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0celouvskyopoulo7
0celouvskyopoulo7
12:36 AM
@Slereah to be fair it's a pretty garbage book
but just about the only place where one can find these results
 
nbro
nbro
1:01 AM
hey
 
0celouvskyopoulo7
0celouvskyopoulo7
1:20 AM
900 page sobolev space book
 
nbro
nbro
1:37 AM
Anyone here has ever had to implement a numerical algorithm where angular velocities were involved?
 
0celouvskyopoulo7
0celouvskyopoulo7
2:26 AM
@dmckee writing a DoE report
it's terrible
 
 
3 hours later…
Albert Einstein
Albert Einstein
5:39 AM
@JohnRennie
 
John Rennie
John Rennie
@AlbertEinstein Morning :-)
 
Albert Einstein
Albert Einstein
@JohnRennie, A very good morning. How are you?
 
John Rennie
John Rennie
Pretty good thanks, and yourself?
 
Albert Einstein
Albert Einstein
I am fine, too
@JohnRennie, when does a man in the lift weigh more, when the lift accelerate upward or downward?
 
John Rennie
John Rennie
@AlbertEinstein This should obvious from your own experience. Do you feel heavier or lighter when the lift starts moving upwards?
 
Albert Einstein
Albert Einstein
5:45 AM
Lighter when it goes upward, is it?
 
John Rennie
John Rennie
Look at it this way. Suppose the lift starts accelerating downwards at 1g i.e. 9.81 m/s². What would you feel then?
 
Albert Einstein
Albert Einstein
@
@JohnRennie, heavier
 
John Rennie
John Rennie
If you jumped off a cliff you'd start accelerating downwards at 9.81 m/s². So if the lift is also accelerating downwards at 9.81 m/s² it means the lift isn't supporting you at all. You'd be falling as if you had jumped off a cliff.
 
Albert Einstein
Albert Einstein
::
 
user228700
6:06 AM
@JohnR: Morning :-)
 
John Rennie
John Rennie
Morning :-)
You must be about to jump on the train by now.
 
user228700
No, no. 11 hours to go...
 
John Rennie
John Rennie
Wow, you board the train around midnight?
 
user228700
10 PM!
 
John Rennie
John Rennie
Then travel overnight. That's a killer journey! Is it a sleeper train or do you have to try and sleep in the seat?
 
user228700
6:12 AM
Yes. Is "killer" a good adjective?
 
user228700
No, the train has berths to sleep in but they're not very comfortable.
 
John Rennie
John Rennie
@Kaumudi.H well, hopefully not. Though if it's literally true you won't be worrying about the exam results :-)
 
user228700
Ah, haha, yes :-) The train is too shaky, a bit too hot and the berth is terribly thin to have a good night's sleep.
 
user228700
Remember the two times I said "I'mma go to the town today"?
 
John Rennie
John Rennie
Yes?
 
user228700
6:23 AM
I wasn't able to go both times because I'm not allowed to roam around here on foot by myself -_-
 
John Rennie
John Rennie
Presumably due to concerns about attacks on women?
 
user228700
No, not even attacks. The people in this village... gawk. A lot.
 
John Rennie
John Rennie
That seems harmless enough, if a bit unsettling. Is the village society that different to Chennai? Do they have rules about unaccompanied young women?
 
user228700
No, they don't have rules but if I walk around wearing sweatpants and a T-shirt, they'll gawk like crazy. Gawk, whisper among themselves, etc.
 
user228700
It's a bit strange and new to them, that's all; women here wear drastically different sorts of clothes.
 
user228700
6:28 AM
In any case, yes, my parents don't want people gawking so yeah, wasn't allowed.
 
user228700
But my dad's taking me out in a bit! (What a lengthy segway!)
 
John Rennie
John Rennie
To be fair it probably wasn't that different here in the UK 50 years ago when teenagers first started wearing radically different clothes.
 
user228700
Yes, I suppose...
 
John Rennie
John Rennie
Though these days you could wear pretty much anything and people would just shrug.
 
user228700
Hmm, yes, OK :-)
 
John Rennie
John Rennie
6:31 AM
So this week you've endured rubbish train and bus journeys, done an exam, and spent the rest of the time effectively in prison!
 
user228700
That's one way to put it, yes :-P
 
John Rennie
John Rennie
... being starved :-)
 
user228700
Haha, no, that would be a bit harsh; I've been well-fed and all but I haven't been liking the food is all :-)
 
John Rennie
John Rennie
I used to be very fussy about food when I was young, but these days I'll eat anything. Yes, there are my favourite foods and foods that I'm not keen on, but at the end of the day food is food and is always better than no food.
 
user228700
> anything
 
user228700
6:35 AM
Oh, I know :-P
 
John Rennie
John Rennie
My sister in law used to work in the Ukraine, and the cooking there is, erm, different.
At one meal she was served cubes of pork fat stewed with cabbage, and she had to eat it to be polite.
 
user228700
That's, erm, wow :-|
 
John Rennie
John Rennie
Yes, that's what she said. Though she expressed herself rather more forcefully :-)
 
user228700
:-/ I...see.
 
John Rennie
John Rennie
If it's too traumatic to discuss I understand, but I'm curious about how th food is different from what you'd eat in Chennai.
The pictures of food you've posted in the past are pretty much what I understood vegetarian Indian food to be. So how does it differ in Kerala?
 
user228700
6:40 AM
Haha, you're being overdramatic! :-) It's certainly not traumatic at all.
 
user228700
Oh, it's not too different from what my mum makes.
 
user228700
Not different at all, actually. It's just the my grandma makes it all in some other way and the end-product doesn't end up tasting just as good.
 
John Rennie
John Rennie
Ah OK, so it's more that the flavours and or textures are different enough to be unappetising?
 
user228700
Sort of, yes.
 
user228700
I'm trying my very best not to be bitter about the food, of all things.
 
John Rennie
John Rennie
6:43 AM
My brother's mother in law (my aunt in law?) is a terrible cook and going for meals at her house is always a bit of an ordeal :-)
Especially as my mother and brother are both excellent cooks.
 
user228700
Ah :-) That's a bummer.
 
John Rennie
John Rennie
:: shrug ::
 
user228700
Right, I gots to go to the town (at last!)
 
John Rennie
John Rennie
We don't eat there often, and as I've said food is food.
@Kaumudi.H Have fun! :-)
 
user228700
Food is foot, yes :-)
 
user228700
6:49 AM
@JohnRennie Bye! :-)
 
Slereah
Slereah
9:47 AM
Now to prove that the musical isomorphisms have components $f_{\mu} g^{\mu\nu}$
 
John Rennie
John Rennie
10:14 AM
@ACuriousMind: well the photon is a massless boson - not a scalar but still a boson - so that seems a reasonable question, if a little ill informed.
 
ACuriousMind
ACuriousMind
@JohnRennie I consider the question utterly lacking in research effort. It's a "reasonable" question, but finding out that the photon is described by quantum electrodynamics where it's associated to a vector field should not be hard for someone reading a book on conformal field theory.
 
John Rennie
John Rennie
@ACuriousMind I must admit I agree with you on this. But in that case I would say so in comment to make it clear what you mean.
 
ACuriousMind
ACuriousMind
On the other hand, if the asker is aware of QED and just wondering whether a conformal massless scalar field might somehow be an alternative description, the question is lacking severely in elaboration.
If it's the former case of no research, then the question is unsalvagable. If it's the latter case, it can be salvaged by answering the comment I posted.
 
Slereah
Slereah
10:31 AM
I just used the term "currying" in a physics thing
Is that widely known enough to not have to explain it
 
John Rennie
John Rennie
As in currying favour?
 
Bernardo Meurer
Bernardo Meurer
I could not do a single question in my Physics exam yesterday
 
ACuriousMind
ACuriousMind
@Slereah Pretty sure it would be better to explain it unless your target audience is computer scientists :P
 
Slereah
Slereah
As in mapping a function of two arguments $f$ to a function of one argument $f(x, -)$
since that is the process by which one obtainds a mapping from vectors to one-forms
 
ACuriousMind
ACuriousMind
That's partial application, not currying
 
Slereah
Slereah
10:36 AM
isn't that what currying is
 
ACuriousMind
ACuriousMind
Currying is making a function $X\times Y \to Z$ into a function $X\to\mathrm{Functions}(Y,Z)$. What you're doing is currying the function and applying it to a specific $x$.
 
Slereah
Slereah
ah alright
 
Secret
Secret
 
ACuriousMind
ACuriousMind
Outside of contexts where the "nature" of functions plays a role, you shouldn't feel the need to use the word currying, since humans are pretty good at "automatically" doing that
 
Slereah
Slereah
I used to be big into lambda calculus so I got a lot of curry on my mind
 
ACuriousMind
ACuriousMind
10:38 AM
That is, just writing $f(x,-)$ is easier than explaining the abstract notion of currying.
 
user228700
@BernardoMeurer What? You're kidding, right?
 
Bernardo Meurer
Bernardo Meurer
@Kaumudi.H Nope
I got a nice fat 0
 
user228700
Dude. Geez, that sucks, man :-/
 
Slereah
Slereah
sorry, that grade is too low, we'll have to ban you from the chat
you'll have to go to the humanities chat now
 
user228700
@Slereah Quit bashing the humanities branch!
 
John Rennie
John Rennie
10:41 AM
@BernardoMeurer: for a computer engineering course you seem to have to do a lot of maths and physics. Not easy maths and physics either.
 
Slereah
Slereah
What if I do it in song
 
Secret
Secret
8
Q: Is there any exception to the law of "Cause and Effect"?

AminI've heard that 'God' is the only exception to the law of Cause and Effect which means that He is not dependent in His existence on anything. Can it be philosophically true? If we accepted this exception how could we make sure that the law would not be broken once again? Can we even call it a phi...

causation
A world without causality is a strange place
 
Bernardo Meurer
Bernardo Meurer
@JohnRennie My course is really bonkers
 
John Rennie
John Rennie
Does the physics course matter? Can you just ignore it and proceed anyway?
 
Secret
Secret
It is a place where only correlations exists, but no way of explaining things (because you don't have the notion of A lead to the occurence of B
 
Bernardo Meurer
Bernardo Meurer
10:42 AM
It's driving me crazy, I'm transferring out of here, this place makes me loose my hair
 
Slereah
Slereah
I wonder what Tom Lehrer's thesis was about
let's see
 
Bernardo Meurer
Bernardo Meurer
All my courses matter, I must pass all of them always
Alas there's still 2 more exams where I can replace my grade
 
Slereah
Slereah
R. E. Fagen and T. A. Lehrer, "Random walks with restraining barrier as applied to the biased binary counter," Journal of the Society for Industrial and Applied Mathematics, vol. 6, pp. 1–14 (March 1958) MR0094856
T. Austin, R. Fagen, T. Lehrer, and W. Penney, "The distribution of the number of locally maximal elements in a random sample," Annals of Mathematical Statistics, vol. 28, pp. 786–790 (1957) MR0091251
Stochastics
 
John Rennie
John Rennie
@Kaumudi.H how was town?
 
Secret
Secret
Annals? (glad they have not mispelt it losing one more n)
 
user228700
10:44 AM
@JohnRennie Oh, it wasn't much :-) I had an ice-cream and a lemon soda. The scenery is beautiful, as always.
 
Balarka Sen
Balarka Sen
I am so bad at doing actual computations.
 
Slereah
Slereah
 
Balarka Sen
Balarka Sen
lol
That's pretty actually accurate for me.
 
Slereah
Slereah
Feynman was the guy who did mental calculation as a hobby
A great party trick
 
Balarka Sen
Balarka Sen
Yeah. Also cool integral computations etc
 
Slereah
Slereah
10:49 AM
I guess that's what people did before television was invented
 
Balarka Sen
Balarka Sen
Trick calculations are actually an important skill I simply just lack.
 
Slereah
Slereah
Well, it's a fine skill to have, I don't know about important
nowadays everyone carries a calculator
good old Tom Lehrer
 
Balarka Sen
Balarka Sen
having a bag of tricks is not a bad thing to have. i guess i just envy people with that skill
on a less frustrating note, watched The Thing yesterday. so awesome
 
Slereah
Slereah
which version
 
Balarka Sen
Balarka Sen
1982
not the prequel shit
 
Slereah
Slereah
10:51 AM
Well, The Thing was itself a remake
 
Balarka Sen
Balarka Sen
Ah yeah
 
Slereah
Slereah
 
Balarka Sen
Balarka Sen
I think it was The Thing from Outer Space.
 
Slereah
Slereah
itself from a book
 
Balarka Sen
Balarka Sen
from another world, got it
well John Carpenter is just great. even though I like left-wing horror movies more
 
Slereah
Slereah
10:53 AM
what
Also John Carpenter made Dark Star, which is great
It's the only country song I know about special relativity
 
Balarka Sen
Balarka Sen
left wing = horror from inside human body instead of outer space
 
Slereah
Slereah
Then just go eat at a kebab
 
Balarka Sen
Balarka Sen
kebab is tasty, not horrifying
 
Slereah
Slereah
The horror only comes later
From inside your human body
 
Balarka Sen
Balarka Sen
only if you're a weakling
 
John Rennie
John Rennie
10:56 AM
@Slereah I've been there :-)
 
Slereah
Slereah
I had a week where my diet was mostly McDonalds, kebab and alcohol
The horror from my human body was very compelling
 
Slereah
Slereah
11:33 AM
How does one prove the existence of the inverse metric
I can prove that there is indeed the components for an inverse metric, but is that enough to prove it's a tensor field
 
ACuriousMind
ACuriousMind
It is a tensor if it transforms like a tensor.
 
0celouvskyopoulo7
0celouvskyopoulo7
11:48 AM
You don't actually believe that, do you?
@Slereah you just prove that the inverse of a matrix is a matrix
 
Slereah
Slereah
Hm
If I have $a \in M_i$ and $b \in M_j$, with $M_i = \{i\} \times M$
 
0celouvskyopoulo7
0celouvskyopoulo7
@Slereah by definition??
 
Slereah
Slereah
How do I write that $a$ and $b$ correspond to the same point
@0celouvskyopoulo7 The definition is just $g(\omega^\sharp, Y) = \omega(Y)$!
It's not terribly hard to prove, but still
 
0celouvskyopoulo7
0celouvskyopoulo7
Plug in basis vectors you fool
Why are people demanding Trump release his tax returns? I thought he did it already.
 
Slereah
Slereah
Do I just write like $\pi(a) = \pi(b)$???
Where $\pi$ is the projection to the second component of the Cartesian product
It seems a bit much
 
0celouvskyopoulo7
0celouvskyopoulo7
11:55 AM
Wot
 
ACuriousMind
ACuriousMind
^I second this wot
 
Slereah
Slereah
I'm trying to write an equivalence relation between points of copies of the same manifold
 
Balarka Sen
Balarka Sen
aka wot wot
 
Slereah
Slereah
I could just write $a = b$, but that is terribly mundane
 
0celouvskyopoulo7
0celouvskyopoulo7
@ACuriousMind skyrim is a buggy piece of crap
I'm not hard saving enough
 
Slereah
Slereah
11:58 AM
I've got a bunch of copies $\bigsqcup_{i \in A} M_i$ and I want to write that two points $a \in M_i, b \in M_j$ correspond to the same point
 
0celouvskyopoulo7
0celouvskyopoulo7
Lydia just vanished and when I player.moveto her, I can't initiate dialogue.
So I have to load my previous save and lose an hour
 
ACuriousMind
ACuriousMind
@Slereah Everyone will understand if you just write that $a$ and $b$ are identified if they correspond to the same point in $M$.
 
Slereah
Slereah
Yeah
It's just so very unrigorous :p
Now to prove that for any closed subset $S \subset M$, $S \neq M$, an identification of $M_i$ is not Hausdorff
 
0celouvskyopoulo7
0celouvskyopoulo7
@BalarkaSen I have a manifold $N$ with a compact embedded hypersurface $M$, and $N$ has positive curvature. By Bochner's theorem $H^1_\mathrm{dR}(N)=0$. Supposedly $M$ now divides $N$ into two pieces. Is this the same argument as for Jordan-Brouwer?
 
Slereah
Slereah
Wait, does the subset even have to be closed
Line with two origins is the identification along $\Bbb R \setminus 0$
 
0celouvskyopoulo7
0celouvskyopoulo7
12:04 PM
I have no idea what you're even talking about.
 
Slereah
Slereah
Actually I think I may have it backward
It needs to be open
 
Jaime Gallego
Jaime Gallego
Hello there
 
Balarka Sen
Balarka Sen
@0celouvskyopoulo7 Nullhomologous hypersurfaces bound manifold on one side. This is not very trivial to prove but is essentially the consequence of being null.
 
Slereah
Slereah
just trying to find a generic method to have non-Hausdorff manifolds
 
0celouvskyopoulo7
0celouvskyopoulo7
@BalarkaSen what?
 
Balarka Sen
Balarka Sen
12:07 PM
That is not a question so I am going to pretend that message does not exist.
 
0celouvskyopoulo7
0celouvskyopoulo7
Why does it have to be hullhomologous
 
Balarka Sen
Balarka Sen
OH. I don't know why I thought that...
Well, it is not true. $S^2 \times p$ in $S^2\times S^1$ is a hypersurface which has $H^1 =0$. But it does not divide it into two pieces...
 
0celouvskyopoulo7
0celouvskyopoulo7
No, the manifold has $H^1=0$.
Not the hypersurface.
 
Balarka Sen
Balarka Sen
Ah, man I am really misreading stuff
Then the hypersurface is nullhomologous :)
 
0celouvskyopoulo7
0celouvskyopoulo7
Is "what" an acceptable question now?
 
Balarka Sen
Balarka Sen
12:11 PM
No, because the hypersurface is a homology class of codimension 1, and it's Poincare dual is a cohomology class of dimension 1. Since dimension 1 has NO cohomology, that is zero
Poincare dual = 0 => homology class = 0
=> nullhomologous
 
0celouvskyopoulo7
0celouvskyopoulo7
Dimension 1 has no cohomology?
 
ACuriousMind
ACuriousMind
@Slereah There is a difference between formality and rigor. It's perfectly rigorous, just not formal :P
 
0celouvskyopoulo7
0celouvskyopoulo7
Oh, by assumption.
 
Balarka Sen
Balarka Sen
:P
Using $N$ for the ambient manifold is really confuzzling man
 
0celouvskyopoulo7
0celouvskyopoulo7
Oh, so it's nullhomologous.
@BalarkaSen This book is nothing but one big confusion.
 
Balarka Sen
Balarka Sen
12:14 PM
what are you even reading
 
ACuriousMind
ACuriousMind
@0celouvskyopoulo7 I see you still do not accept that cohomology does not need a subscript indicating how it was computed :P
 
0celouvskyopoulo7
0celouvskyopoulo7
@ACuriousMind You know, I learned sheaf theory and de Rham's theorem and whatnot, and I decided to reject it all.
The only cohomology is de Rham baby
@BalarkaSen P. Li, "Geometric Analysis."
 
Balarka Sen
Balarka Sen
singular is love, singular is life
 
0celouvskyopoulo7
0celouvskyopoulo7
@BalarkaSen So is this in Hatcher somewhere?
 
Balarka Sen
Balarka Sen
That null hypersurfaces bound an embedded manifold on one side? No, it's nontrivial to prove.
If you want I can try to remember the proof
 
0celouvskyopoulo7
0celouvskyopoulo7
12:19 PM
He says "by an exact sequence argument"
@BalarkaSen Nah, I could probably find it if I wanted
@BalarkaSen In any case, it's used to prove a lower bound for the first eigenvalue for $M$
So nothing very interesting for you
You just need to know that there's a component of $N-M$ with boundary $=M$
@Slereah I'm going to give chap 7 of HE a read
I think I'm ready
 
Slereah
Slereah
Is that the Cauchy one
 
0celouvskyopoulo7
0celouvskyopoulo7
indeed
@ACuriousMind Even HE confuses diffeo and isometry :/
 
 
1 hour later…
mathvc_
mathvc_
1:48 PM
hey guys
 
Slereah
Slereah
hey
 
Secret
Secret
~~~~~~~~~~~~Beginning Transmission~~~~~~~~~~~~~
0
Q: Had any experiment being proposed/done that show that time is linear?

SecretIn classical mechanics and nonrelativistic quantum mechanics, time $t$ is a parameter to describe the evolution of a system. In discrete dynamical systems, we typically take $t$ to be linear and increases in uniform steps. In relativity and quantum field theory, time and space combine to form sp...

experimental-physics reference-frames time
Probably the craziest question I ever wrote in PSE
(an no, I have searched the whole PSE and found no similar questions, afaik)
 
mathvc_
mathvc_
i'm sure it's my fault but i don't understand ur question!
 
John Rennie
John Rennie
@Secret: your question is meaningless. Time is just a coordinate like $x$, $y$ and $z$.
It makes no sense to ask if the $t$ coordinate is linear any more that it does to ask if the $x$ coordinate is linear.
 
Slereah
Slereah
"time" is just defined by events in physics
In the rest frame of a clock, time is just defined by that clock
it's the coordinative definition of time
 
Secret
Secret
2:06 PM
hmm... so whether using proper time or coordinate time, it is a number assigned for each event thus it is meaningless to talk about whether it behaves linearly or nonlinearly?
 
Slereah
Slereah
just ask yourself what it means for time to be nonlinear
 
John Rennie
John Rennie
Proper time is a coordinate time. It is the time coordinate for the observer at rest.
 
Slereah
Slereah
In a physical setting, time is just measured by the repeating of an event that we assume to be periodic
 
John Rennie
John Rennie
The mapping between the time different coordinates of different observers can be, and is, non-linear. But in any one coordinate system time is just the distance along an axis.
 
Slereah
Slereah
If the repeating of an event can't be assumed to be periodic, then you basically have no hope to measure time
 
Secret
Secret
2:12 PM
Slereah: Hmm... then nonlinear time will imply the event is aperiodic. However, if it is aperiodic, then there isn't any well defined standard on how it can be used as some kind of benchmark. Since it does not evolve in some "regular" fashion, I am not sure if one can use such event as some kind of "ruler" to measure time

(I typed too slow, you beat me to it)
I assume a quasiperiodic event will also suffer a similar problem...?
 
mathvc_
mathvc_
its more or less philosophy
not physics
i guess
 
Secret
Secret
Quasiperiodicity has a regular pattern but no fixed period, thus I suppose it can still be used I guess....
 
mathvc_
mathvc_
i think GR says there is no sacred time, and we're all alone
so i think we dunno really what is time, we just measure sth to be social
 
Slereah
Slereah
You can make up some random theory where you have time being nonlinear in rest frame according to specified conditions, and then convert back those times measured to "real" time, but that would be a really dumb theory
It would run afoul of Occam's razor
you are just adding features to the theory that are not necessary
 
0celouvskyopoulo7
0celouvskyopoulo7
All of physics runs afoul of that
An old man in the sky is far simpler than superstrings
 
Slereah
Slereah
2:18 PM
Well, you can make up a physical theory that is 100% without extra features
It's called the Craig axiomatization of a theory
It makes very ugly theories, though
And you can't extend those theories at all
 
mathvc_
mathvc_
@Slereah what's that?
 
Slereah
Slereah
Well for physical theories, you have what are called theoretical constructs and then you have measurable things
You can make a theory with only measurable entities and no theoretical constructs
but then it would be terribly unwieldy
For instance, you won't have a notion of "temperature"
Only measurable events such as what instruments show
you will get 100% the same predictions but those are all disjointed, conceptually
There's no obvious link between what a mercury thermometer shows and what an electronic thermometer shows
 
0celouvskyopoulo7
0celouvskyopoulo7
Millimeters of mercury baby
@Slereah why do you know random things about axiomatization?
 
mathvc_
mathvc_
@Slereah so doesn't it only separate rules?
 
Slereah
Slereah
Craig axiomatizations is discussed in "science without numbers" and "The philosophy of quantum mechanics"
 
mathvc_
mathvc_
2:25 PM
how is science without number?
 
Slereah
Slereah
@mathvc_ It gives you a mathematical formula where, for a list of measurable quantities, you get another measurable quantity
"Science without number" is a book on the axiomatization of classical physics with Hilbert geometry
so there are no numbers and no functions involved
Only points and order relations
and congruence relations
 
mathvc_
mathvc_
oh is it related to geometry interpretation of theories?
 
Slereah
Slereah
Not really
 
mathvc_
mathvc_
nominalism
 
Slereah
Slereah
yes
 
0celouvskyopoulo7
0celouvskyopoulo7
2:32 PM
$$\iint_\Omega h|\nabla f|\, dV=\int_0^\infty dt\int_{\Gamma(t)}h\, dA_t$$
why a double integral on the left?
$$\iint_\Omega d\omega=\int_{\partial\Omega}\omega$$
wot
@ACuriousMind ???
 
Slereah
Slereah
To specify that it's on at least two dimensions?
 
0celouvskyopoulo7
0celouvskyopoulo7
it's a reference text on spectral geometry, I think the reader is supposed to know how integrals work
I found that Stokes theorem from his riem. geo. book
jesus, who knows what he means
 
Slereah
Slereah
does it really matter
 
0celouvskyopoulo7
0celouvskyopoulo7
probably not
 
Slereah
Slereah
2:59 PM
what is the current state of experimental GR, anyway
what's the next big experiment they're planning
More G wave astronomy?
 
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