12:00 AM

woo! oakland!
berkeley!
such a fertile ground for advanced minds, including my own.

i'd donate my organs for research

Kind of related: The Rubber Hand Illusion

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

12:19 AM
reality is an illusion; albeit, a very persistant one

it is but thats kinda moving the goalposts

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.

then an illusion becomes a transient illusion

how are we defining "illusion"?

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)

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

good quote, reality is trippy for sure

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?

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

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

12:36 AM
Madam Currie. now i'm hungry for some reason.

hmm, me too...
currying flavour

wait whats a reflex action?
finding reality trippy/weird?

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

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

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

12:39 AM

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

oh wait, you weren't
now im confused

i keep a supply of radium in my basement

we fumigate our house with radon. as much as we can get.
keeps pests to a minimum.

its the key to the sparkle in my eyes

12:41 AM
forgive me, im really slow atm, may I know what the reflex action was referring to?

look up for the rubber hand illusion

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

> Physics is much too hard for physicists.

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.

@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.

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.

agreed.

@PM2Ring source sir

i am currently a stronger mathematician than newton

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?)

12:51 AM
my suspicion is live performances blow peoples ears out
even if the music was just ok, you can't really tell

sorry, what did you say?

your ears just got blown out
haha

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.

@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"

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

12:55 AM
nukelar, surely?

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

:-p

lol

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

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.

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.

That's true.

democracy is a nice idea

no it isn't

sorry, a beautiful idea

i vote against that too

1:06 AM
you can openly carry any idea you want around without a permit

including hypocrisy

i had a great time yesterday shooting my mouth off

only yesterday?

well, maybe a little more...
gordos for dinner
working on my inner self

1:12 AM
oh i miss gordos.

me too

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.

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

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

the only thing i can get quickly is fairly decent sushi
a pun is always welcome.

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

our minister of decorum

i am very trying

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.

or "The Dogs"?

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.

1:25 AM
in ireland growing up, night clubs were invariably very seedy places, even upscale ones (which i avoided, of course)

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

2 hours later…
3:17 AM
Hello!

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.

i do the same.

Oh, okay. :(

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.

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

it is kind of you to say this.

4:00 AM
Without Sylow's theorem, is it possible to prove group of order 15 is cyclic?

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.
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.

I think you can do elementary arguments here.
For example, the subgroup of smallest index is normal, always.

one of the answers touches on that.

I ain’t looked..

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.

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)

But you inow Cauchy’s Theorem?

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 $G=<a>\times <b>$

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

you're gonna wanna use cauchys theorem.

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

4:28 AM
That's Cauchy.

@TedShifrin Because external direct product of <a> and <b> is G as they have no element in common because $o(<a>\cap <b>)$ 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!

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

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 $<a>\cap <b>$ is identity. Now we know that $|<a><b>|=\frac{|<a>||<b>|}{|<a>\cap <b>|}=|<a>||<b>|=15=|G|$, from here it seemes intuitive to me to conclude $G=<a>\times <b>$ (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 :'(

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.

you are right Ted.

5 hours later…
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)

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

10:47 AM
@Thorgott: what do you suggest here?
@Thorgott noted. That's how I saw internal direct product being defined.

11:13 AM
0

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 ?

11:39 AM
@Koro At which point specifically?

is there any way to avoid class equation?
@Thor
Or should I wait till I learn class equation?

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?

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.

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.

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

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

1 hour later…
1:25 PM
how to find the limit of $\sum_{n=0} n * z ^n$ with z < 1 $without using differential calculus? @MadSpaces I'm not sure that you do. Why are you tying a hand behind your back? I dont understand what you mean. You asked how to find that limit without using differential calculus. This is like fighting with a hand tied behind your back. Why? Why are you disallowing the use of the most appropriate tool? A good question i shall ask my professor, who gave us the homework. I would suggest that you write down the first several terms. 1:33 PM Oh i have been trying now for more than an hour. I only asked since i gave up on it :=) My feeling is that there should be a way of writing$n$as something funny (like$n = (n-1) + 1$, then factoring a$z$out in a clever way to compare to a "nice" series. But, I mean... what tools are you expected to use? As a hint we are told to consider the cauchy product of$ (\sum z^n)^2 $Yeah, that seems reasonable, given that the series is essentially$1/(z-1)^2$. After messing around i have found it that the limit of the given product is the same as the limit of$\sum n * z^{n-1}$which would be$ 1/ (1-z)^2 $And$n z^n = z (nz^{n-1})$, n'est-ce pas? So factor the$z$out and you are done. You've already solved the problem! 1:37 PM I have done this. But this leaves a big gap. Suppose we rewrite the sequence as you suggested and as i have done. We do realiaze that the given hint sequence and our sequence both have the same limit point. How do we connect those two arguments together? I am very unclear about what you have actually done. You expand out the Cauchy product, and see that it is... what? What I understood you to have said is that $$\left( \sum z^n \right)^2 = \sum n z^{n-1},$$ yes? Just factor out a$z$. $$\sum nz^n = z \sum nz^{n-1}$$ I did not reliaze that the first equation holds value. How would one prove that?$ \left( \sum z^n \right)^2 = \sum n z^{n-1}, $@XanderHenderson This one With induction perhaps, any better way where we can rearrange the terms to reach the other side? @MadSpaces I thought you said that you had already done that... No i said that the limit points of both of them are the same. @MadSpaces This is a very confusing comment. How do you know that the two series sum to the same thing? 1:44 PM I dont know if they are per se equal, they do however have teh same limit point. We know that the right sum must have the same limit (using diff calculus ) as the left. The left one is trivial (geometric sequence squared) Actually, they are not equal. i just calculated the first few terms and they are not the same. @MadSpaces Okay, look... start over: the was to use the Cauchy product to expand$( \sum z^n )^2$. Have you done that? No i do not know what that means (To expand the cauchy product) do you mean like.. calculating the limit point ? Do you know what the Cauchy product is? well, we had one difenetion , however i didnt really seem to understand how this connects to this sequence. In other words, not really Give me your definition of the Cauchy product. 1:48 PM Okay. one second the product of two complex sequences$\sum_n a_n$and$\sum_n b_n $is defined as the sequence$ \sum_n c_n $with$ c_n = \sum_{k=0}^n a_k b_{n-k} $is called the cauchy product Great. So$(\sum z^n)^2$is the product of two sequences, yes? What are those two sequences? What is$(a_n)$and what is$(b_n)$? Do you suppose that out of the given hint (since it says consider teh cauchy product of the series) or do you like suppose that because it is squared which implies its the same series multiplied with itself twice I think that if you answer my question, you will have an answer to your question. Let me see. Give me a couple of minutes to mess around with it. 2:19 PM no clue. ( i have been expanding the first terms and trying to figure it, which two other sequences i need to multiply in order to get the same results, but it didnt work out) math people all cross their z's and 7's. to keep them from being mistaken as 2s. @leslietownes Yes, but I started doing it in the first grade, because that't how mah mama dun taught me. how we keep zs from being mistaken as 7s, i dunno. just be careful about that. Honestly, I have difficulty with "h" and "k" in my own handwriting. 2:26 PM i started writing t differently in college. it looked too much like a plus sign. i began curving the bottom. i don't curve it in normal writing but do in math notes. @leslietownes I do the same thing. And "i" has a little tail, too. And "l" is always$\ell$. But my handwriting is still terrible. :( we can see that, it's still on the screen. I completly did not approach like this and instead just instantly used the definition.. There was a four or five year period, starting in high school when I was first learning to write Cyrillics, that my handwriting was okay. However, how do you reach this equality? Sorry if this is a dumb question, but i do not seem to figure it out 2:29 PM @MadSpaces The summand does not depend on$k$. Oh... What is$\sum_{k=0}^{n} C$, where$C$is any constant? Yea i did not notice you are right apparently that's a k. that's what we're learning. @MadSpaces what do you mean what happened? you summed up$z^n,\ n+1$times. 2:29 PM i'm one to talk, my handwriting is worse. @MadSpaces That's just what every narcissist wants to hear! @leslietownes Yes. That is what that is supposed to be. some of those ns could easily be ms. No... Ms is a magazine for modern, liberated women. when i taught i worked very carefully at putting legible letters on the board. it had a side effect of slowing me down to a point where approximately half of the class complained about it on student evaluations. as long as it was not more than half, i figured, job well done. I do not want to change the subject of discussion, but i a pretty sure earlier sevens looked like Z due to the Angle counting thing of arabic numerals 2:31 PM Heh. too fast/too slow is something where it's fine to split the difference. if half of the class complained about legibility i would see that as a problem to be fixed. nobody complained about that. angle counting thing of arabic numerals? that sounds made up. say more about that. @leslietownes It is totally made up. It is this idea that the number of angles in a numeral keeps track of the value of that numeral. If you squint your eyes real hard, it almost makes sense. this sounds like something my mom would have forwarded me after seeing it on facebook. Does not like each number written according to the amount of angles it holds. could have been a fake thing i read i dont know. You have to do some rather contorted things to make it work. Like... where are the angles in a 9? 2:35 PM i'm not a historian but it rubs me the wrong way, where i have a gut feeling that there's no way that that's true. although gut feelings can be both wrong and right. Well could be false, i will read that article. i am still trying to figure out our math problem.. or rather.. my math problem @MadSpaces Nobody write numbers that way. i mean, i did. because of my ancient arabic heritage. i guess i'll stop now if that sets you off. :D Anyway, I've got to go roust my brother from bed so he can go to work. And I should do some dishes. And make more coffee. 2:37 PM I learned this as i was in school in the middle east, and thats how i learned to write 9. But with time i started using the latin 9 @leslietownes The ancient Arabs didn't write their nines that way. :P you may have caught me in a falsehood. @MadSpaces Citation please? Google tells me that modern Arabic numerals are more like these. But Google lies. In any event, I really have to go. these are indians numerals, which some arabic countries use. Thanks for the help Xander Talk to you later 2 hours later… 4:11 PM > truth is a poetically elaborated "mobile army of metaphors, metonymies and anthropomorphisms" 4:22 PM @user85795 Context? Philosophy of language here sir 2 hours later… 6:21 PM Definitely a stupid question but I cannot find a reference for it and I can't figure it out myself: suppose I have a n-dimensional Gaussian distribution$\eta := p(x;\Sigma,0)\,dx$with covariance matrix$\Sigma$and zero mean. Then supposedly$\int_{\mathbb R^n}x_ix_j\,\eta = \Sigma_{ij}$. I don't understand why the covariance matrix has this property. Also, does this property change if we have a more general Gaussian with non-zero mean$p(x;\Sigma,\mu), \mu\neq 0$? Actually it might be as simple as defining covariance as$Cov(f(x),g(x)) = \int f(x)g(x)\eta$... Maybe I did figure it out.... ya it's just expected value, nevermind :( the benefit of asking questions here seems to be that i figure it out when i ask for help about it 7:06 PM hey there i have a question. I posted a question here but then I realized that it is more suitable dsp stack exchange. Is there a way to transfer the question there? @eet It is possible for moderators to migrate questions. However, we typically don't do this, unless we know that the question is likely to be well-received at the target site. On the other hand, you can delete your question here, and post it again on a different SE site. @XanderHenderson there is 40 min waiting time. can you please consider to transfer my last question? omg, a whole 40 mins? I don't know what question you are asking about, and it is unlikely that I would migrate your question, as, again, I am not going to migrate a question unless I know that the question will be well received on the target site. 7:22 PM migration does not put the question on the top of the front page, by the way so if you migrate a question that was last active 2 days ago, it will appear 2 days down on the target site so you're more likely to get the appropriate attention by deleting and re-asking there's a 1 hour waiting time; all i can say is you just have to live with it huge variation in what sites like and do not like in terms of questions. which is totally sensible to me but also hugely important in whether X might migrate to Y in its identical form. most of the time i migrate stuff it's just someone not knowing how to read the tour or site scope :D Hey everybody I have a quick question How do I write$4e^{-5t}$as sines and cosines? ı think I can use$i^2=-1$but I'm not sure 7:56 PM There are injective functions where not all elements in the codomain are mapped to. Is it possible for not all elements of the domain to be mapped (kind of opposite of above case)? What would that be called? Anyone who can link to some good lecture notes summarizing the properties of the little oh (and probably big oh as well) notation, in particular the algebra associated with it? I'd be grateful. Hi everyone. Are there any potential risks to posting a paper on arXiv? @M.ÇağlarTUFAN If you don't imaginary arguments, then$4e^{-5t}=4(\cos(5it)+i\sin(5it))$8:13 PM @Larry The word you are looking for, if I understand your question correctly, is "surjective" or "onto". If a function is both injective and surjective (one-to-one and onto), it is said to be "bijective". @A-LevelStudent What do you mean "risks"? @XanderHenderson I'm not sure exactly to be honest, I'm just thinking of putting something on there and I'm wondering if any harm could come of it. That being said, per CA Prop 65, I am required to warn you that arXiv contains a chemical known to the State of California to cause cancer. i think the cia keep an eye on arXiv lots of scammers on arXiv looking for potential fields medal material. 8:30 PM Is it true that you can never fully remove papers from arXiv? you can never truly remove anything from the internet it is believed that if your result involves the number$-{1\over 12}$then a suspect irish person may appear in your neighbourhood. Hi Thorgott. @Thorgott But will it remain public forever? 8:44 PM "Forever" is a long time. I believe that a pragmatic answer is "assume that it will remain visible until after you don't care any longer." @XanderHenderson I see. Thanks. 1 hour later… 10:09 PM @copper.hat$\sum\limits_{n=1}^\infty n=-\frac1{12}$What sum could be more natural? better check for leprechauns... Not only four leaf clover, but also four fingered leprechaun Hi, I have a quick question. Will the variance for$X>0$,$X \tilde N(0,1)\$ be 4?

:-) i'm not sure how 4 leaf clover because associated, the shamrock is an Irish symbo, not clover

1 hour later…
11:36 PM
Hey y'all, flags should be used for offensive and disruptive messages - not for messages asking for help. @BobSmith This isn't the right place to ask about people willing to tutor you - that's not what this site, nor this network is for.

Specifically, please only use flags for messages that are spam or violate the CoC that should be removed immediately (and warrant the 30 minute suspension that comes with it) - if a message requires moderator action, use a mod flag, and if a message is off-scope for the room or a user is being disruptive in a room, it is better to let a room owner or local mod know instead.

@cairdcoinheringaahing I would argue that requests for tutors are borderline spammy, and likely disruptive.
So, raising a flag is not unreasonable in this case.
Just don't be surprised if it is declined.

@XanderHenderson Then your ROs or mods should move/delete them. Flags raise the attention of all users with 10k+ reputation on chat, and shouldn't be used for messages that are "borderline"

@cairdcoinheringaahing I did delete it.
As a moderator of this site.
The flag is not entirely unreasonable, and I handled it.

@XanderHenderson Ah ok. I can't tell if it was deleted or flag-nuked :)

11:40 PM
@cairdcoinheringaahing I declined the flag and deleted the comment.

If a moderator deletes a message via normal deletion, does a pending flag get validated or declined?

But this kind of "Please tutor me" is a common form of spam---I would get a couple of these every month while I was in grad school. The distinction between "spam" and "legitimate cry for help" is hard to spot.

@hyper-neutrino Neither, I think.

@hyper-neutrino I declined the flag, then deleted the comment, so I don't know.

11:41 PM
@XanderHenderson Yeah. In these cases, I recommend regular users to ping a mod/RO for deletion, so that it attracts less attention

actually, once i nearly hired a guy named bob smith as my ceo
i need help, but probably not of the variety available here :-)

@copper.hat What help do you need?

i need someone to fund my bluewater sailboat

Good luck getting that help on SE :P

11:43 PM
@copper.hat Have you talked to Elon?

@Xnero I apologise, I am just messing, Xander knows I am just kidding.

@XanderHenderson I definitely agree. When I saw it I almost flag nuked it myself but I decided it was on the side of the borderline that I didn't consider spam. I was gonna write up a response telling them this is an inappropriate place but I forgot and then only remembered when the flag appeared.

Elon is not in my social circle

@copper.hat I hear that adding him on Myspace generally gets a response :P

@copper.hat You don't know Elon Jones? Ah, man, bruh! I got's ta introduce you!

11:44 PM
i helped a hs kid get some help once, but that was because i knew someone locally who could assist
i think i do know on elon from a long time ago

@copper.hat you’re beyond help,
2

that would seem to be the general consensus, hence my daughters label of fossil
but i have been very restrained in my PSQs lately

@hyper-neutrino Thanks for that!

yep, no worries - no clue why on earth it wasn't working but ¯\_(ツ)_/¯ chat broke

reviving a latent interest in the Navier Stokes equations
nothing to do with my afternoon fluid consumption

11:55 PM
Almost martooni-time.

tempting
something south american, chilled & white
i'm a simple man of tastes

I'm semisimple.

:-)