like i dont really understand the question and i am not sure if i am not supposed to

it is a question about integration as it is often developed in a second or third course on real analysis or probability theory.

there's a notion of 'absolute continuity' of one measure with respect to another. when $f$ is in $L^1$, $E \mapsto \int_E |f| \, d\mu$ turns out to be a measure. 'absolute continuity with respect to $\mu$' is the name given to the property stated in the problem. on nice spaces, if $\nu$ is any measure absolutely continuous wrt $\mu$, there is $g \geq 0$ for which $\nu(E) = \int_E g d\mu$, with $g$ sometimes called $[\frac{d\nu}{d\mu}]$.

if the measures involved are countably additive, absolute continuity of $\nu$ wrt $\mu$ is equivalent to $\nu$ having every null set of $\mu$ as a null set

Why are hyperbolic functions plotted only on real plane? Do they only give real values? Could anyone explain me this?

@ChristinaMelita introductory measure theory

@leslietownes that's very cool, thanks!

radon-nikodym theorem and absolute continuity are good search terms.

epsilon, davide's answer on math.stackexchange.com/questions/870142/… is a version of the idea, expressed as a proof by contradiction.

the radon nikodym theorem also holds for finitely additive measures on nice enough spaces, if you use the epsilon-delta criterion and not the null set criterion to define absolute continuity. it is actually easy to prove. you can prove it with less work than the proofs you see textbooks give in the countably additive case. but finitely additive measures are not mainstream.

Given sets closed sets $A$ and $B$ in metric space $[0,infty)$, is $A+B$ a closed set?

*metric space under the usual metric.

actually i misspoke. in the finitely additive case you can approximate absolutely continuous measures arbitrarily closely with integrals of functions d mu. which is often enough in practice to assume that your absolutely continuous measure is of the form f dmu.

@buddy001 give an example function!

I am trying using contradiction by assuming the existence of a limit point $p$ of $A+B$ which does not belong to $A+B$ but then I got stuck. Any hints please?

koro: in general, no. i would see where you get stuck in proving that it's true, and try to turn that into a construction of a counterexample.

@shintuku sinh(x)

mathcha.io/editor/qXNKESe8fqmHGLtdEK5DJIMYEE3Psk4Wl4XCP8VjdJ I tried it here Leslie, you may take a look.

seems to me $sinh(x)$ can plot complex values if you want to

wolframalpha.com/input/?i=sinh%28x+%2B+yi%29 @buddy001

So it's like two real and one complex axes? The inputs are real nos. but the output is actually complex too? @shintuku

in the example I sent you the inputs are complex numbers

Yeah my mistake what I meant was that $x$ and $y$ are real nos. @shintuku

koro: actually maybe it's true. supose a_n + b_n is a sequence in A+B (choosing a_n in A and b_n in B for each n) converging to z. by nonnegativity of the sequences, both of the sequences a_n and b_n are bounded. all but finitely many terms will be less than |z| + 1 for example.

$a + bi$ is a complex number, and it has a real part $a$ and an imaginary part $bi$, but $a, b$ are real numbers @buddy001

so z is in the closure of A' + B' where A' and B' are the intersection of A, B with [0, |z| + 1]. these are compact sets. A' + B' is going to be closed. so z is in A' + B' and hence in A + B.

so you reduce to the compact case.

@buddy001 $10 + 2i$, $8i$, $2-i$ are complex numbers. the one in the middle only has an imaginary part, or well its real part is $0$

koro: i'm assuming that you know or are able to prove that A+B is closed if at least one of A, B is compact. that's got to be on math.SE somewhere.

points is a_n and b_n are bounded, hence have convergent subsequences

this has a name, but I forgot it

@leslietownes Yes @leslietownes. I suppose it is correct. Just now I saw your messages. I think I could show it using sequences. Although I didn't quite understand symbols you have used (A' is set of limit points of A, if I am not mistaken). Nonetheless, I think I showed it using sequences.

wolfram alpha seems to have updated how it plots complex stuff. the only thing it used to do would be to plot the real and imaginary parts in different colors on the same axis.

i was using A' to be a bounded truncation of A. i do not acknowledge other uses of '.

to see that it fails in general consider $A=\mathbb{N}$ and $B=\{-n+\frac{1}{n}\mid n\in\mathbb{N},n>1\}$

Ah I see. Compactness of $A$ or $B$ is not required Leslie.

koro had an example like that, and then he deleted it.

i'm not talking about what's "required" but what is capable of solving your problem. i am nothing if not parsimonious.

@Thorgott Thorgott, that's for the case $\mathbb R$

yes

that's why I said in general

another good counterexample would be Z and r Z for any irrational r.

i'm thinking dirichlet's approximation theorem.

maybe something simpler too.

Leslie: If either of A or B is finite. The result is true. Even if $a_n$ and $b_n$ are unbounded (Let's pretend that for a moment), then if $p$ is any limit point of $A+B$, if $p\in A+B$ then we are done. If not, then for $n=2$, we have $1-\frac 12a_2+b_2\lt 1+\frac 12$

finiteness of A and B seems like a weird place to draw the line. i agree with your conclusions but i don't see that as where i would split an argument into cases.

:)

@leslietownes I have heard about it but never used it. I think it's also used to prove sequence (sin n) has limit points.

@leslietownes I see. Let me retract my finiteness argument and continue with the infinite A and B. We create (using induction it can be proven) a sequence $p_n=(a_n+b_n)$ which is such that $p-\frac 1n\lt p_n\lt p+\frac 1n$ for all $n$

any bounded sequence has limit points. you do not need anything relating to approximation theory for that. maybe you don't need it to implement my suggestion either.

proving that lim sin(n) does not exist is a good exercise. there are short proofs and long proofs and proofs in the middle.

But sin n does have a cgt subsequence and hence a subsequential limit.

I have a question to ponder : Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is..

Option (1):$\frac{1}{2}$

Option $(2):\frac{1}{3}$

one route, if you know what pi is numerically: for each k there is an integer n_k between k pi + pi/6 and k pi + 5pi/6. then {sin(n_k)} is an alternating sequence and |sin(n_k)| > 1/2 for all k, so lim sin(n_k) does not exist.

you can use trig identities and limit laws to disprove it without knowing what pi is.

Option$ (3):\frac{2}{3}$

Option (4):$\frac{3}{4}$

@leslietownes That's amazing Leslie. Thank you! :)

rover i'd just write a computer program and see. presumably each ordering of the people is equally probable, this is a very finite probability space.

I don't know about probability spaces..

@Rover: Try making more cases like these GGBBB, GBGBB

i'll keep going on this theme. suppose sin(n) goes to a limit L. if L is nonzero then cos(n)=sin(2n)/(2 sin n) goes to L/(2L) = 1/2 and hence cos(2n) goes to 1/2 also, which contradicts what you get from taking limits on both sides of cos(2n) = 2 cos^2(n) - 1. so L = 0 which implies that cos^2(n) = 1 - sin^2(n) goes to 1. expand cos(2n+1) using the addition formula and double angle formulas to deduce (cos 1)^2 = 1 and hence cos(1) = 1 which for various reasons is your contradiction.

leslie is a sin(n) doesnt converge enthusiast

yes.

you know why this happened to me?

Leslie loves non convergence of (sin n) :)

one time i had a classroom full of calculus students, and a calculus professor, who used this fact on a midterm examination, without proving it.

the professor said something like "sin(n) oscillates." really?

it really bothered me. it caused me to question the quality of the postdoctoral hires at the institution where i was employed as a graduate student instructor.

if you don't want to dive into the weeds, don't go into the weeds.

i agree that sin(x) oscillates. it was just people being lazy about sequences. sin(pi n) does not oscillate.

a lot of my earliest difficulties in math were due to me noticing complexity that my teachers either didn't notice or chose not to acknowledge. so that person tripped over one of my tripwires.

sometimes people who might be inclined to be very talented at math have more difficulty in the earliest classes because they are noticing things that you're not supposed to notice.

[that meme where the guy is pointing at a pin board of photos connected by pieces of string.]

@Koro Ok, I tried that way only and now I got more: BGBGB,GBBGB,GBGBB,GGBBB and..BGGBB so, pb =$\frac{1}{2}$

that's really a $\sin$ Leslie

so, for $\mathbb{R}^n$, how exactly do I visualize local extrema

i have limited imagination and sometimes 3d objects feel nearer than they actually are, which is dangerous when i must relocate

$\sin(\pi n)$ is a big different from $\sin(n)$. I don't find that too questionable a statement. It's not precise, but it's right in spirit.

have you been looking in the side mirrors of your car again?

so what do i do about $ \mathbb{R}^n $

don't do that. nobody else does.

@Rover: I think that's correct.:)

people find me odd for carrying my side mirrors everywhere (i have no car), but i think what's a stake here is, is this a nation of principles?

copper: i appreciate that. i'm getting used to these puns.

Oh, used the fact on a midterm. If he had told them in class that it's a fact, I'm OK with it. This was 1B, not an analysis course.

@shin: No, a nation of principals.

bureaucratization really is the greatest question of our times

it was 1B. hadn't told them in class. i unfortunately know because he made TAs go to each class.

maybe that's what i'm really mad about.

this has been very therapeutic.

1B ?

second semester calculus for math science engineering etc. at uc berkeley. i think it retains that name to this day.

it's where students encounter sequences and series for perhaps the first time.

Ah, I see.

where do people encounter visualizations of local extrema in $\mathbb{R}^n$? or do they just live inside algebra and never properly see (emphasized for dramatic effect)

@epsilon-emperor oh nvm i dont know what that is. i just know to integrate certain functions like indefinite and definite integration. anyways thanks

a surprising number of visitors to this channel have a small number of six-degrees-of-kevin-bacon level of connection to other visitors by virtue of having attended a small number of institutions in the USA.

@leslietownes thanks i dont know what they are xd

shin i think of these things in terms of one and two dimensional slices. i never properly 'see' anything.

outside of degenerate cases, local extrema are determined by first and second order behavior that is detectable along such slices, at least if you have access to all of them.

we won't speak of degenerate cases.

@leslietownes Despite being degenerate ourselves?

yeah slices are the way to go. i guess you might visualize heat-maps in 3d but that is kinda sketchy. you probably need to discretize 3-space in some way to make it so that you can actually "see" the heatmap. local extrema are where there are "dots"

i mean, i don't want to brag. so i remain silent.

that's a bummer, i thought people translated $\mathbb{R}^n$ functions into sublime concertos of classical music, where $x=$ time in the music

Level sets are good, too, in many cases.

well, for the proof of the local extrema means derivative = 0, do you just do it algebraically?

concertos of classical music reminded me of an interesting fact, i'm not sure if it's true. you can detect the route by which sound is transformed in a space by recognizing the kernel of an integral transformation, by convolving it with a delta function.

Yes.

i'm told that they test acoustics in concert halls by firing starting pistols within them, and recording the feedback, approximating the theoretical procedure.

i don't know if this is true. i like it.

you visualize low dimensions and then just try to wing it in high dimensions

It's clear that you should have a horizontal tangent plane — analogous to the 1-variable situation.

sometimes you can also just pretend high dimensions are low dimensions, works with a 50/50 chance

but what would a tangent plane look like in $\mathbb{R}^n$? i guess i could try to cut the Matrix somehow but would that get me in trouble

i was halfway through my dissertation before i realized the pictures i was drawing were off on the dimensions by a factor of 2.

of course i scrubbed all the pictures out of the dissertation itself.

a while ago I drew a lot of S^2s and pretended they're S^3s, it worked out

hyperplanes in R^n are determined by vectors in R^n. just visualize the vector. draw the 2d or 3d pic of a vector.

oh! nice idea

thank you all for the comments

@shin: If you get far enough in my YouTube lectures, there's one on applying Stokes's Theorem in 4 dimensions. So I tried to draw some helpful schematic diagrams there of what was going on.

do you use different colors of chalk? my officemate used to do that. i thought he was pulling my leg. there's no way different colors help.

one time he had a bunch of pieces of paper with these weird multi color diagrams that he was going to use in a talk. because i am childish i drew a marijuana leaf with psychedelic colors emanating from it and slipped it into the middle of the pile. his advisor thought it was funny. a foreign visitor to his talk was confused.

i tried to capture the spirit of the 60s. stick it to the man. be weird. annoy the stuffed shirts.

lol

my advisor was once jailed by the university police because they were clearing a protest (which he happened to be walking through but was not attending). he insisted that he had a right to be there and would not disperse.

that's a good lesson for anybody, although i'm not sure what the lesson is.

i had a dream last night, but i forget what it was.

@leslietownes your dream was you had a dream, in which you had a dream...

i had an infinite number of dreams, and then one more, at the end

$\sqrt{\text{dream}\sqrt{\text{dream}\sqrt{\text{dream}\sqrt{\text{dream}\sqrt{\text{dream}\sqrt{\text{dream}\sqrt{\text{dream}\sqrt{\text{dream}\sqrt{\text{dream}\sqrt{\text{dream}\dots\infty}}}}}}}}}}$

Woah, that's neat...when the roots are big, the vertical line is vertical...as the root gets smaller, it tilts towards right

Yeah I do know that. Now whenever in books they graph $cosh{x}$ or $sinh{x}$ they always show a plane, now what my question was, do these functions give complex outputs? If yes then is the plane that the authors graph in real plane or argand plane? from the link u shared, what I could understand is the function's output is indeed complex is that right? @shintuku

it would depend on the book and the picture. you definitely can get complex values of sinh and cosh, but whether any given diagram in any given book is attempting to depict that is another issue.

i think you can deduce from identities or otherwise that sinh(x + iy) = sinh x cos y + i cosh x sin y for real x, y for example. so there's a real part (sinh x cos y) and an imaginary part (cosh x sinh y) which could be graphed in any number of ways.

I'm actually talking about this @leslietownes

those look like the graphs for real values of x

$\sinh, \cosh$ appear a lot in elementary beam problems in civil eng

@leslietownes yes, so will the output be complex in this scenario?

no. the details depend on the definitions, but most formulas for sinh and cosh make fairly explicit that if the input is real, the output will also be real.

in this respect cosh and sinh are just like cos and sin or exp. you can get complex values of those functions too but you have to put non-real numbers in.

@copper.hat yep like a rope hanging across two level points

how do cosh and sinh arise? i know it's in every calculus book, but physically. is the weight arranging itself to be uniform in the horizontal direction? what problem is it solving?

@leslietownes yeah i get it now when I try to rewrite the function as $(e^{x}-e^{-x})/2$ as this is real for all real $x$

@leslietownes this is a bit simplistic, but the governing equation is often of the form $y''=y$ (ignoring constants and lots of stuff).

hyperbolic secant (squared) appears as solitary wave solutions to the equations for shallow water narrow canal wave propagation (KdV)

are you asking the physical basis? it has to do with a beam bending, shear and all that.

@copper.hat Are you asking me?

yeah, the physical basis. i took a class on this once. i understood it for maybe two weeks.

@buddy001 Leslie...

i like Von Neumann's line "Young man, in mathematics you don't understand things. You just get used to them."

same with the beam equation etc

i definitely feel that way about von neumann algebras.

i really don't get the rush to close & delete many questions. most are obvious noise, but some are reasonable questions that may help others. just because it doesn't have the vapid 'context' where some random fact is quoted as an 'attempt'.

it's quite funny what seems to count as an attempt. if you regurgitate a rephrased version of something in the paragraph before the problem set (or a hint that's included with the problem), that counts.

or if you google your problem, hit "i'm feeling lucky" and paste in whatever the top result is.

i know. i wish there was a little more thought put into some of the deletions.

it kind of reminds me of when benedict became pope. the vibe seemed to be that it would be better if the church went much more in a certain direction even if it meant a whole lot fewer people in the church.

seems a waste of reasonable questions & answers.

weird analogy but that's how my mind works

benedict reminded me a little of contemporary 'populist' politics.

a rabid tiny slice of the population is more politically advantageous than a larger but less nutty slice of the population.

sad that extremes dictate the majority

seems to be true broadly, even on se

nobody's going to march in the streets with signs like 'careful now' and 'down with this sort of thing.' you need snappier messages.

seems it is easier to get people all worked up than to calm people down to think clearly

wonder why the human mind operates like that, must be some evolutionary reason

gorgeous weather in the bay area today. lovely ride this morning.

that seems like it would make some type of sense if survival depended on making a quick decision and getting the tribe/group on board. i feel that in myself at times and it is hard to step back

that seems a reasonable explanation

what i find curious about the current PSQ chase is that if i look at many of the questions that the closers have answered themselves, they fall into what i would characterise as PSQs.

frankly i hate to waste effort. for the moment i have given up writing answers. if i can help someone it will be in chat or comments now.

@Quin i read a summary of a study some time ago which basically said what you said. the thesis was that our intellect evolved to facilitate group coordination rather than any greater intellectual pursuits...

which would explain 'populist' politics.

That makes a lot of sense just from personal experience. It is unfortunate that it has taken such a weird turn lately, in politics and this site. For instance, I am not really sure what to make of all the rules about answering questions on this site and so I basically have opted to not post answers even in cases where I had typed something up for fear of angering the mods lol.

I would guess all these rules will drive people away from answering

i am not particularly bothered by the mods or whatever, but it seems a pity to me to get rid of something that might help more than a few people. mathematics is made inaccessible because of this sort of attitude, in my opinion.

for me the value is part 'interaction', part helping. fitting into some clinical set of vaguely antisocial patterns is not a huge motivator for me.

i stopped contributing to math overflow while still in academia because i felt pushed out. some of the people who were doing the pushing knew me in real life but did not know my pseudonym.

math.SE is going in that direction.

yeah i agree. i guess i dont wanna even think about if im breaking some random rule or not. if i were asking a question and wasn't familiar with the site and it was closed, i probably would not come back. also, different answers to the same question help different people.

i agree. it is a pity, because i think it was doing a great job of demystifying mathematics.

i realise that with online stuff it creates problems for educators, and that needs to be addressed.

i think that it the case with many of the se/so sites. there is a bit of a pull the ladder up approach because you are not an expert.

and i had the feeling if i just said 'hi, it's me, from down the hall' it all would have stopped. that made it worse.

i think it is fair game on mo, because that is research focused.

@copper.hat Don't forget MR. catenary.

@TedShifrin i love that stuff.

some fairly high rep user on there asked a few questions i answered and then somehow deleted them i guess because he was embarrassed that they didn't have 'research level' answers.

i should have been a civil eng

Have you ever worked out the shape of the road you should drive a car with square wheels on to drive level? :P

That's one of the exercises in the first section of my diff geo notes.

It's a classic problem, of course. I take no credit.

my experience is that even with experts, they often make simple mistakes. there is nothing wrong with that. but shooting others for doing same is not ok.

@TedShifrin a cute optimal control problem is the parking problem.

I said a stupid "no" too quickly to Hawk a day or so ago here. I recanted immediately.

we all make mistakes.

@copper.hat That's one of my favorite Lie bracket exercises.

This has made me realize how much I value in-person interaction. everyone is more forgiving with this and there is not so much of an expectation to be "perfect" all the time.

How to slide a car sideways :D

@Quin What is this "in-person interaction" of which you speak?

the fred flintstone problem.

@TedShifrin i like it because it really combines a lot of stuff with a 'fun' problem.

a lot of science museums have working models of that.

Yes, also the bricks stacked to get arbitrarily far. One of my favorite displays at the Exploratorium in SF.

it's this new thing that hopefully will be coming out this next fall where we actually get to talk to people face to face!

i first encountered it in '85 in a controls class.

i loved the exploratorium. i haven't been since it moved from the palace of fine arts.

i loved the exploratorium

Yeah, I was going to go again on a recent Bay Area trip, but out on the wharf the admission is something like $20.

I used to take people there regularly when I was in grad school.

i got to go for free many times as a school chaperone

that's what stopped me the last time. also, the fact that i'd have to be at fisherman's wharf, where no self respecting bay area denizen would go.

One of my classmates from MIT actually worked there for a few years.

the teachers liked having me along because i was immune to IEPs

$-a_{0} \times (-1)^{k+1} \times 1 = (-1)^{k}a_{0}$ ??? How????

what are IEPs?

and the kids knew i would brook no crap.

What is $(-1)(-1)^{k+1}$??????

i forgot the acronym, basically a special plan for a problem child

copper was immune to potential violations of federal law.

ah, gotcha

oooooooohhhhh

it is amazing how kids react to a little discipline. nothing wierd. just being up front with them.

it always worked out well.

Fundamental exercise at the beginning of Spivak or algebra books: Show that $-a = (-1)(a)$. Not trivial at all.

I remember the exercise too

i certainly struggled with it.

Do you mean wired or weird, copper? With your current status, one cannot be sure.

both :-) i am a wirey personality apparently.

I just don't know wierd.

could there be a structure (family of them) that is a quasigroup, but it has finite substructures as groups? The idea is to "lose the 1 in the limit" somehow

at end of terms the teachers gave me bottle of wine, chocolates, etc

I guess by the definition of substructure it's not possible, so that would have to change in some meaningful way

probably why my kids are so embarrased by me

Geez. No wonder you're spoiled.

totally in some ways

both the exploratorium and lawrence hall of science had amazing staff in the 80s. lots of people with deep backgrounds and a whole lot of enthusiasm.

i had the kids in elementary school make a little slide rule.

many of them were hippies but you can't have everything.

What's wrong with hippies?

@leslietownes it is because they cared.

charles pugh was a hippie

i was kidding. i think in many ways as someone who grew up in bay area i benefited from the 1960s in a way that today's kids cannot.

Yup. With very expensive food and wine tastes.

One of my favorite memories was a dinner I contributed to at his house before I graduated. He provided the wines. Unbelievable dinner.

nice fellow. smart non judgemental and nice

He belonged to a wine-tasting group and sent me in his place two or three times when he couldn't go. I was totally intimidated the first time, but then adapted.

He would have been my choice of adviser if I hadn't gone complex geometry.

he wrote up a proof of the rademacher theorem for me :-)

very sweet. he understood what my issue was with the proof i was reading.

Oh, I wrote that up for our dynamical systems course. I had it all typed up and stuff ... but that got trashed when I retired.

remedial work for joe (me)

students absolutely loved him when i was an undergrad.

you couldn't get into his classes if you didn't enroll on the first day of enrollment.

it was an irish friend that connected me to him

I'm surprised. He was hard and not the greatest teacher, but he was a sweetheart. I tried to teach him how to use the triple-layer blackboards, but he never could break his bad habits.

He always got stuck on the bottom board, having to erase it repeatedly.

when people would start on the wrong board! that cracked me up.

i'd forgotten about that.

I talked to him about it and even tried to set the boards up for him and annoy him in class about it, but after two attempts, I gave up.

Reminds me of my colleague (now departed) at UGA who was a horrid mathematician and worse teacher who was contemptuous of me when I talked about the importance of good boardwork and good colored chalk pictures.

it's really about 2 seconds of effort to start on the right board.

Well, even starting on the right board, you have to never use the bottom board. He just couldn't understand that, even with side boards to use.

as i get older i am less able to adapt on the fly.

i can adapt, but the adaptation is quickly forgotten the next time around

Just wait 'til you're my age!

i have an unrelated memory, one semester i taught in a room which had small boards, so i used the slide projector in the room instead. the previous class used the boards. one day the instructor who used the room after me, who was very senior and probably a big wheel in whatever department, came in early and basically yelled, "can you erase these boards before you leave?" i said "i'm sorry, i don't use these boards."

i suspect your still way ahead of my adaptive abilities

he said "you need to erase these before you leave the classroom." i said "i'm not going to do that." my students laughed.

i'm not good with the 'respect' thing.

Some people do throw fits about that. I always loved spying on what the person before me did. Some got paranoid and erased so I couldn't see. I always left mine for the next class to admire the pictures, unless explicitly asked to erase them. It happened one class out of hundreds.

afterward, i was very tempted to depict anatomy on the second board and slide a cleanly erased first board in front of it. but i didn't do that.

another one of my answers deleted.

i deserve a medal for all the stuff i've thought of but didn't do.

i did some stuff like that. a bit juvenile of me. when the instructor raised the board it would generate a laugh.

not entirely pc either

the doors in the basement of evans had little windows into the hallway. sometimes when my friends were teaching i'd pop up in the window and make obscene gestures until they noticed me and began laughing. then i would flee before any students could see the source of the laughter.

i can't do that in my current job because our doors don't have windows in them.

:-)

also because i'm old and mature now. i no longer find it funny to make people laugh with obscene gestures and flee before others can figure out what is happening.

i used to do it to disturb colleagues during presentations.

the worst i do these days is on zoom, sometimes if my cat is in my lap, i'll hold her up and place her in front of the camera so her head is about the size of a human head in the zoom image. you can see who is using 'gallery view' by who starts laughing after the first 30 seconds or so.

my cat is very cooperative with zoom.

how does se make money?

i rarely see ads

i found an answer. apparently i asked the question 8 years ago on meta.

i just found some threads that answer this question. disappointing, i thought it was a pure public service project operated by the Anti PSQ League.

:-). i wonder if anyone evaluates the effectiveness of these campaigns? a lot of closures and deletions are very much warranted, but many PSQs seem like perfectly good stuff to have on mse.

decades ago ibm started firing programmers based on the number of bugs generated. after a while they found they were letting go their most productive staff.

(fred brookes, the mythical man month)

i think a big part of it is a value judgment. that even with PSQs of potential benefit to the community, if someone somewhere might be getting away with something, it is better to keep the site from sliding down a slope into a servant of those people than it is to not have those questions at all.

not my view, but an understandable view.

i am generally a fan of what is termed in my field as 'self help.' if your students can ace your class by copying from the internet, that's your problem as the instructor. or maybe it isn't even a problem.

people who copy from the internet tend not to be able to do it well. they don't know how to change notation to match what the problem is phrased in, etc. if someone can copy well that is almost as good as answering the question.

in my very humble opinion as someone who quit academia and no longer has to deal with the negative consequences of serial copyists winding up in my classroom. :)

@copper.hat "Individualized Education Plan". These are plans mandated under IDEA (the Individuals with Disabilities Education Act) which are meant to ensure that public schools are properly serving students with disabilities. They are not for "problem children".

see my remark above about violations of federal law :)

@leslietownes That seems like something of a straw-man. The most common argument against problem statement questions is that they are unlikely to be of much use to anyone other than the person asking the question. However, if the question can be placed into some larger context, then there is a chance that the surrounding context will make the question more useful for future readers.

(Either by providing a broader theory in which to place the problem, or a citation to a specific section of homework from some text, or whatever).

@XanderHenderson it was a quick characterisation and as such incorrect. many with IEPs are well justified, but, in my limited experience, many are legal justifications for letting kids get away with disruptive behaviour. the issue that that the schools that i have dealt with basically adopt a 'hands off' approach which is disruptive and does nobody any good.

Personally, I wish that we would adopt a more hard-line anti-homework policy, a la Physics, as I don't think that these kinds of questions---even with context---are likely to be of much use to anyone other than the asker, and there are already many sites out there which offer one-on-one tutoring (e.g. quora, reddit, paid tutoring services, etc), but this is a fringe point of view.

@XanderHenderson there are many questions that are PSQs that stand on their own in my opinion. the required 'context' if often noise.

xander i understand that in theory. in practice, i am hesitant to answer a question that cites a textbook and nothing else, even if it is a widely used textbook that many people might be working from.

because rightly or wrongly i have internalized the idea that answering such questions is not the done thing.

@copper.hat Frankly, if context is "just noise", then I suspect that the question really isn't appropriate for Math SE anyway.

Every problem in mathematics occurs in some context. No problem comes from nowhere.

The kinds of problems for which context would be "just noise" tend to be homework-style problems, which really aren't a great fit for the format, anyway.

it seems possible to vault over the 'provide context' line in a very pro forma way by just rephrasing some hypothesis of the question in different words. the line ideally would be something like 'provide meaningful context,' but i understand that this is not an administrable standard.

@leslietownes Indeed. I agree that meaningful context is the goal.

Some explanation of where the problem comes from, and why the heck anyone should care about it.

I think there are many interesting problems (not research problems) for which there is no context other than it appears as part of the subject matter.

"This is problem 4814 from Joe Shmoe's book Calculus for Complete and Utter n00bs. What is the answer?!" is kinda useless. :\

Many reasonable answers which have different than standard approaches are being lost by the close & delete.

@copper.hat Yes, but "part of the subject matter" is context.

I agree with that.

when i find a question that interests me and i think about answering it, i think "this is probably a dupe" and 90% of the time, it is. so many questions don't get over the dupe line for me.

I think context matters when it can help find a solution, but many are standard things for which context adds nothing. Trying to understand duality in optimization is not helped by knowing that you are solving some particular QP. It is standard stuff that folks are having a hard time understanding and a different approach opens things up for them.

"I am studying [foo] out of the book [bar]. [Example] doesn't seem to be easily amenable to the techniques outlined therein. Ideas?" Is a good question, with context, which might provoke nonstandard approaches.

@leslietownes Indeed, this is often a problem with problem statement questions, in that they are duplicate questions, with (perhaps) slightly different parameters. Knowing where a problem came from can help us to know if we should be looking for good duplicate targets.

Unfortunately many people are studying stuff without context.

I think losing different solutions is a problem. It is a lot of work, but it would be nice if they were added to an existing duplicate question?

@copper.hat Losing different solutions is a problem, but having multiple solutions to one problem scattered across multiple questions is, in my mind, a bigger problem.

I agree. It is a pity there is not a way to coalesce the collection of related problems

@copper.hat Questions can be closed as duplicates.

I have found mse very helpful even for basic stuff.

And a moderator or gold-badge bearer can add dupe targets to a post.

So one question can be closed as a duplicate of more than one previous question.

I have found new perspectives that (i'm 60 and have been around the block) are eye opening.

That is entirely resonable.

@copper.hat But this is exactly my point: MSE can be very useful, even to old hands. However, the use of MSE is dependent upon maintaining a fairly good signal to noise ratio, which means aggressively pruning those questions which are unlikely to be of much use in the future.

What is the advantage of deletion over closure?

@copper.hat In an ideal world, I don't have a problem leaving a lot of closed questions around.

I guess that is my concern, I think there are a few problems (without context) that are useful.

@copper.hat I agree. Though most of them are 5+ years old. :D

I think deletion could be put on a longer cycle.

@copper.hat I also agree---my feeling is that the point of closure is to (1) give the asker and community a chance to improve a question and (2) signal potential answerers that they need to help to improve the question, first.

I'm def on board with that.

I am not a huge fan of closure and deletion happening too close together.

But part of the reason that quick deletion is attractive to some is that experience has shown that many askers won't bother to improve their question once they have an answer. So poor questions get answered, closed, then never improved.

I have seen it argued that a shorter deletion cycle sends a stronger signal to the answerers that their behaviour is not okay.

I wonder if it impacts behaviour?

For me it just reduces the impetus to answer.

Hard to say. Though there are enough "Why was my answer deleted?" posts on meta to indicate that, at least, people notice.

I answer in comments instead which is not ideal for anyone.

@copper.hat I mean, that's the point. Quick deletion is supposed to discourage answering---at least, until a question is whipped into shape.

Is it visible when it is deleted?

@copper.hat Honestly, if a question is unlikely to be helpful to anyone but the asker, I am all for answers-in-comments. The asker gets their answer, and the question disappears after a month without polluting the database.

@copper.hat Is what visible when it is deleted?

I guess that would be a better clarification of my concerns. It is a question that prvides leverage for others.

There are too many pronouns... I am confused.

Sorry, I mean if a question is deleted, is it still visible to everyone on MSE.

(I am good at confusion :-)

@copper.hat No. A deleted question is completely invisible to anyone under a certain reputation threshold (10k, I think?), and won't appear in the Math SE search results.

"Deleted" questions and answers are much harder to find.

I know Asaf & Daniel have helped me find deleted some stuff over the years.

@copper.hat Yeah, it's doable, and easier for diamond mods.

Its a bit sad when I go looking for an answer for a problem I am working on and find I have answered it years ago :-(

Heh.

Unrelated: A friend of my daughter was using one of my answers and they realised after reading the profile that it was me. It was funny.

There only perspective prior was a stern helicopter dad who disciplines on class trips.

Heh.

I am happy to see that my 17yo son does some free tutoring online (at his school)

i think many kids are short changed by not having access to basic maths education.

my parents could only afford erdos's brother, pete erdos. he taught me how to cheat at monopoly.

the tao of maths education

@leslietownes My Erdos number magically decreased by 1 at some point in the last five years when I wasn't looking.

how can that happen ? :-)

that's awesome!

sorry ignore that

i thought you meant the other way

@copper.hat A collaborator publishes a paper with someone with a lower number? :P

Yes, I am just slow.

I think mine went up for same reason.

@copper.hat Well, that could happen if a paper were retracted, I suppose.

i remember vaguely wanting a lower one and realizing that none of my coauthors were going to pick up the slack. i had exchanged some mathy emails with someone with erdos 2 but they never led to a paper.

all mine were entirely accidental.

nothing earth shattering unfortunately

lucky to have some smart friends

Weirdly enough, my father (who was a cultural anthropologist) had a finite Erdos number. Any my mother (an archaeologist) arguably has a finite Erdos-Bacon number (she was an extra in Stir Crazy).

:-)

that's an amazing film credit.

@leslietownes I took a class from someone who co-authored a paper with Erdos. But I never managed to turn that into anything (I don't have a lot of interest in discrete optimization nor game theory).

@leslietownes "being an extra"?! :P

in stir crazy. i guess it arguably doesn't count as a credit.