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Math writing is dull when it neglects the human dimension

golem.ph.utexas.edu

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Re: Math writing is dull when it neglects the human dimension

#181

Post by js8 »

Tainnor wrote: post #180
js8 wrote: post #179

Earlier quoted context omitted.

I think you miss the point. I am not disputing FOL being undecidable. What I am saying is that, once we know how to solve SAT well enough, most mathematics will become obsolete (especially for applications). It will be obsoleted the similar way that symbolic solving of equations got obsoleted with numerical solving, once computers (and numerical algorithms) became prevalent enough. Practically minded people will simp…

> symbolic solving of equations got obsoleted with numerical solving That never happened, symbolic and numerical mathematics coexist to this day. Cryptography, for example, relies on exact arithmetic. On that note, good luck trying to solve problems in cryptography with "SAT instances".

Again, you miss the point, there will be a paradigm shift. Yes, symbolic maths still exists, but nobody is looking up a special function to solve an equation. They just plug the numbers (and the state machine approximation of the numerical operations) in the computer and numerically, the result comes out.

Symbolic/numeric is just analogy of the paradigm shift that will come to all (applied) math. Another example is in statistics, shift from parametric to non-parametric.

Cryptography.. relies on unproven belief in ETH or P/=NP or some such (in fact, cryptography has, since Caesar, relied on unproven beliefs about cryptosystems). But that's just a belief, we don't really understand how hard any of these specific problems are. Which is actually a great example of the new paradigm I am talking about, because it shows we don't need proofs (of statements about infinitely many things). We can just quantize things directly (into a state machine that actually does the crypto stuff) and be happy.

We haven't even scratched the surface of what is possible in P vs NP. In particular, CNF representation of SAT instances might be a really crappy one.

Re: Math writing is dull when it neglects the human dimension

#182

Post by skhunted »

atoav wrote: post #178
skhunted wrote: post #83

Earlier quoted context omitted.

What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep. This is precisely what I was referring to about people who come back at a later time and relearn…

I am in education and what you claim here is in contradiction with both my experience and the direct feedback of the people I educated — most of which would say they dislike math or say they are bad at it. The argument that it is like it is for a reason can be made, but it has probably more to do with the historical role of school as an institution that is meant to produce obidient workers than with school as a place…

Feynman’s lectures demonstrate my point. From Wikipedia on the lectures:

As a result, some physics students find the lectures more valuable after they have obtained a good grasp of physics by studying more traditional texts, and the books are sometimes seen as more helpful for teachers than for students.[5]

It does not sound to me that you have much experience with actual teaching.

Re: Math writing is dull when it neglects the human dimension

#183

Post by Tainnor »

js8 wrote: post #181
Tainnor wrote: post #180

Earlier quoted context omitted.

> symbolic solving of equations got obsoleted with numerical solving That never happened, symbolic and numerical mathematics coexist to this day. Cryptography, for example, relies on exact arithmetic. On that note, good luck trying to solve problems in cryptography with "SAT instances".

Again, you miss the point, there will be a paradigm shift. Yes, symbolic maths still exists, but nobody is looking up a special function to solve an equation. They just plug the numbers (and the state machine approximation of the numerical operations) in the computer and numerically, the result comes out. Symbolic/numeric is just analogy of the paradigm shift that will come to all (applied) math. Another example is i…

You should look up provable security. And also, while security proofs typically rely on unproven assumptions, correctness proofs in cryptography are "regular" proofs for all intents and purposes. You can't even do RSA etc. without understanding prime numbers which is impossible if you limit yourself to propositional calculus ("SAT").

> Again, you miss the point, there will be a paradigm shift. Yes, symbolic maths still exists, but nobody is looking up a special function to solve an equation. They just plug the numbers (and the state machine approximation of the numerical operations) in the computer and numerically, the result comes out.

This is false.

Re: Math writing is dull when it neglects the human dimension

#184

Post by SilasX »

araes wrote: post #154
mycologos wrote: post #10

As somebody who works in a mathy subarea of computer science, oh man, I agree. My heart always falls when I need a result and it turns out the original paper is some terse typewritten notice from the 70s whose first sentence is a definition with a bunch of proper nouns and whose main theorem is given at the most general possible level with no applications at all. I have talked with math people about why this is, and…

> c) Is there a field of math that's something like "local actors put in what appear to be rational choices, yet to external observers it often appears 'broken' or 'bad'"? Seems like a field of game theory or something. Many times, those internal view the situation as acceptable. Politics in America seems like it is almost always this type of result. All local actors, all take rational choices, and all America says p…

That's generally referred to as a Prisoner's Dilemma situation, where locally the incentives are to do something that makes it worse for everyone. The SlateStarCodex author generalized the concept into Moloch:

https://slatestarcodex.com/2014/07/30/meditations-on-moloch/

Re: Math writing is dull when it neglects the human dimension

#185

Post by bigbacaloa »

mycologos wrote: post #10

As somebody who works in a mathy subarea of computer science, oh man, I agree. My heart always falls when I need a result and it turns out the original paper is some terse typewritten notice from the 70s whose first sentence is a definition with a bunch of proper nouns and whose main theorem is given at the most general possible level with no applications at all. I have talked with math people about why this is, and…

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Re: Math writing is dull when it neglects the human dimension

#186

Post by bigbacaloa »

noelwelsh wrote: post #61
mycologos wrote: post #10

As somebody who works in a mathy subarea of computer science, oh man, I agree. My heart always falls when I need a result and it turns out the original paper is some terse typewritten notice from the 70s whose first sentence is a definition with a bunch of proper nouns and whose main theorem is given at the most general possible level with no applications at all. I have talked with math people about why this is, and…

I think it's the influence of Bourbaki[1] who were the original mathematical edgelords. I have a book (Creating Symmetry[2]) that explicits rejects this style. It's a lovely book. [1]: https://en.wikipedia.org/wiki/Nicolas_Bourbaki [2]: https://press.princeton.edu/books/hardcover/9780691161730/cr...

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