The h Bar

SchrodingersCat

16:01

Earnest request to all who are reading this: Can you provide me a pdf version of Bertrand Russell's "Analysis of Matter"? I have searched the net and university library but could not find it. I need the entire book . Thanks for helping.

Hari Prasad

16:37

@SchrodingersCat Is this what you are looking for : The Analysis of Matter by Bertrand Russell

0celo7

16:53

@ACuriousMind How does one actually prove that sine and cosine are related by a phase?

ACuriousMind

@0celo7 What have you tried?

0celo7

@ACuriousMind well, tbh I don't know how we're defining cosine and sine in our analysis class

(I'm proving continuity of cos(x))

And we did sin(x) in class

ACuriousMind

@0celo7 So, how am I supposed to know?

dmckee

I know how I'd do it. Two ways, too.

Geometric and analytic.

The analytic way is kinda wordy, though. Suitable for my students but not subtle.

0celo7

If I have access to sum and difference for trig functions it's easy.

So I just define everything via complex exponentials

@dmckee what's the geometric way?

Secret

16:58

Crap, I screwed up another question of mine because of not awaring some maths manipulation rules...
http://physics.stackexchange.com/questions/241628/can-an-entangled-state-act-like-an-operator-when-interacting-with-other-states?noredirect=1#comment528962_241628

The refined question is however too small to ask in the main site (and might already have covered by the main site), I should look it up to find more info on that

If anyone is interested, the refined question is: Since the complex conjugate lies in the dual hilbert space, why will the interaction of the entangled system with a state in one subsystem will result in a state in another subsystem with FLIPPED phase?

DanielSank

@Secret I don't suppose you could post that math as a question with mathjax? It's hard to read.

Secret

Ya I noticed (and insanely hard to proofread without rendering)
Not to mention I could have avoided that question if I am aware I cannot just naively make inner product expressions from bra-kets

Acuriousmind cleared up most of the confusion, the rest can probably be answered via self study

ACuriousMind

@Secret Once again, I don't understand what you're doing at all. Applying an entangled state as a tensor to some random vector in one of the subspaces is not "interacting" with it, and I don't see why you think this operation has physical significance.

If you want to go back to one of the subsystems, the density matrix formalism and the operation of the partial trace is the correct one, see this answer of mine.

Secret

@Acuriousmind I thought in analogy to how 2nd order tensors can be multiplied to (co)vectors to give another (co)vector, I can do the same thing for entangled states and state vectors to give another state vector (because of how the entangled state is basically a 2nd order tensor (if only tw subsystems are invovled). Therefore I tried to do this evaluation to check whether an entangled system can act like an operator, simialr to what matrices does

I will check out the link now

DanielSank

@JohnRennie The moment we use mathematics to do anything beyond counting discrete objects I'm pretty sure I find a lot of infinities.

0celo7

17:07

@ACuriousMind Seriously?

You're magic 99% of the time

ACuriousMind

@0celo7 Yes, seriously. If your problem is that you don't know how the class defined the sine and cosine, how could I possibly tell? I could give you proofs for the phase thingy, sure, but you would just reply "we didn't define it like that" or "I knew that".

dmckee

@0celo7 Triangle ABC has a right angle at vertex C. We see that $\frac{AC}{AB}$ is $\sin b = \cos a = \cos (\frac{\pi}{2} - b)$, then you invoke the evenness of the cosine to get $\sin b = \cos (b - \frac{\pi}{2})$.

0celo7

@ACuriousMind I know how to prove the phase thingy using the angle sum rules.

Is that how you would prove it?

Problem is, we didn't define sine/cosine at all.

ACuriousMind

Then whatever you're taking there is not an analysis class :P

0celo7

@dmckee Hmm.

@ACuriousMind :/

dmckee

17:12

@0celo7 That is easy enough to even south Texas high-schoolers.

0celo7

One more group that I'm not as smart as

Hari Prasad

i changed my profile pic and name but it doesn't change in chat. why?

0celo7

What is vertex C again?

Is that the one opposite to line AB?

dmckee

@0celo7 Yes.

0celo7

What are a and b?

@ACuriousMind lol

dmckee

17:15

The angles at vetecies A and B, respectively. I don't actually recall the notation used in that class, so I'm making it up as I go along and you're suppose to have the intuition to follow.

0celo7

I'm bad at math

ACuriousMind

@HariPrasad It just takes a while

0celo7

Why? Probably caching

ACuriousMind

Exactly ;)

dmckee

Everything excepts posts and comments on the whole Stack Exchange network is aggressively cached. So delays are ubiquitous.

0celo7

17:17

Why are posts and comments not cached

Hari Prasad

@0celo7 its too much maybe

0celo7

get bigger servers

bigger hard drives

Hari Prasad

@0celo7 but everyday the data gets bigger and bigger

0celo7

get bigger hard drives every day

Hari Prasad

@0celo7 lol you must be rich

0celo7

17:19

no

ACuriousMind

...why would caching them require more servers than not caching them? oO

0celo7

@ACuriousMind ::doesn't know what caching is::

beats me

Hari Prasad

@ACuriousMind caching is more proccesor intensive job

ACuriousMind

Posts and comments aren't cached because it would be pretty dumb to think you're the first one to write an answer when someone else answered it an hour ago

0celo7

huh?

ACuriousMind

17:21

@HariPrasad Caching is not a processor intensive job at all. Caching means that the data you're shown (profile picture, reputation, you name it) is possibly a bit old precisely because the database is not updated in real time because that would be processor intensive

@0celo7 If the posts were cached that would mean you would not see answers and edits appear in real-time

0celo7

@ACuriousMind why

ACuriousMind

@0celo7 Because, uh, that's caching means - you don't get the "real" deal, you get some information that was stored previously for fast access and is updated only more or less periodically

0celo7

Hmm.

ACM is now a computer science major.

I give up.

Secret

there goes another broken question...

grrr guess I have to read a lot more to reduce unknown unknowns in my knowledge base so as not to make errors like these

ACuriousMind

@Secret There is nothing there you didn't know. You just, once again, didn't think carefully about what you wrote down. Your "inner product between two different Hilbert space" just has no meaning. It's not that you were missing a rule, it's that you made one up without ever stopping to think about it.

I've told you this before, yet you keep writing down such symbols that don't mean anything in your questions.

Secret

17:37

I know, I am not thinking hard enough that I am not awaring that something I wrote actually makes no sense

sometimes I am wondering whether I am too impatient on trying to understand something by start doing algebra on it

"Applying an entangled state as a tensor to some random vector in one of the subspaces is not "interacting" with it"

I understand now that your answer in that link you give me told how to go to one of the subsystem, or from a mixed state in the subsystem to a pure entangled state

But what is the correct way to write out an entangled state interacting with antoher state. Do I need to express them both in terms of density matrices first?

ACuriousMind

@Secret Interaction is encoded in the time evolution, i.e. the Hamiltonian, not in the states themselves.

Secret

Ok noted, I am thinking way too much into general operators acting on states (e.g. $\hat{p}$, $\hat{x}$, $\hat{L}$ etc.)
In that case, I think the main site already have a related question I have stumbled upon

Secret

Whenever I tried to understand something (especially in physics), I often start to do algebra after reading a bit
I guess I need to think more on whether stuff I wrote is actually makes sense

0celo7

Someone should suggest a phone wallpaper for me

?

Hari Prasad

@0celo7 What's that? phone wallpaper?

Gross Domestic Product

0celo7

17:50

GDP is love, GDP is life

Hari Prasad

@0celo7 GDP is Gross! :P

0celo7

@HariPrasad Huh?

Hari Prasad

@0celo7 just kidding

0celo7

I don't find plays on words funny when it comes to the holy GDP

that's like using the Lord's name in vain

Hari Prasad

@0celo7 holy GDP?

0celo7

18:01

@HariPrasad Yes.

Hari Prasad

What is its Full for?

0celo7

Full?

Hari Prasad

I mean the expansion of GDP

0celo7

Ok now that's just silly

@HariPrasad what

I don't understand what you're asking

Hari Prasad

Is GDP = Gross Domestic Product

0celo7

18:07

yes.

Hari Prasad

@0celo7 Then why do you think GDP is holy X(

0celo7

@HariPrasad because

Hari Prasad

@0celo7 go on

0celo7

oh look a butterfly

Hari Prasad

@0celo7 are you kidding me? again GDP is Gross Gross Gross!

Revolver Ocelot!

0celo7

18:14

what?

I'm busy

Hari Prasad

@0celo7 me too. Bye! peace!

user54412

@tpg2114 I have not seen this done explicitly, though I keep hearing "there are ways to do RK with less memory." One thing is there seems to be different formulas floating around. Compare your stuff to wiki -- the a_i's have to move in and out of F it seems.

user54412

With the wiki definition it seems straightforward: calculate a partial step, accumulate that into the answer with the right coefficient, then overwrite the partial step with the next partial step. This works whenever the Butcher tableau has a_{ij} being nonzero only on the outer diagonal.

dmckee

18:29

@0celo7 Meh! GDP is a flawed measure.

Because it counts activities as useless as having one group of people dig holes and another group fill them as productive as long as someone is writing them pay-checks.

I don't know a better measure, but too much focus on GDP without thinking about what it means opens avenues to considering destructive policies as productive.

Here is a scenario that you might like: every person hired by the government to write and ever changing set of rules with which business have comply increases GDP.

So does the hiring of the people to keep up with the compliance paperwork.

But depending on the nature of the law neither of those things necessarily increases the well being of the country. And in fact, if people are laid off or not hired because of compliance costs then they might destroy real well being.

dmckee

Hmmm and that info graphic is flawed because raw GDP can tell you about either productivity or simply the number of people present. Note that the USA and China are nearly the same tone, but China was four time the population.

SchrodingersCat

And yes, that is the Analysis of Matter by Bertrand Russell that I am talking of.

@HariPrasad The link you have given is just a review of the book. I want the actual full version pdf of the book. Can you help me find it?

0celo7

@dmckee actually no, because taxes are subtracted from GDP

dmckee

18:45

@0celo7 The taxes that are subtracted don't cover the paychecks that are written. And it doesn't effect the point about compliance costs.

0celo7

If paychecks are written, then the work is valuable to someone.

(Assuming it's not the government writing the checks.)

dmckee

@0celo7 Seriously? If you pay someone to do nothing but deal with compliance issues that doesn't generate any value unless the compliance is protecting something of value.

And to assume that all compliance was protecting something valuable would be to assert that the government doesn't get pwn'd by special interests over and over again.

0celo7

@dmckee In a free market, GDP is a good measure.

We're not in a free market.

But the meme of my GDP fetish is here to stay, I'm afraid.

Can't back down now.

@dmckee My physics prof wants me to send him solutions of the wave equation for interesting geometries because we're doing waves/sound and it's actually good review for my upcoming midterm.

dmckee

In some kind of libertarian utopia, sure. But you've never met one, and even with the political will (which doesn't exist) and assuming that human are capable of it (which isn't clear) bootstrapping one from where we are would be a generations long project.

0celo7

@dmckee How do you distinguish between $\Theta$ and $\theta$ in handwriting?

ACuriousMind

18:57

$\theta$ should be $\vartheta$ in handwriting.

0celo7

I can't draw that.

ACuriousMind

Well, that's not $\vartheta$'s fault!

user54412

pretty sure $\Theta$ has two disjoint pieces

ACuriousMind

^also that

It's difficult to see in small print, but the $\Theta$ is an O with a bar not touching the O with serifs at the end in the middle.

0celo7

I have eyes.

dmckee

19:00

I do it Chris' way.

0celo7

Who here knows about the uniqueness of solutions of PDEs

When one says that the "generating function" of the Bessel functions of the first kind is $$\exp\left[\frac{z}{2}(u-1/u)\right]=\sum_{n\in\mathbb{Z}}u^nJ_n(z),$$what does that mean?

dmckee

I know I like to have a uniqueness theorem on my side. Otherwise you never know when you've covered all the bases.

ACuriousMind

@0celo7 Differentiating that function $n$ times and evaluating at $u=0$ gives the $n$-th Bessel function.

0celo7

@ACuriousMind One presumably proves this by doing just that and plugging the result into the Bessel equation?

ACuriousMind

That's like the generating functional in QFT whose $n$-th derivative at $J=0$ gives the $n$-point function. In general, the generating function $F(x,y)$ for a countable set of functions $f_i(x)$ has $\left(\frac{\partial}{\partial y}\right)^n F(x,y)\rvert_{y=0} = f_n(x)$.

0celo7

19:07

@ACuriousMind Um, how do you deal with the division by zero?

$n\in\mathbb{Z}$, not $\mathbb{Z}_{\ge0}$

ACuriousMind

Oh, right

Bernard Meurer

Hai

Mad avatar @0celo7

0celo7

Thanks

@dmckee was this supposed to be a pun?

ACuriousMind

I guess this is an abuse of terminology, that function is not a "generating function" in the sense I wrote above. It is a generating function in the more general sense of being a power series with coefficients the functions it is supposed to generate.

Which I know sounds kind of circular, and it is ;)

0celo7

@ACuriousMind Pretty sure my PDE course is just one giant abuse of terminology

He promised to do a day just on Bessel functions at the end if we have time

user54412

19:15

I can't recall generating functions (in analysis) being anything other than cute diversions.

0celo7

But for how, we should just use Mathematica if we need something about them :/

@ACuriousMind why is $a$ in $f(a)=0$ called a root?

What's the German word for it?

ACuriousMind

Nullstelle. I think the "root" usage evolved because if $f(x) = x^n - c$ then $a$ is an $n$-th root of $c$, but I'm not sure

0celo7

@ACuriousMind It's as good a theory as any.

dmckee

@ChrisWhite I believe they were much more useful in the days when tables of special functions were compiled by hand (as in Abramowitz and Stegun).

You keep manipulating the series forms until you find one which lets you get the first $N$ digits with relatively few computations.

0celo7

19:43

I'm impressed by the volume of stuff my PDE prof manages to put on the board.

Bernard Meurer

He has a 3D board?

0celo7

Yeah.

He 3D prints the notes.

Bernard Meurer

Good stuff

0celo7

just sticks the equations up there

Bernard Meurer

Donald Trump Sings & Dances - Songify This

►

0celo7

19:46

@ACuriousMind Btw, Heine-Borel + Archimedean property implies bounded sets have a sup.

You need the Archimedean property to get $\sup A=\max A$ for $A$ a closed interval.

vzn

21:44

@innisfree this book is on my to-read pile. looks well researched & lively.

amazon.com/The-Age-Entanglement-Quantum-Physics/dp/1400095263

read this one recently, liked it, esp the unorthodox angle, remarkable meticulous research :D

amazon.com/How-Hippies-Saved-Physics-Counterculture/dp/…

Danu

22:14

@ACuriousMind Ask on History of Science and Mathematics?

vzn

@Danu ahem, a considerable point. my povs mesh. am still trying to wrap my brain around your own. on one hand you want to emphatically avoid the ref to anything perelman wrote as "controversial" and then turn around to label my own views (entirely based on highly documented evidence/ other credible authorities albeit minority/ contrarian) "controversial". so the word "controversial" is used like a red flag. as if credible new scientific theories could never be "controversial".

Danu

@vzn You keep on repeating nonsense about what I supposedly "want to" do. I told you to quit that.

Btw @ACuriousMind I think it's related to the word "radical" (recall that radix means root in Latin)

vzn

@ChrisWhite the proof is extremely involved/ intricate and spans many pages. the peer review was not typical because it was not a typical paper/ proof. it was (literally) extraordinary. re the old quote "extraordinary claims require extraordinary evidence". (Sagan)

Danu

Ah, yes I'm correct.

Lo Bello's book on the Origins of Mathematical Terminology has the following:

vzn

@Danu actually the transcript clearly shows you started that. was/ am merely mirroring your own construction. maybe you should consider avoiding that which you demand others to avoid.

Danu

22:23

> The Latin noun radix, radicis means root. Radix is the translation of the Arabic word [insert Arabic word], root, used by al-Khowarizmi for the solution of an equation.

@vzn Actually, the transcript shows this:

yesterday, by vzn

@Danu you seem to reject the human/ social process of proof review by experts...?

First instance of you telling me what I'm "doing" (and I'm not actually doing that)

vzn

yesterday, by Danu

I have a strong suspicion that your POV is heavily by your own controversial views on quantum physics and thus you might want to paint all progress as controversial in order to legitimize your position, but that's besides the point.

ACuriousMind

@Danu Interesting, that clashes a bit with the history of "root"/"radical" as given by Conifold here

Danu

@vzn Note how that is after the quote I just produced.

Stop trying to twist this.

ACuriousMind

I think the question is pretty much answered there already - in a sentence, Conifold says "the name likely spread to general polynomial equations by association", i.e. what I guessed above.

Danu

Nobody who took part in that conversation denies that scientific progress is occasionally controversial. We all know several examples. But you're just dead wrong that in the Perelman case any such thing happened.

ACuriousMind

22:26

Not much of a leap from polynomial equations to equations in general from there

Danu

I have speculated on why you might want to construe it as such, always clearly indicating that this was pure speculation. On the other hand, you have repeatedly and under the pretense of fact said what I, ACM or ChrisWhite "want" to do, always saying things that none of us want.

vzn

@Danu somehow your constructions with roughly the same words are legitimate and mine are not. :(

my sentence you quoted said "you seem..." so apparently your speculation is somehow more privileged than my speculation.

Danu

@vzn Am I supposed to take this seriously? You're trying to play a victim now? Good luck with that. It's obvious to anyone who wants to check that I always kept it clear that my guesses at your motivations are nothing more than guesses.

@vzn Sure, but there are several instances where you left the "seem" out.

Anyways, I'm done with this. Let's stop talking about it.

vzn

@Danu fine, but am not done myself talking about new physics theories. youre free to ignore it or (inaccurately/ unfairly) reject it all as baseless. whatever

Danu

Okay. I'll make sure to ignore it :-)

vzn

22:32

@Danu think some "twisting" is going on elsewhere :(

ACuriousMind

@vzn You didn't really so much speculate about our motives as claim things we haven't said. Saying "You seem to reject the social element" is not an inference about our motives, it is a claim about what we had said. One may find Danu's speculation about your motives inappropriate, but you keep either misunderstanding or misrepresenting the positions of others.

vzn

@Danu furthermore, think you are not fully informed on the perelman proof history. its a dynamic/ extended history, excellent case study of complex sociology of math; you seem to have a rather simplistic pov on it.

Danu

FYI vzn I won't see any further messages, so don't try to continue the discussion with me please (that'd be a waste of your time).

vzn

@ACuriousMind lets not overthink/ split hairs on the statement "you seem". it admits/ concedes ambiguity/ uncertainty. it is hard to understand others complex positions in chat based on short sentences.

Danu

@ACuriousMind I don't think it clashes.

The source I cite brings it back to Arabic authors---which easily predate the part of history that Conifold discusses.

The real question, now, is why al-Khowarizmi used "root" for "solution of equation"

vzn

22:36

@ACuriousMind see no evidence of that. :(

ACuriousMind

@Danu Conifold tries to explain the reasoning - In $x^n = a$, $x$ is the hidden "base" = "root" of $a$

vzn

@Danu chatting with you would be a "waste of time"? sorry you feel that way :(

Danu

@ACuriousMind I don't actually understand that sentence. In what sense is it a "base"?

dmckee

@vzn He means he has ignored you in chat, and that your message will no longer appear to him.

Danu

@dmckee Correct.

dmckee

22:38

Ad now I am going to use my Upset Mommy voice ...

Danu

Bring it :D (and feel free to delete whatever you like)

vzn

@dmckee what are you upset about?

ACuriousMind

@Danu In the sense of base of a number system - $a$ is an "integer" in the system with base $x$

dmckee

The time for scoring rhetorical points on this matter has ended. Why don't you agree to disagree.

Danu

@ACuriousMind Ah, like that. I still don't really find it convincing, but okay.

@dmckee Hey, I already have! :)

By making the discussion impossible to continue

ACuriousMind

22:40

@Danu Well, I find many of the naming choices not really convincing, such is life :P

dmckee

@Danu Well, yes, but the Upset Mommy voice is always dispense equally across all present.

Danu

Really the only issue for me were the assertions on what I was trying to achieve, as well as claims that I am not informed on the issue (when the evidence points in... a different direction). Okay, I'm really doing to stop talking about it now!!!

@ACuriousMind By the way, Lo Bello's book is amazing

He rages so hard against mixing of Latin & Greek

It's hilarious

ACuriousMind

You already said that once, I think.

Danu

> People who know neither Greek nor Latin know the word moral, and some of them even know that the prefix a- negates the sense of the following adjective to which it is attached. The result is the word amoral intended to mean immoral. However, if amoral is to mean anything, it must mean pertaining to love, from the Latin amor, love, and this is the only meaning it has for people who know something.

ACuriousMind

I've gotten used to random mixing, there's nothing to be done about it

Danu

22:43

Heh :)

"for people who know something"

ACuriousMind

He apparently has not yet met people who use "amoral" to mean "devoid of moral value" and "immoral" to mean "of negative moral value"

Danu

BUT IT'S WRONG

(channeling my inner Lo Bello)

> Abelian Not to capitalize the first a is a mistake. Adjectives formed from proper names must always be capitalized, for they otherwise look ridiculous.

> Humanity defers in such matters to those with taste, and only those with no taste write abelian.

ACuriousMind

Reminds me of:

-1

Q: Thanks to let me write "lagrangian" in lowercase

Thank you for your attempt to edit my post better, and I appreciate every edit you make. However please keep in mind that I intentionally use lagrangian, not Lagrangian. I know that Lagrangian is widely accepted and if I write it differently, you will find something not right, and you have the ...

Danu

Yeah... That was a waste of time :P

Another gem:

Bernard Meurer

thingiverse.com/thing:340693

Danu

22:55

> **anticommutative** This is a bad word, the marriage of the Greek preposition ant- (against, opposed to, opposite to) and the Latin-based word commutative. The equivalent Latin preposition contra should have been used at the time of birth. Such absurd words, half Latin and half Greek, are exclusively concocted by people ignorant of both those languages. Dr. Johnson condemns the use of such hybrids as typical of the confused speech of barbarians, conveying by a mixture of signs and grunts ideas that they are unable to get across singly in any one of those way…

[won't let me correct the typesetting, for that would make the message "too long"]

Transcript for