific for CS related papers, then that cheat sheet has to be written by someone with a CS background since a mathematician wont know what is useful to you, and neither will he know what quirky notation CS people use in their own papers since every domain of math has its own quirks.

What you are doing here is the equivalent of a guy wanting to learn python, and then going to the C++ comitee and complaining that no language is well documented online, and even when the C++ committee nicely shows you that in fact there is documentation of python online you still complain and say that nobody cares about your woes because that python documentation was in fact not easy enough for you to read!

Re: Ask HN: How did you learn math notation?

#229

Post by Jensson » Fri, Nov 26, 2021, 7:49 AM UTC

JohnHaugeland wrote: post #214

Jensson wrote: post #204

Earlier quoted context omitted.

> This example works against you. Scope shadowing is nearly universally considered bad practice So you never used the same variable name in two different scopes ever? Like, if a function takes argument "name", no other function you ever write again in any program can have a variable named "name" unless it is the same exact usage? Or, as is commonly complained about in math, every programmer in the world then use the…

> So you never used the same variable name in two different scopes ever? That's not what shadowing is. . > Having different scopes doesn't imply shadowing I didn't say that it did. . > No mathematician knows even close to every domain this is irrelevant to a lightweight two page cheat sheet for simple mathematial symbols part of the problem is that if we ask you for a simple thing that isn't perfect or exhaustive, yo…

> That's not what shadowing is.

But that is what mathematicians do. Why did you bring up shadowing if it isn't relevant?

Re: Ask HN: How did you learn math notation?

#230

Post by Jensson » Fri, Nov 26, 2021, 7:59 AM UTC

JohnHaugeland wrote: post #215

mkl wrote: post #210

Earlier quoted context omitted.

> Programmers want mathematicians to make one of these: https://matela.com.br/pub/cheat-sheets/haskell-cs-1.1.pdf There are lots of maths cheat sheets like that. Maths is big, like all-programming-languages big. Just like in programming, notations are re-used in different areas with different meanings, and different authors sometimes use different notation for the same meaning. A universal cheat sheet is impossible (…

> There are lots of maths cheat sheets like that. I have never found one that gets me through the average undergraduate CS paper. If you know one, I would greatly appreciate a tip. Unfortunately, I saw what you offered, and that's not it. . > A universal cheat sheet is impossible I explicitly stated that this was a non-goal. . > one of which is "the basics", e.g. https://www.pinterest.nz/pin/734016439237543897/ . Tha…

> I have never found one that gets me through the average undergraduate CS paper.

That cheat sheet would be written by CS folks, since every applied domain uses their own quirks in their notations. Mathematicians can't help you there. You can't blame mathematicians for the shortcomings of CS researchers.