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Ask HN: Why is math so obsessed with ancient syntax and frameworks?

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Re: Ask HN: Why is math so obsessed with ancient syntax and frameworks?

#11
post #5
post #4

We use Greek characters simply because it's convenient to have additional symbols at hand. The choice of Greek is historic, but one also sees a little bit of Cyrillic and Hebrew. Notation has evolved since ancient Greece. Euclid, for example, is quite readable in translation, but he did not use modern shorthand. See for yourself: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

That assumes single characters are the only appropriate variable names. There's no reason maths couldn't use a * symbol as multiplication instead of assuming multiplication for any string of characters. People who enjoy the current state of mathematics will probably think the OP is trolling, but it's a reasonable question. Perhaps it could be better put as 'Why doesn't maths concern itself with readability like progr…

An important difference is that to operate with the term is much easier to use short names. If a term is adding in the right side of a equation, and you want to put it on the other side subtracting, you must copy all the equation (and Ctr-C Ctr-V doesn't work in paper.)

A typical program is written one, read a few times (perhaps years later) and executed many times.

A typical math calculation is typed once and read only a few times (a few minutes later) and discarded ("archived").

In the draft, I usually find myself replacing sin(x) and cos(x) by s and c, because it's only a little calculations and in the following 10 minutes I will remember what it means and there is no other s or c in sight and I get bored of writing all the letters.

Re: Ask HN: Why is math so obsessed with ancient syntax and frameworks?

#12
post #9

I agree that this can be frustrating. One of the great benefits of programming languages is that, even though I don't know VisualBasic, for example, I can probably look at the code and know what values the variables represent. It's very difficult to jump into a new mathematical structure, because very often you have to learn the lexicon from scratch.

I'd say that is because when you see a structure you already understand written in a new language (e.g. VB) yu can use your existing mental model.

But when you meet an entirely new structure, as you say, you are starting from scratch.

Re: Ask HN: Why is math so obsessed with ancient syntax and frameworks?

#13
I'm afraid you are overstating the importance of alphabets. For example, try this: http://nedhardy.com/2012/04/25/learn-korean-in-15-minutes-ye... It's not really hard to learn alphabets.

I feel the traditional notation achieves a good tradeoff between clarity and conciseness. I don't want to write the string "integral(sin(x),0,1,x)" on paper - 22 symbols - traditional notation is much more concise. I hate to write parens in (a+b)/c; traditional fractions are clearer. On the other extreme, think about programming in APL.

Also see http://terrytao.wordpress.com/career-advice/there%E2%80%99s-...

Re: Ask HN: Why is math so obsessed with ancient syntax and frameworks?

#14
post #10
post #8

Is programming really so much better off for having so many more languages and means of describing algorithms? At least the language of math that one writes today can be expected to be understandable and readable a hundred or more years from now. A program source code, on the hand, is unlikely to have that kind of long life unless you get lucky and write it in the right language. Also, math is declarative and rigorou…

I find this extremely interesting. I'm a programmer who has had some mental block when it comes to "real math" (whatever that means). I'm very eager to change how I think about math to try to break through the mental barrier. Do you have any books or blogs or anything to recommend that reflect your change in thinking? The summations as for loops is what got my attention, as I am guilty of that. Also the idea of math…

You might try a functional language such as Haskell. It allows you to feel denotational semantics (common in mathematics), rather than operational semantics (common in imperative programming).

Re: Ask HN: Why is math so obsessed with ancient syntax and frameworks?

#15
When mathematicians investigate new types of problems, they often develop new notation. Computer programming languages are an example of this in a very strong sense.

The proliferation of programming languages relative to other systems of mathematical notation may be due to programming being more frequently applied to new types of problems - including the problem of developing new types of notation using computers.

Re: Ask HN: Why is math so obsessed with ancient syntax and frameworks?

#16
there is a more general problem here. why does insist on using domain specific language when ordinary words do fine?

derivative or gradient = slope

is a classic example. mention the word calculus and someone panics in a fit of imagined complexity. describe it in english, clearly, and its very easy...

however the classic counterargument is that it is easier to invent words with context specific meanings for clarity. this makes more sense if you try and describe a functional integral for instance... you need the concept of a function, and an integral which themselves rely on other concepts etc. and would require several sentences to explain well...

also, you have made a faulty assumption about programming - new syntax and language is invented, but the old syntax and language is not replaced - we are stuck with the old stuff too. there are still plenty of areas where C is the only choice - nobody has yet come up with an alternative which addresses the same problems - so 30 years on we still use C - and its use pollutes all of the terminology associated with programming.

(tangent: i still don't understand why we can't compile e.g. Python, C#, Ruby, JavaScript etc. to native code with the benefits of C [Haskell does this quite well for instance - but is held back by general quality of compiler vs. C compilers having billions of dollars and thousands of man years poured into them] - VM or JIT should be a choice if you like spunking away performance - it would be nice if C would die... as much as I enjoy it - GCC, LLVM etc. make the same code gen available for any language with a little work - this feels to me an infinitely better solution than any VM or JIT can hope to be...)

Re: Ask HN: Why is math so obsessed with ancient syntax and frameworks?

#17
post #12
post #9

I agree that this can be frustrating. One of the great benefits of programming languages is that, even though I don't know VisualBasic, for example, I can probably look at the code and know what values the variables represent. It's very difficult to jump into a new mathematical structure, because very often you have to learn the lexicon from scratch.

I'd say that is because when you see a structure you already understand written in a new language (e.g. VB) yu can use your existing mental model. But when you meet an entirely new structure, as you say, you are starting from scratch.

It's not about the structure. It's about the sigils. I have no idea what Xi means in the context that it's used, but if it's named in English it's very easy to understand.

Re: Ask HN: Why is math so obsessed with ancient syntax and frameworks?

#18
post #5
post #4

We use Greek characters simply because it's convenient to have additional symbols at hand. The choice of Greek is historic, but one also sees a little bit of Cyrillic and Hebrew. Notation has evolved since ancient Greece. Euclid, for example, is quite readable in translation, but he did not use modern shorthand. See for yourself: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

That assumes single characters are the only appropriate variable names. There's no reason maths couldn't use a * symbol as multiplication instead of assuming multiplication for any string of characters. People who enjoy the current state of mathematics will probably think the OP is trolling, but it's a reasonable question. Perhaps it could be better put as 'Why doesn't maths concern itself with readability like progr…

> Perhaps it could be better put as 'Why doesn't maths concern itself with readability like programming does?'

Readability is a personal opinion in some ways. I guess I have grown up using mathematical symbols in Physics classes since middle school so those symbols didn't feel arcane to me when I hit my first real math classes.

Re: Ask HN: Why is math so obsessed with ancient syntax and frameworks?

#19
post #10
post #8

Is programming really so much better off for having so many more languages and means of describing algorithms? At least the language of math that one writes today can be expected to be understandable and readable a hundred or more years from now. A program source code, on the hand, is unlikely to have that kind of long life unless you get lucky and write it in the right language. Also, math is declarative and rigorou…

I find this extremely interesting. I'm a programmer who has had some mental block when it comes to "real math" (whatever that means). I'm very eager to change how I think about math to try to break through the mental barrier. Do you have any books or blogs or anything to recommend that reflect your change in thinking? The summations as for loops is what got my attention, as I am guilty of that. Also the idea of math…

Historically, my biggest obstacle to understanding pieces of "real math" was the intimidation factor of the very dense material and the fear that I wouldn't ever be able to understand it.

The best tip I have, one that helps me not be intimidated by "real math," is to find a method of forcing yourself to slow down while reading. I've found that I get intimidated and frustrated only when I'm trying to rush through something. The best method I have for slowing myself down is to keep a notebook open, and write down definitions as I go (and lemmas, and theorems, but from here on I'll just call them definitions). I try to write a definition that is more clear (likely only to myself) than how it was presented in the text I'm reading. I also try to write down important implications of the definitions.

I think the procedural way of thinking about mathematics is natural for someone without much exposure, and is indicative that you're still trying to work out minor details of each definition you encounter. That's fine. If you have to think about a summation as a for-loop to understand it, go for it. After seeing a bunch of summations, eventually they'll carve out their own mental space. I think that writing down definitions will also help to solidify the declarative nature of mathematics, and definitely helps me to move through math more fluidly.

When I'm learning new math, I find that I'm least frustrated when I plan on moving very slowly. I feel that I'm making good time through a mathematics text if I read a page an hour. Next time you encounter some "real math", grab a pen and paper and really dig in to the text.

Re: Ask HN: Why is math so obsessed with ancient syntax and frameworks?

#20

[Mathematician here] Greek leters: It's a feature not a bug! The advantage of Greek letters is that they don't collide with normal variables, you can use short (1 letter) names for symbols. That is also the advantage of using special characters for number (and not using something like a->1, b->2, ...). An additional problem is that some letter has an expected behavior, for example \epsilon usually is small, and M (ca…

I don't know how to explain it but - thank you. You answered so many questions I had about math that I didn't know before until you said it this way.
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