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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

#81

Post by js8 »

constantcrying wrote: post #72
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…

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

Before there was AlphaGo, many top Go players believed that understanding Go is somehow special in helping us to understand the universe. The AlphaGo was a shock, because it turned Go into "just another game", which can be beaten by enough calculations on a powerful computer.

I think the mathematics is the same. Lot of its beauty we cherish, because we don't properly understand it on the "raw" level of SAT (I would write logic, but I really mean the simplest metalogic you need), which is evidenced by our lack of understanding of P vs NP. Once it is understood, the process of "doing math" will be understood algorithmically, and it will become "boring" or "dull".

But as I said, I don't think lack of universal meaning (or lack of mystique) has to detract from the beauty of mathematics.

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

#82

Post by skhunted »

tarkin2 wrote: post #18
skhunted wrote: post #8

Earlier quoted context omitted.

I’ve been teaching mathematics for decades. Know how many students like the cool applications at the time they are taking the class? Very, very few. Usually, it’s later on in one’s journey through life that appreciation for the cool applications occur. At the time of taking the class doing cool applications inspires 1, pisses off 50 because it’s too hard, and leaves 49 rolling their yes.

If you look at the comments in khan academy there are tonnes of people asking for real life applications—that said, they’re given in most of the material there. Inspiring students (and showing the material can help them in their lives additionally) is one of the most important but difficult parts of teaching: good explanations falling on uninspired ears rarely settle. And I’d argue the onus is on the teacher to inspi…

I imagine - but have no data to back me up on this - that a lot of those comments you mentioned on Khan Academy come from two types of people. Those who are relearning the subject and are amenable to applications and those who say they want the cool problems but when they are actually done fall into the 99 category I mentioned above.

It sounds to me like you haven’t taught much. I could be wrong.

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

#83

Post by skhunted »

atoav wrote: post #12
skhunted wrote: post #8

Earlier quoted context omitted.

I’ve been teaching mathematics for decades. Know how many students like the cool applications at the time they are taking the class? Very, very few. Usually, it’s later on in one’s journey through life that appreciation for the cool applications occur. At the time of taking the class doing cool applications inspires 1, pisses off 50 because it’s too hard, and leaves 49 rolling their yes.

Haven't thought is for decades, but was my environments favourite math tutor, because I managed to ground everything in people's reality and rell them a compelling fiction in which knowing how to do the thing was actually a super-power. You know like the survival tricks certain preppers learn and never use — that, but with math. Even if the examples were sometimes over the top, involved flaming moats and other xkcd-l…

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 the stuff. They want applications. At the time a class is taken very few actually want to dive into applications. The subject has been taught the way it is taught for a reason.

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

#84

Post by _dain_ »

culebron21 wrote: post #32

It's not just papers. I tried to learn probabilities theory & statistics, deeper than little knowledge I kept from the uni. For instance, wanted to understand how you solve problems like samples in quality control: if in a sample of N items, m are bad, what's the chance X% are bad in production? Unfortunately, there are either introductory materials (toss a coin -- 50% chance faces) or some robot language. Or schizop…

I find that coding up a Monte Carlo simulation is a tremendous help when I have to deal with some probability/statistics problem. If I can play with the parameters and immediately see how the scatterplot changes, I get a much stronger intuition than I could from formal reasoning.

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

#85

Post by skhunted »

homefree wrote: post #16
skhunted wrote: post #8

Earlier quoted context omitted.

I’ve been teaching mathematics for decades. Know how many students like the cool applications at the time they are taking the class? Very, very few. Usually, it’s later on in one’s journey through life that appreciation for the cool applications occur. At the time of taking the class doing cool applications inspires 1, pisses off 50 because it’s too hard, and leaves 49 rolling their yes.

imo this is largely because of the incentives around the game of school and testing. If you must wait 20yrs before you can do interesting stuff and you’re evaluated primarily on your ability to maximize your grade then anything that gets in the way of that is an annoying distraction for most at best. Even if you’re a student predisposed to find applications and the narrative of the discovery interesting you still hav…

For the vast majority of the students the curiosity, as you put it, isn’t really there. Understanding is very hard work and most people don’t want to put in the work to acquire understanding.

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

#86

Post by constantcrying »

js8 wrote: post #81
constantcrying wrote: post #72

Earlier quoted context omitted.

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

Before there was AlphaGo, many top Go players believed that understanding Go is somehow special in helping us to understand the universe. The AlphaGo was a shock, because it turned Go into "just another game", which can be beaten by enough calculations on a powerful computer. I think the mathematics is the same. Lot of its beauty we cherish, because we don't properly understand it on the "raw" level of SAT (I would w…

Some facts to consider:

- Polynomial problems can still require enormous computing power to the point they are unsolvable. Even if tomorrow there is an algorithm transforming every NP problem to a P problem, not all problems will be feasibly solvable. A O(n^100) Problem is still P.

- P vs. NP is about algorithmic complexity, it has no implications about mathematics being an algorithm or not.

- The most likely outcome is that P and NP are different, in which case there are zero implications on computational efficiency.

- Considering mathematical statements as algorithms has happened for a long time. Any outcome of P vs. NP has limited implications on the philosophy behind it. It just might make it somewhat better.

You just don't understand what P vs. NP is about, your posts are bizarre in the actual context of the problem statement. The implications on mathematics just aren't what you think they are.

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

#87

Post by constantcrying »

vaylian wrote: post #80
constantcrying wrote: post #68

Earlier quoted context omitted.

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.

>but stories are about defining a context and a progression from that context to a more advanced state.

Exactly. Starting a story 80% in makes it nonsensical. If your engineering docs are nonsensical if you open them at 80% you have failed as a technical writer.

>most of the time you want to know in which context the technology has been developed and which problems it can solve.

ABSOLUTELY NOT. Imagine your dish washer manual going over the history of dish washers interspersed with comments about how it functions. That would be insane, useless and unreasonable.

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

#89

Post by sublinear »

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…

Terse statements are easier to prove.

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

#90

Post by js8 »

constantcrying wrote: post #71
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. Plainl…

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

The outcome will matter less than having an answer. And I do think it will be a negative outcome either way, because it will obsolete lot of beautiful math, and replace it with a more mechanical process.

> In basically any field proving the existence of a solution is far, far harder than calculating the solution numerically.

First of all, if you want to ascertain whether the numerical algorithm works correctly, you have to prove the existence of the solution. That's part of the (equation -> solution algorithm) conversion process.

Now, you can possibly get by without proving existence of the solution for the infinite family (and confront the numerical solution directly with reality). But doing that is more complicated than, assuming there is a SAT solver, plug the SAT instance into it and see if there is a solution (and you can get, for a finite family of instances, a similar guarantee you would get from the existence proof).

> Not even the assumption is right.

Not sure what assumption you refer to. Computers don't run algorithms (because algorithms handle unbounded input/output), computers are just a very large state machines. So you need to convert the algorithm to a state machine first. Saying "run algorithm on a computer" is just a useful figure of speech, but somewhat misleading, because it implies certain quantization.

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