Mathematics - 2016-11-07 (page 3 of 4)

Mees de Vries

15:00

@JessyCat, glad I could help.

Well, then I suppose I agree with VSauce or other channels. :-)

Shin Kim

A biologist, a physicist and a mathematician were all drinking coffee and tea and observing a house across the street from them.

They notice that two people walk into the house and then an hour later, three people walk out.

Physicist: An experimental error. Our first measurement was incorrect.

Biologist: No, they've obviously reproduced.

Mathematician: No, now when a one person enters the house, it'll be empty again.

from MO

Jessy Cat

And one more thing, every isomorphism is also an embedding, right?

@MeesdeVries wait a sec. If $\sigma$ and $\rho$ are even and odd, respectively, then $\sigma \rho$ is odd, so $\phi(\sigma\rho) = \sigma\rho\tau$, which I need to equal $\sigma \tau \rho$ in order to show that $\phi$ is a homomorphism, but $\rho$ and $\tau$ don't commute, do they?

Ooh, wait a minute, I saw what you did there, @MeesdeVries. Nevermind.

@MeesdeVries sorry to keep bugging you, but what about when they're both odd?

Mees de Vries

What about it?

Jessy Cat

How to show it's a homomorphism in that case.

Mees de Vries

Well. Which two things have to be equal for that to be true?

Jessy Cat

15:11

I have that $\sigma \rho$ is even, so $\phi(\sigma \rho) = \sigma \rho$.

But, since $\sigma, \, \rho$ both odd, we have that $\phi(\sigma) = \sigma \tau$, $\phi (\rho) = \rho \tau$

Wait a minute...the $\tau$'s are inverses of each other.

Silly Jessy. Trix are for kids.

Mees de Vries

Exactly. Always write down what you have to prove, and what you know. It so often turns out to be easier than you thought.

Jessy Cat

I have a tendency to be extremely impulsive in speaking and asking questions - tends to make people think I'm either stupid or know nothing...and always to their detriment later.. bwahahaha

Aksel'sRose

hello all, trying to prove that norm of v =norm of w iff v+w is orthogonal to v-w.

DHMO

It fascinates me that the natural numbers can be expressed as sets...

sasha

any help will be appreciated

0

Q: Inductive proof for Bauer's theorem

Pre requisite Hardy and Wright first prove the following theorem $$\prod_{t(p)} (x-t)=x^{p-1}-1 \pmod{p}\; ...(1),$$ where $p$ is a prime number. $t(p)$ represents the set of numbers less than $p$ and co-prime to $p$. $t$ represents a number from the set $t(p)$. Bauers Theorem The authors la...

thanks :)

Aksel'sRose

15:16

ive worked the norms to <v,v>-<w,w>=0 and im trying to get to <v+w, v-w>=0

Balarka Sen

@Aksel'sRose Back calculate. Start from <v+w, v-w> = 0.

Then you'd get a pretty good idea how to get the other direction.

Aksel'sRose

@BalarkaSen okay, i will try that. thanks

Balarka Sen

@DHMO Every natural number is trivially a set: {n}.

DHMO

@BalarkaSen no, I mean the number itself.

Jessy Cat

@MeesdeVries and for injectivity, since the identity permutaiton is even, we will get that only when $\sigma = id$, right?

Balarka Sen

15:18

By which, I mean there is a correspondence between N and the singletons of N.

Jessy Cat

No way to get there for an odd $\sigma$?

Balarka Sen

@DHMO A natural number is an element of a set. That is not itself a set, per se.

What do you have in mind?

DHMO

@BalarkaSen the set definition of natural numbers

Mees de Vries

In ZF(C), everything is a set.

In particular, $n = \{0,\ldots,n-1\}$.

(At least, typically, you could take different definitions.)

DHMO

and $0 = \varnothing$

Balarka Sen

15:20

@DHMO My definition of natural number is the plain one, from Peano axioms :P

But sure, there are many many definitions.

DHMO

@BalarkaSen the definitions are equivalent

Balarka Sen

Of course they are

DHMO

you can also incorporate sets with Peano axioms

by defining the successor function in terms of sets

Balarka Sen

I am aware

DHMO

I find the set-theory definition quite neat.

Balarka Sen

15:21

I was just objecting to saying "a natural number is a set". You can define them as a set.

But you can also define them in ten thousand different - but equivalent - ways.

DHMO

you do have a point

Balarka Sen

There's e.g., a definition of $\Bbb N$ in Church's lambda calculus.

DHMO

I am aware

exercise: prove that $\omega^2 = \omega + \omega^2$.

Hanno

hi all

Balarka Sen

Hi

DHMO

15:32

@Hanno Che hanno?

Hanno

hm?

DHMO

italian for "what do they have"

in your language it would be "Was haben sie"

Hanno

ah right, could have known that :)

DHMO

"hanno" means "they have"

Hanno

yep I remember

DHMO

15:34

nice

Tobias Kildetoft

@DHMO Sorry, was away for a while there. $\omega$ is the smallest ordinal strictly larger than any finite ordinal.

DHMO

@TobiasKildetoft yes, but it is not how it is defined...

Tobias Kildetoft

@DHMO how is it defined then?

DHMO

@TobiasKildetoft you know, $4 = \{0,1,2,3\}$

then $\omega = \cup \Bbb N$

Hanno

whats the problem?

DHMO

15:43

17 mins ago, by DHMO

exercise: prove that $\omega^2 = \omega + \omega^2$.

here is the exercise

Tobias Kildetoft

@DHMO Well, that definition is clearly the same given that inequalities between ordinals is given by containment

DHMO

@TobiasKildetoft you win

Hanno

DHMO: do you already know about distributivity of ordinal multiplication?

Tobias Kildetoft

@Hanno Hi. Long time no see

Hanno

@TobiasKildetoft yes indeed, hope you are doing well? are you still in upsala?

Tobias Kildetoft

15:48

@Hanno My employment there ended last week, so now I am unemployed for a while (I will go back to Aarhus as a postdoc August next year).

though I will probably meet with Walter occationally anyway

Hanno

ah ok... good that you already have a new position in sight

Tobias Kildetoft

Yeah, it is a shame that there is a break between, but better to have it already than not

I could also have had it start earlier, but this way is better for the timing on when my daughter will have to switch from pre-school to school (so we can move when she has to switch anyway)

Hanno

yes that makes sense

DHMO

@Hanno yes...

well of course you can use any way to prove it

it's just a simple exercise

Tobias Kildetoft

@Hanno Still doing research?

Hanno

15:53

@TobiasKildetoft not really, i think about math from time to time and enjoy it, but no research at the moment

Tobias Kildetoft

ok

Hanno

though i at times thinking about trying to return

computer science is fun but - at least in what i have been doing last year - lacking the depth and beauty of math

but its also less frustrating ;)

Martin Thoma

Do functions of the form f(x) = a / (x^s + c) + b have a name (such as "polynomial functions" or "exponential functions")? (with a, b, c, s > 0)

s.harp

Does somebody know basic commutative algebra?

I'm trying to see why $\mathrm{ht}(I/(xA))+1≥\mathrm{ht}(I)$ if $x\in I$ with $I$ an ideal in $A$.

($A$ noetherian)

Hanno

16:11

@s.harp you can reduce to the case where A is local and I is the maximal ideal

then its the statement that passing to the 'zero set' of an element does not drop dimension by more than one

s.harp

16:34

@Hanno if $I$ is prime I can pass to the localisation of $A$ at $A-I$, which is lokal and $I$ is the maximal ideal, is that what you meant? (And is it true?)

Hanno

yes and if I is not prime you instead consider the (minimal) primes containing it

Fargle

Good morning chat.

s.harp

Thanks, I think that I can see how to do it :)

Hanno

@s.harp alright :)

s.harp

@Hanno if I set an element of $A$ zero by passing to the quotient (say in lokal case), does $\mathrm{Spec}(A)$ do something simple/understandable?

The points that contain $x$ remain points still, and also the closed sets that only contain such points remain closed, but I don't see whats going to happen to the prime ideals that dont contain $x$

Hey-men-whatsup

17:03

guys may i ask something

I need interpretation help

s.harp

ask

saturatedexpo

is every subspace a dimension smaller then its supspace?

s.harp

if your vector space is finite dimensional, then yes

for a counterexampe with an infinte dimensional vectorspace consider the functions of finite support from $\mathbb N\to\mathbb C$ and the subspace where $f(0)=0$, both spaces have same dimension (there is an isomorphism between them) but one is a strict subspace of the other

Hey-men-whatsup

about limit (area under the curve), where does the writer get the equation (in the red box)? I've read it about 2 hours haven't got any clear understanding

Astyx

Hi

saturatedexpo

17:08

bon sois @Astyx

s.harp

@hey-men check here for example math.stackexchange.com/questions/122546/…

Hey-men-whatsup

@s.harp thank you let me read it

s.harp

the standard way to do it would be over $(k+1)^3-k^3= 3k^2+3k+1$, you can see that
$$\sum_{k=0}^n (k+1)^3-k^3 = (n+1)^3$$
and the sums of the right terms are $3\sum_k^n k^2+3\sum_k^n k + n$, where only the first term is unknown

Hey-men-whatsup

thank you

Astyx

Can you define a norm on a Vector space on a field that is neither $\Bbb R$ nor $\Bbb C$ ?

And can you define a vector space on a ring ?

s.harp

17:14

@Astyx that depends on what you mean with norm, ultrametric fields ($\mathbb Q_p$) have an absolute value and with that you can define norms on their vector spaces

saturatedexpo

@Astyx isnt $\mathbb{Z}_p$ satisfieing everything?

Tobias Kildetoft

@Astyx "Vector spaces" on general rings are called modules

@saturatedexpo satisfying all what?

Astyx

@TobiasKildetoft Oh yes of course thank you

saturatedexpo

@TobiasKildetoft satisifieing being a space.

Tobias Kildetoft

@saturatedexpo you mean a vector space? Sure

but not one with a norm

saturatedexpo

17:17

ah ok

Astyx

@s.harp I see thank you !

teadawg1337

17:31

I found this identity while flipping through my notebook, is there a simple way to prove it? $$\sum_{n=1}^\infty\sum_{k=1}^n\frac{(-1)^{n+k}}{nk}=\frac{\pi^2}{12}+\frac12\ln‌^2 2$$

saturatedexpo

if $\frac{a}{b}<\frac{c}{d}$, show that $\frac{a}{b}<\frac{a+c}{b+d}<\frac{c}{d}$. All variables are positive. is this strongly connected to: $a<\frac{a+b}{2}<b$?

Astyx

How do you make mathjax text appear correctly ?

Here on the chat

saturatedexpo

tinyurl.com/cfqcvpc @Astyx

Astyx

Thanks !

Fargle

Howdy @Balarka

Balarka Sen

17:36

hi

Astyx

Hi

Fargle

How goes it?

Balarka Sen

@s.harp Prime ideals in A/I are in 1-1 correspondence with prime ideals of A containing I.

@Fargle 'salright

arctic tern

@saturatedexpo intuitively, it means if you combine the numbers behind two averages, you get a new average in between the original two. here's one way to prove it. first prove with c=d. then prove with c<d using a/b<(a+c)/(b+c)<(a+c)/(b+d). then do c>d with a/b<(a+d)/(b+d)<(a+c)/(b+d). assuming everything's positive.

@teadawg1337 take the mercator series for ln(2), square it, look at symmetry along diagonal n=k

teadawg1337

@arctictern Ah, that works

Balarka Sen

17:41

@Fargle What's up with you?

Fargle

About to leave to get a job, actually. Waiting tables. Not glamorous but it'll be money in the pocket.

Balarka Sen

I wish you luck on your job!

Fargle

That said I'll be leaving for a bit but I'll leave the chat open so you can make my computer go "doonk" constantly.

Thank you!

Balarka Sen

I'll have to leave too though. Gotta get to work.

Astyx

Bye !

teadawg1337

17:45

@arctictern I just found my work a couple of pages afterward, and that's actually exactly what I did to derive it in the first place

saturatedexpo

18:04

i like the idea of partitions. The humans i like and the humans i not like are two disjunct sets that form all humanity. brilliant.

Astyx

What about the humans you do not care about ?

saturatedexpo

@Astyx well, humans i don't care about i don't like, or i like them. depending on the context.

but they'd fall into exactly one of those sets

teadawg1337

@Astyx The humans not cared about are a subset of the humans that are disliked

Astyx

How can you like something you do not know ?

How can you dislike something you do not know ? :)

saturatedexpo

if someone didn't disappoint me i like them.

or: if someone has made me happy i like them.

i mean $\neg$ like. not dislike ;)

(or hate)

Astyx

18:09

I think we should formalize the idea of "liking"

saturatedexpo

haha

maybe just say 3 disjunct sets

easier and fits all discussions ;)

like, not known, dislike

arctic tern

disjoint

saturatedexpo

oh, typical german

meh, i think i write all my math now in english

Astyx

The symbols don't vary that much from german to english do they ? :)

saturatedexpo

i think to 99% not

But translating for MSE and a german board is silly

(or MSE and my homework)

but it helped me so far to understand what is meant

because you can't translate if you don't know what it means. example: positive in french

Astyx

18:18

Mm ?

saturatedexpo

positive in french is $a\geq 0$, whereas normally $a>0$

Astyx

Oh yes

I'm always outraged by people claiming 0 is not positive :)

saturatedexpo

that's why writing mostly with symbols and equations is so much better because it's international.

Astyx

I don't agree

Writing with words makes the proof so much clearer and easy to read

saturatedexpo

yes, but only if the text is properly paragraphed IMO

Astyx

18:21

Of course

saturatedexpo

otherwise it's stupid, just my pov

basicly i always paragraph for a "then" or "therefore"

Astyx

What's more with words you can tell the reader exactly what you are trying to prove which makes the proof require far less concentration that without it, and this is not something you can do with symbols

saturatedexpo

yes words can be a great additional guide

but having a precise symbolic definition helps precision?

Tobias Kildetoft

In my experience, people just learning math use way too few symbols at first, then graduately start using way too many and finally scale down to an appropriate balance

Astyx

In mine too :)

saturatedexpo

18:28

To the symbols: i read that "while" is a byproduct of laziness. Do you agree?

Tobias Kildetoft

@saturatedexpo Not sure what you mean

saturatedexpo

$a\cdot b>0$ while $a,b\in \mathbb{N}_1$ for example

i dont think i nailed it tho, wait i look the thread up ;)

arctic tern

so "[condition holds] while [hypothesis is true]"?

sounds efficient to me

saturatedexpo

oh, i confused it with "where"

3

Q: Math Symbol for "Where"

Pretty much any math text I've read introduces notation through a similar format of equation-notation or notation-equation form e.g ax+b+c where a = ..., b = ..., etc. or Let a = ..., b = ..., etc. ax+b+c I tend to see the former more and was wondering if there has been an offici...

notation

Astyx

As long as one understands your writing ...

saturatedexpo

18:34

not even me understands what i write. that doesn't say someone else doesn't, just that sometimes i don't haha

Tobias Kildetoft

@saturatedexpo I think "where" is fine for some purposes.

"while" seems rare, at least in my own papers so far (except in ordinary English sentences)

saturatedexpo

@TobiasKildetoft do you think tho, that i should, if possible, avoid "where"? as a beginner

Tobias Kildetoft

@saturatedexpo Not necessarily

saturatedexpo

i mean to me it's analogous to programming.

Tobias Kildetoft

Sometimes it is more natural to have the main object first, then mention what everything was afterwards. Sometimes, this makes for a more natural read than introducing everything beforehand

saturatedexpo

18:36

where you first have to define all variables and THEN make a statement

like a=b+c, while b and c are reals. this would not compile nicely

Tobias Kildetoft

it also does not make much sense mathematically

saturatedexpo

$\{\forall a\in A:a=b+c\}$ where $b,c\in \mathbb{R}$

Astyx

That is kind of the point : no one wants to read a algorithm, we're humans not computers ... It requires a huge amount of attention to read and understand a large enough algorithm

Tobias Kildetoft

now we are getting into the "where" being ambiguous

saturatedexpo

But wouldn't it be more proper: Let $b,c\in\mathbb{R}$ ....?

Tobias Kildetoft

18:43

basically, "where" mainly belongs in definitions

saturatedexpo

ah ok

just learning how to speak "userfriendly" math ;)

Tobias Kildetoft

Best way to learn is to read stuff written by people write well

And these are easy to recognize, since they are the ones that are the easiest to understand

Astyx

I couldn't agree more

saturatedexpo

that way I did not thought of!

altho it kinda is obvious^^

Akiva Weinberger

XKCD has endorsed Clinton

Astyx

18:48

Mmm ?

saturatedexpo

@TobiasKildetoft if you think that further, there lies alot of truth in "a great [artist] copies"?

just exchange artist with what you want

Tobias Kildetoft

Certainly

teadawg1337

math.stackexchange.com/questions/2003926/…

I think this is a half-decent question. It's a shame it's posed so poorly

john smith

Hi , I want a permutation that first increases, reaches a maximal , then decreases, for example [1,3,4,6,5,2] but not [1,3,2,4,6,5] . Can anyone explain in how many ways I can do it ?

Tobias Kildetoft

19:04

@johnsmith So that corresponds to choosing a subset of the numbers being permuted

well, of the numbers being permuted except the largest one

john smith

@TobiasKildetoft I want to calculate " Given N, count how many permutations of [1, 2, 3, ..., N] satisfy the above property "

saturatedexpo

@teadawg1337 you mean with posed "presented"?

teadawg1337

@saturatedexpo Yes

Tobias Kildetoft

@johnsmith Right, so that means there are $2^{N-1}$ such.

john smith

@TobiasKildetoft Can you explain how?

Tobias Kildetoft

19:07

@johnsmith choose the elements in the increasing part

saturatedexpo

@teadawg1337 is the question: "is there a function that intersects with a halfcircle at more then 2 points"?

john smith

@TobiasKildetoft Sorry but I am not getting the point

Tobias Kildetoft

@johnsmith the increasing part is uniquely determined by which elements are in it. And once this is determined, the decreasing part will consist of the remaining elements.

teadawg1337

@saturatedexpo Yes, specifically of the form $x^n+y^n=1$. And with that specific haf-circle

john smith

@TobiasKildetoft How does this lead to 2^(n-1)

Tobias Kildetoft

19:12

@johnsmith because that is the number of subsets of a set with $n-1$ elements

saturatedexpo

@teadawg1337 won't fit a sinus curve with slight adjustments? (leftright slided and updown slided)

teadawg1337

I don't know, I haven't tried manipulating the constraints of the problem. As it stands, brute force calculation shows that $n<\frac{200}{113}$ within the original problem description

Astyx

@johnsmith funnily enough someone had exactly the same question yesterday ...

john smith

@Astyx He might also be solving the same problem

Astyx

@johnsmith See chat.stackexchange.com/transcript/36/2016/11/6/16-21

Sarvin was his name

john smith

19:21

@Astyx Yes I am also solving the same problem

Astyx

And did you understand the solution ?

s.harp

@teadawg1337 shouldn't the interior of $x^n+y^n=1$ in the first quadrant always be convex? maybe from stuff like that it can be seen to be impossible?

teadawg1337

it holds computationally

It appears to be possible

s.harp

what do you mean it holds? As in ther exist $n\in\mathbb Q$ so that $x^n+y^n=1$ intersects the circle line more than twice?

john smith

@Astyx I don't know why But I am not able to understand the solution

Astyx

19:23

You want a permutation that first increases then decreases

teadawg1337

@s.harp Yes, at least according to WolframAlpha (and, by extension, Mathematica)

I'm just as confused by it myself

john smith

@Astyx Yes

s.harp

funky

teadawg1337

$n$ may very well be irrational

Astyx

@johnsmith Such a permutation is uniquely defined by the elements that are in the increasing part
For instance [1,3,4,6,7,5,2] is uniquely defined by $\{1,3,4,6\}$ in the sense that if you are told the numbers in the increasing sequence are 1,3,4 and 6, the only permutation allowed is [1,3,4,6,7,5,2]

Does this help ?

teadawg1337

19:28

@s.harp The curves still maintain convexity, their slope just varies such that it intersects a unit circle. By the intermediate value theorem, there have to be at least two values of $n$ such that $x^n+y^n=1$ intersects a unit circle centered at $(1,1)$ exactly three times. The OP gave the value of $65/116$, which intersects said circle four times.

s.harp

The map $(0,1)\times\mathbb R_{>0}\to\mathbb R^2$, $(t,h)\mapsto (t^{1/h},(1-t)^{1/h}) =(\exp(ln(t)/h),\exp(ln(1-t)/h) )$is continuous, and $(1/2,h)\mapsto (1/2^{1/h},1/2^{1/h})$

john smith

@Astyx I think I understand : I compute all the subsets except the largest number in it

s.harp

This point always lies on the diagonal and for $h\to\infty$ it goes to $(1,1)$, for $h\to0$ it goes to $(0,0)$

so it has to intsersect the circle line

Astyx

@johnsmith Exactly

john smith

@Astyx That was easy , don't know why I could not think of this

s.harp

19:31

the intersection of the circle with the diagonal line is at the point $(1-\sqrt{2},1-\sqrt{2})$, so if you find an $h$ so that $1/2^{1/h}=1-\sqrt{2}$ you have an $h$ with $3$ intersection points

john smith

@Astyx @TobiasKildetoft Thanks for your help and patience

s.harp

$h=-\ln(2)/\ln(1-\sqrt{2})$ would be a solution, lets see if im an idiot or it actually works

teadawg1337

Wait, but $\ln(1-\sqrt{2})$ is complex

s.harp

oooooh i need $1/\sqrt{2}$ not $\sqrt{2}$, that was a mistake

teadawg1337

That does work

Balarka Sen

19:37

@teadawg1337 Even $x^3 + y^3 =1$ intersects a lot of circles centered at $0$ exactly 4 times.

teadawg1337

The OP is asking for $x^{1/n}+y^{1/n}=1$, so the exponents are less than one

s.harp

those are two curves, they do look like they intersect

teadawg1337

Mhm

s.harp

@Balarka its not a circle centered at $0$, but one centered at $(1,1)$ and its supposed to intresect the $x^h+y^h=1$ line

Balarka Sen

I didn't read the original question.

teadawg1337

19:41

@BalarkaSen math.stackexchange.com/questions/2003926/…

It's phrased somewhat poorly

s.harp

$h\approx 0.564476$ is the expression from above

teadawg1337

But $h=1/2$ intersects only twice, and $h=.53$ intersects four times according to WolframAlpha

So there's another $h$ value

I'm too tired to do the actual working out, though.

s.harp

the intersection cannot be on the diagonal then though

teadawg1337

I don't think that's a constraint within the original problem, though

Your $h$ value does indeed work, though

s.harp

yeah, I was just remarking that the ansatz from above can only find the intersections on the diagonal, so gotta try something new

Balarka Sen

19:51

nice question

you can probably set up bounds for $h$ where you might get more than than 2 intersections, because for $h \to 1$ it becomes like a line and $h \to 0$ it becomes a closer and closer approximation for $xy = 0$.

I don't know how to deal with such questions for curves cut out by nonpolynomial equations. The best tool to count intersections for polynomial cases is Bezout's theorem.

alright, gotta go

Semiclassical

hi chat

teadawg1337

Hey @Semiclassical

Astyx

Hi

What example of the use of topology to solve problems not directly linked to topology would you give to someone to show how useful it is ?

Semiclassical

20:07

point set or algebraic?

Astyx

Both

Tobias Kildetoft

@Astyx In arxiv.org/abs/1601.06975 we ended up using topological considerations a couple of places, even though the topic is very far from topology

Astyx

Thanks I'll give it a read ! However I was looking for more "direct" applications

Tobias Kildetoft

What do you mean by "direct"?

Astyx

That does not require a large mathematical background to understand

Something a beginner would understand easily enough

Alessandro

20:15

@Astyx If you're aiming at a general audience you might be interested in this video youtube.com/watch?v=AmgkSdhK4K8

Tobias Kildetoft

That seems tough, since just the amount of topology needed will generally be more than a complete beginner knows

Astyx

Thanks a lot

saturatedexpo

is topology all about bending figures with some special ruleset?

Tobias Kildetoft

@saturatedexpo No

Astyx

Thankfully

Alessandro

20:24

No, those are the pretty pictures that are shown in pop science books and videos

saturatedexpo

good, that i know now!

so would a topologian question be: "what is the average distant between 2 points in a square?"

or is this too banal?

s.harp

distance is usually understood as an analytic notion and not as a topological one

Semiclassical

if you have to invoke distance, you're probably not doing topology

that's too strong a statement, I'm sure, but 'the average distance between two points in a square' is certainly not topological

saturatedexpo

but: "when does the average distance of points in a wierd loop equal the average distance of points on a circle?"

Semiclassical

I'd still chalk that up to analysis not topology

saturatedexpo

20:38

ok!^^

s.harp

the best resource to learn about topology is the movie "El topo"

Semiclassical

Topology tends to be less "what computations can you do" and more "what mappings can you make", I guess?

saturatedexpo

so topology is not (all) about loops

Semiclassical

@s.harp what

oh. topo-logy

Tobias Kildetoft

@Semiclassical To be honest, I have very little idea what sort of questions topologists are interested in these days

s.harp

20:39

( youtube.com/watch?time_continue=35&v=3joYVNyyi5w )

Semiclassical

Nor I

s.harp

isn't this chatroom normally full of algebraic topologists?

Tobias Kildetoft

@s.harp Yeah, and I have no idea what they talk about most of the time :)

Semiclassical

heh

I'm not sure where Gauge Theory would fall in all of that

Alessandro

Jodorowski? Western sure doesn't look like his style! I think I'll check that out

Semiclassical

20:42

I tend to see a lot of differential geometry in chat

Alessandro

that's @Balarka's fault

Semiclassical

El Topo is quite bizarre from what I've heard of it

s.harp

ill watch it tonight

saturatedexpo

how would you make a loop that doesn't contain a square formed by 4 distinct points ón the loop? that video is a cool teaser

s.harp

I saw "A field in england" yesterday, I loved it :=)

Astyx

20:45

What is it about ?

Alessandro

we don't know whether it's possible to make one @saturatedexpo

saturatedexpo

is this on the Gödel list? or "we wait for the next Fermat"-thingy?

Alessandro

actually the unsolved cases are pretty pathological curves, for all the well behaved loops it is known that you can find a square with its vertices on the loop

s.harp

@saturatedexpo connect the ends of hte limit of this curve: en.wikipedia.org/wiki/Hilbert_curve

Semiclassical

the more pathological the case, the less interesting I find it.

s.harp

20:48

indeed, the morgue is the worst place to do mathematics

Astyx

Haha

saturatedexpo

but for any morgue there winks some cool prize?

(if it's more then 100 years old, i guess)

Semiclassical

Is there a name for this conjecture?

Ah, the inscribed square problem (wikipedia has a page)

Alessandro

yes it's that one

s.harp

oooh I misunderstood it, I thought it was asking whether or not you had a curve that does not contain a square on the interior :)

anyway im going to go home now, have fun people

Astyx

20:51

Bye

saturatedexpo

do science papers get submitted that don't solve a particular problem but introtduce to it?

Tobias Kildetoft

@saturatedexpo Certainly plenty of papers introduce the very problem they also solve

Semiclassical

Usually they at least offer some sort of progress, though

otherwise it's hard to explain why anyone should care about it

saturatedexpo

@Semiclassical so that is not unheard of, maybe i read some of those.

i mean it's more fun that way. To know that you are not the only dumb person haha

Transcript for

$Mathematics$ Mathematics