Mathematics - 2023-06-30 (page 2 of 2)

Xander Henderson

23:00

@robjohn Gross.

Ted Shifrin

@D.C. This is a concrete "solution" of one of my favorite problems in elementary projective geometry: How many lines meet three lines in space in general position? You can find a complete discussion of this in the last chapter of my algebra book, if you ever decide you want to learn projective geometry.

Xander Henderson

@TedShifrin Oh, that sounds like fun.

@TedShifrin Because it don't render right?

Ted Shifrin

Yeah, I've forgotten the syntax with underset.

Jakobian

{}{} ?

Xander Henderson

$M^n = \underbrace{M\times\dots\times M}_{\text{$n$ times}}$?

Ted Shifrin

23:03

There you go. I used to be good at that, but I'm rusty.

Xander Henderson

I'll go get the WD-40.

Ted Shifrin

@XanderHenderson Were you being sarcastic again?

Xander Henderson

@TedShifrin No, that sounds like a genuinely interesting problem.

Ted Shifrin

I'm shocked!

robjohn

@XanderHenderson Is there a big X operator?

Xander Henderson

23:05

Seems like it should be amenable to elementary tools, but I don't immediately see how one would go about working it out. But I am not in a place where I can get out pen and paper to try things out.

Ted Shifrin

To get the "universal" answer, you want projective space and complex numbers; but over $\Bbb R$, you can certainly say "at most."

D.C. the III

@TedShifrin your linear algebra book? I do have an interest in projective geometry actually. I have sen its application to statistics and least informally in something I read. I didn't understand the whole treatment but I saw its use.

Xander Henderson

And I'm guessing that there is a clever geometry trick that reduces it to a two liner. :D

D.C. the III

you defintiely have infected me with the geometry bug......

Xander Henderson

@robjohn Not that I know of.

robjohn

23:05

yeah, that was why I went the ugly way

Ted Shifrin

There's a section on projective geometry in the lin. alg. book, but no, I meant the actual algebra book. There's a whole chapter on projective geometry (and also affine and also a bit of hyperbolic).

D.C. the III

Oh you have a big boy algebra book too?

hmmm before I can tackle that I need to look at introductory and intermediate geometry first. Any suggestions for a good place to start?

Ted Shifrin

My favorite sophisticated geometry book is by Pedoe. It's the book I was trying to force Hades to read instead of doing all his infernal high school problems with angles :P

D.C. the III

Well you know I can't start with that.....I do have it earmarked because I rememebr you suggesting it

there's proabably a book recommendation list on MSE

leslie townes

1. hop on pop and other dr seuss books. 2. eisenbud 3. hartshorne

there's your royal road to geometry

Ted Shifrin

23:11

Um ...

D.C. the III

@leslietownes Heartless........

leslie townes

maybe that's an unfair characterization of what an MSE recommendation list would be

Ted Shifrin

Hartshorne actually has a sophisticated book on Euclidean geometry — did he used to teach the course for teachers?

leslie townes

i don't know if he ever taught it, but that book (published under various titles including "geometry: euclid and beyond") is really good

Ted Shifrin

I actually do not know it, but I think he has stuff over a general field $\Bbb F$ in there.

leslie townes

23:12

yes

shintuku

if there is a bijection between sets $A,B$ then the free abelian groups generated on them are isomorphic right?

leslie townes

i took a class based on that book, great stuff

D.C. the III

Actually since I am intending on doing abstract algebra next year sometime, I could use your book instead of Gallian's? Same treatment?

leslie townes

shin: yes, there is even an isomorphism between the groups that 'is' the bijection on the generators

shintuku

great thank you!

Ted Shifrin

23:16

Both are rings first, @D.C. Mine is definitely more geometry-oriented (big surprise). Symmetries of polyhedra, for example.

But I think you've had enough of me, so I won't encourage it.

D.C. the III

I like the geometry, even though I suck at it at the moment it produces a calming effect on seeing what all the symbol pushing is doing

leslie townes

dc3 gets a call from his credit card company. "someone keeps ordering books by ted shifrin, this is highly suspicious activity so we've blocked your-- ... uh, what? ... you sure about this?"

Ted Shifrin

For once, I have to concur with @leslie. Probably Munchkin put him up to it.

D.C. the III

She asked me to do it by offering me a key to infinite LeslieCoin

Ted Shifrin

Maybe she can get me the lesliecoin that leslie refuses to pay up.

mick

23:33

hi all

D.C. the III

Gallian does Groups first then Rings

mick

0

Q: Looking for $\zeta(s)$ such that $\zeta(s) = 0$ IFF $0 = \zeta(\frac{2}{3}-s)$

I am looking for a zeta function $$ \zeta(s) = \sum \frac{1}{a_n^s}$$ Where $a_n$ is a sequence of distinct positive integers, such that $\zeta(s)$ is analytic for all $Re(s) > 1$ $\zeta(s)$ has a simple pole at $s=1$. $\zeta(s)$ has an analytic continuation to the entire plane. $\zeta(s) = 0...

Ted Shifrin

Oh, I thought he was a ring first person.

There is sound pedagogy for rings first, but only about 25% of the books do it.

mick

i prefer rings over groups

shintuku

strongly recommend gallian because there is a full solution manual for the millions of exercises

mick

23:34

lack of group understanding that is

even more than lack of ring understanding

D.C. the III

Interesting because the Algebra course here is divided into Groups and Rings. I did do the Groups part, but no surprise I really didin't learn anything because I wasn't ready for it.

shintuku

abelian groups important for rings, had to go back and do abelian group theory a couple of times after starting rings

mick

why downvote ?

Ted Shifrin

I wish people would stop coming in here asking us to explain downvotes. We all get them, and we have no explanations.

D.C. the III

Even MSE can't escape being hypnotized by the Clout demon

Xander Henderson

23:47

@D.C.theIII "Clout demon"?

Ted Shifrin

That said, the post will probably be closed for lack of context and effort.

D.C. the III

@XanderHenderson The concern for whether you got downvoted or not and it hurting your "reputation". Online "status" being something of grave importance to an individual's identity.

Xander Henderson

@D.C.theIII Ah.

Gotta get them XPs.

D.C. the III

In the social media (instagram) world people doing anything for attention. Called by the young folks "clout chasing"

shintuku

i dont care about the reputation i care about the downvote

D.C. the III

23:51

why?

like i said maybe there is an importance to a high reputation beyond getting a mug (sorry Copper)

shintuku

because i put effort in my question and it is a problem that is consuming my time and this asshole just presses a button and fks my chance to have a decent answer

D.C. the III

and what of it? So you get the green checkmark for giving the best answer or not. You still answered it and did it for your own development

shintuku

i mean downvote for questions

Xander Henderson

@shintuku This seems like an awfully selfish approach to the site. As long as you get your answer, everything is hunky-dory, eh? And anything which reduces the chances of you getting your answer is automatically "assholes trying to fuck you"?

shintuku

yes

Xander Henderson

23:54

Yeah, you are incredibly selfish.

shintuku

ok buddah

2

Xander Henderson

Catering to the whims of single users is not the goal of Math SE. The goal is to create a repository of high quality questions with authoritative answers. There are pages and pages of discussion in the Help Center and on meta which describe what kinds of questions are a good fit for this site.

It is very common for downvotes to indicate that a particular question (or answer) does not meet the consensus standards, and should, therefore, not be a part of that high quality repository. It isn't that "assholes" are out to get you; it is that you didn't follow the rules.

Which, frankly, is rather selfish.

shintuku

i find that very uncommon, mostly they're assholes

D.C. the III

@shintuku Same premise. So somebody won't see it right away. It will eventually get some traction by people interested in it. Funny I'm in essence talking about being relaxed and free about it, yet I'm fuming about not being able to work the problem I was working on before....lol

Xander Henderson

@shintuku (1) I think that you don't know what you are talking about and (2) keep in mind that, while I am not moderating now, if/when the strike is resolved, I will be catching up on old flags, including chat flags---I would stop with the name calling.

D.C. the III

23:58

I disagree.....to come to MSE you have to have a vested interest. I doubt assholes are going to be strolling in here to vote on high level math questions just for kicks

The strike still going on Xander?

Xander Henderson

@D.C.theIII Yup.

shintuku

@XanderHenderson you don't know what you're talking about

Xander Henderson

449

Q: Moderation Strike update: Data dumps, choosing representatives, GPT data, and where we’re holding

Introduction Since our strike announcement, a number of new developments have occurred. Philippe, VP of Community, posted data they have regarding GPT content on the platform. Stack Exchange staff reached out to strike organizers and asked us to choose three moderator representatives for the str...

discussion moderation community company

D.C. the III

@XanderHenderson Good. Don't fold like the subreddits folded after a few days

Transcript for

$Mathematics$ Mathematics