The h Bar

0celo7

12:00 AM

local extrema

Balarka Sen

where the induced metric and the subspace metric will not agree upto 1st order, I'm very sure

there's tight corners there

0celo7

I mean take like $f(x)=x^2/\epsilon$ and look near $0$

the tangent plane will approximate the base

so the graph metric agrees to first order with the base metric near $0$

Balarka Sen

Yes, but I mean take $x = -\epsilon$ and $y = \epsilon$. Then the corresponding images on the graph have large distance in the induced metric compared to subspace metric

0celo7

I agree, but you're saying this $\forall x,y$

If you add $\forall x,y$ such that $d_M(x,y)\ge\delta$ then it's fine

(for some $\delta$ that exists)

Balarka Sen

$d_M((-\epsilon, \epsilon^2), (\epsilon, \epsilon^2)) >> \|(-\epsilon, \epsilon^2) - (\epsilon, \epsilon^2)\|$

0celo7

12:04 AM

@BalarkaSen again, my problem is when $x\to y$. I don't doubt that for points far away it's true

Balarka Sen

$-\epsilon$ and $\epsilon$ are far away??

Wut

0celo7

far away compared to $x\to y$

on a length scale of say $\epsilon^\text{googol}$, the graph of $f$ is almost flat

Balarka Sen

Hmmm that is true

0celo7

assuming $\epsilon<1$ ofc...

@BalarkaSen I believe the existence of such a wiggly thing only if $x$ and $y$ are not meant to be too close

Balarka Sen

@0celo7 Maybe this is right...

0celo7

12:06 AM

what does the paper say exactly?

Balarka Sen

And as $\epsilon \to 0$, we could take $\delta$ closer and closer to $0$ of course...

@0celo7 arxiv.org/pdf/math/0003026.pdf page 433

0celo7

right, it should be a usual "given $\epsilon>0$ there exists $\delta>0$ blah blah" thing

@BalarkaSen is this a variant of the statement of the ripple lemma?

Balarka Sen

What I am saying? A special case, I think, yes.

0celo7

well what is this $R$ supposed to be, morally

ok, $\epsilon\ll 1\ll R$

you're saying $R=O(1/\epsilon)$

Balarka Sen

They said pick any given real numbers

I just picked $\epsilon$ and $1/\epsilon$

Seems like a fair choice

0celo7

12:11 AM

oh ok R is given, right

@BalarkaSen While I'm thinking about this, symplectic boy, what is the uniform C^1 topology on the group of symplectomorphisms?

Balarka Sen

Is giving it the induced C^1 Whitney topology from Diff(M) a good idea?

Are symplectomorphisms stable under perturbation?

0celo7

I don't know, if they said that then I'd be happy but the "uniform" bit is strange

the manifold isn't compact...

Balarka Sen

Yikes

0celo7

@BalarkaSen no idea, this is unexpected symplectic stuff, I don't really know anything about it

@BalarkaSen so looking at this figure, I definitely don't think it proves what the authors think it does...

the points near the peaks are definitely not being moved far apart!!

Balarka Sen

Yeah that's strange

But maybe your reformulation is enough idk

0celo7

12:17 AM

"Further we can choose this isotopy to finish with a diffeomorphism
which nowhere shrinks distances"

wot

ok I agree that this curve increases distances

Balarka Sen

Yeah that is fine

but the scaling up by R ...

0celo7

what is it with symplectic topologists giving really vague proofs

Balarka Sen

that only works outside an nbhd of the crit points apparently....

lol

0celo7

drawing a fucking curve is not a correct Riemannian geometry proof

Balarka Sen

@0celo7 staff.science.uu.nl/~zilte001/holo_curves_spring_2015/…

page 2

They say it's induced from C^1(M, M)

0celo7

12:20 AM

yeah, thanks

Balarka Sen

@0celo7 what I'm really confused about is how this proves the flattening lemma

I didn't even think much about rippling before you asked about it

0celo7

@BalarkaSen The proof is written so strangely too

Clearly M can be replaced by S via an isotopy which moves points at most
A + 1
ω
. Further we can choose this isotopy to finish with a diffeomorphism
which nowhere shrinks distances, is fixed near {0, 1}, and which outside a given
neighbourhood of {0, 1} scales length up (measured in M ) by a constant scale
factor.

Is he saying one should modify $S$ more here?

Balarka Sen

I think he just wants S to be flat near 0 and 1

0celo7

what does he mean by "scales length up" though??

that might be the key

how is he gonna scale lengths up by a constant factor without stretching the whole thing somehow

Balarka Sen

R*d(x, y), maybe? He says the same thing in a very vague way in the proof of flattening; check it out

page 437

bottom

0celo7

12:25 AM

lmao fuck that proof

Balarka Sen

lololol

0celo7

imagine turning this in as homework

Balarka Sen

"We do this and this and this and the embedding is now as flat as we please"

wtf

0celo7

@BalarkaSen This encapsulates my beef with Russian math perfectly

Balarka Sen

it's written by british people lol

0celo7

12:27 AM

intellectual traitors!

Balarka Sen

But!

"We are very grateful to both Yasha Eliashberg and the referee for comments
which have greatly improved the clarity of the proof of the ripple lemma."

0celo7

hahaaaaaaaaaaaaaaaaaaaaaaaaaa

Balarka Sen

Yes, you did clarify that one very well

0celo7

that's the sound of me having a stroke

Balarka Sen

get stroked

rip

0celo7

12:28 AM

my stomach is growling and my dinner takes > 1 hour to prepare

gtg

hmu if you have an insight

Balarka Sen

for sure

0celo7

I will find the error :)

Balarka Sen

bon apetite

looool

skeptic fuck

0celo7

@BalarkaSen I don't like the statement of the ripple lemma. Try my modified version (no guarantees on its truth, but it's weaker than theirs so shrug) and see if the flattening proof goes through

Balarka Sen

I'll try that. Thanks

0celo7

12:30 AM

@BalarkaSen "compressible" means that the function looks like a graph locally?

er

graph of a nice function locally

^ retarded

Balarka Sen

$M^n$, a submanifold of $Q^q \times \Bbb R^k$ is compressible if $M$ is nowhere tangent to the vertical $\Bbb R^k$

0celo7

yeah I'm reading that

Balarka Sen

Or better, the projection map $M^n \to Q^q$ is an immersion

0celo7

@BalarkaSen ah yes

Balarka Sen

ah ok

0celo7

12:32 AM

always prefer things that can be stated in terms of analysis

Balarka Sen

I prefer some amount of rigor... unless rippling happens

0celo7

ugh, the statement of the flattening lemma is already hard...

Balarka Sen

I can explain if you want. It's pictorial

0celo7

@BalarkaSen if you're up when I'm done eating

I really need food, I don't think I had lunch :/

Balarka Sen

Do eat

0celo7

1:06 AM

@BalarkaSen stage 1 is cooking

figure this out yet?

Balarka Sen

I have been reading their first paper. The ideas there are completely different

Want to hear about the flattening lemma?

0celo7

go for it

Balarka Sen

Suppose $M^n$ is a compressible submanifold of $Q^q \times \Bbb R^k$, i.e., the projection map gives an immersion $M^n \to Q^q$.

Consider the Grassmannian $\text{Gr}_n(Q^q \times \Bbb R^k)$ of $n$-plane distributions on $Q^q \times \Bbb R^k$. We could look at the subspace $H$ of that Grassmannian consisting of "horizontal" $n$-plane bundles

Horizontal means sits inside the $q$-plane distribution $\pi^* TQ^q$ in $Q^q \times \Bbb R^k$, where $\pi$ is projection to the $Q$ factor.

Fix any neighborhood $U$ of this subspace $H$ in the Grassmannian. So elements of $U$ are $\epsilon$-horizontal $n$-plane distributions on $Q \times \Bbb R^k$

0celo7

are these distributions in $T(Q\times R^k)$?

Balarka Sen

Yep

0celo7

1:13 AM

ok

Balarka Sen

Tangent distrubutions

0celo7

ok you keep saying on $Q \times R^k$ which could mean something different

(that's a vector bundle)

@BalarkaSen $\epsilon$-horizontal?

Balarka Sen

Ahhh I see, by on I mean at each point of Q x R^k you have a tangent plane stuck

0celo7

@BalarkaSen ok, the language could also mean you have at each $q\in Q$ a plane of $R^k$ stuck

Balarka Sen

Yeah I realized

Didn't mean that

0celo7

1:15 AM

ok, so epsilon horizontal means?

Balarka Sen

You could make that rigorous because you have a Riemannian metric... but there's no need to. Take it to definitionally mean that it's an element of $U$

0celo7

is $Q$ kompakt?

and $M$

Balarka Sen

It's an element of a fixed neighborhood of $H \subset \text{Gr}_n(Q \times \Bbb R^k)$ consisting of horizontal $n$-plane distributions.

@0celo7 They don't seem to mention that

0celo7

@BalarkaSen I am just wondering if elements of $U$ can get "arbitrarily close" to being vertical.

Balarka Sen

Oh $M$ is compact

@0celo7 I see

Well I mean Q x R^k is noncompact...

0celo7

1:19 AM

yeah true

ok continue

Balarka Sen

Claim: You can produce a $C^0$-small isotopy $h^t$ of $M$ in $Q \times \Bbb R^k$ such that the tangent bundle of the final manifold $h^1(M)$ is restriction of an element of $U$ to $h^1(M)$.

So $Th^1(M)$ is $\epsilon$-horizontal, i.e.

Ah, should mention $ q\geq n + 1$

0celo7

i.e. what??

Balarka Sen

I put the i.e. in the back of the statement instead of at the front.

:P

0celo7

************** Indian English

Balarka Sen

lmao

that's a microaggression

i don't identify as an indian

i identify as jaden smith

0celo7

1:27 AM

I see what the thing is saying, I think

yes, $q>n$ makes sense

well why not $q=n$

Balarka Sen

mhm

0celo7

probably not enough "ripple room" ;)

Balarka Sen

ya

0celo7

ok so I see what the lemma is saying

have you figured out the ripple yet

@BalarkaSen two new D. Chappelle specials!

Balarka Sen

Not yet

@0celo7 Sounds delicious

Fawad

1:53 AM

Angle of contact 180 degrees is same as 0 degrees?

Anyone?

HsMjstyMstdn

@Fawad What do you mean "angle of contact" ?

Anyone know what do the squiggles above dQ and dW mean ?

0celo7

impossible without more info

HsMjstyMstdn

I assume Ocelo's talking to Fawad

0celo7

@HsMjstyMstdn I'm talking to you

HsMjstyMstdn

@0celo7 Oh sheez, alright. It was on a lab writeup, representation of the First Law of Thermodynamics. There is mention in the paragraph before it that neither the Q nor the W can be perfect differentials. Could that be related to the tildes ?

Fawad

2:31 AM

Angle of contact between liquid and solid

HsMjstyMstdn

Unless you're talking about something very specific with regards to directionality, I don't think there's going to be much of a difference between 0 and 180 degrees, Fawad. It just might mean that one is going left to right and the other vice versa.

dmckee

3:08 AM

Huh?

0

Q: Converting radioactivity levels to radiation doses

You stand in an environment where the air is 5% radon-222. How long does it take to absorb a lethal dose of radiation? I'm making the following simplifying assumptions: The only decays that matter are the beta decays of Pb-214 and Bi-214. The alpha decays can be ignored because skin and ...

radioactivity

I make it kilowats per cubic meter. Hundreds of kilowatts per cubic meter.

HsMjstyMstdn

Yeah, the decay heat would be terrific

Anonymous

@HsMjstyMstdn Imperfect differentials

HsMjstyMstdn

@Blue Thank you

Does the "imperfect" have any mathematical definition ? Or is it merely an expression of this differential not being perfect

Anonymous

3:23 AM

@HsMjstyMstdn mathworld.wolfram.com/InexactDifferential.html

HsMjstyMstdn

@Blue Thanks

Captain Bohemian

5:21 AM

I am wondering what are Gauss transformations.

John Rennie

6:41 AM

@Fawad the contact angle is measured through the liquid:

Slereah

7:34 AM

mornin

Schwartz Witten has a pretty neat history of string theory

I didn't know of the dual mode theory

dexterdev

8:10 AM

Hi all... @dexterdev here. I have a question to ask here. Since this is a general chat room, I guess this is the best place for my issue.

I meant general chat room for physics

I recently posted a biophysics question in bio.SE and now I feel it should have been more appropriate in physics.SE

Can any of you guys suggest me what to do regarding my question : biology.stackexchange.com/questions/69321/…

2

Should I delete it and move to physics.SE ?

John Rennie

@dexterdev Hi Dexter. That's really physical chemistry and there isn't a physical chemistry SE so it doesn't fit anywhere :-)

I don't know anything about the ripple phase in cell membranes, but I did work as a physical chemist and I did study lamellar phases of surfactants.

And I'd be surprised if the ripple phase was as well defined as the diagram suggests. I would have guessed it was a rather poorly defined intermediate state between ordered and disordered.

I very much doubt it is a travelling wave like a ripple travelling along the membrane because I would guess the dampling is far too fast for a wave to propagate very far.

dexterdev

8:29 AM

@john-rennie Hi. As far as I understand ripple state is a meta stable state. Not really sure though. And I observed it in MD simulations. We have no clue why this happened as the temperature was above transition temperature where it should have been in fluid state. There must be some other reasons. Most probably it is not a travelling wave as you mentioned. But in literature sometimes ripple phase is explained along with "undulations".

See Page8 here : physics.iitm.ac.in/~iol/lecture_notes/vani/general-lipid-stuff/…

I will catch you later

David Z

@JohnRennie Hm, I would have thought it might be okay here, but you know the topic better than I do. Of course it would need some explanation of relevant background information, for people who don't know about lipid membranes.

Mithrandir24601

@Blue So, this is another 'general noise type' :) (presumably as a result of uncertainty intrinsic to the system). As a quantum Turing machine uses states (and is entirely equivalent to a classical Turing machine), it's not quite so clear cut as to whether this is taken into account or not. It probably depends how you model the problem or something.

Also remember that you can repeat simulations as many times as you like, so you can recreate the exact state using an ideal quantum simulation, but maybe that's what you're saying. More also: To properly look into this would be very interesting, but would require a fair bit of time delving into it (has anyone properly proven this claim, or is this just another thing that everyone takes for granted?)

David Z

@dexterdev One thing I'd definitely suggest is narrowing down your post to contain only one question. I'm not sure how much they care about that on Biology but here I would put it on hold as too broad simply because you're asking two questions - that's before even considering whether it's on topic.

CooperCape

Oh wait is the span of 2D vectors a plane?

Balarka Sen

8:53 AM

depends on the vectors

span of $\hat{i}$ and $2\hat{i}$ is a line.

(Namely, the x-axis)

CooperCape

Oh right...

Course

Balarka Sen

When is it true?

CooperCape

Just for all vectors which aren’t on the same line right?

I guess mathematically when $\lambda v_1\neq v_2$

Balarka Sen

For all $\lambda$. Yes.

What if you have more than 2 vectors? How would you state it mathematically, then?

CooperCape

It depends if you want a plane of like a cube right

Balarka Sen

8:57 AM

You're in $\Bbb R^2$.

CooperCape

So for a plane two would have to be in the same line with the other not

Oh yeah oops

Sorry I went 3D there.

Balarka Sen

Well, two need not be on the same line. Consider $\hat{i}, \hat{i}+\hat{j}, \hat{j}$.

The three span the whole of $\Bbb R^2$.

None of them are on the same line.

CooperCape

Ah right

Balarka Sen

So (1) state the property (2) write down the mathematical version

CooperCape

So to span the whole of R^2 there just need to be at least 2 vectors not on the same line?

Balarka Sen

8:59 AM

Good, yes.

CooperCape

Now mathematically...

Balarka Sen

There's a clean way to write this down without using quantifiers.

i.e., without saying "there exists" or "for all"

CooperCape

Hmmmm

Okay

Balarka Sen

Should I spoil it?

@0celo7 I got it. I understand the idea of the proof of flattening.

This ain't bad actually, but they should have been way more rigorous about it

Constantine Black

Hi. Is there any possibility any of you knows some matlab? When a problem asks to simulate the change of particles inside a box as a function of time, is it ok to just define the appropriate vectors and make the plot or does it mean something else? Thanks.

Slereah

9:10 AM

journals.aps.org.https.sci-hub.tw/rmp/pdf/10.1103/…

that's an old ass string theory paper

"particles coupled through imaginary coupling constants are usually referred to as "ghosts" and are according to our last axiom, highly undesirable in any theory"

Why does QFT have so many ghosts

bolbteppa

@Slereah that paper is incredible

That's a famous article, I love how he sticks to Nambu-Goto through and through

I don't get what he's doing in I.70 to I.75 properly, kind of bluff with another perspective

My eyes keep glazing over when I try to find out about dual models and the links to qcd

dexterdev

9:31 AM

@DavidZ OK . I will do so.

Slereah

"An additional property of the model emerged namely that the no-ghost theorem held only if the dimension of spacetime was smaller or equal to a critical dimension (26 in the conventional model)."

How strange!

Oh man it has pomerons

I completely forget what those are

CooperCape

@BalarkaSen Sorry I had to go to school assembly (yes We still have those ugh). I’ll think about it and if I can’t think of anything I’ll probabky end up asking you later... Thanks for your help, tho :)

Slereah

Possible example of a pomeron

Balarka Sen

@CooperCape For sure

dexterdev

@DavidZ I will ask one question here. But can I post it in physics.SE now? I dont have necessary tags even here. :(

Slereah

9:37 AM

"In early particle physics, the 'pomeron sector' was what is now called the 'closed string sector' while what was called the 'reggeon sector' is now the 'open string theory'."

bolbteppa

@Slereah if you ever see section I.6 explained similarly but better elsewhere let me know

Slereah

Hm, did Nambu really invent the point particle action in 1970?

Seems fairly late

Action of a point particle seems like an important thing to model from the beginning of GR

Even SR

Oh wait, Nambu only did the string action apparently

Who invented the point particle action

bolbteppa

point particle action existed for ages

I think Loren(t?)z or someone back then did it

Slereah

Do you mean Lorentz, Lorentz or Loren

bolbteppa

Another paper like this is the GGRT paper they reference, but this one is more of an overview

Slereah

9:51 AM

GGRT?

bolbteppa

footnote on page 4

David Z

10:31 AM

@dexterdev If you can't find appropriate tags for your question, that's usually a sign the question is off topic.

Slereah

Lorentz–Lorenz equation

The Lorentz–Lorenz equation, also known as the Clausius–Mossotti relation and Maxwell's formula, relates the refractive index of a substance to its polarizability. Named after Hendrik Antoon Lorentz and Ludvig Lorenz. The most general form of the Lorentz–Lorenz equation is n 2 − 1 n 2 +...

Slereah

10:59 AM

why does string field theory have a trilinear form

The hell is $\langle \Psi, \Psi, \Psi\rangle$ supposed to mean

Fawad

11:22 AM

@Slereah kong the savage?

@JohnRennie cool representation. So does it mean 0 degrees and 180 genres are different?

dexterdev

@DavidZ So where do you post biophysics usually involving lipids? bio.SE has tags, but physics.SE is more active! :(

Qmechanic

@Slereah : FWIW, it is part of a Chern-Simons-like action.

John Rennie

@Fawad yes. 0º means the liquid perfectly wets the surface while 180º means the liquid doesn't wet the surface at all.

i.e. with a 0º contact angle the liquid spreads out on the surface to form a thin film. With a 180º contact angle the liquid rolls up to from a drop.

Slereah

12:07 PM

Oh apparently it's $\langle \Sigma, \Psi_1 \star \Psi_2 \rangle = \langle \Sigma, \Psi_1, \Psi_2 \rangle$

for some operator $\star$

"An explicit description of the second-quantization of the light-cone string was given by Michio Kaku and Keiji Kikkawa."

First time I actually hear of Kaku on a real thing!

bolbteppa

The guy came up with it

Unbelievable

Slereah

it's pretty rare for a dude to be a pop science icon and actually known for your contribution to physics

Feynman and Hawking are probably the two good examples

bolbteppa

Weinberg I'd say too

Fawad

@JohnRennie thanks. Surface tension concept is tough for me :(

bolbteppa

Bill Nye another /s

Slereah

12:19 PM

Does Weinberg do pop science?

bolbteppa

He writes popular articles, talks with Dawkins on video etc

Oh yeah he wrote 'the first 3 minutes' an awesome pop sci book I read ages ago

He's got a section in his 'intro' string book on 2nd quantization, one chapter in it on lightcone field theory, another chapter on brst field theory, there's an element of magic to the way he writes

as in 'insane path integral $\sim \delta$ function' and voila, answer!

Slereah

breast field theory you say

bolbteppa

Well he does know how to write for the masses...

Balarka Sen

@Slereah Neil deGrasse Tyson

bolbteppa

(Lot of interpretations there :p)

Balarka Sen

12:26 PM

counterexample right in your face

Slereah

@BalarkaSen Have you ever actually seen a paper by Tyson

I'm sure he wrote some

But I've never seen one

Let's see

Neil deGrasse Tyson

Neil deGrasse Tyson (; born October 5, 1958) is an American astrophysicist, author, and science communicator. Since 1996, he has been the Frederick P. Rose Director of the Hayden Planetarium at the Rose Center for Earth and Space in New York City. The center is part of the American Museum of Natural History, where Tyson founded the Department of Astrophysics in 1997 and has been a research associate in the department since 2003. Born and raised in New York City, Tyson became interested in astronomy at the age of nine after a visit to the Hayden Planetarium. After graduating from the Bronx High...

it's all boring astrophysics

snooze

bolbteppa

That part of his book comes after teichmuller spaces, moduli spaces, spinors and trees, superconformal ghosts, etc etc so yeah the guy is a maniac (in a good way)

Slereah

Oh no

the worst ghosts

Does he use interuniversal Teichmuller universes

bolbteppa

Maybe in his crazy advanced string book for all I know

Balarka Sen

physicists like moduli spaces

it's like their spirit animal

their pop dream

I have yet to learn the right definition of a moduli space

It's too komcplicated

Slereah

12:35 PM

I don't know what a moduli space is

Balarka Sen

it's a space which parameterizes objects

Slereah

that's pretty broad

Is it like a configuration space?

Balarka Sen

yeah it's a philosophy rather than a definition

exactly so

Slereah

o

Is it exactly a configuration space?

Balarka Sen

every point corresponds to certain arrangement/configuration/object

@Slereah Not really

A configuration space is an example of a moduli space.

Slereah

12:37 PM

what's a moduli space that isn't a configuration space

bolbteppa

For him he takes the space of constant curvature metrics after quotienting out overcounting by diffeomorphisms to be the moduli space, and then, in spinor like fashion, if we instead throw away only diffeomorphisms connected to the identity, we get a Teichmuller space

Balarka Sen

@Slereah There's the moduli space of conformal structures on surface of genus $g$, eg.

bolbteppa

Interactions are Riemann surfaces, RS's are conformally equivalent to constant curvature surfaces, etc

Balarka Sen

Although it's not a very interesting space if $g \geq 2$

It's just $\Bbb R^{6g - 6}$ I think

bolbteppa

Still haven't gotten close to interacting string theory properly, that Scherk article gets you there pretty fast as an intro but I of course got side tracked

Balarka Sen

12:41 PM

It's not the moduli space that's interesting to be honest, it's how you model it

The "usual" model for moduli space of conformal structure on surfaces of genus $g \geq 2$ is to consider the length function on the induced hyperbolic metric on the surface

Slereah

@bolbteppa something something sum over manifolds

bolbteppa

Space of circles is a moduli space where the moduli speecifying different circles is the radius (= modulus) or something

Now we are just in 26 dimensions with insane spacetime 'circles' :p

Balarka Sen

Also, the topology matters. You want to understand how the objects change if you move around points in the moduli space

It's a cool reformulation of various changing shit

@Slereah Oh yeah the simplest example is of course projective spaces

Slereah

They always say that Polyakov for non-string doesn't work but I'd like to see the actual proof of it sometimes

Like why membrane theory no works

Balarka Sen

I need to learn measure theory

Slereah

12:49 PM

ask @0celo7

he'll tell u all about it

Balarka Sen

No doubt

bolbteppa

What do you mean Polkakov for non-string doesn't work? In BBS they show Polyakov doesn't work with a cosmological constant term for strings and only works with a cosmological constant term for non-strings i.e. branes, maybe that?

Slereah

I usually read that if you try to have 3D Polyakov theories (or more), you end up with divergences

Hence why there is no membrane theory or SHAPE theory

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