Community college is a good way, low commitment as well.
Ask HN: How did you learn math notation?
201–210 of 258 posts
Re: Ask HN: How did you learn math notation?
#202Earlier quoted context omitted.
I really, really appreciate your reply and its tone. Thank you for that. You've given me some things to think about. I often wish people were more like computers. It probably wouldn't make the world better but it would make it more comprehensible.
Thanks for the pingback ... I appreciate that. And thanks for acknowledging that I'm trying to help. It might also help to think of "scope" in the computing sense. Often you have a paragraph in a math paper using symbols one way, then somewhere else the same symbols crop up with a different meaning. But the scope has changed, and when you practise, you can recognise the change of scope. We reuse variable names in dif…
> We reuse variable names in different scopes
This example works against you. Scope shadowing is nearly universally considered bad practice, to the point that essentially every linter is pre-configured to warn about it, as are many languages themselves (eg prolog, erlang, c#, etc)
To a programmer, you're saying "see, we do it just like the things you're taught to never ever do"
.
> You may still not like math, or the notation,
The notation is probably fine
What I personally don't like is mathematicians' refusal to provide easy reference material
Programmers want mathematicians to make one of these: https://matela.com.br/pub/cheat-sheets/haskell-cs-1.1.pdf
It doesn't have to be perfect. We don't need every possibility of what y-hat or vertical double bars means. An 85% job would be huge.
Re: Ask HN: How did you learn math notation?
#203Earlier 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.
No.
Leave math notation whatever it is
Just do a better job of documenting it
Re: Ask HN: How did you learn math notation?
#204Earlier quoted context omitted.
Thanks for the pingback ... I appreciate that. And thanks for acknowledging that I'm trying to help. It might also help to think of "scope" in the computing sense. Often you have a paragraph in a math paper using symbols one way, then somewhere else the same symbols crop up with a different meaning. But the scope has changed, and when you practise, you can recognise the change of scope. We reuse variable names in dif…
> We reuse variable names in different scopes This example works against you. Scope shadowing is nearly universally considered bad practice, to the point that essentially every linter is pre-configured to warn about it, as are many languages themselves (eg prolog, erlang, c#, etc) To a programmer, you're saying "see, we do it just like the things you're taught to never ever do" . > You may still not like math, or the…
> 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 variable "name" only for that usecase and otherwise comes up with a new name for it?
Having different scopes doesn't imply shadowing, it just means that you define it and then use it and then scope goes out and it no longer exists. No mathematician knows even close to every domain, so different domains of math uses notation differently. It is like how different programmers programs in different programming languages. It is such a waste to have so many programming languages, but people still do it for legacy reasons.
Re: Ask HN: How did you learn math notation?
#205Earlier quoted context omitted.
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?
Math notation has evolved to be what it is because it is useful for the actual doing of math, and the communication of math to those who have sufficient background. It's not deliberately designed to keep people out, and there are literally hundreds of thousands of books that introduce people to the notations used, to help on-board them. Haskell is unreadable to one who has not trained in it or similar languages ... w…
> It's not deliberately designed to keep people out
Surely you must realize that you're protesting this because it has this reputation, though?
And surely you must realize that it has this reputation for a reason?
When I was a teenager and took my first calculus course, I struggled with summation for three days. When I finally went to my dad he looked at me funny and said "your teacher is an idiot, isn't he? It's a for loop."
I had been writing for loops for seven years at that age. I almost cried. It was like a lightswitch.
The problem was always that nobody had ever actually explained what the symbol meant in any practical way. Every piece of terminology was explained with other terminology, when there was absolutely no reason to do so.
Mathematics has the reputation for impermeability and unwelcomingness for a reason.
It's because you guys are ignoring us saying "we want to learn, please write out a cheat sheet" and saying "yes, but don't you see" instead of just building the easy on-ramp that every other field on earth has built
.
> > You might be tired of wandering into someone else's area of expertise and telling them: > > You must change! You must make it more accessible!
No, we generally just fix the problem. If people are saying "this isn't accessible enough," we just work on it.
I would like for you personally to be aware of Bret Victor's work. He's incredibly potent and clear on these topics.
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.
http://worrydream.com/LearnableProgramming/
We have, in fact, mostly given up on waiting for you, and started to make our own tooling to understand your work, using obvious principles like live editors and witnessable effects.
http://worrydream.com/MediaForThinkingTheUnthinkable/
Edit: those are the talk notes. Wrong link, sorry. I should have used this instead: https://vimeo.com/67076984
This is a big part of how we criticize ourselves, is for failing to provide the tooling to allow new modes of approach.
https://www.youtube.com/watch?v=PUv66718DII
We frequently think of our programming languages as new modes for thought. This line of discussion is particularly popular in the Lisp, Haskell, and Forth communities, though it crops up at some level everywhere.
We frequently think that the more opaque the language, the less useful it is in this way.
That's why programming languages, which are arguably 70 years old as a field, have so much more powerful tools for teaching and explanation than math, which is literally older than spoken language
You guys don't even have documentation extraction going yet. We have documentation where you have a little code box and you can type things and try it. You can screw with it. You can see what happens.
This is why we care about things like Active Reading and explorable explanations.
http://worrydream.com/ExplorableExplanations/
This is why we care about things like live reactive documents. It really changes your ability to intuitively understand things.
Math hasn't grokked non-symbolic communication since Archimedes, that's why it took nearly two thousand years to catch up with him.
We are asking you to come into step with the didactic tools of the modern world. It's not the 1850s anymore. We have better stuff than blackboards.
Are these flat symbolic equations cutting it for you guys to communicate with one another? Sure.
Are they cutting it for you guys to onboard new talent, or make your wealth available to the outside? No. (Do you realize that there is an outside to you, which isn't true of most technical fields anymore?)
These problems are not unique to mathematics, of course. Formal logic is similar. Within my own field of programming, the AI field is similar, as is control theory, as tends to be database work. They don't want to open the doors. You have to spend six years earning it.
But the hard truth is there are more difficult fields than mathematics that have managed to surmount these problems, such as physics (which no, is not applied mathematics,) and I think it might be time to stop protesting and start asking yourself "am I failing the next generation of mathematicians?"
An example of who I believe to be genuinely good math communicators in the modern era are Three Blue One Brown.
.
> > Believe me, mathematicians are tired of non-mathematicians wandering up and saying: > > Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that!
Then fix the problem.
It IS fixable.
.
> Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it?
Given the way you guys push back on being asked to write simple reference material?
No, but I understand why they do.
.
> Do you really believe that no one has tried to make it more accessible?
No. Instead, I believe that nobody has succeeded.
Try to calm down a bit, won't you? People tried to explain Berkeley sockets in a simple way for 12 years before Beej showed up and succeeded. The Little Schemer was 16 years after Lisp.
Explaining is one of the very hardest things that exists.
We're not saying you didn't try! The battlefield is littered with the corpses of attempts to get past Flatland.
We're just saying "you haven't succeeded yet and this is important. Keep trying."
.
> Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do?
No. The literal ask is for you to repair that. Crimeny.
Re: Ask HN: How did you learn math notation?
#206Earlier quoted context omitted.
Math notation has evolved to be what it is because it is useful for the actual doing of math, and the communication of math to those who have sufficient background. It's not deliberately designed to keep people out, and there are literally hundreds of thousands of books that introduce people to the notations used, to help on-board them. Haskell is unreadable to one who has not trained in it or similar languages ... w…
> It's not deliberately designed to keep people out Surely you must realize that you're protesting this because it has this reputation, though? And surely you must realize that it has this reputation for a reason? When I was a teenager and took my first calculus course, I struggled with summation for three days. When I finally went to my dad he looked at me funny and said "your teacher is an idiot, isn't he? It's a f…
> 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 one of the most studied topics in education since it is so extremely important for so many outcomes. People learn programming faster since programming is simply easier, not because more effort has been done to make programming easy. There hasn't, way more effort has been put into making math easy and the math we have is the results of all that work.
https://en.wikipedia.org/wiki/List_of_mathematics_education_...
> Given the way you guys push back on being asked to write simple reference material?
Nobody pushes back on writing simple reference manuals. There are tons of simple reference manuals for math everywhere on the internet, in most math papers, in most math books, everywhere! Yet still people fail to understand it. Many billions has been put trying to improve math education, trying to find shortcuts, trying to do anything at all. You are simply ignorant thinking that there are some quick fix super easy to implement things that would magically make people understand math. There isn't. It is possible that math education could get improved, but it wont be a simple thing.
Re: Ask HN: How did you learn math notation?
#207after starting to take quantum chemistry the professor wrote up on the board:
E Psi = H Psi
and we all joked you could just cancel the Psi and so E=H.
several very kind people explained vector calculus to me ("bold means a matrix, and this dot means matrix multiplication") but to be honest, I still can't read math notation but if you show me anything in numpy I'll understand it immediately.
Re: Ask HN: How did you learn math notation?
#208Earlier 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. No, that belief isn't the problem; that actual status quo itself is obviously the problem. There are numerous notations and authors don't explain what they are using, assuming everyone has recursively read all of their references depth-first before reading their paper.
Why does RTFM not apply to mathematics dependencies?
The dependencies are not manuals. This could in fact be avoided if citation #1 were a Fine Manual.
Re: Ask HN: How did you learn math notation?
#209Earlier quoted context omitted.
Because there usually isn’t anything resembling an actual manual.
Sure there is, read these and you will understand most math papers people here struggle with: https://mathblog.com/mathematics-books/ Of course you still wont be able to understand most math papers written by pure mathematicians, but it should be fine for whatever you need in CS. I know all the topics on that page, it is just a very fleshed out math major.
That's "read all the fine manuals", not "read the fine manual".
In the end you might eventually read all of them, but it's not the efficient thing now.
Re: Ask HN: How did you learn math notation?
#210Earlier quoted context omitted.
Thanks for the pingback ... I appreciate that. And thanks for acknowledging that I'm trying to help. It might also help to think of "scope" in the computing sense. Often you have a paragraph in a math paper using symbols one way, then somewhere else the same symbols crop up with a different meaning. But the scope has changed, and when you practise, you can recognise the change of scope. We reuse variable names in dif…
> We reuse variable names in different scopes This example works against you. Scope shadowing is nearly universally considered bad practice, to the point that essentially every linter is pre-configured to warn about it, as are many languages themselves (eg prolog, erlang, c#, etc) To a programmer, you're saying "see, we do it just like the things you're taught to never ever do" . > You may still not like math, or the…
> 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 (just like a general programming cheat sheet is), but many cheat sheets or notation reference pages exist for particular contexts, one of which is "the basics", e.g. https://www.pinterest.nz/pin/734016439237543897/. Try searching or image searching for [math cheat sheet], [linear algebra cheat sheet], etc.
> mathematicians' refusal to provide easy reference material
This is an absurd claim. There is no such general refusal. On the contrary, many mathematicians provide their students with relevant easy reference material constantly. We sometimes spend entire semester-long courses providing easy reference material, and there are many books with exactly the kind of cheat-sheet you want inside the cover, or in an appendix or front matter (as well as the ones on the internet mentioned above).