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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

#71

Post by constantcrying »

js8 wrote: post #28

IMHO it's even worse. Once we figure out P vs NP, we will understand what it means to invert boolean functions algorithmically, and all mathematics will be replaced with an automated process. Today, most of the math is figuring out how to solve an equation, i.e. to give an algorithm to calculate the solution. We then "quantize" the algorithm to a state machine (e.g. convert reals to floats, algorithm steps to machine…

>IMHO it's even worse. Once we figure out P vs NP, we will understand what it means to invert boolean functions algorithmically, and all mathematics will be replaced with an automated process.

Literal nonsense. Do you not realize that P vs. NP might have a negative outcome (extremely likely)?

>Today, most of the math is figuring out how to solve an equation, i.e. to give an algorithm to calculate the solution.

Plainly false. In basically any field proving the existence of a solution is far, far harder than calculating the solution numerically. See e.g. PDEs.

>We then "quantize" the algorithm to a state machine (e.g. convert reals to floats, algorithm steps to machine code), so that we could run the state machine on a computer and get a result.

Literally not true. Not even the assumption is right.

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

#72

Post by constantcrying »

js8 wrote: post #35
yau8edq12i wrote: post #31

Earlier quoted context omitted.

> IMHO it's even worse. Once we figure out P vs NP, we will understand what it means to invert boolean functions algorithmically, and all mathematics will be replaced with an automated process. I'm sorry, but that's just naive techno-solutionism. Maybe the computer will be able to solve your syntax problems, i.e., write proofs. It will never know anything about the semantics. Said differently. Maybe the computer will…

My point is, the need for semantics is a human construct, it's not required to solve practical problems. Practical value of MVT is that we can apply it in the process of describing a solution, i.e. an algorithm. But if you have a SAT algorithm that can somehow inherently apply a finite instance of MVT, you no longer need to know what MVT is. And this is at the heart of P vs NP question, how to solve SAT, and once we…

None of this is true and your understanding of the subject is obviously very poor.

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

#73

Post by eternityforest »

serf wrote: post #27
daxfohl wrote: post #13

The same should be said for engineering design docs tbh

absolutely disagree. an engineering design document is about information retrieval, not education. It's not made to entertain or educate about new concepts, it's made to be terse and rigidly structured for the sake of aiding the work of the reader and to provide reliable information recall methods for those reading it. I don't want to know what 'problems are worth attacking' when reading a design document, I want to…

I might want to know why the hole on the left flange needs such insane tolerance though.

Maybe it's not relevant in a specific version, or maybe I have an idea for how to solve the issue so it can be made cheaper, etc.

Maybe it's absolutely integral to the whole application and I should stop wasting my time trying to make a printed PLA version, etc.

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

#74

Post by eternityforest »

bedobi wrote: post #2

I’m no mathematician, so I only took basic school math, but I hated every moment of it. Mostly because overwhelmingly there was never any context or justification for learning any of it. Why does this exist? What actual real world problems does it solve? How did folks come up with and it, prove it works and start using it? Crickets. Just learn this formula, then that. The first time I heard the ancients calculated th…

I did a (not fully third party reviewed for errors, watch out) project to record all the math related "cool shit I'm glad to have discovered": https://github.com/EternityForest/AnyoneCanDoIt/blob/master/...

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

#75

Post by mycologos »

xelxebar wrote: post #42
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…

While gatekeeping is definitely a thing, I really suspect it's not the major incentive here. In writing (both prose and code!) there is always a question of target audience, which inevitably excludes the not-target audience. Personally, for a field in which I'm an expert, it's really annoying to continually wade through introductory material and hand-holding just to get to some small nugget of substance. In that case…

The target audience point is fair. There are basic concepts that I don't bother defining in any paper I write, and I'm sure there are people who would make the same argument about them that I'm making here. But I'm not suggesting writing everything like "An Extremely Gentle And Slow Introduction to X, With Lots of Reassurances That You Can Do It".

The question probably comes down to how accessible a paper should be. Personally, I think a reasonable bar is something like: a third-year PhD student in your broad area should be able to skim the paper and say a couple of paragraphs about what's happening and why it matters, and upon reading the paper more closely, present it in a seminar and defend it at least a couple of questions deep. IMO, most papers are not at this level, and are instead pitched at actual experts.

I think my point (and TFA's point as well) is that going from an experts-only paper to a seminar-ready one is actually not a ton of text. It might increase a paper's length by 5%. It's not about making everything longer, but adding enough context and signposting that the story can be followed at multiple levels, from the 5-minute pitch you'd get at a poster session to the every-detail one the author has. So I think we can have a paper that both the grad students and experts like.

I think doing this takes some skill and effort, which is well within the reach of most of the people who can write these papers, but way less effort is expended on this non-technical aspect.

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

#76

Post by culebron21 »

constantcrying wrote: post #67
culebron21 wrote: post #49

Earlier quoted context omitted.

That's what I tried to avoid in the first place :)

So you tried to avoid an instructive text which is set up to allow readers to learn about the details of the subject starting from the ground up? And you are complaining that you can't find a resource which does exactly that?

I don't need ground up. I've even passed the exams on prob.theory and statistics. I need particular parts of it, but not in a cryptic form. I've had read enough of textbooks in the uni to see they're just as cryptic as research papers.

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

#77

Post by protomolecule »

saithound wrote: post #24
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…

In my experience, (c) is a very large part of it. At one point in my career, I decided to try writing good, accessible articles, which properly motivated definitions and well-explained arguments with plenty of hand-holding. When I did that, a version of the derogatory sentence "The proofs are easy / non-technical." would appear in the reviews. Every. Single. Time. Of course, I have some independent confirmation that…

Yeah, when the result is easy to understand people think it was easy to arrive at. What surprises me that smart people don't correct for that bias.

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

#78

Post by constantcrying »

culebron21 wrote: post #76
constantcrying wrote: post #67

Earlier quoted context omitted.

So you tried to avoid an instructive text which is set up to allow readers to learn about the details of the subject starting from the ground up? And you are complaining that you can't find a resource which does exactly that?

I don't need ground up. I've even passed the exams on prob.theory and statistics. I need particular parts of it, but not in a cryptic form. I've had read enough of textbooks in the uni to see they're just as cryptic as research papers.

You can skip chapters you already understand.

I don't know what textbooks you are reading, but almost every single one I have read tried very hard to present the content in a matter which focuses on understanding, unlike papers which focus on pure information.

I am afraid if you find either cryptic you have a serious lack in the prerequisite knowledge and that is what you need to focus on if you want to understand the subject. From first hand experience I can tell you that I have passed exams on a lot of things I have very little knowledge of right now. Textbooks are essentially the only way to reliable self study academic materials.

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

#79

Post by js8 »

seanhunter wrote: post #46
js8 wrote: post #35

Earlier quoted context omitted.

My point is, the need for semantics is a human construct, it's not required to solve practical problems. Practical value of MVT is that we can apply it in the process of describing a solution, i.e. an algorithm. But if you have a SAT algorithm that can somehow inherently apply a finite instance of MVT, you no longer need to know what MVT is. And this is at the heart of P vs NP question, how to solve SAT, and once we…

Most equations that can be solved can already be solved symbolically by things like mathematica or numerically by a grab-bag of numerical techniques that every maths, engineering and physics student learns at some point. You don't need to have found the solution to P vs NP to do any of that. I think most mathematicians would say that most of maths is not in solving equations because once you get the right equations,…

I disagree that converting from an equation to a solution algorithm is a straightforward process. It is very much where mathematics helps, for example just to ensure convergence of the method.

Also, the way you model reality (choose the equation) is often done with the limitations of solvability in mind.

I also disagree that maths can help you pick the right equations, just like there is no formal method that can verify whether a program specification is appropriate to the problem.

Equation (or a model) is just an infinite family of SAT problems, typically parametrized on our understanding what a "number" is. If we had a really good SAT solver, then getting a solution would indeed be a really straightforward process (just pick the number representation) of solving the instance. The same is also true for checking "legitimacy" (which I interpret as consistency) of the model - SAT solver would tell you that the instance is unsatisfiable and why. But you can never formally determine that the chosen SAT instance is appropriate model for the task at hand.

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

#80

Post by vaylian »

constantcrying wrote: post #68
daxfohl wrote: post #13

The same should be said for engineering design docs tbh

Absolutely not. Engineering design docs should be terse and to the point. Documentation is not a medium where you want to tell a story, because that makes it instantly much less usable, since people will read it at random parts to attain specific information.

Maybe we have different ideas about what a "story" is, but stories are about defining a context and a progression from that context to a more advanced state. You can use technology in ways that the inventors never intended, but most of the time you want to know in which context the technology has been developed and which problems it can solve. That is why it makes sense to have stories in technical documentation.
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