Perhaps

← doesnt have all the answers but does not preclude/ can note when others do not seem to be asking the right questions ... do have alternative approaches, have blogged at length about them, the "community" is not receptive right now, think it will chg gradually over "the long haul/ run" aka years

@CuriousOne research is not merely/ cannot nec be reduced just to competing agendas although it sometimes plays out that way historically

@vzn: I have not seen any "alternative approaches" that I would take seriously. There is a difference between being imaginative and being knowledgable with an idea that works.

@CuriousOne lol then you can join the crowd! research/ new directions never arrive fully baked in ones lap/ on ones doorstep...

@vzn: I never had a problem with the crowd. :-)

@vzn: Anyway, one of my oldies but goodies is "Put up or shut up!" and I invite everybody to put up. :-)

@CuriousOne your dodging the "citation needed" is noted and you dont seem to be bothered by the omission. actually was expressing some sympathy for your frustration about the possible approaching/ oncoming desert of new LHC findings esp wrt history.

@CuriousOne sounds like black or white thinking to me. ps DS was criticizing your comment style in here awhile back, dont know if you saw that

@vzn: I am not that frustrated about the desert. I have expected it since, at least, 1994 or so. The Higgs and nothing else was my only expectation for LHC.

@vzn: Anybody with a serious suggestion is highly welcome, I am just not seeing it.

@vzn: That I am not into into intellectual nonsense is based on experience: it doesn't seem to work.

@CuriousOne what is your own recommendation/ "serious suggestion"? higher energy?

@CuriousOne dont know what "intellectual nonsense" you are referring to

@vzn: I don't have any recommendations. I only follow what nature says. If it doesn't say anything at 1TeV, one has to look at 100TeV.

@CuriousOne aka higher energy

@vzn: We have plenty of people who are looking at 1neV. :-)

reminds me of the 11 setting from spinal tap :P

@vzn: "Intellectual nonsense" is when you think that you are smarter than nature.

@CuriousOne "stop telling god what to do" supposed quote, bohr to einstein

@vzn: "It's not even wrong!" :-)

To put it another way... the average string theorist is a third rate mathematician who would never get tenure in a quality math department. Witten and some others are excluded from this opinion, of course, but Witten would have done better with his career/life if he had spent it on something with substance/data.

@Slereah hey

Turns out $nR_{ij}R^{ij}\ge R^2$.

Oh Javascript

@Slereah: With more freedom comes more responsibility. Anybody who thinks that the average programmer writes better software in oppressive languages like C/C++ doesn't know the extent of the human ingenuity to mess up.

Obviouslu Javascript has no mathematical structure

It wasn't supposed to.... :-)

I am curious how the people write compiler in a consistent way

They don't.

They don't do that for C, either. :-)

I think it somehow do, chrome and firefox run the same with my Javascript

You have benign Javascript. :-)

I don't have JavaScript

We've been over this

On C one can kill consistency with a simple union that exposes the endianness of the machine... :-)

Never ask how many endianness bugs of the DAQ are built into the SM. :-)

Turning a couple of bytes around can be easily mistaken for a bunch of jets by theoretical physicists who don't (care to) know how the DAQ works. :-)

The only really bad thing about Javascript is the debugger... or absence of anything but a toy version thereof.

"Some constructs could be defined but are so ugly that they should not be. A classic variant that makes my eyes bleed and that should not be defined is: i = ++i + p[++i];"

heh

$$\frac{\partial }{\partial t}R(X,Y,Z,W)=(\Delta R)(X,Y,Z,Y)+\sum_{pq}R(X,Y,e_p,e_q)R(Z,W,e_p,e_q)+2\sum_{pq}R(X,e_p,Z,e_q)R(Y,e_‌​p,W,e_q)-2\sum_{pq}R(X,e_p,W,e_q)R(Y,e_p,Z,e_q)$$$$-\sum_k\mathrm{Ric}(X,e_k)R(e_‌​k,Y,Z,W)-\sum_k\mathrm{Ric}(Y,e_k)R(E,e_k,Z,W)-\sum_k\mathrm{Ric}(Z,e_k)R(X,Y,e_k‌​,W)-\sum_k\mathrm{Ric}(W,e_k)R(X,Y,Z,e_k)$$

@Slereah how do you like that PDE

too long m8

Obfuscation is the first step to tenure...

@Slereah can you solve it?

Well, $R = 0$ is a solution

given an initial metric $g_0$ m8

might not be flat

A bit tougher then

You mean we can't even tell how many 40 page GR papers were written about flat spacetime?

what

Is there a simple test if a non-trivial looking metric is flat?

Compute the Riemann tensor

What do you mean by "flat"

Ricci flat or flat flat

Riemann tensor vanishes iff metric is locally flat

Doesn't that have thousands of terms in the worst case?

@Slereah Flat means "isometric to Euclidean space"

No

Then Riemann indeed

@CuriousOne You can write the full thing down in about 10 pages

But that's the absolute worst case

OK...

Riemann tensor for Minkowski space is 0 and all diffeomorphisms of 0 will still be 0

There are usually symmetries and other things that make computing it not terrible

And a computer can do it

@Slereah The proof of what I said is very nontrivial and requires PDE theory

you can have a flat space without symmetries

Huh? Is there a simple example for that?

Yeah, I'm curious too

Minkowski space with chunks removed

chunks ?

That's not physical... but mathematically I get it.

Although I guess it's flat but not technically diffeomorphic to Minkowski space

what does physical even mean

@Slereah correct

Physically it's just Minkowski with naked singularities

Something nature actually makes?

This really is not physical

Maybe

@CuriousOne No

Damn physicists and their "physical"

There's no way you know either way

Thats the point of physics, isnt it ?

That's why physics is not math... or we could all go home. The mathematicians are better at that than we are.

math is objectively better

And cheaper.

Can't turn the lights on, though...

Maths are just a tool for the REAL sciene (physics)

Neither can modern physicists @CuriousOne

Not even.

Electricity is not modern physics?

Yeah, maybe.

@CuriousOneNo, calabi-yaus in curved spacetime are modern physics

String theory is a joke

I like it.

I doubt nature does those. :-)

The background is not even dynamical

Why ?

@Ocelo7 String theory is pure mathematical beauty.

String theory debates sound suspiciously like religion debates

Naaah...

String theory is not a joke! I bet with all of you it's approximately correct 10fs from the singularity.

Neither side has any evidence @PhysicsGuy

There could be a proof for it in the not too distant future.

Physics cannot be proven

qOcelo7 Then occupied.

Is someone willing to write an NSF grant for the purchase of a black hole with me?

@CuriousOne No, we need the money for wars

It doesnt matter then. it describes the nature very good, thats it.

Wait

Can we drop a black hole on China

A black hole is the ultimate weapon!

Yeah

Does it destroy us too?

Elon Musk will move us to Mars, first, then we can.

I think a kind of warp, or alcubierre drive is the better technology

Ah, good

If we drop it while Mars is on the opposite side of the sun, we will be OK.

yup

How do you want to "drop" a black hole ?

And where ?

The same way you drop all bombs... with laser guidance.

@PhysicsGuy China.

But....

@CuriousOne The atom bombs were dropped the old fashioned way

This will effect us, too.

drop, then gtfo

Not if we are on Mars.

Ok, not then. It could orbit the sun.

Although, I rather move to Titan. On Titan people can fly.

By "it", I mean the black hole.

@CuriousOne What do you want to write ?

We already have black holes

@Slereah Let $M^n$ be compact and let $g(t), t\in[0,\tau]$ be a solution to the Ricci flow satisfying $\sup_M |R_{g(t)}|\le \tau^{-1}$ for all $ t\in[0,\tau]$. Given any integer $m\ge 1$, there is a positive constant $C$ such that $\sup_M|D^mR_{g(t)}|^2\le C\tau^{-2}t^{-m}$ for all $t\in(0,\tau]$.

For the grant?

(Sonic black holes)

Something about testing string theory, of course. :-)

Wonderful PDE nonsense

Why can't I see it typeset correctly? I always see the MathJax...

@Ocelo7 And now ?

and now what

Why did you write this definition ?

that's a result, not a definition

@Slereah can probably apply Ricci flow to his wormholes

That would be interesting.

Can I

So when is the NSF going to pay for the acquisition of a wormhole?

What does NSF mean ?

National Science Foundation

Sorry, Im a foreigner.

Ok.

Not Safe For

That's the guys who used to pay my salary.

I think you mean to type NSFW

:-)

@Slereah Most likely

Actually... DOE might be better for the black hole bomb thing...

@Slereah Suppose I'm doing induction on $P(n)$

I don't know what you're talking about

you crazy man

can I assume $P(0),\dotsc,P(n-1)$ are all true

or just $P(n-1)$

The assumptions on induction are $P(0)$ is true and if $P(n)$ is true, then $P(n+1)$ is true

can I also assume the others are true

up to $n$

If you know they're true, why not

But of course that doesn't help

$$\frac{\partial}{\partial t} D^mR=\Delta D^mR+\sum_{l=0}^m D^l*D^{m-l}R$$

what is this

@Ocelo7 Did you deal with Poincare-Conjecture ?

That appears to be maths

@PhysicsGuy not yet

qOcelo7 What d you mean by What is this ?

@Slereah no, it does here

@Ocelo7 What do you mean by "What is this" ?

I don't know :/

great.

i know

@ Did you find out ?

@Ocelo7

No

I'm having a crisis

Do you even know what this is related to ?

no

@Ocelo7 Why do you treat it then ?

@PhysicsGuy this Ricci flow is actually insanely hard to understand

Isn't that a statement relative to effective brain size?

No

Whales have huge brains and they won't understand it

Hence the qualifier "effective". The whale brain is not effective.

ah, I did not see that word

I need to estimate $$\frac{\partial}{\partial t}|D^{m-1}R|^2$$ given that weird equation above

Problem is, I don't even know how they're defining $|-|^2$

frick

@Slereah @yuggib this is a legit PhD level book :/

Ricci flow is really hard to understand

you're supposed to pull everything back to a fucking bundle, then use an induced connection on that bundle, then push everything back and let the $\le $ absorb all of the terms

???

@PhysicsGuy well if you know anything about Shi estimates now's the time to tell me

Holy guacamole @CuriousOne is here!

@DanielSank: I am watching the Ricci flow... can't decide yet, if this is about geography or rare medical conditions.

@Ocelo7 Not spontaneously, Im sorry.

So we really have

@CuriousOne ::Daniel cocks an eyebrow... is very confused::

$$D_{\partial_t}D^mR=\Delta D^mR+\sum D^lR* D^{m-l}R+\mathrm{stuff}$$

maybe?

oooo, maybe I can absorb that stuff into the sum

@DanielSank: Somebody in university told me confusion is the first step to learning... for me it was the first step to failing the exams. ;-)

@CuriousOne It's about estimating curvatures right now

@CuriousOne har har

That person was probably on to something.

I have a hard time believing you failed exams.

@0celo7: Don't waste your time... I know my limits. This is way over. :-)

@Ocelo7 mathoverflow.net/questions/109474/…

@DanielSank: I failed an oral plasma physics exam once. After that my question evasion strategies improved considerably.

@Ocelo7 Why dont yo ask sb here on PSE ?

Why would I ask about Ricci flow on PSE

I am looking in Chow's book right now for what they do

But I think this book is skipping a step

I have to go from $\partial/\partial t$ to $D_{\partial/\partial t}$ and then chuck the extra terms

@Ocelo7 citeseerx.ist.psu.edu/viewdoc/…

@PhysicsGuy yeah, but no one does it like this book, and I'm trying to figure out what they're doing

Ok. Good luck. I think you wont get to a result, im sorry.

Why do you think that

Because it seems hopeless.

what

I think I'm quite close

Like CuriousOne said....

I will soon understand line 2 in this 2 page proof

:<

what did he say

"Don't waste your time... I know my limits. This is way over. :-)" Or maybe I misinterpreted that sentence.

I think you did

Ok.

What is actually your aim ?

Why are you working on Ricci-Flow, what do you want to achieve ?

I remember somebody else claiming that one can't produce original research by publishing things one understands. ;-)

Poorly written proofs are so frustrating

I get an error term $\sim R\ast D^{m-1}R\ast D^{m-1}R$

I think that's fine

Yes, that is ABSOLUTELY fine

I need some results on Licernowitcz laplacians

Whats that ?

Not even Google knows that term... :-)

Because I cannot spell Polish surnames @CuriousOne

@PhysicsGuy A Laplacian on tensor fields IIRC

Ah, okay

Hmm, shouldn't Petersen have stuff about this

Or maybe Lee

What has this to do with Ricci-Flow, If I may ask this naive question ?

I'm still trying to calculate $$\frac{\partial}{\partial t}|D^{m-1}R|^2$$

This will involve a tensor Laplacian

And ?

And I need to show that $$\Delta |D^{m-1}R|^2=2\langle \Delta D^{m-1}R,D^{m-1}R\rangle+2|D^mR|^2$$

where $\Delta$ is the tensor Laplacian

Ok.

the idea is to get a bound on the derivatives of the Riemann tensor

Oh no, it's not the Lichnerowicz Laplacian I need

@Ocelo7 Its nice to follow your ideas through the chat....

I hope I don't have to explicitly prove this...

;)

$$\Delta T=\sum_k D^2_{e_k,e_k}T$$

::sobs quietly::

If I must...

I think I am catching up... with regards to the spelling of Polish surnames. :-)

$D^2_{X,Y}S=D_XD_YS-D_{D_XY}S$

oh gosh

Oh, Christoffel symbols appear!

Now it has something to do with GR

The calculation is $$\Delta|A|^2=\sum_k (D_{e_k}D_{e_k}-D_{D_{e_k}e_k})\langle A,A\rangle$$

Anyone want to do that?

no?

Where are the Christoffel-Symbols ?

$D_{e_k}e_k=\Gamma_{kk}^le_l$

Now it looks familiar.

I swear I've done this calculation before in my life

Really ?

Something similar at least

oh well

@CuriousOne My goodness that explains a lot about our previous discussions ;)

oh my god

magic

@DanielSank: Did it sound like Polish to you or like failed plasma physics? :-)

@PhysicsGuy I'm reading the book by Brendle btw

I'll ask for Chow, Lu and Ni for my birthday :)

@CuriousOne I meant the slippery conversational techniques.

Which, to be clear, are entirely infuriating.

@DanielSank: If you can't do, you have to fake. :-)

@CuriousOne :(

You know a lot though...

@PhysicsGuy Lol, it's trivial

@CuriousOne Coming to the AMA?

@Ocelo7 What ?

@DanielSank: Mostly about experimental techniques. As far as theory is concerned I am sticking to the basic definitions.

$$\Delta |A|^2=\sum_k\left[2\left(\langle D_kD_kA,A\rangle+\langle D_kA,D_kA\rangle\right)-2\Gamma^l_{kk}\langle D_lA,A\rangle\right]$$

@CuriousOne Theory is about explaining data as concisely as possible.

That equals $2\langle \Delta A,A\rangle+2|DA|^2$ after a battle

It's important for experimentalists to throw in their lot.

@DanielSank: What makes me mad, though, is that theorists who have the formulary under total control seem to have trouble linking it to observable phenomenology.

@CuriousOne Try not to get mad. It's not useful. Having formal mathematics under control is no small feat.

We need to recognize the diligence and importance of people like that and help make the bridge between their amazing skills and the data we measure.

@DanielSank: It's not that. We can totally agree that the math describes the experiments and observations really well.

So that gives $$\frac{\partial}{\partial t}|D^{m-1}R|^2\le \Delta |D^{m-1}R|^2-2|D^mR|^2+C_2\sum_{l=0}^{m-1}|D^lR||D^{m-l-1}R||D^{m-1}R|$$

I think we estimate that using compactness?

I dunno

I'm done for today with Ricci flow

Ok.

Tensors are all fun and games until you have to differentiate them a bunch of times

How do you want to use compactness ?

@PhysicsGuy continuous functions on a compact set are bounded

Tensors are fun....in physics

@DanielSank: What has happened since the 1970s is that generation after generation of theorist have written books about the theoretical descriptions that, unfortunately, over-interpret the theory. There is no need for that and it becomes ever harder to pull the layman back from these ideas to where physics really is as a science.

Also there's an induction hypothesis floating around

@Ocelo7 Yeah.

this book sketches a lot of proofs

filling in the details is challenging

What book ?

Brendle, I just said it

It's an informal intro to Ricci Flow

@DanielSank: I do get the frustration of the theoretical folks, I really do. Nature has really given us this puzzle where only the most ambiguous pieces are on the table... :-(

@CuriousOne Unless you give me examples I'm going to have to regard this as yet another "everything is always getting worse" proclamation. I find those tiresome.

@Ocelo7 I understand. Go on, how do you want to use compactness ?

@PhysicsGuy see that sum with the products?

yeah.

Please note that having more bad books doesn't mean the community is degrading. If we have 100x more books now then we did before, then we also have 100x more bad books.

Part of it I can relate to $t$ using the hypothesis of the theorem, and some parts I think I have to bound from above using compactness, that is all

There is a similar fallacy often made about pop culture; the idea is that music and movies are getting worse.

I need to get that sum to be $\le C_3 \tau^{-2}t^{-m}$

where $t$ is the time parameter and $\tau$ is a constant from the hypothesis

It's false. As anyone who watches old movies and listens to old music (i.e. me) knows, there was crap back then too.

and $C_3$ is just some constant

@DanielSank: It starts with "The First Three Minutes" containing Weinberg's religious preferences for a cyclical universe and now we have Krauss preaching the zero energy universe. :-)

Only the good stuff gets attention fifty years after original publication, so there's a strong sampling bias and we all think "the good ol' days" enjoyed better pop culture.

@CuriousOne I've never heard of either of those. Is it possible you are attracted to things you don't like because you enjoy being offended and then complaining?

That's really common, unfortunately.

We're all guilty of it.

@DanielSank: If you haven't notices, I am still trying to exorcise wave-particle duality, which officially should have died in 1929... :-)

Source: People pay attention to television news.

@CuriousOne Have you talked to John D. before?

@CuriousOne As an experimentalist I strongly disagree with that statement.

As a theorist I would agree.

And as a physicist who pays attention to both theory and experiment I'd say it's all subtle.

@PhysicsGuy Now I will move to some algebraic topology

@DanielSank: They are not paying attention to Phys. Rev. A-D articles...

to calm down after that battle

Čech cohomology

@CuriousOne Who's "they"? (By the way, it helps follow the flow of chat if you respond to specific messages).

@0celo7: Yes. :-)

@Ocelo7 Thats better. Start with simplicial complexes.

What's wrong with wave particle duality

@DanielSank: Pretty much everybody except for the people who are reading Phys. Rev., I am afraid.

@Ocelo7 It shouldnt occur.

@PhysicsGuy I am reading Bott & Tu

Whats that ?

A book

@0celo7: It gives people the wrong ideas.

On cohomology

It's very interesting

They try to motivate the simplical stuff by first doing de Rham

@CuriousOne what does that mean

I want to learn algebraic topology so I can study either twistors or surgery next

now let me read!

Ok, bye.

@CuriousOne I'm sorry, what? You're defining "people who don't pay attention to Phys. Rev. A-D" as "people who are reading Phys. Rev."?

confused

The library's copy of Bredon smells like a centipede

very characteristic smell

@ChrisWhite: Thanks! It drives me crazy.