Mathematics

user 85795

12:00 AM

PM 2Ring

Wikipedia has some info: en.wikipedia.org/wiki/Upside_down_goggles & en.wikipedia.org/wiki/George_M._Stratton

leslie townes

woo! oakland!

berkeley!

such a fertile ground for advanced minds, including my own.

porridgemathematics

i'd donate my organs for research

PM 2Ring

Kind of related: The Rubber Hand Illusion

copper.hat

not quite sure i get the illusion part? it is more of a visual reflex

user 85795

12:19 AM

reality is an illusion; albeit, a very persistant one

porridgemathematics

it is but thats kinda moving the goalposts

PM 2Ring

The illusion part is that when the experimenter suddenly hits the rubber hand with the hammer, part of you feels like he's hitting your hand.

porridgemathematics

then an illusion becomes a transient illusion

user 85795

how are we defining "illusion"?

porridgemathematics

i presumed you were defining it as 'sensory experience', which would blur the lines between hallucination/'reality'/experience

I suppose if you can't figure out your senses are not being consistent, whatever you're experiencing is non-illusion (or so I presumed you were sorta saying)

user 85795

12:31 AM

hmmm, interesting

> Summary: Albert Einstein once quipped, "Reality is merely an illusion, albeit a very persistent one." The famous scientist might have added that the illusion of reality shifts over time. According to a new study in the journal Psychological Science, age influences how we perceive the future

porridgemathematics

good quote, reality is trippy for sure

leslie townes

just found what is probably uranium glass in a storage space in our attic. previous owner left a lot of junk here. anybody want to be irradiated?

copper.hat

that is just a reflex action, like when one reacts when watching a movie.

that is entertainment 'science'

i went for a cycle this morning, got my dose of radiation

leslie townes

i stay inside but i still do get my gamma rays.

user 85795

Madam Currie's lab note book is still radioactive to this day!

leslie townes

12:36 AM

Madam Currie. now i'm hungry for some reason.

copper.hat

hmm, me too...

currying flavour

porridgemathematics

wait whats a reflex action?

finding reality trippy/weird?

PM 2Ring

Uranium glass is pretty safe. Unless you grind it up & eat it or inhale it.

leslie townes

yeah, i was kidding. you're not getting anything worse than background from it unless you, as you say, somehow want to.

user 85795

> Marie Curie's Belongings Will Be Radioactive For Another 1,500 Years

porridgemathematics

12:39 AM

oh, you were referring to worrying about radiation from uranium glass

copper.hat

reflex is probably the wrong term, but a response based on correlations rather than actual stimulus.

porridgemathematics

oh wait, you weren't

now im confused

copper.hat

i keep a supply of radium in my basement

leslie townes

we fumigate our house with radon. as much as we can get.

keeps pests to a minimum.

copper.hat

its the key to the sparkle in my eyes

porridgemathematics

12:41 AM

forgive me, im really slow atm, may I know what the reflex action was referring to?

copper.hat

look up for the rubber hand illusion

porridgemathematics

ohhhhh

i was confused, I was under the assumption pretty much every mathematician finds reality 'weird'

in some way or another

well, every is a generalisation, a lot, weird -> curiosity -> physics -> mathematics

user 85795

> Physics is much too hard for physicists.

leslie townes

i'm reminded of a mitch hedberg joke about reality. when i was on acid, i would see things like beams of light. and i would hear things that sounded an awful lot like car horns.

PM 2Ring

@user85795 Whoever said that doesn't understand exponential decay. Radium-226 has a half-life of 1600 years. It decays to radon-222 gas, which has a half-life of ~3.8 days.

leslie townes

12:47 AM

it's because of acid i know that butter is better than margarine. i saw through all the bulls---.

i miss mitch hedberg he was an amazing live performer.

copper.hat

better than a dead one

leslie townes

agreed.

user 85795

@PM2Ring source sir

porridgemathematics

i am currently a stronger mathematician than newton

copper.hat

my siblings all rave about leonard cohen live (when he was) even though not all are fans of his music. something about an in-person performance

(out-person performance?)

porridgemathematics

12:51 AM

my suspicion is live performances blow peoples ears out

even if the music was just ok, you can't really tell

copper.hat

sorry, what did you say?

porridgemathematics

your ears just got blown out

haha

leslie townes

the mitch hedberg clips on youtube are usually fairly stupid. there's definitely something about the experience of being bombarded with jokes, each stupider than the last, for over 45 minutes.

it wears you down and then eventually you're in pieces. my wife and i were talking about this the other night. i love what i refer to as "anti-humor" where the joke is just being as unfunny as possible for as long as possible. she doesn't.

PM 2Ring

@user85795 Ah, Business Insider. Not necessarily a reliable source of info on nuclear physics. They can't even spell "atomic". See the caption of the image at the top of the page: "Marie and Pierre Curie. Credit: Atmoic Heritage Fund"

porridgemathematics

i think anti-humor requires a little bombardment before things click

copper.hat

12:55 AM

nukelar, surely?

leslie townes

PM, as legal counsel for the Atmoic Heritage Fund, i insist that you retract your defamatory allegations and insinuations.

PM 2Ring

:-p

user 85795

lol

copper.hat

let me get hold of my representation from my halliburton friends...

PM 2Ring

In the early days, people just didn't get that you need to be careful with radioactive stuff. The Curies first isolated radium by processing around a ton of uranium oxide. In their kitchen.

leslie townes

1:02 AM

we're also involved in a furious trademark dispute with the Atomic Heritage Fund. we think they switched a letter to deceive the public and trade on our good reputation.

the idea of something completely silent, invisible, and yet lethal is still counterintuitive. somebody had to take those risks for everyone to figure it out.

i'd have given them the nobel prize just for that.

PM 2Ring

That's true.

copper.hat

democracy is a nice idea

leslie townes

no it isn't

copper.hat

sorry, a beautiful idea

leslie townes

i vote against that too

copper.hat

1:06 AM

you can openly carry any idea you want around without a permit

user 85795

including hypocrisy

copper.hat

i had a great time yesterday shooting my mouth off

leslie townes

only yesterday?

PM 2Ring

Also see en.wikipedia.org/wiki/Human_radiation_experiments

copper.hat

well, maybe a little more...

gordos for dinner

working on my inner self

leslie townes

1:12 AM

oh i miss gordos.

copper.hat

me too

leslie townes

there is good mexican food here but due to accidents of location it is more than a 15 minute drive away, which means i don't eat it very much.

copper.hat

there are many eating places nearby, but the real variety is not great.

PM 2Ring

There's an Australian restaurant chain that does Mexican food named Mad Mex.

leslie townes

the only thing i can get quickly is fairly decent sushi

a pun is always welcome.

copper.hat

1:15 AM

nothing appropriate, with emphasis on the latter word

something about the cardinality of items tasting like something else

i always strive to extremise the tone of the convo

something to do with the lagrunge multipliers

leslie townes

our minister of decorum

copper.hat

i am very trying

PM 2Ring

I always thought that Extremes would be a good name for a nightclub. People could say "I go to Extremes". OTOH, maybe a name like that would just attract trouble.

copper.hat

or "The Dogs"?

leslie townes

used to be one near by called The Office. sorry honey, long day at the office.

there was a place in my hometown called the brass rail which should have been called the third rail, for what happened to most people who came into contact with it.

copper.hat

1:25 AM

in ireland growing up, night clubs were invariably very seedy places, even upscale ones (which i avoided, of course)

user 85795

Indeed, when the freaks come out at night, they invariably end up in night clubs.

Anitej Palur

3:17 AM

Hello!

leslie townes

hi

Anitej Palur

Hello. :)

I always find it difficult to open chats from MSE. Is there a faster way to do it?

I always enter the URL to enter chats.

leslie townes

i do the same.

Anitej Palur

Oh, okay. :(

user 85795

can you bookmark this page?

leslie townes

3:27 AM

i think so. because i'm a caveman i begin typing 'chat.stack' and then my browser fills in the rest.

so it must be possible to just bookmark that.

user 85795

i would never judge a caveman by his ability to bookmark pages on the internet :-)

leslie townes

it is kind of you to say this.

Koro

4:00 AM

Without Sylow's theorem, is it possible to prove group of order 15 is cyclic?

leslie townes

there's definitely a way to get there although the simplest ones do go somewhat through group actions.

which is basically sylow theory even if you just talk about a group action.

math.stackexchange.com/questions/208760/… is one route.

one you talk about groups operating on groups you are doing sylow theory whether it fits into that list of theorems or not. is my view.

but you don't need the full theory.

Ted Shifrin

I think you can do elementary arguments here.

For example, the subgroup of smallest index is normal, always.

leslie townes

one of the answers touches on that.

Ted Shifrin

I ain’t looked..

leslie townes

some people, if they don't know, you can't tell 'em.

and if they do know, you definitely can't tell em.

can't tell what's been told. that's all i'm saying.

Koro

4:20 AM

@TedShifrin I don't know this result yet Ted. I am allowed to use cosets. I will also tell exactly what is the problem that got me stuck so that my problem is more expressed.

@leslietownes Leslie, I'll take a look at that as well after I discuss my proof (not yet complete)

Ted Shifrin

But you inow Cauchy’s Theorem?

Koro

Ted, no

I managed to show that a group of order 15 (henceforth called G) must have atleast one element of order 5 (say b) and at least one element of order 3 (say a). It follows that $G=<a>\times $

Ted Shifrin

So you don't know there are elements of order 3 and 5? Hopeless, then.

It follows?

leslie townes

you're gonna wanna use cauchys theorem.

Koro

@TedShifrin Ted: I know that there are elements of order 5 and 3

Ted Shifrin

4:28 AM

That's Cauchy.

Koro

@TedShifrin Because external direct product of <a> and is G as they have no element in common because $o(<a>\cap )$ must divide 3 and 5 that is gcd(3,5)=1

Then I want to claim that <a> is normal subgroup of G. By doing so, I'll be able to prove at least that G is abelian.

Then I can try to work my way out to prove cycle ...

@leslietownes the first answer by prof. Eigen answers my question I think. Than you!

Ted Shifrin

I think you need one normal for that direct product argument. But I'm way too rusty on algebra. So I pass.

Koro

Ted, that's what's been confusing me a lot lately. You are right if we talk about internal direct product which by definition considers normal subgroups. But what confuses me is this: It's clear that $<a>\cap $ is identity. Now we know that $|<a>|=\frac{|<a>|||}{|<a>\cap |}=|<a>|||=15=|G|$, from here it seemes intuitive to me to conclude $G=<a>\times $ (external direct product), which may be wrong. May be Leslie can enlighten me on this.

:58329475, group action has been used in the answer. I don't know that :'(

Ted Shifrin

4:51 AM

You haven't shown that the external direct product is isomorphic to $G$. You need to get an isomorphism. Otherwise you prove this in great generality when it’s false.

Koro

you are right Ted.

Russian Bot Who Knows Your IP

5:12 AM

Sha Vuklia

10:15 AM

@Astyx Yea, this is indeed the argument (I expected it to be obscure, so I didn't even try to think about it ;v)

(My book defines an isogeny to be a rational map (and hence a morphism) between elliptic curves. This induces a map between function fields, and if the corresponding field extension is separable, the isogeny is said to be separable)

Thorgott

@Koro This conclusion is false in this generality. You need both subgroups to be normal to obtain a direct product.

Koro

10:47 AM

@Thorgott: what do you suggest here?

@Thorgott noted. That's how I saw internal direct product being defined.

mick

11:13 AM

0

Q: How many primes of the form $3^n + n^3 $ exist?

I was looking for primes of the form $3^n + n^3$ or equivalently of the form $9^m + 8 m^3$. I was not able to find any ?? How many exist ? What are the first few ? It seems like a trivial thing I missed. Or maybe not since it somewhat resembles questions about fermat primes or mersenne primes. My...

any ideas ?

Thorgott

11:39 AM

@Koro At which point specifically?

Koro

is there any way to avoid class equation?

@Thor

Or should I wait till I learn class equation?

Sayan Chattopadhyay

For a complex vector bundle $E \to X$ what would the notation $\mathcal{A}^1(X, End(E))$ mean? I would guess one forms, but what kind of one forms?

Thorgott

Finite group theory is like a sandbox. There's tons of ways of playing around with what is there to reach the desired conclusion. I do believe a modestly non-trivial input is necessary, but Cauchy's theorem does that job. In short, you can certainly avoid the class equation.

Koro

I am allowed to use Cauchy's theorem

With that it is easy to conclude order 3 and order 5 elements exist. So far I know Cauchy theorem's proof only when the group is abelian.

I'll think more on this.

Thorgott

@SayanChattopadhyay probably just complex ones? I think I recall that notation from Huybrechts

Sayan Chattopadhyay

11:56 AM

Right for the trivial vector bundle case it would be just a matrix of one forms, where the size of the matrix will be the rank of the vector bundle

Mad Spaces

1:25 PM

how to find the limit of $ \sum_{n=0} n * z ^n $ with z < 1 $ without using differential calculus?

Transcript for

$Mathematics$ Mathematics