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Mathematical Notation Is Awful

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Re: Mathematical Notation Is Awful

#4

Post by efz1005 »

Real maths is done either in books or papers, where the authors explain every bit of notation they will use. This is not the case in online resources, which is indeed a bad practice... But hey, don't blame maths for that.

And regarding the "understanding maths in terms of computer programs", sure that's possible to do with _some_ topics, but you just can't expect a computer to represent _every_ concept you'd like.

Re: Mathematical Notation Is Awful

#5

Post by efz1005 »

k__ wrote: post #2

their naming isn't that good either. All these words that are already used for other things. Magma, ring, group, body, lense, optic...

You should learn what the concepts mean instead of judging the names associated to them. We call something a Ring to avoid saying "a set with two operations which behave in a certain way [...]" every time we refer to it.

Re: Mathematical Notation Is Awful

#6

Post by krapht »

Domain-specific languages, notation, and vocabulary exist for many disciplines. They are for the benefit of experienced practitioners and allow them to express common concepts and ideas in a precise and concise fashion to those who have been also been trained in the art.

Sometimes jargon, abbreviations, and cryptic notation exist to artificially make it harder for outsiders to understand what's going on, but the examples in this post don't convince me. The true issue here is that the appropriate Wikipedia article has no link to the "Simple English" version.

Most humans are capable of using context to distinguish usage. Operator overloading in programming languages and in mathematics can be useful sometimes.

Re: Mathematical Notation Is Awful

#7

Post by bjornsing »

efz1005 wrote: post #4

Real maths is done either in books or papers, where the authors explain every bit of notation they will use. This is not the case in online resources, which is indeed a bad practice... But hey, don't blame maths for that. And regarding the "understanding maths in terms of computer programs", sure that's possible to do with _some_ topics, but you just can't expect a computer to represent _every_ concept you'd like.

Show me a paper that explains "every bit of notation they will use"! ;P

(I understand there's a difference between "explaining" and "stringently defining", but I can't help thinking of the only book I know that actually tried to stringently define all notation: Principia Mathematica. If I remember correctly it took Bertrand Russel about 160 pages to define addition and prove that 1 + 1 = 2. :P)

Re: Mathematical Notation Is Awful

#8

Post by klibertp »

efz1005 wrote: post #5
k__ wrote: post #2

their naming isn't that good either. All these words that are already used for other things. Magma, ring, group, body, lense, optic...

You should learn what the concepts mean instead of judging the names associated to them. We call something a Ring to avoid saying "a set with two operations which behave in a certain way [...]" every time we refer to it.

"We call something a Ring to avoid saying"

Why a "Ring" and not an "asda2+"?

Re: Mathematical Notation Is Awful

#9

Post by erdewit »

In my experience people that are very verbose, that talk or write at great length and with ease, tend to have a dislike for terse formulations. Sometimes to the point of being offended by it. Math is just about the ultimate in terse notation and perhaps the author is one of these verbose people.

The same thing can be seen with programmers: The verbose programmer writes a lot of lines of code and is proud of it, while the terse programmer is proud to remove or simplify code.

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