Mathematics - 2018-04-04 (page 1 of 5)

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12:58 AM

[Random]

Set zoo

$\varnothing$

$U$ (DNE)

$\mathscr{P}(A)$

$\{x : \phi (x)\}$

Totally unordered

Partially ordered

Linearly ordered

Cyclically ordered

Directed

Well ordered

Compact

Bounded

...

Finite

Infinite Dedekind finite

Amorphous

1:11 AM

Hey guys, I have a question about an attempted edit on this question https://math.stackexchange.com/questions/1629629/clarifications-regarding-lagrange-resolvent

I tried to edit the tags on the question to be more relevant to the subject matter, but the tags were rejected. Specifically I tried to remove the "linear-algebra" tag because I don't think it has anything to do with the question, and add tags for galois theory and abstract algebra.

I would like to get some clarification as to why these edits were rejected. Could anyone tell me?

1:36 AM

Perhaps the above would be an appropriate question to post on Math meta?

Xander Henderson

@WilliamOliver It looks like amWhy chose the "Reject and Edit" option from the review queue; looking at the edits that amWhy made, I suspect that they thought that your additional tags were not that relevant, and that you failed to fix some of the grammatical problems.

@XanderHenderson I suppose I am confused as to why the additional tags wouldn't be relevant

(Thank you for replying btw)

Xander Henderson

@WilliamOliver shrugs

That is a part of math that I don't know well, so I can't comment on whether or not I agree with the rejection of the additional tags. Perhaps @amWhy didn't see the additional tags?

Hm, okay. Do you think it would be bad practice to attempt the edit again but with a subset of the tags? I think the tags are one of the main reasons this question never got an answer

Xander Henderson

1:54 AM

I'm not sure that I am the right person to answer that question. I don't see any harm in attempting the edit again.

You might also bring up the question on Meta

@XanderHenderson Alright thanks!

Xander Henderson

This link might be helpful, too.

It looks like you got one approval, and a "Reject and Edit", so you probably have a good case; I just don't know that topic well enough to do anything other than prevaricate.

Okay, I will bring it up on meta first

if an element in a monoid has a left inverse, must it have a right inverse?

@LeakyNun I think this might help

https://math.stackexchange.com/questions/655186/in-a-non-commutative-monoid-is-the-left-inverse-of-an-element-also-the-right-in

2:02 AM

Can I ask a question here? Or is that not what this is for?

@EvanWeissburg You can ask questions here. See the description in the top right.

Oops, easily missed I guess.

@WilliamOliver thanks

@LeakyNun np

I'm curious about conic sections of the form Ax^2 + Bxy + Cy^2 ... = D

The Bxy is the rotation term, and my textbook mentions that we can calculate angle of rotation as tan(2alpha) = B/(A-C).

It also states that alpha is between 0 and pi/2, which seems wrong since the alpha should be between -pi/4 and pi/4, right?

2:15 AM

@Semiclassical hey

I have faith in you

@Semiclassical I don't

@Semiclassical me neither

Does no one have any intuition about the answer

2:31 AM

goo.gl/images/F58DRU

[Random]

Thinking about routes on isolating some chemical product as a function of its various methods. Imagine each isolation method form the axes, and then the probability of isolating a product is some sequence formed by these axe. Then what you have is a hyper surface which detailed how much yield of the product you will get given some inputs

Often, the surface has some kind of ridges in certain directions, such that if one isolation method fails, some others will work wonders

But later's imagine some homogenous surface where the isolation probability is lower everywhere. Then clearly this means the product is close to not isolatable

However, in real life, these surfaces are more complicated in shape. Perhaps an interesting question that may or may not have been addressed by machine learning, is to find the optimal route to the isolation of the product

Akiva Weinberger

@EvanWeissburg I'd guess that you can choose any interval of length pi/2 from which to choose alpha

given that tan(2alpha) is periodic with period pi/2

pubs.acs.org/doi/full/10.1021/acscentsci.7b00492

ok nvm they have done it

2:57 AM

@AkivaWeinberger how do you know which direction the conic section is rotated them? you only know the alpha for a single quadrant, not which quadrant you are in?

Akiva Weinberger

I don't actually know what alpha refers to in this context

Unrelated: xkcd.com/743

Facebook was just always evil I guess

Xander Henderson

it annoys me that xkcd gives a number to each comic, but no easily discernible date

So, I was googling some news, and found something about there's a female shooter in youtube HQ

Xander Henderson

Yes.

That is a thing that happened today.

besides that, there seemed to be a host of crazy things going on in the world since yesterday

Strangely however, nothing depressing happened during the easter long weekend that is 28/3/2018-2/4/2018

3:03 AM

I wish she came to my house. I wouldn’t need to finish this work

it's as if chaos itself is having a easter holiday

alpha is the angle of rotation of the conic

and then everything explodes as soon the holiday is over

Would that mean we all need more holidays? :P

Akiva Weinberger

@XanderHenderson May 21, 2010

Xander Henderson

Where can that be found?

@AkivaWeinberger

Oi... "In the mouseover text of the archive page" Jeebus... what a terrible system :\

3:14 AM

Or you can just stop wasting your time on that website

Xander Henderson

Very helpful, Zee. Thank you for sharing your thoughts.

4

I just want the best for you

3:47 AM

[Random]

Sometimes I think Zee is a bot constructed from the combined consciousness of Albert Einstein, Lubos Motl, and Alex Grothendieck

meanwhile, I still don't know whether he is that Zee who wrote that QFT book

he's too smart to have written that book

and don't even talk about the QFT book

the GR book is far better

btw, what am I in terms of consciousness combination of historical people?

Jack the Ripper, Alex Jones, and Abe Lincoln

3:52 AM

I fear to ask what I'd be.

You're pretty careful to reveal very little about your personality

hah

Alexander Emric Jones (born February 11, 1974) is an American radio show host and conspiracy theorist. He hosts The Alex Jones Show from Austin, Texas, which airs on the Genesis Communications Network and shortwave radio station WWCR across the United States and online. His website, Infowars.com, is a conspiracy theories and fake news website. Jones has been the center of many controversies, including his promotion of Sandy Hook Elementary School shooting conspiracy theories, and his aggressive opposition to gun control in a debate with Piers Morgan. He has accused the U.S. government of being...

lol

> fake news website

reeeeeee

on the one hand, I think that's editorializing

on the other hand, I think it's also correct

3:55 AM

Abe Lincoln puzzles me the most though, probably because other than he is involved in freeing the black slaves I knew nothing about him

whenever GMT and [] occur in the same line, the chance that it's federer is 78%

Am fighting the forces of evil but in my weak moments, I fantasize about selling my soul to algebra

abrahamlincolnsclassroom.org/abraham-lincoln-in-depth/…

Hmm.. in what way I resemble Lincoln...

you should be more concerned that your primary personality is Jack the Ripper

That's because the dark side is much stronger in cyberspace, lol

4:00 AM

Plot twist: Lincoln IS Jack the Ripper

I suppose it’s what I would call mathematical nihilism, am a visual person but sometimes I just wanna go “ it all means nothing , it’s just marks on a paper , so you may as well become a marks on a paper expert “

anybody understand model theory?

Abraham Lincoln (February 12, 1809 – April 15, 1865)
Jack the Ripper 1888–1891(?)
Time travel = confirmed :P:P:P:P

you guys are discussing flat earth?

did you know dihydrogen-monoxide is one of the most lethal substances on earth, yet it's sold absolutely everywhere

the government is putting that stuff in our food

it's what made up our bodies :P

so model theory connoisseurs anybody?

4:05 AM

and responsible for the evil behaviour of homosapiens as the stuff constantly corrode us from the inside out :P

the government is pretty evil

that's what i've been saying all along

nobody will listen to me

finally some good fellas you can talk some sense to

@JoeShmo model theory people are not on atm. But you may try leave the question at logic chatroom

these guys aren't responsive

♦ $Mathematics$ Logic

This room is meant for discussion about logic, including found...

4:07 AM

and i suspect half of them don't actually know what they're talking about

unfortunately

i belong to that half

Your best chance is the computer science room

Or even philosophy

these guys are finite model theory people..

they dont know the good stuff

you won’t find the goodies here I think

philosophy.... potentially. haven't tried.

Idk if their is even a philo room

4:08 AM

The Symposium

A Party Space for Philosophy.SE! Both philosophy and mundane c...

A residential MO mathematician resides there

im trying to produce essence from MT

Mozibur Ullah

Secret has his hands everywhere

I am a delocalised wave function you know

Frankly the only model theory I know is how to get rejected by one

4:10 AM

if there is a joke hiding in there it went right over my head

I think Akiva also knew a bit of model theory

@Secret well, at least we'll know how fast you're moving

i think he did. im looking for somebody to pick his brains

@Semiclassical true true, even in an outside the joke perspective, because my walking pace is quite constant

heh

4:12 AM

I can find many ways to relate my life to quantum phenomena, showing that I love quantum among the physics

For example, some of my friends behave like entanglement: Long distance and long time, yet very fragile

and as soon as you shine light on them they disappear?

What I relate to is a more technical notion, namely linear response theory

well, except that the light is not really photons, but yeah, they do ghost like crazy

I have 45 ghosting so far

Idk how they gave me a college degree without taking a single science course

which in essence says that, if you think in terms of various frequencies of the external field, then the response at each frequency is proportional.

Though what I really have in mind is not that, but nonlinear response

which is to say, when that linear response assumption fails

4:17 AM

what nonlinear response you identify yourself to?

not a particular one. just more that notion of not being able to respond to external stressors in a linear way

materials obey linear stress-strain relations. you apply a certain amount of stress, you get a proportionate amount of strain

for some kinds of stress, that's a fine description. give me some math to crunch out on the board, and it'll scale in a sensible way

Let me ask you guys a physics question

this better be a good question

If I had a strip of metal and I twist it , what do you call the energy stored in it ?

but give me a writing assignment, and...nooope

it's pretty much immediately stressful. nothing linear about it

4:20 AM

@EricSilva yo, do you know how to do the $[[S]]$ thing for currents

@Zee elastic energy?

@Zee if it's a small strain, then the metal will respond elastically and I'd say it's elastic potential energy

well , this is completely cracknpot thinking

but if you twist it so much that it deforms, then there's not going to be a tendency of that metal to return to its original shape and so there's really no energy stored that way

But I was thinking if there was a relation between orientation of a manifold and whatever this energy is

4:22 AM

I think you can write down versions of elastic energy for manifolds.

though that relies on some notion of 'deformation'

@Semiclassical For me, small stress like a one page assignment will die off very quickly, followed by speedy completion of the assignment. For larger stress like an essay, I will procrastinate and the stress will build up to some point and eventually I stop responding to it. For something big like an entire PhD, though, the response is something like a bunch of step functions convolved with some smooth curve, (i.e. it rises over time)

@EricSilva in latex

I have a similar problem actually , skipped the last 2 days of school and I doubt am gonna be able to turn this shit tomorrow

I guess what I have in mind is that, with 'linear response' to stress, you can reduce the stress by narrowing what you have to work on

It makes no sense , you KNOW you should do work , yet you don’t , Gromov said cockroaches are more logical than human beings , I agree

Cockroaches don’t procrastinate

They just work

4:27 AM

everything becomes boring when the label "work" is assigned to them

Akiva Weinberger

I know like the minimal amount of model theory

With nonlinear response, though, you don't necessarily have that being the case. Even just a small exposure to it can stimulate a huge response

Akiva Weinberger

but if you were to ask me an actual question you'd probably quickly discover that I know nothing

Ok Socrates

I suppose another bit which could be added to this is the assumption of an equilibrium system

4:28 AM

My set on maths knowledge is dense except in logic

(well, mostly...)

dense in what topology?

you apply an external field to that system, and it'll change to a different equilibrium. but it can't change drastically

@JoeShmo I don't know what topology we can give to the set of all mathematics

Probably the coarsest topology

Akiva Weinberger

@Zee There are some topics about which I know enough to know that I know nothing. Like agriculture.

Apparently it's hard.

I thought, you know, seeds -> food, but apparently it's more complicated

4:29 AM

$\llbracket N \rrb$

some coarse nontrivial topology I think

@AkivaWeinberger that’s not true , you know a lot about it

but writing stress can seriously discombobulate me

It is hard to have much self-esteem in those moments when you know you should be doing something and you just can't bring yourself to even look at it

@AkivaWeinberger sheafs , germs , stacks , fields , these were all mathematical concepts before they were applied to agriculture

riiiight

4:31 AM

@Semiclassical My uncle is a farmer, I can confirm.

oic

Finite strain theory

In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which both rotations and strains are arbitrarily large, i.e. invalidates the assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different and a clear distinction has to be made between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue. == Displacement == The displacement of a body has tw...

not sure how to apply that to manifolds

But sounds appropriate

Ya

does riemannian curvature tensor (plus some torsion) account for all possible manifold deformations?

4:33 AM

Depends how you define deformation am guessing

That sounds too vague in formulation to be true.

it sounds like a physics theorem

whats the difference between physics and diff geo?

Although diff geo people like to think tensors can describe any geometrically meaningful change

(ew, ew)

4:34 AM

@0celo7 Have trouble finding a mathematical one, as "Deformation Theory" is really about perturbing solutions in PDEs etc., not twisting stuff

deformation theory is really complex analysis

That has to do with solutions to polynomials from what I know

well, if a manifold with tensors at every point is sufficient and necessary to capture arbitrary deformations, then the energy is probably a functional of the tensor field

cannot guarantee it is a linear functional though, though in physics linear functionals are common

I think am gonna go cry and rock back and forth

Note to self: When finally learn enough about manifolds to be confident about it, check how the action functional changes as a function of some paths on a manifold

4:39 AM

Whatever you do , don’t read lee books

TheLittleNaruto

Can someone help me with a noob question ?

Lee smooth manifolds is by far the worst text I ever had to read through

TheLittleNaruto

Zee ~ Lee

>: /

@TheLittleNaruto Depends on what quesrtion

TheLittleNaruto

4:41 AM

It's about Linear Algebra

ok

That’s secret s type of shit

TheLittleNaruto

I see.

He’s a linear algebra guru

TheLittleNaruto

Woah!

4:42 AM

"Just ask, don't ask to ask."

World renowned and known , he’s the real deal in it

TheLittleNaruto

I want to understand in simple way

The tutorial I found online are too much to digest @Secret

@Semiclassical I did that last night, But nobody responded. :/

Just ask the question already

Secret?

@TheLittleNaruto what is the question?

That is the question...

TheLittleNaruto

4:44 AM

@Secret I want to understand this equation y=mx+c

Well y is a letter

TheLittleNaruto

@Zee xP

c as well , it comes after b I believe

what about it, you want to know what each term means, or something else?

TheLittleNaruto

Yes

4:45 AM

...

TheLittleNaruto

something like that

= is two minuses , so that changes into +

TheLittleNaruto

@Zee That is high level concept, I would rather avoid it ;)

@TheLittleNaruto desmos.com/calculator/zcc9qswolg play around with this, and you will come to realise c is the y intercept and m is the slope (how steep the line is)

and y is just the value of the function, the y coordinate on the graph

TheLittleNaruto

@Secret Thank You :)

4:48 AM

Is this defined on a topos ?

TheLittleNaruto

@Secret value as in output of the function ?

yes

TheLittleNaruto

Ok

which on a graph it is the y value

TheLittleNaruto

I see.

4:49 AM

What is the technical definition of a matrix ?

I never met anybody who knew it

A linear function that maps vectors to vectors

which is why it is a linear map

a matrix is distinct from an array (more commonly encountered in computer science and programming) in that the latter usually don't have operations defined on them nor have geometric properties

@Zee an element of $\Bbb R^{n\times m}$ written in a funny way

@0celo7 yup that’s what I always get told but I find this definition to be funny frankly

TheLittleNaruto

@Secret Can't a matrix considered as XY-Plane ?

@TheLittleNaruto no it cannot, as there are directional dependence for each axes

it's effect however can be plotted as a vector field for n x n matrices

TheLittleNaruto

4:52 AM

Ohk

@Secret I mean a matrix is associated with a linear transformation but they aren’t the same thing

is "Ohk" an indian thing

Probably oh ok

@Zee it's more like, what happens when you express a linear map under some basis, since the components of a matrix varies with the basis

so matrix is like a linear map given the coordinates

Well that certainly is true

But I still don’t see a technical definition of what a matrix

4:54 AM

I think they call that a representation of the linear map? (but then I knew little about representation theory)

Think of an $n\times m$ matrix as a map $\{1,\ldots,n\} \times \{1,\ldots,m\} \to \mathbb{R}$

Which is the same data as $\mathbb{R}^{n\times m}$, as Ocelot mentioned above

I gave a definition that can be made technical if anyone gave a shit

I am not sure what you are after as $M : \Bbb{F}^n \to \Bbb{F}^m$ where M linear pretty much defines what a matrix is

Frankly am trying to decipher the filler sign stuff

@Secret so here's the thing, a matrix is a different type of object from a linear map

4:59 AM

Frankly am trying to decipher the doller sign stuff

the great and powerful zee can't read latex?

how do you get a college degree without knowing latex

No, I am anti tech

Also , I never took a science course so there that too

seriously, are you a real human. or are we talking to some AI

@Daminark how is mine differ from yours (PS. $\Bbb{F}=\Bbb{C} \text{ or } \Bbb{R}$)?

@Secret to get a matrix you need a basis.

5:00 AM

I said that already many posts above

7 mins ago, by Secret

@Zee it's more like, what happens when you express a linear map under some basis, since the components of a matrix varies with the basis

@Daminark can you write that again without Latex ?

exactly

so what is the issue

@Daminark Do not give in.

Zee then replies:

6 mins ago, by Zee

But I still don’t see a technical definition of what a matrix

so I am not sure what he is looking for

the technical definition can be written down very easily using what I said

@Daminark gave a sketch

it's not even worth talking about

You need a basis for a matrix but that still does not tell me what. Matrix is

5:02 AM

A matrix is a block of numbers you get after expressing a linear map under a basis

You may think it’s silly but I honestly believe such a definition does not exist

@Secret that’s pretty much the canonical answer

Well. At the very least, one part of that last statement was true.

Except it’s no good

@Secret the point is this, technically the objects are formally defined differently. I'm saying this on a set-theoretic level. Now, it's a fact that when you define matrix multiplication properly, then for any linear map $T:\mathbb{F}^n\to\mathbb{F}^m$, there is a matrix $A$ such that $T(v) = Av$

This fact is borderline trivial, but very technically it's not purely a matter of definitions

A matrix is a “table of numbers “ that represents a linear transformation

But wtf is a table of numbers?

Well it looks like this hdkbxjdndb

5:05 AM

@Zee Ocelot and I literally gave formal definitions above

Ok , so you have no rigorous definition just know this by intuition

100% formal

@Zee uh... a well ordered set under lexicographical ordering?

Mar 24 at 18:27, by Eric Silva

TIL if something doesn't make sense to you it's not your fault, it's the theory's fault for not making sense

Again, this guy is an AI sent to troll us

5:06 AM

Omg , why are you guys being like that

Because you're being stupid

@Daminark hmm, if I understood correctly, the definition of matrix multiplication ensures a one to one correspondence between linear maps and matrices, thus by the abuse of notion, they get conflated into each other in linear algebra courses and contexts?

Shhh...time out guys :-)

I think it’s. Very reasonable point

If your inability to read TeX or listen to reason is getting in the way of your understanding what we're saying and you know this to be the case, you don't start going off like "Oh yeah this mathematical theory cannot be formally defined! :O"

5:08 AM

He's learning something new.

Go online and look at some LaTeX documentation, read what I said. It's a formal definition of a matrix.

It’s ok @skullpatrol I been going through this countless time

And this ain’t new, matrices is low level stuff

@skullpatrol Don't give undeserved credit, when someone's making an honest attempt to learn you can tell

Am discussing it from a subtle high level Grothendieck point of view

Learning is usually predicated on the willingness of the reader to change their mind.

3

5:09 AM

Sorry your minds cannot see that

a lexicographical ordering of 2-tuples is how a table is formally defined

Alright Zee, tell me now. Why is a map $\{1,\ldots,n\} \times \{1,\ldots,m\} \to \mathbb{F}$ not formal?

Until somebody gives me a formal definition of Matrix , I ain’ buying

And I refuse to read your Latex nonsense

Why are you being so difficult?

People are like wolfs, I was discussing this softly, but once they smelled that , they pounced

5:13 AM

If you want a definition, look it up in a dictionary :-)

Little they know , they have no idea what a matrix is

Akiva Weinberger

One day I'm gonna meet you sober

If LaTeX existed during Grothendieck's time, believe me he'd have no gripes with reading it or using the link at the side so that the screen renders

If you were truly anti-tech you wouldn't even be on a computer right now

Am not perfect

Nobody is pal.

5:15 AM

If I used Latex then next thing your gonna ask me to use ode solvers , and then ode solvers and then algebra solvers , and then I’ll just be some IT guy

Just show some willingness to learn.

This guy is an AI. I’m going to bed. Night y’all.

@Daminark Eh. Maybe he would, maybe he wouldn't. But what Grothendieck would have done is neither here nor there, since none of us are Grothendieck.

Well, you can always improve. Take the first step to living up to being anti-tech and turn off your device

@Daminark your right , thank you

5:17 AM

:)

5:29 AM

Also @Secret from some time back, representation theory is different from the matrix representation of a linear map

Just in case it improved chances of this getting noticed I will point out that there is a user who is interested in discussing "differential geometry as in first two chapters of Kobayashi and Nomizu" and "Stacks as in Angelo Vistoli’s notes."

Madhuchhanda Mandal

user image

How can I approach this problem?

@Daminark hmm? I knew representation theory is often used in the context of groups by somehow mapping a group to a vector space, but otherwise I don't know much about it

Let $G$ be a group and let $V$ be a vector space. Then a representation of $G$ on $V$ is a homomorphism $\phi:G\to GL(V)$

I have forgotten even the things I knew about this topic (which was very little). But I remember that there were some results which looked almost as magic. For example, that order of a group is sum of squares of degrees of irreducible characters. (I would never guess that something like that should hold after being told the definitions.)

Akiva Weinberger

5:36 AM

"Nomizu" means "river flowing through a field"

literally "field water", no=field, mizu=water

I should sleep

@MadhuchhandaMandal You can find using Approach0 some posts which contain at least the LHS of your equation. Maybe looking at them might help.

Akiva Weinberger

"Kobayashi" is "little forest"

"Ko" little, "hayashi" forest, pronounced bayashi here 'cause I dunno

Madhuchhanda Mandal

5:52 AM

@MartinSleziak Thanks!!

6:35 AM

[Random]

Extremely delocalised space

@AkivaWeinberger it’s called rendaku, changing the first consonant in a compound word

literally “link” “unclear”, meaning that when it links another word, its consonant becomes “unclear”, ie voiced (t->d, k->g, h->b,...)

Let $S$ be a set which contains points $p \in S$. Each point $p$ is a R-tuple (where R is some unordered set) and hence represent a location. Now construct edges (a tuple of tuples) between points p. This generate a relation between these points and give rise to geometric properties

now the key idea is that these edges and hyperedges can be made time dependent, thus they and hence the topology etc. and the very structure of what space is defined by S changes all the time

Therefore, space is reduced to a family of undirected relations between points, i.e. an undirected graph where points represents notions of position

7:34 AM

@Lozansky : I think is more easy to proove that the Bonnet's formula define the Legendre Polynomials, and the formule of Rodrigues too.

Please someone look at this

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