Is there any particular topic? I agree with other posters though that the notation is a short hand for the concepts and you need the concepts, not the notation.
Ask HN: How did you learn math notation?
131–140 of 258 posts
Re: Ask HN: How did you learn math notation?
#132Earlier quoted context omitted.
> I think a real problem in this area is the belief that there is "one true notation" and that everything is unambiguous and clearly defined. One main cause for this belief is that in a programming there is one true noation (or rather, a separate one for each language) that is unambiguous and clearly defined. I dislike maths notation as I find it lacks rigour.
> I dislike maths notation as I find it lacks rigour. I see this a lot from programmers, but in essence, you seem to be complaining that maths notation isn't what you want it to be, but is instead something else that mathematicians (and physicists and engineers) find useful.
I think "useful" is doing a lot of work here. A lot of math notation exists clearly to gate keep. It's often nonsensical. It's a shame because it really makes mathematicians look bad (re:annoying) to those who can see through it. It's not hard to see through it or anything, but it is obnoxious. All you need is an english explanation of the notation, and then you're good, but often all of the sources on the topic are written in the same obnoxious babble language.
Take sequential Monte Carlo / sequential importance sampling for instance. This powerpoint on it is clownishly bad: http://people.eecs.berkeley.edu/~jordan/courses/260-spring10...
This is supposed to be an algorithm implemented in code. It's essentially illegible without code examples, which it doesn't feature. Code examples tell you what the cipher signifies; at no point does the cipher provide any value to the learner. Fanciful bayes-theoretical statements and so on basically reduce to "iteratively build enlarging valid states." Given the fact that this simple statement is missing, I question if the professor has some sort of communication disorder or if they're just a troll. Similar to pomo philosophers, it's probably a mix.
Re: Ask HN: How did you learn math notation?
#133I think a real problem in this area is the belief that there is "one true notation" and that everything is unambiguous and clearly defined. Yes, conventions have emerged, people tend to use the same sort of notation in a given context, but in the main, the notation should be regarded as an aide memoire , something to guide you. You say that you're struggling because of "the math notations and zero explanation of it i…
Why are you telling OP what his problem is? Shouldn't you address his pain points, not your rationalization of them?
I wrote it many times already and am bit tired of it, so just a quick summary:
- programmers[1] also use cryptic notation and tend to think in concepts rather than syntax
- nevertheless, programmers spend a lot of time commenting the code, documenting it, specifying it, and so on.
- why can't mathematicians emulate it? What is so wrong about attaching additional few pages to every paper that nobody wants to do it? Pages with explanation of the syntax used, even the common bits. And you know what they could also do? Link to external resources with explanations! But no. This is not happening. Do their PDFs have a size limit or something? Is inserting a link into a paper considered some kind of blasphemy?
I don't know the reason, but in all the discussions on this topic mathematicians almost always underestimate the importance of knowing the syntax. It's much more important for comprehension than they tend to admit. And in the end they do exactly nothing to make the syntax more approachable for newcomers. And then newcomers are out-goers in a heartbeat. It's so obvious that I can't help thinking it's premeditated...
EDIT: [1] Among many others, of course.
Re: Ask HN: How did you learn math notation?
#134Earlier quoted context omitted.
> I think a real problem in this area is the belief that there is "one true notation" and that everything is unambiguous and clearly defined. One main cause for this belief is that in a programming there is one true noation (or rather, a separate one for each language) that is unambiguous and clearly defined. I dislike maths notation as I find it lacks rigour.
> I dislike maths notation as I find it lacks rigour. I see this a lot from programmers, but in essence, you seem to be complaining that maths notation isn't what you want it to be, but is instead something else that mathematicians (and physicists and engineers) find useful.
Yes. What's wrong with changing math notation? Why wouldn't you do it if you know that it would make it easier for others to approach? What's the rationale behind doing exactly nothing to make the notation more approachable for the masses?
Re: Ask HN: How did you learn math notation?
#135Earlier quoted context omitted.
Undefined behavior isn't a feature. A spec isn't an implementation, either. All behavior in an implementation can be teased-out if given sufficient time. > if you were an alien trying to reconstruct it, for example - you'd hit serious problems. I can't speak to alien minds. Considering the feats of reverse-engineering I've seen in the IT world (software security, semiconductor reverse-engineering) or cryptography (th…
> All behavior in an implementation can be teased-out if given sufficient time. Can it? Given what? You would need to understand how the CPU is supposed to execute the compiled code to do that. In order to understand the CPU you would need to read the manual for its instruction set, which is written in human language and hence not any better defined than math. At best you get the same level of strictness as math. If…
> 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 explicitly.
Math, though, is more like prose in this respect – while any given novel probably has a lot of structure, terminology, and notation in common with other works in its genre, unless it is extremely derivative it almost certainly has a few quirks and innovations specific to the author or even unique to that particular work that you can absorb while reading or puzzle out due to context, as long as you accept that the context is quite a lot of other works in the genre (this is more true of some genres/subfields than others). Unlike novels, at least in math papers (but not necessarily books) you get explicit references to the other works that the author considered most relevant, but those references are not usually sufficient on their own, nor necessarily complete, and you have to do more spelunking or happen to have done it already.
Finally, like prose, with math you have to rely on other (subsequent) sources to point out deficiencies in the work, or figure them out on your own. Math papers, once published, don't usually get bug fixes and new releases, you're expected to be aware (from the context that has grown around the paper post-publication) what the problems are. Which means reading citations forward in time as well as backward for each referenced paper. The combinatorial explosion is ridiculous.
It would be great if there were something like tour guides published that just marked out the branching garden paths of concepts and notation borrowed and adapted between publications, but textbooks tend to focus on teaching one particular garden path.
Re: Ask HN: How did you learn math notation?
#136I think a real problem in this area is the belief that there is "one true notation" and that everything is unambiguous and clearly defined. Yes, conventions have emerged, people tend to use the same sort of notation in a given context, but in the main, the notation should be regarded as an aide memoire , something to guide you. You say that you're struggling because of "the math notations and zero explanation of it i…
Why are you telling OP what his problem is? Shouldn't you address his pain points, not your rationalization of them? I wrote it many times already and am bit tired of it, so just a quick summary: - programmers[1] also use cryptic notation and tend to think in concepts rather than syntax - nevertheless, programmers spend a lot of time commenting the code, documenting it, specifying it, and so on. - why can't mathemati…
Mathematicians do document and comment, that's what papers and textbooks are: commentary on the math. They don't throw out formulae and equations and call it a day. Attaching a full tutorial for every level of reader is tantamount to attaching Stroustrup's C++ books to every C++ program, or K&R to every C program. You wouldn't do that, you'd expect the reader to ask you for references or to seek them out themselves.
Re: Ask HN: How did you learn math notation?
#137By doing math. Khanacademy has a lot of higher than highschool math courses you could check out.
Re: Ask HN: How did you learn math notation?
#138Earlier quoted context omitted.
Why are you telling OP what his problem is? Shouldn't you address his pain points, not your rationalization of them? I wrote it many times already and am bit tired of it, so just a quick summary: - programmers[1] also use cryptic notation and tend to think in concepts rather than syntax - nevertheless, programmers spend a lot of time commenting the code, documenting it, specifying it, and so on. - why can't mathemati…
Mathematicians do document and comment, that's what papers and textbooks are: commentary on the math. They don't throw out formulae and equations and call it a day. Attaching a full tutorial for every level of reader is tantamount to attaching Stroustrup's C++ books to every C++ program, or K&R to every C program. You wouldn't do that, you'd expect the reader to ask you for references or to seek them out themselves.
> or K&R to every C program.
That's actually doable... ;) K&R is rather terse, what, 1/5 of Stroustrup or something like that. But I digress.
More on topic: there's also a class of programs that DO come with a book attached - or rather, multiple books, for every level; if not included outright in the distribution then at least linked to in the "learn" tab on a homepage. They're called programming languages. So, it can be done. That's all I want to say.
Re: Ask HN: How did you learn math notation?
#139Earlier quoted context omitted.
> I think a real problem in this area is the belief that there is "one true notation" and that everything is unambiguous and clearly defined. One main cause for this belief is that in a programming there is one true noation (or rather, a separate one for each language) that is unambiguous and clearly defined. I dislike maths notation as I find it lacks rigour.
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…
There are formal grammars. The formal grammars are really hard to understand in my humble opinion. The best examples I think are COQ (see e.g. https://en.wikipedia.org/wiki/Coq) and Lean (see e.g https://en.wikipedia.org/wiki/Lean_(proof_assistant) ).
Yes, we are too lazy to be 100% formal and many times we are too lazy to be mostly formal. This is mostly because we target our writing to other mathematicians who have no need to see every small step and including every step makes the proofs long. On the other hand, I do feel that generally speaking mathematicians should show more of their work and skip fewer steps.
I find your statement "People can't be bothered to be exact about things because being exact is hard and people avoid hard work." to be very true. Being precise is difficult.
Re: Ask HN: How did you learn math notation?
#140Earlier quoted context omitted.
> I dislike maths notation as I find it lacks rigour. I see this a lot from programmers, but in essence, you seem to be complaining that maths notation isn't what you want it to be, but is instead something else that mathematicians (and physicists and engineers) find useful.
I think "useful" is doing a lot of work here. A lot of math notation exists clearly to gate keep. It's often nonsensical. It's a shame because it really makes mathematicians look bad (re:annoying) to those who can see through it. It's not hard to see through it or anything, but it is obnoxious. All you need is an english explanation of the notation, and then you're good, but often all of the sources on the topic are…
Lecture powerpoints are bad everywhere since you are meant to listen to the lecturer speaking about them, they aren't meant to be read independently like this.
Try to understand programming based on a programming lecture powerpoint, it is usually impossible.
Edit: Also you can't write code for what he is talking about in that lecture. Code cannot deal with infinities or continuous values. You'd get approximations which isn't the same thing, then you'd need to prove that those approximations are good enough which would have to be done without code anyway.