Mathematical Notation Is Awful • Hacker News Board

Re: Mathematical Notation Is Awful

#91

Post by setr » Sun, Jul 31, 2016, 9:06 PM UTC

paxcoder wrote: post #86

mcphage wrote: post #71

Earlier quoted context omitted.

Years of studying what, though? Calculus, most of linear algebra, discrete math are all calculation based. Math papers are proof based. If you spend years studying proof based math (analysis, algebra, topology, and so on) then you'll be familiar enough with proof based math to understand it. It's like saying "why isn't spending years studying spelling not sufficient to understand Ulysses?"

Ok, then why are we spending years learning "spelling"?

Probably because the goal was different from read Ulysses.

And I doubt most subject areas have the goal of reading proofs.

Re: Mathematical Notation Is Awful

#92

Post by mcphage » Sun, Jul 31, 2016, 9:42 PM UTC

panic wrote: post #74

mcphage wrote: post #70

Earlier quoted context omitted.

The answer to all of your questions: computer programs are written for computers to understand, and computers aren't very smart. Mathematical papers are written for mathematicians to understand, and they tend to be a lot smarter than computers.

Machine language is also written for computers to understand, but it's not easy to read. Computer-formalized math is usually even harder to read than regular notation. I don't think computers have much to do with this.

True, I should have said it better as, programming languages are written for compilers to read, and they're not very smart. Machine language is written for computers themselves. Computer-formalized math I don't think is written for anyone to read.

Re: Mathematical Notation Is Awful

#93

Post by paxcoder » Mon, Aug 01, 2016, 6:22 AM UTC

setr wrote: post #91

paxcoder wrote: post #86

Earlier quoted context omitted.

Ok, then why are we spending years learning "spelling"?

Probably because the goal was different from read Ulysses. And I doubt most subject areas have the goal of reading proofs.

I'm sorry but I don't see how this is an answer to my question.

Re: Mathematical Notation Is Awful

#94

Post by mcphage » Mon, Aug 01, 2016, 4:44 PM UTC

paxcoder wrote: post #93

setr wrote: post #91

Earlier quoted context omitted.

Probably because the goal was different from read Ulysses. And I doubt most subject areas have the goal of reading proofs.

I'm sorry but I don't see how this is an answer to my question.

We spend years learning "spelling", because the mathematical equivalent (arithmetic, up through calculus, linear algebra, differential equations, discrete math, etc) is incredibly valuable on its own—and that that value doesn't really require familiarity with the proof-based foundations underpinning it. Learning real analysis is valuable if you're going to be a mathematician, but as an engineer it won't help you get more out of calculus (at least, not compared to the cost of learning it).

Re: Mathematical Notation Is Awful

#95

Post by epicaricacy » Mon, Aug 01, 2016, 7:49 PM UTC

chilie wrote: post #13

These are just issues that someone unfamiliar with a field would face. None of them are problems for those of us in the field. First, the expectation thing. He's using a special case, E(X), and complaining that the more general case doesn't follow the general case. It's like saying "Well the plural of mouse is mice but the plural of house isn't hice!". The general definition of expectation (for a discrete probability…

>It's like saying "Well the plural of mouse is mice but the plural of house isn't hice!".

Just because English sucks and doesn't make any sense doesn't help the case for mathematical notation.

Re: Mathematical Notation Is Awful

#96

Post by paxcoder » Sat, Aug 06, 2016, 11:05 PM UTC

mcphage wrote: post #94

paxcoder wrote: post #93

Earlier quoted context omitted.

I'm sorry but I don't see how this is an answer to my question.

We spend years learning "spelling", because the mathematical equivalent (arithmetic, up through calculus, linear algebra, differential equations, discrete math, etc) is incredibly valuable on its own—and that that value doesn't really require familiarity with the proof-based foundations underpinning it. Learning real analysis is valuable if you're going to be a mathematician, but as an engineer it won't help you get…

I believe you have adopted your opinion of what should go into the first set of brackets of yours.

An engineer is expected to allot too much time to math to turn out unfamiliar with it. I think we should spend less effort on practicing cleaning fish and more on learning to forage for fish.

Re: Mathematical Notation Is Awful

#97

Post by mcphage » Thu, Aug 11, 2016, 2:46 PM UTC

paxcoder wrote: post #96

mcphage wrote: post #94

Earlier quoted context omitted.

We spend years learning "spelling", because the mathematical equivalent (arithmetic, up through calculus, linear algebra, differential equations, discrete math, etc) is incredibly valuable on its own—and that that value doesn't really require familiarity with the proof-based foundations underpinning it. Learning real analysis is valuable if you're going to be a mathematician, but as an engineer it won't help you get…

I believe you have adopted your opinion of what should go into the first set of brackets of yours. An engineer is expected to allot too much time to math to turn out unfamiliar with it. I think we should spend less effort on practicing cleaning fish and more on learning to forage for fish.

> I believe you have adopted your opinion of what should go into the first set of brackets of yours.

I'm not really sure what you mean by that.

Certainly I'm not of the opinion that proof-based math is useless; I studied math in grad school, and stayed as far away from anything applied as I could. But I don't think it offers much value to engineers or scientists. Let mathematicians establish the foundations, and let scientists and engineers build on top of that. They're different skill sets, with different goals.