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user116211
12:00 PM
@heather example: Partial ordering.
 
user116211
Not all pairs are comparable.
 
@MAFIA36790, what is that?
 
user228700
@JohnRennie Do u like to cycle a lot?
 
(::googling::)
 
user116211
@heather I can tell if you want.
 
12:02 PM
@MAFIA36790, sure, yeah.
 
user116211
Let $(S, \preceq)$ be an ordered set.
 
user116211
If not all pairs are connected, then $\preceq$ is a partial ordering.
 
I think that makes some sense...thanks!
 
user116211
Connected means $\forall a,b \in S: a\ne b \implies (a,b)\in \mathcal R ~\lor~ (b,a)\in \mathcal R$ where $\mathcal R$ is a relation.
 
@heather why are you up?????
 
12:08 PM
@0celo7, school, sadly. I get up at 6am on weekdays.
 
?????????
 
Have to leave in a minute to catch the bus.
 
Why do we do this to our children
 
@0celo7, I have no idea.
 
@heather you should drive
 
user116211
12:08 PM
@0celo7 We had to go to school at 5:30 am :(
 
@MAFIA36790 Nothing India does is shocking any more, sorry
 
user116211
In winter, it was delayed to 7 am.
 
user116211
@0celo7 ohh ._.
 
@MAFIA36790 Kelley is not basic
 
@0celo7, dude, don't have my learner's permit yet
 
12:10 PM
@heather You should learn real analysis first
 
got to go, thanks everyone
 
not topology
real analysis motivates topology
 
user116211
@0celo7 yeh, you told me earlier.
 
not blind yet
 
user116211
@0celo7 Then it's not cancer.
 
12:15 PM
engineers are the worst when it comes to math
 
user116211
Maybe signs of cataract.
 
So I'll need laser surgery?
 
user116211
I'm not a medical guy.
 
user116211
You are not old; so may be that can be ruled out.
 
user116211
0
Q: Passing a wall when travelling at a very high speed

Vaibhav SharmaI want to know whether it is possible to escape through a wall or any solid obstacle while travelling at a very high speed,greater than speed of light.Is there any relation between speed,mass and wall force so that if someone achieved that ratio may escape the wall?

 
user116211
12:20 PM
Flash can does that.
 
Omg you're obsessed with him
I agree he's kinda cute but dude
 
user116211
No.
 
@bl00 I summon thee
Also I should do homework
@ACuriousMind Dude let's change our avatars
 
user116211
@0celo7 Why? Your current one is the best of all your prev avatars.
 
user116211
12:34 PM
Good.
 
user116211
Any more?
 
user116211
hmm; okay.
 
@ACuriousMind Not interested?
 
I don't think I'm tired of Triss yet
 
12:40 PM
@ACuriousMind So I started the Sierra Madre DLC
Seems pretty boring tbh
Does it get better?
I found God and got him to come with me
@ACuriousMind Is there a level cap in this game?
 
@0celo7 Yes, $30 + (5\cdot \text{number of DLCs installed})$.
 
Weird. I can't seem to go beyond 29.
The exp bar doesn't increase any more.
 
Maybe something went wrong when activating the DLCs. It is Bethesda's crappy engine, after all :P
 
lol yeah
hmm, what to do now
Maybe I shouldn't play video games with this eye
I really should be learning algebraic topology
 
12:56 PM
@ACuriousMind I think I might be an analyst, not a geometer.
 
1:18 PM
Hi guys! @ACuriousMind why in extended-susy one usually take N<= 8 and not higher values?
 
@FrancescoS The maximal $\mathcal{N}$ is dependent on the dimensions of the spacetime. You must examine the "smallest" multiplet possible (the one with the lowest spin) for a SUSY algebra with a given $\mathcal{N}$ and make sure that it doesn't contain any particle with spin greater than 2 and that the only spin 2 particle is the graviton.
 
@ACuriousMind why no spin greater than 2?
 
@0celo7 which one is that one from?
Arnold?
 
@FrancescoS There are no consistent QFTs with spin-greater-than-2 and spin-2-and-not-graviton fields. It's called the...Weinberg-Witten theorem, I think
 
@ACuriousMind Also for massive higher-spin particles?
 
1:28 PM
Why are people hating on Newton, for his standing on the shoulders of giants quote?
 
@FrancescoS Yes, it has nothing to do with whether they mediate forces or not. They'd have to couple to Lorentz- and gauge-invariant conserved currents, and the content of the theorem is exactly that there are no such currents for spin > 2.
 
user116211
Newton was such a jerk. — MissMonicaE 1 hour ago
 
user116211
they are trolling.
 
@ACuriousMind Ok, thanks. Now, look at arxiv.org/pdf/0907.2441v3.pdf at the beginning of pag.7. They use an extended SUSY for generic N and they conclude that the higher-spin super partners of the Goldstino field generates multi-particles states (and then consistency ) . Do you have any idea of that?
My question arises form this paragraph
 
@FrancescoS That's about "in finite volume". I don't think that the Weinberg-Witten arguments hold in finite volume.
And I don't know much about QFT in finite volume, only that many other no-go theorems of QFT also fail there
 
1:38 PM
@ACuriousMind but they say "the finite volume intuition is still valid", do you think the mean "the conclusion is the same also in the infinite volume case"?
 
@EmilioPisanty yes
 
@FrancescoS Yes - they explicitly say that also in infinite volume, the superpartner will create a two-goldstino state. I'm not actually sure what the problem is
 
@ACuriousMind so in this case I could take N > 8...
My problem is that from this conclusion it is not clear that N>8 is forbidden. I mean, if the higher-spin super partners are just multi-particles states, I don't care if they have spin greater of 2. not?
 
@FrancescoS Yes, if for some reason you can argue that the higher-spin states are not states of fundamental particles, then yes. The restriction on $\mathcal{N}$ is meant for standard SUSY field theories where everything in the multplet is supposed to be a fundamental field.
 
@ACuriousMind Thanks ;)
 
1:45 PM
hey, @ACuriousMind, you remember this one?
15
A: Photons with half integer angular momentum - what's happening?

ACuriousMindNothing is happening. At least, nothing except that a new generalized quantity suggestively called "angular momentum" was defined and subsequently measured. But nothing we know about the usual angular momentum of photons is changed by this in any way. Standard total angular momentum is $J = L + ...

 
@EmilioPisanty sure, what about it?
 
@ACuriousMind I'm trying to go through it in a bit more detail
might use it for nonlinear opticsy stuff
not sure how they actually make the fields in question
> Photons in a variable superposition of two angular momentum eigenstates |j = ±1/2〉 can be generated from the Gaussian input beam using a linear polarizer (LP), a quarter–wave plate (QWP), and a biaxial crystal (BC).
and also
> As shown in Fig. 1, the light is first elliptically polarized before passing through a biaxial crystal, leading to a superposition of angular momentum eigenstates. The amplitudes in the superposition are controlled by the angle of the QWP, $\theta_{qwp}$, with the beam varying from purely $|j_{1/2} = 1/2〉$ to purely $|j_{1/2} = −1/2〉$ as the QWP rotates by 90°.
 
2:02 PM
Oh, I just read the theoretical part, I think. No idea how the experimental setup actually worked, sorry
 
@ACuriousMind fair enough =/
still, doesn't make sense to me
they're claiming that an elliptically polarized gaussian mode going through a "biaxial crystal" (i.e. just a birefringent plate?) will magically look as in the inset
 
user228700
2:54 PM
@JohnRennie: So, do you like cycling?
 
@Kaumudi I don't cycle for a hobby, only as a form of transport. But I do enjoy cycling.
 
user228700
Ah, OK...
 
I find cycling to be nice level of exercise. I find running is too intense, and to be honest as I get old and rickety running puts too much strain on my knees. And it's nice to feel the wind in your hair as you whizz along ona cycle.
 
3:30 PM
Has anyone here read through The Feynman Lectures (at least the first 2 volumes) ?
 
user218912
@0celo7 yes?
 
user218912
I slept in because I forgot to set an alarm and it was dark.
 
user218912
missed qft...
 
user228700
@JohnRennie It sure is :-) I cycled to school for 6.5 years.
 
user228700
(That's about 8 Kms everyday, so not much, but yeah, so many years :-D)
 
3:39 PM
@Kaumudi I used to cycle to school as well, and I must admit I didn't enjoy that much. I think there's a difference between cycling because you want to and cycling because you have to :-)
 
user228700
@JohnRennie Again, I'm unable to discern the two. Okay, it was very stressful during the morning time, when I was usually always late, but coming back was always fun :-) Half of my journey was inside the IIT campus, which is mostly just forest and very few vehicles so I didn't have to deal with traffic that much.
 
user228700
Still, it was definitely more enjoyable when I could go wherever, without worrying about being late for assembly or whatever.
 
I think when I was a schoolboy there always seemed to be so many more important things to do, and time spent cycling seemed like time wasted. Now I'm (semi) retired cycling seems like an excellent way to use up the copious amounts of free time I have :-)
 
user228700
Hm, I see :-)
 
@JohnRennie you should read Wald in your copious free time
 
3:48 PM
Yes. I should. But if I were going to read a textbook it would be one on quantum field theory rather than GR.
Instead of either I read Sci-Fi, which is less educational but more relaxing.
 
user218912
@JohnRennie you're not even that old, you can still learn stuff just as well as anyone.
 
scifi real
bonus point for cool sounds
 
@bl00 I find these days I'm less interested in detail, but more interested in getting a big picture view of a subject. I'd really like to have an intuitive understanding of QFT in the same way I've managed to get an intuitive view of GR. But no QFT book I've ever started has managed this for me.
 
user218912
@JohnRennie lancaster qft? did you read that one?
 
user218912
I found it really intuitive.
 
3:54 PM
You mean QFT for the gifted amateur?
 
user218912
yes
 
user228700
Hey, what happened to Ice Lord?
 
@bl00 I've got the book, and I've started reading it a few times but always got bored and given up. I will read it one day!!
 
user218912
@Kaumudi it's me
 
user228700
@bl00 Aaah! I've been meaning to ask for a long time. OK, hi :-P
 
user218912
3:57 PM
@JohnRennie I think it's a pretty good book to learn QFT from for the first time.
 
user218912
@Kaumudi hey
 
user218912
well time to go to class bye guys
 
user218912
wait before that @0celo7 did you need anything? you pinged me earlier
 
user228700
4:25 PM
@JohnRennie: Halp!
 
user228700
Are u busy atm?
 
What is it with this word halp? Is this some cool teen speak with which we old timers are unfamiliar?
But assuming it means help then no I'm not busy, though i've recently eaten a large lunch so I'm sleepier than usual :-)
 
user228700
@JohnRennie No, I think it's just supposed to be me SHOUTING help so it kinda sounds like halp?
 
user228700
I might be completely wrong tho :-P
 
Anyhow, what's up?
 
user228700
4:27 PM
Bond angles. Again.
 
user116211
@JohnRennie internet slang.
 
@Kaumudi Yes?
 
user116211
Anyways, I have just encountered an edit where US version words were changed to UK version words.
 
user228700
So I'm trying to understand how various factors change the bond angle of molecules. U'd be able to help, no? (Pls pls pls :-P)
 
user116211
Since the main edit was relevant, I approved it.
 
4:30 PM
@Kaumudi yes of course
But bear in mind that all the rules for how bond angles change are rather qualitative ...
 
user228700
Bond lengths. How in the world would they affect bond angles?!
 
Suppose you have a molecule $AB_2$ and the two $B$ atoms are large. That means the B-A-B angle may be increased because the two B atoms bump into each other.
 
user228700
Huh. OK, this is the same as something I read on a post.
 
user228700
OK, it makes sense.
 
For example in diiodomethane the I-C-I bond angle is greater that 109.5 because the two iodine atoms simply can't get close enough to make the angle that narrow.
But if you increase the bond length you can get the atoms closer together and therefore decrease the bond angle.
 
user228700
4:37 PM
Yeah, OK, this makes sense...
 
user228700
:-) Alright, I've already discussed quite a lot of points with DHMO over at CSE Chat. The last point is about:
 
user228700
 
I'd guess that's also down to the size of the atoms. The $PX_3$ molecule is like a pyramid with the P at the top. As you make X bigger, e.g. going from Chlorine to Iodine then the X atoms push each other and widen the bond angle.
 
Wtf someone in QM asked for a hard exam
 
user228700
@JohnRennie The atoms push each other..?
 
user228700
4:42 PM
@0celo7 Good luck!
 
It's tomorrow
I don't know how to study
 
user228700
Oh, wow :/
 
@Kaumudi I mean as the size of the X atoms increases you can't squeeze the X atoms closely enough together to keep the bond angle the same.
 
user228700
Hey, what happened to ur eye?
 
Haven't been to the doctor yet. Two hours
 
user228700
4:45 PM
@JohnRennie Hm, OK...
 
user228700
@0celo7 Ohk...
 
user116211
@0celo7 Dude, don't die being blind :(
 
I have a damn appointment
Chill
 
user116211
:)
 
But then the $NF_3$ bond angle is less than $NH_3$, which shows how dangerous these arm waving arguments are.
 
user228700
4:46 PM
Hm, I guess if I keep the basic concepts of VSEPR in mind, I'd be able to figure out all this about bond angles...
 
Lol
Chemistry is arm waving
Even worse than physics
 
user228700
Oh, totally x-(
 
3
Q: Why the bond angle of PH3 is lesser that that of PF3?

AneekWe can explain why the bond angle of $\ce{NF3}$ (102°29') is lesser than $\ce{NH3}$ (107°48') by the VSEPR theory, since lone pair lone pair repulsion is greater than lone pair bond pair repulsion. Then for $\ce{PH3}$ and $\ce{PF3}$, also, it is expected that the bond angle of $\ce{PF3}$ will be ...

 
user228700
@JohnRennie Yes, but I think (Oh, I do hope) that I can provide sound reasoning for these exceptions now...
 
Hmm, yes, are you familiar with the term post rationalisation :-)
 
user228700
4:50 PM
@JohnRennie Sheepishly smiles Hehe.
 
> Because of (3), an instanton in a p-brane will be an magnetic source of $H^{12−p}$ or electric source of $H^{p−2}$). This generalizes the result of [9], for the solitonic 5-brane constructed from a type I instanton (p = 9), to general p. It motivates a generalization of Witten’s proposal: the zero scale size limit of the instanton in a p-brane will be a Dirichlet p − 4 brane, bound to the p-brane.
Either I or the author fail at basic arithmetic here
 
user228700
Ah, back bonding :/
 
user228700
God, I'm starting to hate Chem. more than I hate Biology!
 
@ACuriousMind why?
@Kaumudi don't do chemistry then
 
Hi @TheLoneMilkMan. What brings you to a physics chat room?
 
user228700
4:53 PM
@0celo7 I have no choice. Sigh.
 
If the brane is supposed to couple to $H^{12-p}$ ($H^{p-2}$), then the field strength $F^{13-p}$ ($F^{p-1}$) must be able to be integrated over the brane, i.e. the brane must itself have 13-p or p-1 dimensional worldvolume. But a p-4 brane has p-3 dimensional worldvolume.
Either I'm completely misunderstanding the reasoning, or the p-4 claim just doesn't follow
 
@Kaumudi to be fair all these arm waving rules are popular at school level but ignored at university.
 
Where does the 13 come from?
 
@0celo7 differentiating raises dimension by 1, no?
 
@JohnRennie Either we're low on milk, or physics.
 
user228700
4:54 PM
@JohnRennie Just. So. Ugh. Okay, I'm going to bed.
 
Ah right
Where does the 12 come from :P
 
@Kaumudi see, that's why I ended up in physical chemistry. It's a lot more logical and mathematical.
 
so the gauge potential is a 12-p form?
 
those arm waving rules only work in first order. After that, everything is calculating transition states and energy manifolds in order to predict what those species are doing
 
@Kaumudi Biology is very awesome.
 
4:56 PM
Because the dual of a p form in 10D has dimension $10-p$, so the dual of the $p-2$ form has $10-(p-2)$. Why it's p-2 is in yet another paper I don't really wish to open because I'm already like four papers deep trying to understand this (originally rather tangential)claim :P
 
user228700
@JohnRennie It is, and I have always like physical chemistry more.
 
I also like the rigor of physical chemistry, but for some reason I also have no problem arm waving with organic chemsitry arguments
 
This is an interesting question:
2
Q: Trajectory of safe descent into a black hole

Naveen BalajiIs there any specific trajectory that an object can take in a black hole without it getting spaghettified? I am aware that the intance gravity of a black hole would rip apart any object if it falls into one, but would there be any points or paths in the black hole's gravitational field that does...

 
Hm, wait
 
@ACuriousMind well are you dualizing the field strength or the potential?
 
4:56 PM
in fact, among my peers, I am very rare in being a person who like BOTH organic and inorganic chemsitry
most of my peers have a preference of one or the other
 
@0celo7 Yeah, I just realized that might be where the problem is
 
user228700
@DanielSank I imagine that Biology is a okay! Just not my cup of tea.
 
It's presumably possible to calculate the tidal force in the rest frame of the infalling observer, though offhand I don't know how to do it. But how will that tidal force depend on the geodesic they follow towards the singuilarity?
 
@Kaumudi A good physicist with interest in biology can be a very effective researcher.
 
I am also rare among my peers to be a physicist that is not disgusted by biology
 
4:58 PM
@JohnRennie it won't, it should depend on the point
*point alone
 
All of this is one reason I will have many question marks whenever PhD comics that mention the wars between the fields were shared
 
@0celo7 Proof?
 
because to me, all science exists in harmony
 
Tidal force is the GR version of sectional curvature
 
user228700
@DanielSank I am very interested in some parts of biology :-) I was just exaggerating before. I don't hate it or anything, but again, I don't love it either. How is this so? (About the research thing)
 
4:59 PM
And perhaps not long coporate finance and politics will soon join the party along with culture and art
 
Now, the usual dualizing would be - $H^p \to F^{p+1}\to ({\star}F)^{9-p} \to \tilde{H}^{8-p}$
 
oh wait it's not normalized
@JohnRennie stop distracting me
 
user228700
@Secret :-)
 
@ACuriousMind what is H?
 
Yeah, that paper has totally messed up the dimension counting
 
5:01 PM
@Kaumudi Well, it's just that biologists and medical researchers are not trained in the same experimental and theoretical techniques as a physicist. A friend of mine is in bio-chemistry, and her lab has zero people who know basic electronics. Yet, they're trying to build "lab on a chip" characterization devices.
 
@0celo7 Some gauge potential form
 
A physicist or engineer with real lab, metrology, and analysis skills can bring a lot to those fields.
 
@DanielSank are you a microbiology cup of tea person?
 
Hm, maybe I'm not understanding how exactly the instanton is supposed to be a "source", though
 
user228700
@DanielSank Hm, OK, I see ur point...
 
5:02 PM
So I have a stupid question. Is the gauge potential in string theory not a connection?
 
user228700
Anyway. I should really go not talk for 7 hours now. Bye! :-)
 
@0celo7 Only if you define "higher geometry" and "higher connections", cf. nLab for more on that craziness :P
 
Sigh
What???
 
Ahaaa, I had been misreading eq. (3)
 
@Secret I think biology is interesting at all levels.
 
5:04 PM
me too, though my interest is much stronger for ecolology and microbiology
(one big one small ,lol)
 
Okay, now I understand the p-2 instead of p.
 
I like plants very much, and I like learning about and observing interesting animals.
I am always fascinated by plants, particularly that they eat sunlight. That's just amazing.
I find natural selection to be a very interesting subject, and I consider it a sort of "fundamental law" of the universe.
 
@ACuriousMind you must have been really stuck to have complained in chat :P
 
yeah, especially when you realise plants knew how to use entanglement photsynthesis a long long time before we humans knew it existed.
Animals are also interesting. I like birds mainly, but I also like to watch individual insects
 
Rubber ducking by typing in here does help :P
And I'm still stuck because I still don'T get the p-4 :P
 
5:09 PM
@Secret I still don't buy that, actually. Has anyone proved that there's anything coherent in photosynthesis?
@ACuriousMind I actually bought a rubber ducky for my office.
 
Proof?
 
I am not sure, I have not followed up much on its recent development, because I am too deep in group theory and topology in the current month. The last thing I heard from my biophysicists professors is that there is some kind of long term coherence in the photosystems, but that piece of news is about 5 months ago
 
@Secret If you have a reference for that I'd like to read it.
Last time I really paid attention to this, the argument was that the speed of transport was faster than you'd expect for a diffusion process.
 
Arrrrgh, I hate people who don't state what their variables denote. This author is using $H$ for the field strength. Which it also often denotes -.-
 
However, since photosynthesis carries the photon only a small number of steps, diffusion (which is a continuum and large step number limit) shouldn't apply in the first place.
If you look at particles moving around in a gas/liquid, on short time scales the motion is expected to be faster than the diffusive limit.
@ACuriousMind Preaching to the choir, bro.
 
5:15 PM
@ACuriousMind I don't understand what the issue is
 
@DanielSank In retrospect I think their notation is actually the more common one; still this cost me an unreasonable amount of time to figure out
 
user116211
 
studying hyperbolic geometry recently?
 
user116211
No.
 
user116211
5:23 PM
Saw this while editing a post.
 
user116211
0
A: Is it possible to say we are inside a black hole?

Lawrence B. CrowellThere is a lot in this question, and some of this is not answerable or I don't think the writer of the question has some of the right concept of things. However, it is not entirely impossible that the universe is in some respect the physical product of a black hole. The Maldecena $\rm AdS/CFT$ co...

 
6:11 PM
@ACuriousMind I can't parse this message :P
 
@Danu I earlier said $H$ should denote a gauge potential. The "which it also often denotes" is intended to be an admission that I might have jumped to conclusions in this case
 
Ah.
I didn't see the $H$ should be a gauge potential thing
 
Any idea whether the octonions have a co-algebra structure, and if yes, which one?
 
No idea.
 
I have found out why calibrated 3-folds inside a 7D $G_2$-fold are called associative, now I'm trying to figure out why calibrated 4-folds would be called coassociative.
 
6:14 PM
Should probably be what you need
"calibrated"?
 
@ACuriousMind oh but when I say the exact same thing I get no response
Nice!
 
The "wayback machine" applied to the first (defunct!) link suggests that Kock's book on Frobenius algebras has the answer.
Then I'm willing to bet that the answer is yes because Frobenius algebras have a coalgebra structure.
 
@Danu An d-dimensional submanifold $\Sigma$ is called calibrated if there's a calibration d-form $\omega$ such that $\int_\Sigma \omega = \mathrm{vol}(\Sigma)$. (a form is a calibration form if it's always less than or equal to the volume of any submanifold when integrated)
 
Nope, Kock's book doesn't mention octonions.
@ACuriousMind And it's still nonzero everywhere, or what?
Else the zero section would work
 
@Danu The zero section wouldn't have any calibrated manifolds, so it would be useless
 
6:19 PM
@ACuriousMind Still would make for a sloppy definition :P
 
@Danu I'm reading physics papers here :P
 
3/10
 
@Danu ok I definitely recognize his music
 
plz cloz dis qtion
0
Q: Theoretical estimation of vacuum energy of the universe

NionIt is said that there is about $120$ order of magnitude discrepancy between the theoretical and measured values of the vacuum energy. My question is, how does one calculate, theoretically, the total vacuum energy of the universe? My understanding of vacuum energy is that it is the ground state en...

 
Hey ACM, can I ask you a question?
 
6:22 PM
Don't ask to ask
Wtf is wrong with you
 
@0celo7 jeez
@ACuriousMind Do you know of any metrics in which black holes have an upper mass limit?
 
Ahaaaa
Just like the associative folds are fixed points of involutions, the coassociative folds are fixed points of anti-involutions
 
Btw TIL the equivalent for black holes in Newtonian mechanics is a "dark star"
A dark star is a theoretical object compatible with Newtonian mechanics that, due to its large mass, has a surface escape velocity that equals or exceeds the speed of light. Whether light is affected by gravity under Newtonian mechanics is questionable but if it were accelerated the same way as projectiles, any light emitted at the surface of a dark star would be trapped by the star's gravity, rendering it dark, hence the name. == Dark star theory history == === John Michell and dark stars === During 1783 geologist John Michell wrote a letter to Henry Cavendish outlining the expected pr...
Crap
 
@SirCumference I've never heard about an upper limit on a BH mass
Then again, I don't care much about black holes and don't know much about them
@Danu get a gold QFT badge and close it yourself!
 
Darnit
Who knows about em here?
 
6:32 PM
@ACuriousMind Eww
Ain't nobody got time :(
@ACuriousMind What's an anti-involution? Square to -1?
Also I hate using "folds" for manifolds :P
 
@0celo7 Can I ask you a question?
 
@Danu No, it means it's an anti-homomorphism.
(that squares to 1)
 
@ACuriousMind Homomorphism? Of what
Anti-homomorphism---what does that even mean
 
@Danu It inverts the order of multplication!
Nothing more
That is, $f(ab) = f(b)f(a)$
 
Homomorphisms of what?
 
6:41 PM
@Danu in this case, algebras
 
@ACuriousMind I thought you were talking about submanifolds
 
Ah, okay :D
The terminology "(co)associative submanifolds" is motivated by the fact that if one takes $\mathbb{R}^7$ as the local model of a $G_2$-manifold and identifies it with the imaginary part of the octonions, then these submanifolds correspond to the fixed loci of (anti-)involutions of the octonions.
 
ah
 
What is a G2 manifold?
 
A manifold whose holonomy is (a subgroup of) $G_2$, one of the exceptional Lie groups
 
6:54 PM
@ACuriousMind I know what G2 is
 
Oh yeah? So define it :D
 
@Danu Automorphism group of some 3 form on a 7 dim vector space
 
That sentence makes no sense.
You tried to copy what I said, but failed :D
 
Or something something isometry group of octonions
@Danu sucks for you then
 
no, for you :)
 
6:57 PM
I've never needed G2, so actually it doesn't matter for me
 
Don't fight plz
 
If I do need it, I'll google
In any case, I did once know but I have Alzheimer's
 
:'(
 
I'm trying to get in the Guinness book btw
But when I called them they said to stop smoking pot and my memory will improve
 

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