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Ask HN: How did you learn math notation?

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

#251

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. 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…

> 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.

Where is the legend/key?

I recall my disappointment when as an artist I started studying different maths for use in animation. I would open a book from a university library and expected to find a page with summary of notation used in the book. Maps have this, I would grumble, why not math books?

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

#252

Earlier quoted context omitted.

> 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.

If math were like code: the program relies on macros that are not defined in the program. Those who have the author's previous two programs loaded in the image don't notice any problem.

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

#253

Earlier quoted context omitted.

As someone who's studied math and CS extensively, it's not that mathematicians don't need that rigor it's only certain sub-fields have a culture of this kind of notational rigor. You absolutely see little bubbles of research, 2-4 professors, get sealed off from the rest of the research community because their notational practices are so sloppy that no one wants to bother whereas others make it easy to understand thei…

> CS are just better about this, and I can only explain it as a part of the culture and tradition. CS professors writes just as incomprehensible math as everyone else, as you can see many here brings up examples of CS professors writing incomprehensible math in their papers.

I think you can easily pick examples from any field of terribly written papers but I'm attempting to describe my experience of interacting with both disciplines over many years; reading many books and papers from both.

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

#254

I'm a math professor, and my students find it revelatory to understand math as I talk and draw. Math notation is not math, any more than music notation is music. Notably, the Beatles couldn't read sheet music, and it didn't hold them back. The best comparison would be is reading someone else's computer code. At its best computer code is poetry, and the most gifted programmers learn quickly by reading code. Still, let…

Super answer! I wish you were one of my professors, and I had excellent professors. If I may humbly add, try making your own notation and playing around with it. Very rapidly one realizes just how hard a problem good notation is.

Actually, making my own notation is how I start puzzling out any problem. When one reformulates a problem, the appearance keeps changing but the problem is still there. It often takes multiple reformulations to "see" a problem, unencumbered by artifacts of birth.

The other day an EE grad student came to my office to show me his lab's research. After changing notation a couple of times, I was able to recognize that their novel combinatorial problem was an instance of graph coloring.

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

#255
post #147

Earlier quoted context omitted.

People can also understand each other through combinations of obscure slang, garbled audio, thick accents, and drunken slurring. It's still an unpleasant way to communicate. Shall we be satisfied with the same low standards in a technical field, because it is how it is ? Hands-on users of math notation are complaining that it sucks. I'm not sure why a dismissive "works for me" is so often the default response.

> Hands-on users of math notation are complaining that it sucks. I'm not sure why a dismissive "works for me" is so often the default response. It is really easy to complain. People also complain about every popular programming language, but it is really hard to make something that is actually better. It is easy to make something that you yourself think is better, but it is hard to make something that is better in pr…

Personally, I stopped complaining about Java, Perl, and PHP when I didn't have to read or write them anymore for work.

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

#256

Earlier quoted context omitted.

> 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.

Why are you ignoring the fact that I specifically said I wasn't basing my criticism on the worst examples I could find?

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

#257

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…

Imagine saying that it's impossible to make a 2 page PDF because there's no money for it

Honestly

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

#258

Earlier quoted context omitted.

Super answer! I wish you were one of my professors, and I had excellent professors. If I may humbly add, try making your own notation and playing around with it. Very rapidly one realizes just how hard a problem good notation is.

Actually, making my own notation is how I start puzzling out any problem. When one reformulates a problem, the appearance keeps changing but the problem is still there. It often takes multiple reformulations to "see" a problem, unencumbered by artifacts of birth. The other day an EE grad student came to my office to show me his lab's research. After changing notation a couple of times, I was able to recognize that th…

Can your lectures be shared online?

I would love to watch you create notation.

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