Mathematics - 2021-06-06 (page 3 of 5)

Permutator

06:00

I don't have a green card :(

and I want one

Balarka Sen

@copper.hat Ahh yes

Permutator

any suggestion?

copper.hat

there is areason to get married

Balarka Sen

So you'd know for sure

Permutator

@copper.hat what's that?

copper.hat

06:00

i am very open minded

really, shooting goldfish is no fun

sorry.

Permutator

What's the reason for getting married?

copper.hat

so you can divorce and get half the proceeds

Permutator

That's pathetic

why will anyone marry you if you're divorced?

copper.hat

you need to expand your diction

Balarka Sen

@copper.hat rip

copper.hat

06:02

are you Euler by any chance?

Permutator

RIP

Yes

why?

what's wrong with Euler?

why will anyone marry you if you're divorced?

copper.hat

it really should be spelled oiler

Koro

@BalarkaSen Never mind. It was one of my elective courses during my graduation. It comes in civil engineering en.wikipedia.org/wiki/….

copper.hat

i think FEA is cool.

Permutator

@copper.hat DUDE

copper.hat

06:03

and related methods

Koro

woah @copper knows that :)

Permutator

You sound like Bob Marley

or Shawn Mendes

copper.hat

who is bob marley?

Permutator

RIP

You don't know him?

Balarka Sen

@Koro interesting, i know very little about numerical methods.

Permutator

06:04

He's Thanos

MIGHTY THANOS

6 INFINITY STONES

Koro

Balarka, it has many applications for example when you design bridges

Permutator

And boom half population wiped out by snapping a finger

Balarka Sen

sounds interesting!

Permutator

that sounds so COOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOL

Koro

In civil engineering, it has many applications.

Permutator

06:05

@robjohn Any significant progress on ym integral?

copper.hat

similar methods used to analyse transistors, etc.

i wish i had done either civil or aeronautical

Permutator

@copper.hat math major?

CS minor?

or linguistics? XD

copper.hat

ee mainly

Permutator

RIP

Engineers are of not much use

Koro

@copper.hat: You can still study structural analysis and design and study random vibrations also

copper.hat

06:07

optimisation as in continuous parameter/control

Balarka Sen

@Koro discretization is something that i think about on and off but it is always a rather firmly on the side of will-o'-the-wisp for me

Permutator

I decided that I didn't want to be an engineer when I was 7

Balarka Sen

for example, i find discrete differential geometry fascinating

copper.hat

@Koro we used it once to study structural failure in a 2d building model

Permutator

@BalarkaSen Diff geo! Yeah! I took a course on it this year at Stanford

copper.hat

06:08

we were optimising beam parameters to reduce non elastic stuff

@Permutator i can guarantee that you own something that was designed with software i wrote.

Permutator

Any recommendation for a nice dating website?

@copper.hat NO WAY

coz I own nothing except a f*** labror-dog

Balarka Sen

copper, are you aware of what control theory is? i have found the word being thrown around in certain circles but i never tried to explore what it is

Permutator

which dies 2 weeks ago :(

*died

RIP

copper.hat

@BalarkaSen you are correct. at the time is was using algebraic methods to design compensators for linear control systems. also a little optimal control.

Balarka Sen

oh very cool

Koro

06:12

In civil engineering, I had maths only for first 3 semesters (real analysis, complex analysis, linear algebra, ordinary/partial diff. eqns). I didn't know anything about group theory. I started studying group theory during lockdown and more real analysis etc. I'm still learning. This differential geometry sounds very new to me @BalarkaSen

copper.hat

unfortunately many involved do not pay attention to detail.

non differentiable analysis (as in Clarke) was an interest of mine for a while

but you really need to be an analyst to go much deeper than $\mathbb{R}^n$.

and i am pretty weak$^*$ in that area

Balarka Sen

@copper.hat i know of the following problem which the literature says "is well known in optimal control theory": let $A \subset \Bbb R^n$ be an open connected subset and $f : I \to \Bbb R^n$ be a $C^1$-curve with $f'(t) \in \mathrm{Conv}(A)$ for all $t \in I$; then find $g : I \to \Bbb R^n$, $C^1$, such that $g'(t) \in A$ and $\|f - g\|$ is as small as possible

Koro

I have been doing that-trying to go deeper than Rn, so far I have reached metric spaces only :)

Balarka Sen

maybe you know something about this

Conv(A) = convex hull of A

copper.hat

sounds like what was known as relaxed controls

hmm. maybe not

Balarka Sen

06:16

yeah no, you seem right. something something filippov's relaxation theorem

copper.hat

well, it is going in the 'opposite' direction, given $f'$ find a $g'$.

Balarka Sen

apparently Gromov rediscovered much of this stuff later in geometry and it became a staple food. led to ideas which are used to prove Nash's deep results in Riemannian geometry

ahh

copper.hat

joking apart, it gets too deep for me pretty quickly

i like convex stuff because it is straightforward :-)

Balarka Sen

i find the result to be so interesting just even in the case of $n = 3$, $A = \{(x, y, z) \in \Bbb R^3 : x^2 + y^2 < z^2\}$

hm, not quite. one second

OK, $n = 2$, $A = \{(x, y) \in \Bbb R^2 : x^2 + y^2 < 1\}$

Koro

Dear Balarka, are you a professor?

copper.hat

06:22

a tracking problem of sorts

Balarka Sen

Any trajectory on $\Bbb R^2$ can be though in-time as a trajectory in $\Bbb R^2 \times \Bbb R$ which moves monotonically in the $* \times \Bbb R$-direction, something like trajectory of a particle

derivative being constrained in $A$ means it's contained in the light cone

derivative being constrained in $Conv(A)$ means its literally photon

its always tangential to the light cone

so trajectory of any particle can be approximated by photon trajectories

the approximant will be very swirly in general yeah

copper.hat

i was thinking more mundane stuff like tracking a missile :-)

Balarka Sen

thats a much more practical phrasing :)

copper.hat

@BalarkaSen i choose to go into the software/hardware world not because i am a pacifist, just didn't want the missile tracking to be my answer for what do you do

Balarka Sen

@Koro no, far from it. i became officially a grad student a week ago :)

hahah

copper.hat

06:25

one of my early jobs would have been working for a prof tom kailath at stanford

Koro

I ask because you talk about stuff that I have never heard of...manifolds, hulls etc. I hope to learn it all some day $\ddot \smile$ @BalarkaSen

Balarka Sen

@Koro with persistence and interest, you will definitely. think of it as playing a video game

thats what math is at the end of the day. just a cheaper way to entertain yourself in the off time

2

copper.hat

disappointing as it is to acknowledge one's one limitations, i realise that there is a limit to the degree of abstraction i can handle. i need to be near concrete not abstract nonsense

Balarka Sen

thats pretty respectable imho

copper.hat

i want it all and i want it now :-)

Koro

06:30

I don't quite like my current job. It's just that it's not even remotely related to maths or my area of engineering.

copper.hat

few jobs are

all of the people i know who are doing what they want to do are academics

Stéphane Jaouen

@TedShifrin : hello. The problem was : "can we fill the space with tetraedron with no overlap or gap?" my idea was based on the animation that you will find in the following link:fr.wikipedia.org/wiki/T%C3%A9tra%C3%A8dre, in the paragraph "volume of the tetrahedron". With 6 tetrahedra, you get a parallelepiped that fills the space. If this is wrong, where is my mistake?

Russian Bot Who Knows Your IP

08:52

tip: try to create folder called 'con' in your windows computer

if it gives an error then there is a problem in your device

trust me this can be done

let me show you a proof:

(screenshot of my computer)

Leaky Nun

09:38

@RussianBotWhoKnowsYourIP now what

user21820

11:32

@LeakyNun: You just got trolled by a dot who does not know your ip.

Leaky Nun

oh no did i

user21820

I think so.

Russian Bot Who Knows Your IP

12:26

Trolling isy profession

Russian Bot Who Knows Your IP

14:40

Open notepad

Write '(1<<19**8,)*2' (without the quotes)

Save it as main.py

Run it if you have a Python 3 installed

no don't do it

hyper-neutrino

i ran it and nothing really happened

Russian Bot Who Knows Your IP

It will create a file of 8.5 gb space

Somewhere

hyper-neutrino

lol no it won't

it just creates a large integer somewhere in RAM and then the program ends so presumably it gets collected pretty quickly

leslie townes

here's a thought. open a web browser, put math.stackexchange.com into the browser window, review the questions you see there, offer thoughtful input if anything strikes your interest, or check back later for something interesting to pop up

Russian Bot Who Knows Your IP

There is a version which creates a file of some tb of size

leslie townes

14:44

it's possible to do constructive things on a computer. even yours, russian bot

Russian Bot Who Knows Your IP

I once posted a fork bomb

@hyper-neutrino deleted it

Now i posted a compiler bomb!

How about a zip bomb

hyper-neutrino

here's an additional tip on top of leslie's excellent advice

read the chat guidelines posted in the room topic itself. it's hard to miss

Russian Bot Who Knows Your IP

The don't troll rule is unnecessary

leslie townes

i'm tempted to respond to math.stackexchange.com/questions/4164989/… with geometrical input. somebody stop me.

Russian Bot Who Knows Your IP

I once felt really bad

Someone actually tried the fork bomb i told him as a joke

But he later confessed that he was on a vm

leslie townes

14:50

classic example of rudin suppressing geometrical insight. i do respect the fact that the book has not a single picture in it. but it's hard to justify giving exercises like that without arming people with some amount of g__m___ intuition

russian bot it is one thing to reflect on the past and another thing to learn from it.

Russian Bot Who Knows Your IP

Yup

Thorgott

oh god, that exercise is giving me bad flashbacks

Russian Bot Who Knows Your IP

But i will never stop trolling and giving people zip and fork bombs

Thorgott

I think it's the one I struggled the most with from that chapter back when I tried reading Rudin

leslie townes

my daughter keeps jumping off a step in our bathroom and slipping on the floor, hurting herself. every few days she tries again.

i appreciate tenacity, but here i think she should focus on learning from mistakes.

Thorgott

14:52

of course, I did not understand the geometry back then

It's pretty trivial looking at it now

leslie townes

thorgott, that's why it's such a bizarre exercise. there's nothing in the book to prepare you for it.

Russian Bot Who Knows Your IP

leslie w h a t

leslie townes

i'm not really sure how helpful it is. it might be interesting to pose the problem in different metric spaces and see how you could vary the solution set.

if i wrote an analysis book it would probably just be some kind of easier knockoff of rudin, also with no pictures.

Russian Bot Who Knows Your IP

Splashing Around

►

U know this

We all know this

Everybody knows this

leslie townes

then when i'd get to the implicit function theorem, and stuff where you have to think about level sets and what they look like, i'd just stop. i'd say, sorry, there is no more analysis.

Koro

15:08

Has any of you attended Rudin's lectures ?

Like when he taught at some university

I like Rudin's style :)

When I saw this theorem: Real valued monotonic functions on (a,b) can't have uncountable discontinuities.

I struggled with the proof a lot and that's when I saw Rudin book probably for the first time...

Thorgott

that theorem has a name, which I always forget

it starts with F, I think

Koro

I was amazed as to how between one sided limits, he chose a rational number

leslie townes

every theorem has a name, man. you just need to give it one.

wikipedia says froda's theorem.

Koro

and then injected set of discontinuities into set of rationals :)

leslie townes

i would have thought dini, or someone like that.

lots of people thinking about discontinuities back then.

Koro

15:13

That's when I started studying Rudin. But then got pushed back by words like "metric spaces"

So I started with chapter 1 onwards

leslie townes

things start normally enough and then for some reason, a ton of metric space topology.

then it's back to analysis.

Koro

and then I understood metric spaces, solved exercises also. I enjoyed it.

I still enjoy it.

I agree he doesn't use many pictures and all but that's what you have to fill in

That's what I think

leslie townes

i did find topology easier to understand after rudin. but it was a struggle.

"many" pictures?

ahaha

Koro

Leslie, someone complained in messages above about pictures

So that's what.

PM 2Ring

@RussianBotWhoKnowsYourIP If you persist in behaving like an idiot, people will naturally assume that you are, in fact, an idiot.

leslie townes

15:15

it may even have been me.

Koro

I was scrolling above to see who.. Glad you mentioned that :)

PM 2Ring

Which are better? Imperial spaces, or metric spaces? :)

Koro

scrolling above or down , zoom in or zoom out, push or pull (at doors), it's very typical of me to confuse these :)

Thorgott

@leslietownes ah, right

Koro

Sometimes at doors, I pause for a moment whether to push or pull :)

leslie townes

15:17

"rudin doesn't use many pictures" is the equivalent of my "i don't own many yachts."

there's a far side cartoon for that.

and the opening sketch of 'i think you should leave' with tim robinson.

Thorgott

Rudin's exposition of topology is offensively bad, probably the worst part of the book

Koro

Thorgot you mean chapter 2?

Because topology word was never mentioned if I recall

I'm talking about baby Rudin by the way

leslie townes

yes, chapter 2.

Thorgott

the chapter is literally called "Basic Topology"

Koro

Yes..

I forgot :'(

Thorgott

15:20

also, leslie, wasn't Dini's theorem the one about monotonic pointwise convergence on a compactum being uniform or something?

leslie townes

yes, although it's funny, because i don't think he ever defines what a topology is

Thorgott

I forgot most of these theorems by now

leslie townes

he's certainly doing topology but doesn't go that far.

Koro

I wonder what exact meaning of topology is!

leslie townes

thorgott that is definitely one of them.

Koro

15:20

I know the definition though

But like dictionary meaning of topology

The word origin etc.

leslie townes

i just checked. 'basic topology' is the title of the chapter, but the book never otherwise addresses the term 'topology.' it isn't even in the index.

at least in my edition.

that's funny. a rare hiccup from rudin.

Koro

Right Leslie

Topology is never mentioned inside the chapter

Thorgott

I mean, I don't think that's what's wrong with it

Koro

It exists only on the title

Thorgott

he's just restricting himself to metric topology

leslie townes

15:23

if i were his editor i would have said, let's call chapter 2, "metric spaces."

Thorgott

though it's funny, because he still uses definitions and proofs straight out of general topology

Koro

Thorgott you know better about generalized topology. Seeing from my perspective (who knows up to metric spaces), I didn't find any issues with chapter 2

Except that I don't know the dictionary meaning of topology

or what is the origin of the word topology

I searched it online but... I didn't get it

Often the term Point set topology is used for example in Apostol mathematical analysis

Thorgott

he does compactness via open covers in metric spaces, it's funny

Koro

PST = Study of sets which consist of elements called points. is what I understand by PST.

@Thorgott Isn't that how it's usually done?

Thorgott

not in metric spaces

it just makes the concept a lot less accessible without any benefit

I never finished the book, but I'm pretty certain that this definition of compactness never becomes relevant

like most of that chapter

Koro

15:30

@Thorgott With my current understanding, I'll politely disagree with this as the concept was used many times for example in exercises and then in continuity chapter and in sequences/series chapters too etc. Extensive usage of compactness (using open covers) I must say.

PM 2Ring

@Koro Dictionary compilers aren't mathematicians, (unless it's an actual mathematical dictionary), so dictionary definitions of mathematical terms are generally not very illuminating. Wikipedia does ok, I think: "A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity.

(cont) "Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property."

Thorgott

compactness is important, the definition via open covers is not

it appears in exactly two places after chapter 2

one is in proving that the continuous image of a compact space is compact (which can just as easily be checked with any alternative definition), the other is in proving that a continuous function on a compact metric space is uniformly continuous (which can just as easily be rewritten to accommodate a more standard definition of compactness in metric spaces)

Koro

It appears in exercise of chapter 2 also many times :)

But may be you are right about more useful version of compactness (which is without open covers). I don't know.

Thorgott

he also puts a lot of emphasis on perfect sets in chapter 2, which is a concept that appears nowhere except in one remark that just recalls chapter 2anywhere else in the book

it's ridiculous how frontloaded that chapter is with abstract technicalities that don't get motivated in the slightest and are in parts hardly relevant to anything else

Koro

@leslietownes I have observed that usually Rudin doesn't mention names for example: No mention of cantor's diagonal theorem, Cauchy mean value theorem etc. :) Cauchy mean value theorem is simply called one of the mean value theorems etc.

@Thorgott appears in exercises

Thorgott

15:42

not past chapter 2

Rover

The value of $6+log_{3/2}(\frac{1}{3\sqrt2} \sqrt{4-\frac{1}{3\sqrt2}\sqrt{4-\frac{1}{3\sqrt2 }...}} )$ is

Thorgott

the fact that concepts from chapter 2 appear in the exercises of that same chapter doesn't really make them more relevant or useful in the large scope of the book, that's just self-sufficiency

Koro

@Thorgott I see. I don't know.

Rajorshi Koyal

15:58

-1

Q: Doubt in a combinatorics question.

Mohan is 35th from the top and Geeta is 21st from the top among students. Mohan is 14th from the top and 12 th from the bottom among boys. Geeta is 18th from the top among girls. What could be the total minimum number of students? I am unable to approach the problem whole heartedly.

combinatorics

I am having doubt with this

Please assist me with this.

leslie townes

i'm not a huge fan of naming theorems after people. at least older stuff where cauchy (for example) would have been working with different definitions even if he was making essentially the same argument.

also the surprisingly consistent rule that basically anything named after anyone is not actually attributable to them.

Rajorshi Koyal

@Wolgwang Sir can we get in touch once?

leslie townes

in functional analysis there are lots of results that textbooks end up calling the A-B-C-D-E-F theorem. where A, B, C, D, E, and F were people who added onto the form that you see in the reference. at some point it seems silly.

except for anything that anyone wants to name after me.

Rajorshi Koyal

@leslietownes Did you reply to me?

If so.. Let assume them as M and G

Instead of there full names.

leslie townes

i was responding to koro but will also give aliases to the people in your problem. :) thanks.

Rajorshi Koyal

16:11

:-) Would you mind assisting me @leslietownes ?

Koro

@leslietownes Actually when I see theorems with names, I find them very motivating :)

I like to see names :)

and a biography also of those who invented them ...

Rajorshi Koyal

Same here @Koro ;P

Koro

:)

Rover

16:30

@leslietownes Hi :-)

Any hint on abooove problem.

Koro

16:41

@Rover: first solve the repeating nested radicals. There’s a very standard way to solve these.

Mehdi Slimani

16:55

hello people, linear algebra question

There is this proof of the eigenvectors of a symmetric matrix being orthogonal that goes as follows:
take two eigenvectors $v_i, v_k$ of $A$, consider $v_i^T A v_j = \lambda_i v_i^T v_j = \lambda_j v_i^T v_j$.
If the two eigenvalues are different then $v_i^T v_j = 0$.

I always bugged a bit on how to extend this to eigenvalues with multiplicity>1. i found a different proof that doesnt care about that but im still wondering on how to proceed to extend the first proof

could somebody point me in the right direction please?

Thorgott

what precisely is it that you want to prove?

Mehdi Slimani

eigenvectors of symmetric matrix are mutually orthogonal

Thorgott

not all of them are

Mehdi Slimani

@Thorgott do you have in mind rank defficient matrices ?

leslie townes

think of the identity matrix

Thorgott

17:00

I have in mind the fact that e.g. any eigenvector is not orthogonal to itself

Mehdi Slimani

hmm true. what about this statement: you can find n eigenvectors orthogonal to each other for a nxn symmetric matrix

Thorgott

yes, that's pretty much the spectral theorem

leslie townes

within eigenspaces for eigenvalues of multiplicity > 1, you will need to make some arbitrary choices and maybe do a gram schmidt kind of thing

Thorgott

yeah, that part is easy, to be clear

leslie townes

as you see for example with the identity matrix. :) any nonzero vector is an eigenvector. some choices of these will be mutually orthogonal, others won't

Thorgott

17:04

the hard part is that the Eigenspaces add up to the entire space

Mehdi Slimani

thank you for the indications. i came across a proof that uses gram schmidt and induction to cover the whole space

leslie townes

if you use induction you do have to work gram-schmidt into the middle of it, depending on how it's structured. i think axler does it this way.

Mehdi Slimani

i realize that the first proof is a dead end for eigenvalues of multiplicity > 1

that was my main doubt. thanks a lot for the help people

leslie townes

sure thing. it's a very good question.

i'm a huge fan of thinking deeply about ways of proving the spectral theorem.

i've yet to see a book that dares to prove the infinite dimensional case and then specialize for matrices. maybe that will be my contribution to the linear algebra literature.

Thorgott

you ought to start with the most general case and then devote the rest of the book to corollaries

leslie townes

17:15

haha, the book with only one theorem.

then corollary 1, corollary 2, . . . corollary 95

Buddhini Angelika

17:26

Hello all.

Consider two groups, $(\mathbb{Z}_p \times \mathbb{Z}_p) \rtimes_{\phi} \mathbb{Z}_q$ and $(\mathbb{Z}_p \times \mathbb{Z}_p) \rtimes_{\theta} \mathbb{Z}_q$, where $p,q$ are distinct primes. For these two groups, is the following statement correct?

The above two are two groups of the same isomorphic type, where each semidirect product is defined by $\phi: \mathbb{Z}_q \rightarrow Aut(\mathbb{Z}_p \times \mathbb{Z}_p)$ and $\theta: \mathbb{Z}_q \rightarrow Aut(\mathbb{Z}_p \times \mathbb{Z}_p)$, respectively. The set of ordered pairs representing elements of the group (i.e. ordered pairs of the form $((a,b),c)$, where $a,b, \in

\mathbb{Z}_p, c \in \mathbb{Z}_q$ ) is the same, whereas the product of two elements should be computed using $\phi$ and $\theta$ when doing computations with each group respectively.

I mean is there anything wrong with the terms used, like "isomorphism type" inappropriately used? Thanks a lot in advance.

leslie townes

i'd need to know more about phi and theta before concluding that the groups are isomorphic. if this falls out of some abstract theory of cyclic groups, it isn't clear to me how.

i agree that both semidirect products could be represented as sets of pairs of the form ((a,b),c). that seems non controversial.

copper.hat

pronounced fee of course

leslie townes

generally speaking if you have two actions of one group on another group, the isomorphism type of the semidirect product can depend on the choice of action.

if it doesn't in some case that seems significant and maybe worth saying more about.

copper i was thinking this morning when talking to my daughter that i pronounce 'the' in two ways. sometimes 'thuh,' sometimes 'thee.' she does it too unconsciously.

i'm a member of team fie. no fee for me.

Buddhini Angelika

Okay, thanks @leslietownes when $q|p-1$ but does not divide $p+1$, there are $(q+3)/2$ conjugacy classes of $GL_2(p)$ and hence $(q+3)/2$ semidirect products.

copper.hat

i still use ye for you plural, accidentally used it with non irish folks yesterday

leslie townes

17:33

wow, this got very algebraic very quickly. i will back away slowly without making eye contact. :)

Buddhini Angelika

They are non-isomorphic semidirect products right?

leslie townes

if the question was simply whether the english sentence read like a well composed and understandable sentence, my answer is yes; i was just curious about the internal math mechanics.

Buddhini Angelika

:)

Wolgwang

$\require{action}\toggle{\text{Something is hidden here, click to see.}}{\toggle{\text{Mathematics is the most beautiful and most powerful creation of the human spirit.}}{\text{Isn't this amazing?}}\endtoggle}\endtoggle$

leslie townes

my daughter was obsessed with gender this morning. she and the cat were being difficult in the same way. again. i said 'you have something in common,' and before i could complete the thought, she said 'yes, we're both girls and you're a boy. and mama is a girl.' then she started naming all the people at school and assigning them in categories.

Buddhini Angelika

17:35

Like if it was said that there are $(q+3)/2$ semidirect products, they are not isomorphic, so if $\phi, \theta$ above define two out of those semidirect products then, the above statement has an error, right?

leslie townes

so i said 'what you have in common is that you get very rude when you want more food and we won't give it to you.'

lesson learned, hopefully.

if the isomorphism type of the semidirect product can depend on the choice of map, the statement seems to need more context. it seems to be assuming we already know what theta and phi are. if we do, maybe that's fine.

if not, maybe we need more information, or qualification

Buddhini Angelika

Okay,

leslie townes

i've figured out my neighbor's code for his garage door. it uses the same tone coding as phones do (or used to). and i've heard it every day for the last year.

copper.hat

the first time i realised the difference in us english was when i used the word fortnight

DTMF I used to carry a dtmf dialler when i used to travel to europe for work

leslie townes

yeah.

it's 1067. maybe his birthday is october 1967.

copper.hat

17:41

probably the default setting

leslie townes

maybe that's when the garage door ai was hatched in its laboratory, like HAL 9000.

copper.hat

:-) i have forgotten what ours is. easily hackable.

leslie townes

i used to use 1066 as an arbitrary number in made up problems. one day a student asked why, and i said because it's big enough to not be too small, and the norman invasion. they said, what's the norman invasion.

i said, this isn't history class.

copper.hat

decades ago i had set up this system where i could text my garage door for status & operation

:) i like your rationale !

leslie townes

there used to be a server you could ping and see how many sodas there were in a vending machine in the basement of evans hall.

i miss the old internet, that kind of stuff was fun. now it's just five or six companies running platforms for people to yell at each other.

Buddhini Angelika

17:46

What if it was said like follows. When considering the groups of order $p^2q$, $p>q$, both $p,q$ are prime, we consider a case: $G \cong S_p \rtimes_{\theta} \mathbb{Z}_q$, when $ S_p \cong (\mathbb{Z}_p \times \mathbb{Z}_p)$.

$ S_p \rtimes_{\theta_1} \mathbb{Z}_q \cong S_p \rtimes_{\theta_2} \mathbb{Z}_q$ iff $ \theta_1(\mathbb{Z}_q)$ and $\theta_2(\mathbb{Z}_q)$ are conjugate subgroups of $Aut(S_p)$. Thus the classification problem becomes the linear-algebra problem of determining
the conjugacy classes of order-$q$ subgroups of $GL_2(p)$. And for $q|p-1$ case they have got $(q+3)/2$ conjugacy classes and have concluded that there are $(q+3)/2$ non abelian semidirect products.

Then still in order to determine whether they are not isomorphic, we need to know about $\phi, \theta$, or from this can we say there are $(q+3)/2$ non-isomorphic groups?

copper.hat

@leslietownes at some point a camera was mounted on the top of evans that would upload bay pics periodically. that way you could have the screen backdrop show the outside when stuck in your interior office

that was the fun internet

leslie townes

i never had an interior office. always had a window. sometimes even a balcony.

Xander Henderson

@leslietownes I taught for a semester at Scripps College. They gave me an office with windows which looked out over a really lovely little courtyard. That courtyard was later used for filming the last scene in The Bird Box. It was entertaining to watch that movie, get to the end, and be able to say "Hey! Look! My office!"

copper.hat

i was always in an interior office (including my unabomber one) until i moved to the cad group in cory hall. then i had a cubicle which had an interior facing window on the other side. certainly no visual inspiration for research...

most of the cad group had microvax which made for great late night sessions of xtrek

leslie townes

ha! xander that is amazing.

copper.hat

17:59

there is a convex PSQ which shows absolutely no effort but which i am dying to answer for some practice

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$Mathematics$ Mathematics