The h Bar - 2015-09-09 (page 3 of 4)

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1:00 PM

@0celo7 You don't muck about with that string perturbation series/sum over worldsheets

@JohnDuffield No, it does not. That you detect single electron blips and not a continuous intensity on the screen means it's neither "a wave" nor "a particle".

@0celo7 : no. A 551keV is a wave in space in an open path, a 511keV electron is a wave in space on a closed spin ½ "spinor" path. There are no strings.

Oh man we need Lumo in here.

IT'S A QUANTUM WAVE

@JohnDuffield what is "waving"?

what is it waving in?

@ACuriousMind Well you don't actually do that much with the perturbation series...at least not in BBS.

They mention it but never actually calculate any terms.

BLT on the other hand...

@0celo7 Ah, good :D

1:04 PM

@ACuriousMind : no, it's a wave. A standing wave. Standing wave, standing field. You see dots when you do an optical Fourier transform and you understand why. Don't think the electron is some speck.

@Slereah @ACuriousMind @etc About that Lagrangian thingy I post up there, did I have a correct understanding?

@ACuriousMind Yeah, it's briefly in chapter 3.

BLT has about 60 pages on the bosonic partition function.

@JohnDuffield I think you would do well to read the first few chapters of some standard QM textbook. Sakurai's Modern Quantum Mechanics covers the double slit experiment in detail.

And another like 40 for superstrings.

@Slereah lol :D

1:06 PM

@JohnDuffield I don't think the electron is a speck. I don't think the electron is a wave. It's a quantum object. It has properties of both, but it is neither. It's best described by a ray in a Hilbert space. Go and learn quantum mechanics before talking about it.

It's a string dammit!

Kawaii little electron string

@0celo7 You go learn some string theory before you talk about it ;)

Some more

I know something

Some :D

11 mins ago, by John Duffield

@0celo7 : no, electron diffraction implies it literally is a wave.

^ Perhaps I didn't get the joke, why is it worthy of 2 stars?

1:12 PM

because of the word "literally"

1:24 PM

@skillpatrol : when a seismic wave moves through the ground, the ground waves. When an ocean wave moves through the sea, the sea waves. When a gravitational wave moves through space, space waves. At least, that's what the LIGO guys expect, hence: “if the two arms have identical lengths”. It's the same for an electromagnetic wave. Read what Maxwell said.

is there an aether?

Dude quoting maxwell is a bit ridiculous.

@Danu : ask a question about it and I'll give you an answer. I'm afraid some of the things in your textbooks aren't right. You surely must know this by now.

Perhaps more suited to this point than any other:

41 mins ago, by Slereah

user image

@skillpatrol : yes there is an aether. See this. We call it space. It isn't nothing. It's something that you can curve.

@ACuriousMind : well regardless of what you think, electron diffraction is a fact of life. Go and learn about it before talking about it.

1:28 PM

Luminiferous aether

In the late 19th century, luminiferous aether, æther or ether, meaning light-bearing aether, was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space, something that waves should not be able to do. The concept was the topic of considerable debate throughout its history, as it required the existence of an invisible and infinite material with no interaction with physical objects. As the nature of light was explored, especially in the 19th century, the physical qualities required of the aether...

@0celo7 : as ridiculous as quoting Einstein, and you think you know better because you've read a book by Penrose.

@skillpatrol : follow my link, Robert B Laughlin is no joker: "it rather nicely captures the way most physicists actually think about the vacuum".

Sorry guy, gotta go. Ask some questions, and I'll answer them to the best of my ability.

later pal

How can someone be so consistently wrong? It's an amazing feat to twist and misinterpret all of modern physics so thoroughly.

4

Bump, since this one is at least more sensible than my longer question far back:
Is there any significant meaning when the classical lagrangian vanishes, other than it means the total kinetic energy has the same value as its total potential energy?

If I have a lagrangian that vanishes for all times between t1 and t2, then the action of that system in question between t1 and t2 will be zero, what will that mean?

@ACuriousMind Occam's razor would suggest: "he is doing it on purpose, just to contradict everyone else". In my humble opinion, that's probably true; the motivation being just to entertain and at the same time anger every frequenter of this chat.

1:36 PM

@Secret No, because you can add total derivatives to the Lagrangian without changing anything, so it vanishing carries no meaning at all.

Ah that reminds me...

my memory constantly failed for small things like these

And again, with that feature of physics to allow different interpretations (and the relative difficulty to prove that a not-so-reckless interpretation contradicts experimental facts) he has a decent success.

Any one got any idea what this guy is trying to do here?

Smoke Detector School

Where Smoke Detectors learn

@yuggib Combined with all the answers he writes, that'd be a considerable investment of time just to annoy people he doesn't know

@TheDarkSide The smoke detector is there to automatically detect bad questions and post them in chat so the community can react swiftly

If a site wants to use it, you only need to tell the creator of it that, it he will start an instance of it in their chat.

@ACuriousMind everyone is entitled to have his own way of wasting time/slacking off

1:40 PM

The detector reacts to e.g. ALL CAPS TITLES, Korean or Chinese symbols, word repetition, unusual density of links, etc.

@ACuriousMind OH MY GOD. I thought he was a user spamming some chat with nonsense!

@JohnDuffield I haven't read a book by Penrose.

@TheDarkSide lol

Why do you keep telling me I've read books I haven't.

The "Smoke Detector School" is where he tests these bots :D

So yes, that chat is just completely filled with their alerts.

1:41 PM

@ACuriousMind Ohh...

And I went there on two occasions. Most recently, I posted :: sigh ::

Haha

:D

@ACuriousMind What irks me is that he never uses equations to explain anything

I could dig the electron being a photon going around a belt-like roller coaster

but there's no mathematical evidence

@0celo7 That's perhaps the reason why it rolls the way it does!

@0celo7 He is much smarter than that...within a mathematical framework, his assertions would be more easily falsifiable; in the realm of almost philosophical interpretations, it is harder to contradict

1:48 PM

Are these equations related in that that all describe some kind of minimal curves?
$$\delta \int_{t_1}^{t_2}L(\mathbf{q},\dot{q},t)dt=0$$
$$\dot{\phi}=0=-\nabla V(\phi)^{\perp}-\lambda \hat{\tau}$$
$$\ddot{x}^{\lambda}+\Gamma^{\lambda}_{\mu \nu}\dot{x}^{\mu}\dot{x}^{\nu}=0$$ ?

PS 2nd equation is from a reading of my honours project
http://scitation.aip.org/content/aip/journal/jcp/126/16/10.1063/1.2720838

@Secret Yes, e.g. the geodesic equation is the Euler-Lagrange equation for a specific action.

is it

prove it

@0celo7 Left as an exercise to the reader (to google for "length functional" and "energy functional" in the context of differential geometry).

@0celo7 Congratulations : You did there : physics.stackexchange.com/questions/201462/…, as a 1-year-user and member of the genious gang , what you didn't want to do others to you here, when a 2-month user. — diracpaul 2 hours ago

@ACuriousMind fyi I know how to do it

I'm not that terribad

diracpaul is right

I need to stand up to the tyranny of this site

lol

1:55 PM

I'm only half kidding there

I dislike the homework policy here

2 days ago, by Danu

diracpaul doesn't mess around

@0celo7 I was almost certain you knew

@ACuriousMind I mean, I have like 7 books that discuss it

BBS does it too

Let's see... Zee (x2), Weinberg (x2), Straumann, Wald, Hawking-Ellis, BBS, Cahill, Parker-Toms

maybe BLT but I haven't seen it

also

"genius gang"

tfw not as smart as the average german math or physics student

who's the most well known physicist to use Physics.SE

't Hooft

Gerard

well that's a modest answer

it is, of course, me

after 900 hours in battlefield and 1000 in CoD

I'm pretty famous

2:06 PM

The 2nd equation is part of some transition state finding algorithm called string method

the del part is the gradient of the potential energy V for some configuration of atoms in a molecule (V is thus a hypersurface that depends on the position of atoms)

$\perp$ means we are taking vectors normal to the curve at some point. The normal vectors depends on the gradient as follows:
$$\nabla V(\phi)^{\perp}=\nabla V (\phi)-\langle\phi|\hat{\tau}\rangle\hat{\tau}$$

the $\phi$ is a curve on this potential which connected between two configurations (the products and the reactants)

gerard the gerbil

jesus man your chat posts

"string method"

why are strings so cool

they aren't though

@Secret what is $\langle\phi|\hat\tau\rangle$?

@FenderLesPaul depends on the string tension

which is somehow a free parameter?

@ACuriousMind please explain

what is this free parameter business

why do people say ST has none

$\langle \phi|\hat{\tau} \rangle$ is the inner product between the curve and the unit tangent vector at a certain point. Thus it describes a projection, the tangential component of the curve

2:11 PM

ah ok

@0celo7 Didn't we have this discussion already once?

@ACuriousMind it was unsatisfactory

I'm pretty sure you said "I don't know string theory, I don't know"

Then why would asking the same person again be more satisfactory? :D

Go ask Lubos.

I would like to talk to him

I would love to see Lumo v. JD

that would be epic

You could also ask that as a question on the main site. Someone might answer. (You should source the statement "ST has no free parameter" first, though)

2:14 PM

"intellectual garbage man vs. Einstein and the evidence" it would be better than Mayweather v. Pacquiao

@ACuriousMind because you've learned some more string theory in the meantime

I don't know where I got that from tbh

> Actually, string theory model building is more constrained than plain QFT model building, due to the fact that at the heart of it there are no free parameters, since all parameters are instead fields of the theory

> The undertaking called string theory started out as perturbative string theory where the idea was to encode spacetime physics in perturbation theory by an S-matrix that is obtained by a sum of the integrals of the correlators of a fixed 2-dimensional conformal field theory over the moduli spaces of conformal structures on surfaces of all possible genera – thought of as the second quantization of a string sigma-model.

That's a very good summary!

@ACuriousMind nLab is cool!

2:29 PM

Are there other theory of everything candidates besides string theory that are competative in terms of support by the community?

I don't think so.

People might throw out LQG, but the following is not nearly as large.

@0celo7 You need not tell me that!

Damn now I want to get back to BBS

@ACuriousMind Seriously, please explain the section starting on page 211 when you get to it

I read that (mainly from popsci) LQG is only trying to make quantum gravity, but have made no attempt at unifying the other 3 fundamental forces

I do find one idea from LQG quite attractive, that it is independent of the background, on whatever the underlying spacetime is

No, a theory of everything should determine the background.

2:32 PM

legend has it that even the most silent utterance of the phrase "LQG" will have Lubos rushing to flame and rage in a moment's notice

string theory is intellectual garbage

::waits::

I want to sit down with one of the Becker sisters and Schwarz and have them tell me exactly what I need to know to read their book.

I feel like they won't explain any of the Kahler holonomy stuff at all.

Also a review of RG flow would be nice.

Also I'd love it if they explained spinors.

About string theory, I first made aware of this term from popscif like scientific american and newscientist, and like most people in the public excited at the idea of extras dimensions (though we don't understand that dimensions here has a precise meaning)

Later I was a bit demotivated because of such a long time no practical test to test its predictions since the energy required is still too high

Despite that, since it is not ruld out, I still considered as a candidate and I would like to learn about it and other Quantum gravity candidates in the future

And then 2-3 years ago, I learnt form sciencedaily that some condensed matter people found that there are equations analogous to those in string theory that help describe various phenomenon in condensed matter physics

I then have the following comment “it seems they have found some uses in condesned matter physics, but how far can a mathematical analogue stretch?”

Tldr: My position on string theory is: I want to learn it, but I am kinda ambivalent about it due to the experiment problems

PS If I post this in one go, Slereah will see "see full text" again

I have no interest in working with string theory in my real life, but there's no harm in reading about it.

> A global Lorentz symmetry of spacetime with all matter and force fields in it would mean that the world looks the same if we arbitrarily translate in some direction, or arbitrarily rotate in some plane.

nLab confused Lorentz and Poincare group?

what on Earth is "local supersymmetry"

damn superpeople

2:49 PM

https://en.wikipedia.org/wiki/Principle_of_least_action
@ACuriousMind What is physically happening to the evolution of the system as the action is minimised until it becomes stationary to first order?

I don't think it is ever "not minimized"

I understand a stationary action give the euler lagrange equations which for some given lagrangian one can extract the equation of motion from it

Yeah, classically, it is never "not minimized"

@Secret @0celo7 is correct. The classically occuring paths always minimize the action.

:3

2:52 PM

3 coffees in 2 hours

new record for me this semester

addict

ok, new reading plan:

analysis and Zee's QFT

so the non minimised paths only exists in the quantum domain?

I have it so I might as well read it

@0celo7 If I had to guess, I'd say supersymmetry as a gauge group.

@Secret ...not really

@ACuriousMind eh, what

oh the SUSY parameters are functions

du bist doch ein kluger Bursch(e)

2:54 PM

Junge

uh I forgot that word

e or no e?

@Secret Quantumly, you can't really speak of "paths existing" - the path integral formalism integrates over all fields/paths, but it's unclear what "existing" might mean. The quantum object does not follow any path (unless you are a Bohmian)

@0celo7 Hochdeutsch it's with e

@ACuriousMind what I thought

it's funny, even though Lang and I are both from the Pfalz, we always work back into hochdeutsch

gah, I really need to read a lot more before I can get my questions sensible

omg coffee high

yuussssssss

2:56 PM

@Secret where are you in your education

hopefully my honours will indirecly help me to advance more in my qunatum mechanics...

@ ocelo7 generating full background, please give a sec when infromation is being retrieved...

I'm currently learning parabolic motion!

yay!

WARNING the next post is HUGE!

(Note the list may not be exhaustive, anything not mention you can ask or assume I only know a bit)

Background:
Degree: Bachelor of Science (Physics and chemistry)

Chemistry:
=================
Inorganic chemistry:
-----------------------------------
Electronic structure of atoms (molecular orbital theory on diatomics, isotope effects, bonding (intra and intermolecular), quantum numbers, overlap integral, moorse potential, vibrational modes, radial distribution functions)

Solid state chemistry (types of solids, bonding (intra and intermolecular), bravis lattice, space groups and point gro…

and to top that:
I am currently in my honours in chemsitry, subfield photochemsitry , molecular dynamics and computational chemsitry

How did it let you make such a large post

I have no idea

3:08 PM

was that a one semester or two for ODEs

one semester, it's pretty basic stuff. We have not cover much on the complex number side of ODEs

and we are only introduced 3 types of PDEs, and they are all homogenous PDEs

what school

UNSW

that's a lot of material for one semester

one thing of note is that: I have a classical mechanics knowledge gap due to our physics school before the 2016 overhaul does not list this course as compulsory and double majors CANNOT do it without overloading

I also have zero experience in numerical calculations, which makes my honours a pretty steep learning curve

3:12 PM

tbh man you've asked questions that I would expect you to know based on that background

like that Lagrangian question should have been made clear in your quantum class

no they skipped that compeltely

because they thought it is covered in classical mechanics course, but they don't realise double majors have all electives filled in that they cannot take that couse

I mostly try to close my classical mechanics gap by workign wiht my friends and reading goldstein

was that one semester for linear algebra

and yes

what the heck

that's an insane amount of material

Our uni consider a full load to be equal to 4 courses, thus >4 is overloading
Some of my friends who do the same double major as I have done that, but I know I cannot handle overloading thus I have not overload and hence the classical mechanics gap

1 hour later…

4:20 PM

@ACuriousMind : I'm not consistently wrong. I don't make up stuff like electron diffraction or the Einstein-de Haas effect or the wave nature of matter.

@yuggib : I'm not "doing it on purpose just to contradict everyone else". I'm doing it to tell you about the correct physics.

@0celo7 : OK. But Hawking-Penrose has had a few mentions here. As you know I am not a fan of either.

You have to be pretty stubborn to argue against a mathematical fact.

@0celo7 : mathematics doesn't provide evidence. Science provides evidence. You know, things like Einstein-de Haas and electron diffraction?

@JohnDuffield The best way to get us to believe you is to show us mathematically why mainstream physics is incorrect.

@0celo7 : I'm not arguing against "mathematical fact". I'm pointing out the facts.

The singularity theorems are mathematical facts of general relativity.

To argue against them is to argue against the mathematical foundation of GR.

If you want to do that, fine, please read Hawking-Ellis and point out the line where the mistake is.

Who knows, they might have misused a topology theorem somewhere. If you can find it, great, write a paper.

4:32 PM

@0celo7 : aaargh! The wave nature of matter is mainstream physics. Singularity theorems are hypotheses, not facts. Learn to distinguish physics from mathematics. And stop dismissing Einstein in favour of mathematicians like Hawking who have never ever come up with anything that has been validated by hard scientific evidence.

Are the singularity theorems incorrect?

And the wave nature of matter is cargo cult popsci.

What? The wave nature of matter is not popscience. Where did you get that from? Some mathematician who dismisses the evidence and finds it easier to pretend the electron is some point particle? Tsk. OK, I've got to go, ask a question about the singularity theorems and I will tell you about the problem.

Can you formulate a fully consistent quantum theory of electrodynamics while treating a electron as a photon going around a Dirac belt? Awesome. I'd love to see it. If not, then I'll go with the theory that actually makes measurable predictions.

@JohnDuffield And what about the other leptons? Are quarks just gluons going around Dirac belts?

@JohnDuffield No, you don't make up these phenomena. But you do make up your own interpretation of these phenomena, which is completely at odds with modern physics, and does not yield a consistent theory making quantitative predictions. And you pretending to "teach physics" to others by telling them your personal ideas is dishonest and harmful to the goals of this site.

2

4:52 PM

@ACuriousMind How does a neutral gauge boson obtain a charge by fluttering around in a special pattern?

@JohnDuffield The electron is neither. It's a quantum object.

@0celo7 Why do you ping me with these rhetoric questions? If I'm pinged, I fell inclined to answer more or less seriously :P

@JohnDuffield I do not wish to ask a question about the singularity theorems. I want to know why you dislike them/think they are wrong.

@ACuriousMind How does the whole "fractional charge" thing work, anyway. Gluon magic?

I just don't see how gluons, which have no EM interactions, somehow produce charged particles.

@JohnDuffield How do electrons obtain mass? Saying $E=mc^2$ does not work because electrons have rest mass, photons do not.

Furthermore, how do electrons not zoom around at the speed of light if they're made out of photons?

@JohnDuffield What about neutrinos? Why is their mass so small and why are they neutral?

@ACuriousMind I think that's a nice array of questions for the meantime.

@JohnDuffield If you want to convince me and the chat of your ideas, explain them to us. Don't tell us to "ask a question" (it would get closed very quickly) or "do research." My time is valuable and I don't want to hunt down your links that are sometimes completely irrelevant!

And I never see you use actual equations to back your stuff up.

You're all about predictions but I haven't seen any evidence for your Dirac belt idea!

@JohnDuffield Mathematics allows us to extract predictions from a scientific theory. Assuming one does the mathematics correctly, one will obtain a truth within that theory. Thus, if you say a prediction of a theory is wrong or does not make sense, you either have to find a math error or make a correction to the theory itself.

Now, it is perfectly possible that the theory is wrong. Newtonian gravity is wrong. Einstein gravity is wrong as well. But once you accept that, it does not make sense to reference papers from before we knew that.

Now, if you want to argue that the singularity theorems are incorrect because GR is not a quantum theory of gravity...that's fine. But don't come shoving "Einstein and the evidence" in my face because there's nothing about quantum gravity in there.

@ACuriousMind Does that make sense?

5:08 PM

Yeah, to me, it does.

::cringe::

@ACuriousMind $$\frac{\mathrm{D}}{\mathrm{d}\tau}$$

that's the ugliest notation ever

make the lower $\mathrm{d}$ capital

5:32 PM

I didn't invent that one, OP used it first :P

@ACuriousMind We both agree that $\nabla_{\dot\gamma}$ is better, right

Yup.

good, good

@ACuriousMind do you upright the capital D for gauge cov. derivatives?

Can I derive the levi civita connection from geodesic deviation? (Obviously using the properties of that specific connection)

what do you mean "derive the Levi civita connection"?

like $\Gamma\sim \partial g$?

5:39 PM

@0celo7 I don't like writing it with the capital D, but yeah, when I write it, I typeset it upright.

@ACuriousMind whaaat

how do you like writing it

Or, um, I say that now. I can't exclude that I've done otherwise at places.

and how do you write the gauge cov derivative in curved spacetime

@0celo7 $\mathrm{d}_A$, where $A$ is the connection form.

ew

@ACuriousMind can you explain @NeuroFuzzy's question

5:42 PM

No, not exactly sure what it's about either

Okay, basically I am just unsure about deriving the christoffel symbols from the metric (which woukd solve me oroblem b/c the christoffel symbols relate to the connection). No idea what \Gamma or \sim or partial g mean in your eq 0celo7

I'd like to understand it in a more geometric way than the abstract defs in my book

I see that the connection is like a generalized jacobian, but then some extra properties are added to the connection relating it to the metric. The book says "there's a unique connection satisfying this" and moves on.

@NeuroFuzzy heuristically, the christoffel symbols are the first derivative of the metric

$\Gamma\sim\partial g$ means they are of the form of first partial derivatives of the metric

@NeuroFuzzy ah

this is true, the LC connection is unique

I think Wald and Straumann prove this.

HE perhaps

user image

hold up for the second part

Nonono I've seen that

I just have zero geometric intuition for that

Gyazo is broken

I'm not sure that there is any intuition

what kind of intuition are you looking for

user image

there we go

Well I mean

If $\nabla _x x=0$ is the equation for geodesics and comes from the levi civita connection, but extremizing the path length also gives the eqs for geodesics

5:58 PM

the LC connection is the only one that works that way

I think that's the principal argument for using the LC connection in GR

There should be some way to go from geodesics (minimizing path length) to defining the proper connection. And I'm wondering if anyone has experience with that and if that's a worthwhile line of inquiry.

@NeuroFuzzy: Do you have intuition for parallel transport? Then the Levi-Civita connection is the unique connection parallel transporting vectors in a way that preserves the length and angles between vectors

^^

remember that "length" and "angle" is defined by the metric

@FenderLesPaul you should catch up on the chat history

The shortest lines between points are "straight lines" - those where the tangent vectors doesn't change at all, so the curves of minimal path length (the geodesics) are the curves along which the tangent vector is parallel transported such that is it unchanged along the curve.

@0celo7 why?

6:01 PM

is good mane

@ACuriousMind hmm... I don't really for parallel transport. Geodesics, yes. Can yiu go from one to the other?

Yes

OH. like, parallel transport preserves angles between geodesics along the path and is torsion free?? Thay sounds good

See Straumann, who defines the covariant derivative in terms of a "parallel transport map"

@NeuroFuzzy: You can probably reverse this thought process, first define the geodesic as minimizing path lengths, then demand the tangent vectors are parallel transported such that they don't change along these shortest paths (because the geodesics are thought to be the "straight lines"), and then the only connection that does that is Levi-Civita again.

6:04 PM

@ACuriousMind I'll try working that out! Thanks!

" Those of you who have said it can't be done are right. That's because no one on the planet knows how QFT relates to our illusively physical cosmos. It is relatively easy to understand the math, but, contrary to a few notable mathematicians, the cosmos in not mathematics at its foundation. Math is a tool, a language, a model of reality, but is not reality itself." @yuggib another soul confused about what is a model of what ;)

and I am homle

@ACuriousMind : But a geodesic can be non-minimal! :O

Haha I understood though

@0celo7 1000? You n00b

6:22 PM

@0celo7 where's the good stuff?

I just see fruitless back and forth with John Duffield :p

@Danu :(

I'm terrible at everything

3

I'm on my phone so I cant star that message right now, but rest assured I will.

6:42 PM

@ACuriousMind Ahahahah exactly...I thought a little bit about that, and the mathematical notion clearly makes sense to me. Mathematics can describe structures with no physical meaning, so it makes sense that a specific instance of a theory should be called a model of that theory.

If that instance is our formalization of reality/physics (whatever that means), then it perfectly makes sense as a model in the mathematical sense

and you should say in that case the physical universe is a model of, say, the theory of unital $C^*$ algebras :D :D :D

In addition the metamathematical theorem of Gödel about completeness makes automatically the mathematical theory consistent (for it has a model)

It is extremely far fetched, and very few people would agree with me, but I find it reasonable.... :-P

The linguistic form of that last bunch of statements is horrible, but some sense still can be made out of it

7:11 PM

why would anyone star that

people are mean

"I am a philosopher of physics and have a pretty good understanding of all this"

Red flag right there

^

Slightly above "I am no physicist but I have common sense"

mr. astronomer is having a field day today

7:29 PM

"Thank you for playing!"

Aug 22 at 11:59, by John Duffield

Don't you want to play?

Playa gotta play.

The Warriors Luther "Come Out To Play"

7:53 PM

The Warriors - Can You Dig It

8:06 PM

Swing your arms from side to side

Come on, it's time to go, do the Mario

Phonics The Hedgehog

8:28 PM

@Secret I see, interesting. Thank you for your detailed answer.

8:39 PM

@Slereah you down for helping an impoverished college student with an ODE

I'll give it a shot

$xy'-y-x\sin (y/x)=0$

I did the substitution $u=y/x$

and then used the variables $u,x$.

what does that get you

after some simplification I ended up with $$\int \frac{\mathrm{d}u}{\sin u}=\int\frac{\mathrm{d}x}{x}$$

No clue how to do that integral, but my handy Abramowitz and Stegun gives $-\log(\cot u+\csc u)$

Ooh csc/sec integrals are annoying

8:43 PM

so $-\log(\cot u+\csc u)=-\log x+C$

John Baez (mathematician/mathematical physicist at UCR) has said "the only way I know of doing it is remembering the clever substitution"

What is the Clever Substitution

now how on Earth did the book end up with $y=2x\tan^{-1}Cx$

The Clever Substitution is something something probably just u=\cot u+\csc u

yeah that's it

it's dumb

8:44 PM

Just memorize it.

Well if you memorize it, you might as well get the solution from a reference book :p

note that Wolfram actually disagrees with the book solution

what does it say

well now that I think about it

is $\tan^{-1}x=\cot^{-1}1/x$

hm

Let's see

8:47 PM

I caught some communicable disease when I was with my nephews

I'm not in ODE solving shape

$ \tan (\arccot x) = \frac{1}{x}$

Apparently

I meant memorize the clever substitution

you don't need to specify communicable

You can't catch down syndrome or inbreeding from someone

wtf

whatever, how do I do this

user image

what

that's not what the integral is

you dun gooved

Or did you

csc is 1/sin

no goofin

8:50 PM

no that's right

but that integral...

nono iirc there are a bunch of equivalent forms of the integral iirc

it's a very annoying integral wherever it pops up

well how the hell do I do that integral

and get it in that form

ok that does give the right answer

but how on Earth does one calculate that

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Sep '159

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