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12:16 AM
Guys, someone explained my way of thinking about quantum mechanics for me!
http://en.wikipedia.org/wiki/Relational_quantum_mechanics
@ACuriousMind ping, since I know you respect this sort of thing.
 
@DanielSank "zero world interpretation". I like it.
 
@ACuriousMind Can it be experimentally verified?
 
@0celo7 No, but that's fine, because it seems to make no statements about the world at all. It just makes explicit the fact that all physical theories essentially are descriptions of information available to us rather than descriptions of "reality", I think.
 
12:31 AM
This is scarily accurate I think.
Although "scientist" should include engineer.
Although my dad (engineer) made me memorize pi to five digits when I was too young to know what pi is.
 
@ACuriousMind is it the case then that quantum interpretations amount to a choice of 'gauge'?
 
@ACuriousMind I'm retarded...pls halp smbc-comics.com/index.php?id=393!!
 
@AlfredCentauri Hm...it would be the most hotly contested gauge choice of all time, then.
They indeed always seem to boil down to a choice of what is "real", though.
@0celo7 Not all SMBCs make sense to me, either.
 
@DanielSank "someone explained my way of thinking about ____ for me! " hehehe
 
@ACuriousMind Is SMBC a troll?
I feel like some of these webcomics are either a reference to something or are just nonsense trolls.
 
12:38 AM
@0celo7 the earlier ones can be pretty dumb. I think "insulin shots" could be replaced by "food and water" or any other thing. The joke is taking "all we need is each other" too literally.
They're hit or miss but... doesn't he write one basically EVERY day? They can't all be good haha
 
@0celo7 ...sometimes, I guess
@NeuroFuzzy Yes, one comic every day. The quality is surprisingly high for that rate
 
@ACuriousMind Does parallelizable imply zero curvature?
(I think Nakahara is saying this, but he's being cryptic.)
 
@0celo7 Yes, parallelizability implies the tangent bundle is trivial, and trivial bundles cannot have non-zero curvature
 
@ACuriousMind Hmm, are Lie groups parallelizable?
 
@0celo7 Yes
why?
 
12:50 AM
How does Yang-Mills work then?
Isn't the field strength trivially zero?
(I don't actually know what I'm talking about, have not studied bundles yet.)
 
Yep, you don't know what you are talking about ;) The Yang-Mills curvature is not the curvature of the tangent bundle of spacetime (or the Lie group), but of a principal bundle over spacetime with the gauge group as its structure group
 
Ok, 150 pages to go for the first reference of "principal bundle"
Gimme a week.
@ACuriousMind This whole business with the contorsion tensor is new to me. It seems that we can almost "gauge transform" it away since $\Gamma+t$ with $t\in\mathcal{T}^1{}_2(M)$ is another connection.
Is that an appropriate view?
 
@0celo7 Why would that be a gauge transform?
 
@ACuriousMind Quotes.
We have a degree of freedom, so we use it to eliminate a term we don't like, i.e. the contorsion.
 
@0celo7 I don't follow why $\Gamma \mapsto \Gamma + t$ would be a degree of freedom.
You aren't free to choose the connection.
 
1:02 AM
@ACuriousMind I thought there were many different connections.
 
Yes. But they aren't equivalent
 
I know they aren't equivalent.
I'm saying if you have a valid connection $\Gamma$, then you can construct $\Gamma+t$ which is also valid.
 
That's true
Given a connection with torsion, you can always construct a canonical torsion-free variant of it
But I would not call that a gauge freedom in any sense, since things related by a "gauge transform" should be equivalent in some sense.
 
Ok.
@ACuriousMind Has Sofia held up her promise never to return?
 
Did she? I hadn't heard that lol
 
1:08 AM
@0celo7 I've not tracked that, but I don't think I've seen anything from her, so probably: Yes.
 
@ACuriousMind I just poured the last bit of a sampler of this. Have you ever tried it? Wonderful vanilla finish and aroma.
 
1:25 AM
@0celo7 Nope, I don't know that one.
 
@ACuriousMind Do Germans like bourbon or is it seen as a heathen drink?
50%+ corn isn't for everyone.
 
@0celo7 I personally don't like bourbon, but the German as such isn't really a whisky drinker, so no cultural preference here, I think
 
@ACuriousMind Do you similarly dislike rye whiskey?
There's something about it that I dislike, but can't put my finger on it.
 
I don't think I've ever tried rye whisky
 
@ACuriousMind Pedantic note: American whiskeys are spelt with "ey".
@ACuriousMind Holy crap this exercise: Calculate the Riemann tensor of $\mathbb{R}^3$ using the metric in spherical coordinates, the Robertson-Walker metric and the Schwarzschild Metric.
Riemannian geometry exercises are ridiculous.
 
2:15 AM
0
Q: Age - Score Relation

Kyle KanosHT to Danu on this one. So there was this recent post inquiring about answering 0-answer questions in which a comment read, It is not evident that votes on answers to old questions are fewer than on new ones and, elsewhere on the site, it was mentioned that late answers are typically eithe...

 
 
1 hour later…
3:26 AM
Nice post @KyleKanos ^
:: hat tip :: lol
 
Thanks
 
Is spacetime curved whether or not other objects are present? In other words, the sun curves spacetime irrespective of whether other objects are there, right?
 
@StanShunpike correct. In fact, spacetime can be curved without the presence of any objects if the so-called cosmological constant isn't zero.
 
3:46 AM
@AlfredCentauri true, I hadn't thought of that. Question: are the effects of gravity still considered to extend to infinity in GR? If so, how do we know this? Or is it just an assumption?
 
@StanShunpike gravity is spacetime curvature. If the the spacetime is asymptotically flat, then, 'at infinity', the curvature is zero and there is no gravity. But, honestly, 'infinity' is not obliged by what we 'know'.
 
@AlfredCentauri in other words, infinity might not be a physically meaningful concept?
 
4:03 AM
@StanShunpike it's meaningful but subtle. I can't do the subject justice here (maybe someone else can). It would be great to get you and a few others here around the fire pit for some libations and BBQ here in sunny FL to discuss. Maybe some day...
 
@AlfredCentauri That would epic :D
 
4:53 AM
@ACuriousMind YES!
Yes yes yes yes a thousand times YES!
 
5:39 AM
The book Curvature and Homology by Goldberg, despite having lengthy sections on complex geometry, does not use $\mathrm{i}$ but instead writes $\sqrt{-1}$ everywhere. Seriously.
 
 
4 hours later…
9:28 AM
@StanShunpike I have friends who are researching that sort of thing
 
9:43 AM
Before Einstein came up with General Relativity, was there any serious reason to doubt Newton's theory (and its various developments)? I only know about the discrepancy in Mercury's orbit, which may have been caused by an error (e.g. similar to the one that caused people to make up Planet X).
Also, is this an okay question to ask here? (e.g. history of physics)
 
any empirical reason?
or can one consider theoretical arguments?
 
9:58 AM
I don't know. It's a history question, so it's about whatever reasons people had in the past.
0
Q: Before Einstein came up with General Relativity, were there serious reasons to doubt Newton's theory?

Just GregBefore Einstein came up with General Relativity, was there any serious reason to doubt Newton's theory (and its various developments)? I only know about the discrepancy in Mercury's orbit, which may have been caused by an error (e.g. similar to the one that caused people to make up Planet X).

Right now we have tons of reasons, but it seems to me we only knew why Newton's theory was wrong after the better theory came up. We certainly didn't know the kinds of experiments to perform.
 
10:22 AM
i;ve written a quick answer
" we only knew why Newton's theory was wrong after the better theory came up" -< Yes, theories are rarely/never abandoned if no better explanation is available.
 
 
5 hours later…
3:00 PM
@JustGreg I disagree with the perception that Newton's theory was/is wrong. It's not wrong, it actually works quite well. It just cannot be extended to "bigger" things.
That would be like saying QM is wrong because it doesn't work the same as classical mechanics
 
They simply cover different size regimes
o/ @ManishEarth!
 
Calling newton's theory wrong is fine, as long as you call every other modern theory wrong too, because they all have the same problems :P
o/
 
How goes it?
 
Badly. Really swamped :/
 
3:06 PM
With schoolwork? Or lifework?
 
schoolwork
 
Well on that note, I hear you! I've got my dissertation due to the committee on Weds
 
@KyleKanos Ah, good luck!
 
TY, but this is the easy part. The hard part comes next week when I actually defend :\
 
3:25 PM
@DavidZ friends who are researching whether gravity is infinite? How?
 
3:52 PM
I'm done talking to this guy:
20
Q: If the LHC-calculated mass of the Higgs is wrong, how long will it take to determine this with confidence?

PurposeNationAfter I watched "Particle Fever"--the movie about Large Hadron Collider (LHC) and the successful identification of the Higgs boson--I became a bit concerned with that team's handling of various negative PR incidents. Further, with the amount of money spent and the pressure to produce results, al...

I no longer believe he is asking in good faith or that he actually wants to know the answer.
 
@StanShunpike studying the asymptotic behavior of spacetime with nonzero cosmological constant
 
I had that suspicion from the start, tbh.
 
@ACuriousMind Well, it had occurred to me to, but it is a reasonable question on the face of it and there is an answer.
 
@KyleKanos hm, isn't the defense kind of a formality? Not literally, but in the sense that if there are any legitimate doubts about whether you can pass, your advisor wouldn't let you defend in the first place
@StanShunpike see e.g. this
 
@DavidZ I've heard of cases where students insisted. And of ones where the advisor just wasn't looking out for the student like that. But those are rare enough that you always hear of them nth hand.
Certainly that is part of the advisor's job.
 
3:56 PM
@dmckee I think "How much confidence can we put in this?" is either trivially answered by the Sigma confidence levels or opinion based. Putting "scientific" in front of confidence doesn't make it less so.
 
@dmckee Yeah, I've heard of those cases too, but I think Kyle would know if that was him :-P
 
@ACuriousMind I'm more ticked off by his comments than the late edit. He's asked how can we trust this stuff if it isn't replicated and I showed him the process for replication and he's simply dismissed it.
He also implies that he can guess how collaboration work better than people who've been there.
In any case, I'm done.
 
@DavidZ Well, I suppose that is kinda true. But I do have one member on the committee who is not an astrophysicist and is a bit of a stickler when it comes to certain things that I may or may not be prepared for. So the nerves are based on him alone, really
There was one girl here a number of years ago who was asked at her defense to redo some experiment (a small undertaking, from what I was told) and she said no and quit the program.
 
Ah, I see what you're saying. Though still, even if someone on your committee is a stickler, you really have to crash and burn to actually fail. From what I understand.
 
Right. So long as I present the work in a coherent manner and explain why it's important & how it connects to the observables, I should be okay to pass.
 
4:02 PM
@KyleKanos that's all on her. (Though it really does say something about burnout in grad students)
Sounds about right
Honestly, I was so relieved to be done writing the actual thesis that I didn't really care about the defense.
 
Then I get to spend some time (hopefully not much) adding/subtracting from the dissertation. And then off to learn C++
 
woohoo real fun! (C++)
(lol)
I'm starting to think of C++ rather like quantum mechanics, in that nobody understands it, and anyone who says they do is either lying or clueless
3
 
4:22 PM
@DavidZ that's Ashtekar as in Ashtekar variables, right? That's a name i've seen crop up many times when I have searched QG
 
Yeah, he's kind of the pioneer of the theory
or, one of the pioneers, really
 
@DavidZ is that of LQG? I don't know much obviously but I thought Witten was the string theory guru. I know Carlo Rovelli is another LQG guy.
 
4:37 PM
Yeah, Witten is big in string theory
and Carlo Rovelli is (as far as I know) one of the other LQG pioneers who got involved in it around the same time as Ashtekar
(yes, I meant Ashtekar is a pioneer of LQG)
It's probably somewhat analogous to the big names in quantum field theory in its early days - Feynman, Schwinger, Dyson, etc. Similarly LQG has Ashtekar, Rovelli, and others
 
Yeah, most fields need pioneers. Knowledge doesn't just fall from the sky.
Funny debate with Carlo Rovelli m.youtube.com/watch?v=jEr038WOKFI
 
5:37 PM
Well that kinda sucks:
123
Q: Do I have the legal right to demand information on plagiarism of my work from another university?

Need legal adviseA student of a German institute has translated my Russian thesis word by word to English and submitted it as her own work in 2014. I informed the university providing them with my work in Russian and presentations of the work I made in 2013. Upon receiving my email, university examinations first...

 
5:57 PM
@DavidZ: What does it mean to understand QM? Understanding anything, like hydrocarbon chemistry say, I would quantify by knowledge of it. I think there are people who can answer the bulk of well formed questions, so I'd say they understand it. If you extend QM to it's philsophical context, then it's also fair to say that nobody understands power, death, etc.
@ACuriousMind: In the thread about cold fusion, you speak of the merit of non-mainstream theories. What's the merit of theories in general (apart from reasearch of non-non-mainstream theories having the advantage of easier getting grant money)
 
@NikolajK The merit of a theory consists in it predicting the results of experiments/measurements as accurately as possible, I'd say. Among those that perform equally well, we use variants of Occam's razor to choose those that have the fewest and most elegant axioms.
 
@ACuriousMind: Mhm, k, I don't know who looks at the predictions of fringe theories to see if they are accurate. I feel the label is just assigned with reference to what's been published in the bigger pictures. New areas energy as perturbations of old research, or if a famous person decided to work on them.
Everybody "knows" that cold-fusion is fringe science. I don't know anyone who dislikes the theories and has read more than 5 papers on it seriously. I feel the arguments against those theories is "these theories we learned about in university say to opposite - so it must be false". That's of course a ridiculous perspective, exactly what doesn't work. You can't argue with the established theory against the new one, only with experiment.
"Quantum electrodynamics predicts A and B. A has been confirmed. Fringe theory predicts not B. But quantum electrodynamics is true! So Fringe theory is false!"
"Conversation of energy!" ... "No perpetuum mobile!!"... etc.
 
@NikolajK You're correct, but I think that many non-mainstream theories (the "crackpot" ones) actually say "not A". I've honestly no idea where cold fusion falls on the scale of "crackpot" to "reasonable theory that has not been pursued for unclear reasons".
 
6:13 PM
That being said, I don't want fringde theory content on SE, just like I don't want homework threads. You only have finite time in your life so (unless you have your own money for experiments) you focus on the things where people know about it.
 
user54412
6:49 PM
@DavidZ Well, certain departments have hard time limits for the PhD, so at the end you either quit or defend what you have.
 
user54412
Also, professors in at least one such department are known to, during the defense, pull out a list of questions the student got wrong during oral quals 3 years earlier, to make sure they improved their breadth of knowledge about the field as a whole...
 
user54412
um what?
3
 
user54412
Apparently an answer from 2.5 years ago needed more cheese
 
Well it's true, you do need more cheese
 
user54412
Is there a good reason for allowing unregistered edit suggestions?
 
6:56 PM
In case they make good suggestions?
 
user54412
Who with good intentions and enough time to make good edits is scared away from registering an account?
 
user54412
It's still anonymous after all
 
user54412
oh well
 
At least it wasn't accepted
 
user54412
as it turns out I am eating more cheese right now, so maybe they had a point
 
6:58 PM
They're psychic
Also, I was reallllly tempted to use backwards axes for my Meta post because you mentioned it in your Meta post @ChrisWhite
 
user54412
ha!
 
user54412
it would sort of make sense too
 
user54412
or maybe not -- I've seen too many HR diagrams to know anymore
 
7:30 PM
@NikolajK Conversation of energy... heh.
 
@Danu We have those often 'round these parts ;)
 
@KyleKanos :) Hi Kyle
 
Hi!
 
How are you doing
 
Tired of writing mostly.
But otherwise fine. Yourself?
 
7:41 PM
Pretty tired because I forgot about summer time so lost out on an hour of sleep last night, haha
Otherwise very well. Still on holidays (2 more weeks to go), and pretty relaxed
 
@Danu: Conversation ... didn't notice this ^^
 
8:09 PM
So usually I see the precursor to the Schwarzchild solution written as $$ds^2 = -A(r)dt^2+B(r)dr^2+r^2 d\theta^2 + r^2 \sin^2\theta d\phi^2$$.
Oh, nvm. I figured it out. Yay. Self learning.
 
@StanShunpike page 14 of this maths.tcd.ie/~ipde/GR_Notes.pdf has a good construction
@StanShunpike you might enjoy joining @NikolajK 's Landau reddit boards.4chan.org/sci/thread/7156940
 
Says reddit, links 4chan
suspicious behavior
 
ahhh weird!
Says a lot about my state of mind right now, fcuk
"Landau's style is quite percuilar. There's that common joke about Lifshitz who comes to Landau and says "Hey Lev, I'm afraid that I forgot those ten pages of calculations in the tram", and Landau replies "Don't worry, we'll write as usual: 'It's obvious that...' ""
The beauty of Landau is that most things are like 2-3 frickin' pages, I have 3 50-page math articles about to force me to quit math, I mean enjoy the 10 Landau's while you can!
 
@DavidZ If in doubt, check the ISO standard :)
 
Also it's sheer crazy people are merging that Wildberger nonsense with Landau lolz
@NikolajK is that you?
 
8:21 PM
@bolbteppa Which articles? Lol
@bolbteppa Wildberger? Was dat?
 
The thing in post boards.4chan.org/sci/thread/7156940#p7160748 is called 'The Fundamental Lemma of the Calculus of Variations'
@Danu they are translating Landau's stuff into 'Rational trigonometry' on that 4chan page and even link to a video, this is a guy who denies the real numbers and invented a form of trigonometry trying to avoid it
 
@bolbteppa How does one deny the real numbers?
How does one invalidate Cantor's construction based on equivalence classes of rationals
(I don't know the Dedekind construction well enough to comment on that)
 
He doesn't really say anything about why it doesn't work
Pretty stupid though, yeah
Real numbers make so much sense :P
 
@bolbteppa nice! That looks like a good idea. I went over the Einstein Hilbert action right after I learned how the EL equation worked. But I just successfully derived the Schwarzschild solution for the first time yesterday (:D) so now might be a good time to try relearning that stuff again since i have a better feel for the EFEs
 
8:29 PM
@bolbteppa Honestly I dont really care to have many conversations on the basics of the first few pages of Landau
It made really fine sense to me about 2 years ago, and I've been content since :P
 
@StanShunpike just be aware you are working with Euler-Lagrange equations for a metric tensor, that's tough and most derivations of E-L do things a bit differently to how they do it with scalars and vectors (as in Landau vol. 1 & early sections of 2 for example), Susskind should go over them all
 
@ChrisWhite Did someone say CHEEEEESE? youtube.com/watch?v=C7rzSslub6U
 
8:51 PM
@DavidZ says a physicist!
 
@DavidZ Or - If you think you understand C++, you don't understand C++
 
@AlfredCentauri I think people on the standards committee probably can say they 'understand' some subset of it at least.
 
I just don't think physicists or mathematicians have the right to really say that...
 
@NeuroFuzzy Yeah, I don't think C++ is that bad - I certainly love C++. However, admittedly, there are some things which can be confusing sometimes like the different rules for type deduction, referencing collapsing, template metaprogramming, etc.
 
@bolbteppa: Yes, I did the Wildberger calculations
 
9:00 PM
@NikolajK do you deny the real numbers?
 
what does that even mean
 
Do you have a problem with $\sqrt{2}$?
 
the set of real numbers is a troublesome concept, of course.
What Wildberger does it boring, though
 
@JamalS Heheh I don't use any of those things! I stick to my little valley of OOP, almost always w/o even templates! nor type deduction.
 
@NikolajK What's troublesome about it?
 
9:02 PM
Maybe it would be fun to learn though.
 
"Do you deny the real numbers?" - Sounds like a good question to ask in a witch hunt.
 
@NeuroFuzzy Erm... the moment you type 'auto' you're using type deduction...
 
@JamalS and I never type auto!
 
@NeuroFuzzy Then that's not good...
 
Thank you?
 
9:03 PM
the undefinable reals form a "set" in any of the stronger set theories, but you can be definition not think or talk about any of its elements
 
@JamalS Hmm? Why not? Isn't kind of a recent feature anyways? I like strictly typed stuff.
 
@NikolajK I think you have been fed some crazy propaganda, the reals are definable in tons of ways amazon.com/From-Numbers-Analysis-Inder-Rana/dp/9810233043 it is sheerly crazy to say they are undefinable
 
@NeuroFuzzy And auto doesn't mean you're not using strict typing.
C++ is statically and strongly typed.
if you write 'vector<int>::iterator' instead of something like auto in a for ranged-based loop, then you're in the dark ages.
 
@bolbteppa: I have been fed... believe me when I say I have a strong grip of logic/set theory/category theory
 
@bolbteppa The term "undefinable" has a precise set-theoretic/logical meaning here that doesn't imply that you can't "define" the reals in the sense you understand. Be careful what you call crazy propaganda.
 
9:08 PM
@NeuroFuzzy Also, if you don't write exactly the right type explicitly in say, a for loop, but it still works, you may be suffering from an unnecessary copy for every iteration of the loop. So, using auto can actually give you a performance boost.
 
@JamalS Oh, wow, I didn't know that. Not going to lie, I use ints and vector::size for that... (usually it's nested so I need to check "i!=j")
 
@NeuroFuzzy Also, if you use iterators in for loops explicitly using v.begin() and v.end(), you are calling begin() and end() during every iteration, whereas something like for (auto& element : v), you only call it once.
 
@JamalS well neat. Thanks, I didn't know that.
 
@ACuriousMind but that use of the word completely assumes their validity, (s)/he is using it as a means to try to cast aspersions on the very existence of the reals as a concept, that sounds like a witch hunt to me rather than (correctly) challenging someone on the meaning of their explicit statements, do you have issues with real numbers too?
 
@NeuroFuzzy You do use algorithms from <algorithm>, right?
And lambdas... right?
 
9:15 PM
@bolbteppa Issues...not really. They are quite weird from a set-theoretic viewpoint, though. (Such as there being models of ZF where the reals gain very different properties than what we're used to)
 
@JamalS Erm... well I don't write my own binary search from scratch, for one! So that's good right? :p
 
@bolbteppa: Take the collection of any language/formal system/syntax anybody has ever come up with and will come up with in the next 50000 years. They are symbols written in a line. E.g. A book might have 26 different letters and "_" for word seperation. You can take Moby Dick and translate it to a number by giving every position a number and saying which letter (also encoded in a number), is there. Clearly you can encode every book/text/data that's possible to write down in to such a number.
 
@NeuroFuzzy Okay, you're practically writing in C...
 
All information you can write down and work with fits into a countable scheme. The rational numbers are countable and you can describe every single one of them. There is „one over two“, „seven over a million“, etc. The set of real numbers are uncountable (or rather, we can express a concept involving injective functions and so on and prove a certain predicate expressing „uncountablilty“ is provable for the real numbers).
 
@JamalS I have not used lambdas ever no... but you're making me think I should get up to speed...
 
9:16 PM
So most of the real numbers can’t eve be expressed or discussed. Now you can define the set of definable reals, call it D. Then R without D, which we write as R\D is an object of our theory, the symbol 'R\D' is a "set". But by construction you can’t talk about any of it’s elements. You can't think of a single one. The "set" doesn't really have element in any constructive way. The reals is mostly unconstructive.
 
@NeuroFuzzy I've reduced 20+ lines of code to a few lines using lambdas and std::algorithm.
 
@JamalS of course not! Still using all the object oriented memory management features and smart pointers. Way better than C there. Am I mistaken in thinking auto and lambdas are c++11 things?
 
@NeuroFuzzy They are C++11.
 
Btw. your example of sqrt{2} is much more tame, you can specify it by its function and use it, like i. I know that Wildberger is a finitists who has some unpractical and useless ideas (e.g. he doens't want to permit a theory with infintite primes, because you can't express infinite numbers in a universe of finite energy/atoms). The fact that he's a dogmatic goof doesn't mean he's formally wrong with anything though.
 
@NikolajK Use $$ for the LaTeX to render in chat (assuming you have the app, but even if you don't, most of us do).
 
9:21 PM
@JamalS: k will. I don't have it, but I though there were not many formulas in my text anyhow
 
@JamalS Heh, well that must by why I don't use them! Thanks though, sounds like good stuff.
 
I read that $$g_{aj}\ddot{x}^{j} + \left(\partial_i g_{aj} -\frac{1}{2} \partial g_{ij} \right)\dot{x}^j \dot{x}^i=0$$ is equivalent to the usually way we write geodesic equation with the Christoffel symbol. Does anyone know off hand why/how these are equivalent?
 
@NikolajK just because something is too difficult for our brains to comprehend at the moment that somehow casts doubts on it's existence? There is a very clear, easy proof of the uncountability of the reals, just because we can't list all the numbers in a line that doesn't mean their existence is troublesome, they have been proven to behave that way, but by your logic this is enough to put them into question.
 
@NeuroFuzzy The YouTube videos from C++ Going Native, C++ Con, and C++ and Beyond will bring you somewhat up to speed.
 
@NikolajK do you accept the existence of $\sqrt{2}$ or does that cause you problems? Clearly the theory is built to make sure they end up with this number, you can do it many ways, but the concept of $\sqrt{2}$ is what I'm asking about, that number which cannot be written as a finite string of decimals.
 
9:23 PM
@bolbteppa: I don't think we two mean the same things by the words we use. Do you have a clear notion of "existence" in mind when you use that word?
 
@bolbteppa: What do you mean with "accept the existence"? Is there Plato's heaven for you where all the sets of numbers live?
 
@JamalS Thanks!
 
@StanShunpike Have a look at the Christoffels in terms of the metric. Using a bit of index gymnastics, you should be able to show both expressions are the same.
 
@StanShunpike find out how to write Christoffel symbols in terms of the metric, I linked this to you weeks ago in the Borisenko book where he gives many ways of expressing Christoffel symbols, you have just written the geodesic equation which comes about in diff geom when you have a metric by extremization
 
@ACuriousMind Commentary: thought it was something like that.
@bolbteppa thx I'll take a look amigo.
 
9:28 PM
@NikolajK By Pythagoras theorem $1^2 + 1^2 = 2 = a^2$, does such a number as $a$ exist in any way, shape or form?
@StanShunpike cool, this is equivalent to 'parallel transport' in diff geom too (for when you don't have a metric) and if you're really clever you'll notice this is all just the baby Fermat's theorem from basic calculus generalized to allow for a moving basis :)
@ACuriousMind the existence of that $a$ is what I mean
 
@NikolajK Correct me if I'm mistaken, isn't "there exists" left as a sort of "undefined" symbol in first order logic?
 
@bolbteppa: We have comprehension. You can view a as the thing solving the equation and then it "exists", if you will. What's another story is Platonic existence of number, that doesn't matter here, but I'm pretty much a relativist on most things.
@NeuroFuzzy: well, you have formation and elimination rules - but it's nonconstructive in first order logic in any case!
 
@bolbteppa Yeah, but what does it mean for $a$ to "exist"? In what sense do $1$ and $2$ in your example "exist"? You need to fix the axiom scheme and possibly the model in order to meaningfully talk about existence.
 
@NeuroFuzzy: That's different, for exmaple, in PerMartin Löfs type theory, the constructive logic with quantifiers that emerged in CS in the 70's
 
@JamalS Not that I have checked, but Id be very surprised if there was a compiler in use that didnt handle idiomatic C++ this old
 
9:34 PM
Here \Sigma plays the role of \exists, but it's not just the statement some thingy exists, but a pair where the first entry is the thing, and the second entry is the prove that it has the descibing property
Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics based on the principles of mathematical constructivism. Intuitionistic type theory was introduced by Per Martin-Löf, a Swedish mathematician and philosopher, in 1972. Martin-Löf has modified his proposal a few times; his 1971 impredicative formulation was inconsistent as demonstrated by Girard's paradox. Later formulations were predicative. He proposed both intensional and extensional variants of the theory. Intuitionistic type theory is based...
 
@alarge Well, the advice I mentioned is quite recent, so I presume they don't.
Either way, ranged-based for loops are much cleaner.
 
user54412
@JamalS You'd shutter at the type of code we write in my group. No auto, no std::vector, essentially no external libraries
 
@NikolajK I wouldn't say that learning a form of mathematics (rational trig) explicitly based on denying the real numbers is relativist, that's hardcore tbh, the guy is defining concepts like area (quadrance or spread or something?) that explicitly uses real numbers to talk about length and area but pretends it doesn't apply, that's a huge joke and it takes serious ideology to ignore that.
Pythagoras irrefutably establishes the concept of $\sqrt{2}$, we built our foundations to give us this result, if the foundations don't we change the foundations, but you said this was troublesome which reeks of either half-thought (which I don't believe since you devoted so much time to Wildberger) or serious ideology. I asked Wilberger this and he gave me tons of nonsense, I am wondering why you find the reals existence troublesome,
just because you can't list them all with our deficient mathematics means we have to work harder, you seem to be taking the reverse lazy route tbh I'd like to see why.
 
@ChrisWhite Well, you could always copy and paste the gcc implementation of std::vector, and use it if 'std' is considered external.
@ChrisWhite What do you compile with? C++98 or C++03 then?
 
@JamalS Ranged fors are cleaner, sure, but I dont think the compilers would actually be computing v.end() (or rather std::end(v)) every iteration (much less begin)
 
9:38 PM
@alarge I heard Scott Meyers say that about gcc I think.
 
user54412
@JamalS One of those. We wanted C++11, but seeing as gcc only fully supported it last year, and icc still doesn't fully support it, we have to be careful
 
user54412
We have one major restiction -- must compile on as many supercomputers as possible -- and one major goal -- performance
 
user54412
fancy things work against both of those
 
Fancy things work against performance? What?
 
@JamalS It probably was some edge case. You can trick the compiler into doing stupid things (a recent talk by Meyers had an example of false sharing from a paper by Sutter)
 
user54412
9:41 PM
it takes a while for compilers to work new language features into efficient hardware calls
 
@bolbteppa: "I am wondering why you find the reals existence troublesome" I think I've made it clear in which sense I find it "troublesome". I have no storng feeling about using them - I wouldn't necessarily if there was an alternative (because constructive math is the more creative basis), but since I don't think that's feasible I'll also use real numbers all my life - at least I will use those which are thinkable, haha ;)
 
@ACuriousMind you again seem to be at complete odds with Bourbaki
 
user54412
also, fancy things are often very general -- you can often get performance out of rolling your own, custom-built version
 
Oh, so @bolbteppa @ACuriousMind it would help me a lot if you could answer this because this will help me decide what courses to take for the next 11 weeks. Doesn't the material in this course: keni.ucsd.edu/s10 seem approachable for someone with only a bit of experience in finite groups and rings? It lists a whole year of graduate level quantum mechanics as a prerequisite but doesn't appear to use it!!!
or @anyone else, really.
 
@alarge By the way, are you aware you can implement concepts lite in C++14 already using SFINAE?
Or did I already mention that?
 
9:44 PM
@bolbteppa I'm not sure Bourbaki ever delves into the abyss of set-theory and logic. But anyway, I'm not saying I don't "accept" the reals, and I certainly am happy to use powerful axioms/models where the reals and much more exist happily, but it is important to realize that there is quite a large amount of choice (pun intended) in constructing the "mathematical world of things which exist".
 
(Drifting off in the constructive math department a little, there are theories like Synthetic differential geometry, which are only possible once you drop the law of excluded middle, i.e. if you drop the axiom "P or not P". This is because this theory needs the (also non-constructive but nonstandard) axiom that you have a set of "reals" {x | x^2=0} that is strictly bigger than the set {0}. This is the used to set up differentiation syntetically)
 
@JamalS I havent looked into concepts yet (as the original non-lite version didnt make the cut)
 
@NeuroFuzzy it is a smattering of Lie groups, Lie algebras, representation theory, every step is motivated by quantum mechanics/particle physics and that stuff is crazy hard without motivation but doable, but it looks like it's written for someone who wants to use group theory to apply to particle physics properly, are you into it for that and would you be able to read stuff on particle physics on the side to motivate it?
 
user54412
@NeuroFuzzy After a brief glimpse, my guess is that the prereq is there so that you know how these things apply to real physics (they'd probably seem rather ad hoc without context). I agree it doesn't seem to directly use the physics.
 
9:46 PM
@alarge It's worth watching the talk about metaprogramming by Walter Brown as well, if you're not familiar with the basics, and void_t.
 
My guess would be the same as @ChrisWhite's
 
@ChrisWhite Hm. The only thing I know is the relation between SU(2) and spin
 
@alarge I've tested it on vc++ and it works.
 
@ACuriousMind they do, their whole 300 page first book is on logic and set theory starting from nothing, they used Hilbert's old system of logic, what they did has issues but conceptually they did everything phenomenally, they defined the reals using topology!
 
@ACuriousMind: Bourbakis first book is indeed "Set theory".
Related to @NeuroFuzzy question, they use a concept to define \exists and \forall that has been since long forgotten en.wikipedia.org/wiki/Epsilon_calculus#Bourbaki_notation
Wildberger in his videos points out the problems with sets that have been pointed out in the same year as Cantor has come up with his set theory (for example the critique that I made above, that set theory doesn't capture the meaning of "set" very well, if you can prove the existence of "sets" like R\D, which have no element you could even start to describe if you have a whole book), those are established conceptual problems.
Wildberger is silly, because he draws the conclusion we should do a handwaving kind of constructivism only. There are constructivist programs, but less elementary and
And don't get me wrong, I don't have a Vendetta against set theory in the least, I see and understand the issue and take it for what it is. Although be aware that if you set up mathematics in standard set theory using standard definitions (which no working mathematician does anyway), then you can prove that 1 is an element of the ordered pair (0,7). This is because standard set theory is material and you have to make some choices (oh, not again). (category theory eliminates this problem, btw.)
 
9:52 PM
@JamalS Ill look into this, thanks.
 
@ChrisWhite @ACuriousMind thanks for your thoughts. I'll have to talk to the professor.
 
@NikolajK I think this is all like childish stuff tbh, just about no serious math or physics actually depends on the exact value of a number, it's all explicitly built to avoid that dependency, further your problem about $1$ being in $(0,7)$ is just because the minimal amount of axioms are used, seeing a problem with that is really missing the point, it's like a Fox news /Christian-values argument tbh ('isn't this weird, surely ag'inst god's will')
Also this creativity argument only holds for like high school math really, also pretending category theory is some solution is again just missing the point of category theory, which is all about relating well-defined disparate areas of maths and showing their similarities, it's like taking wallpaper and saying 'oh we could cut this into letter shapes and re-create Shakespeare and as a new thing our letters will have weird designs on them, did Shakespeare have that?' lol
 
Can someone tell me what's happening at this question? The mess in the question has six upvotes, and a long-time user is saying not to close it because he finds the topic the question apparently is about interesting.
 
@NikolajK In the nicest possible way, I genuinely think you need some guidance if you think it's okay to read Bourbaki and Landau and at the same time give any credence to things like rational trigonometry, I mean the guy is there drawing squares on the board and you don't stop to think if he asks about the length of the diagonal of his unit square and how his whole theory is built on saying that question doesn't make sense?
 
How does it get six upvotes without even asking a goddamn question?
 
10:06 PM
@ACuriousMind: It's odd. Friends of him?
 
@ACuriousMind that's a completely fine question, he asked for a reference to understand unique commutation relations in some set in gauge theory and someone answered completely knowing what he was talking about?
Why try to close things down just because you don't know what's going on
uh oh
 
@bolbteppa: Lastly, the fact that Wildberger is a Nut doesn't mean he's a bad person or that whatever he does it bad. His rational geometry project is probably doing nothing mathematicans form the 17 century would have disliked. I've never read his stuff before. I did the Landau exercises of chapter one, where you express the Lagrangian for a pendulum in spherical coordinates,
then recalled having read on /sci/ that Wildberger uses "quadrance" and "spread" instead of edge lenght and angles and just suggest and performed the exercises in the Landau books in those Wilbergerian coordinates. I did it, it was fun, the coordinates weren’t really suitable as polar coordinates for the pendulum (duh), but I read the article on his plane geometry and learned something. The world isn’t black and white and his geometry is just (maybe) useless and cute.
Like a romance movie. But why not.
On the later post: You're wrong in some accounts here. The artifact of definition, $1\in(0,7)$, can be eliminated but adding more axioms will not change the fact that there will always remain such incidence in such set theories. Category theory comes from combinatorics in homological algebra, shows similarities etc., nontheless
it also enriches the conceptual real of maths by showing structural definitions are possible - a set theoretic group is a pair where the first entry is a set and the second is a function... a set theoretic product is a set of pairs, where a pair is a set, where … in category theory, you define product structurally by projections and no modeling accidence happen. Anyway, I could also list downsides of categories, that#s not my point.
 
@bolbteppa Look at the question. It is of no use to anyone but the people already knowing the answer. That's not how questions here are supposed to work. Give a bit of context, explain the symbols you use, ask something more specific than "I don't understand this" (which isn't even a question). This isn't about the topic of the question at all, it's about the utter lack of effort and accessibility.
 
@NikolajK yeah I completely get you, I never said he was a bad person and would never lol, but this is what I mean about guidance, I have 8 hours to write up 2 fucking posters on crazy subjects but I'll be back someday soon to go into this shit properly, I'd love to talk to people who merge Bourbaki, Landau, Wildberger lol I thought I was the only one ;)
 
10:11 PM
I asked Wildberger if he read into the type theory activity that's currently going on, but he doesn't know about it
essentially, I watched a video and said he should maybe give his version of foundation, formally, but he now only seems to post on basic algebraic geometry
I'd like to learn more about his spread polynomials, which are basically Chebychev polynomials en.wikipedia.org/wiki/Rational_trigonometry#Spread_polynomials
 
@ACuriousMind regarding that Christoffel question I had from earlier, if i make the assumption $\partial_{i}g_{aj} = \partial_{j}g_{ai}$ then it works out. Why can I make that? Does that follow from the symmetry of the Christoffel symbols, ie $\Gamma^{\lambda}_{\mu\nu}=\Gamma^{\lambda}_{\nu\mu}$?
 
@StanShunpike No, I don't think that's a true assumption. I'm pretty sure it's false in general.
The symmetry of the Christoffels you cite only needs that the metric is symmetric, i.e. $g_{ij} = g_{ji}$.
 
@StanShunpike I'm not sure you wrote the geodesic equation correctly even but that's definitely wrong
 
Okay I go now.
 
@StanShunpike if you check that Russian book and see how the $\mu \nu$ indices are naturally associated to derivatives of basis vectors you'll never worry about some parts of Christoffel symbols again ;)
 
10:23 PM
But lastly, this just in, next week we'll also start reading amazon.com/… on /sci/ :)
There's some indian at Caltech, starting a PhD in string, who said he'll lead the dicussion
(the book is stealable online, so I hear)
 
@bolbteppa smartypants! that's clever! I will look. That sounds much easier. I just wanted to get a basic derivation all smoothed out but clearly the math formulas i used could be written more elegantly
 
Yeah in virtually every book you are given some non-intuitive formulation of this stuff, how they define covariant derivatives as though it's some axiomatic concept is horrendous, just take a derivative of a vector field and invent the theory yourself ;)
@StanShunpike how is Susskind going?
 
thanks for drawing my attention to the Fundamental lemma of calculus of variations, whoever it was
 
@NikolajK if you're reading Landau and find it tough or just think more mathematically I advise reading Gel'fand's Calculus of Variations for the math for Landau book 1 & 2 (I call it Landau book 0 it's that good), it has this lemma (in like 4 forms, Arnold's Mechanics book has it too)
Also the NPTEL videos on CoV follow Elsgolts book which is similar (but not as good) and there's also a Krasnov-Kiselev problem book that's definitely worth checking out
@NikolajK I have a mnemonic for the first two chapters of Landau and a pdf of notes I made like a year or so ago, as soon as I can find time I'll join and add it, in the meantime I'd advise trying to find out what Gel'fand says Noether's theorem actually is and compare it to virtually every other formulation of it to see sheer magic ;)
 
10:42 PM
@bolbteppa susskind is going well. the Entanglement lectures and the classical mechanics ones overlap nicely. I am wondering if i need exercises though. The lecture notes you gave me were great, but i didn't see exercises with it. Any suggestions? I have always found exercises are important to do
@bolbteppa since @Danu told me there were solutions of Grifiths, i started doing the problems and was very surprised how easy it was once i got used to the terminology. Im half way through chapter 1 exercises. Mostly just been calculus. Calculating expectation values.
 
@StanShunpike you have Griffith for QM exercises, you have Calkin for mechanics exercises, you have Jackson for EM exercises, I just advise Susskind for you to conceptually start from the beginning and get a half-honest ground-up view of all of physics and the math necessary, after Susskind I think you should go back to your old ways, but until then I really think Susskind should be a priority, you'll see why you need so much of the math your so gung-ho to learn from first principles :)
 
@bolbteppa okay, I've definitely made the lectures more of a priority, but I will shift more of my attention to just watching and won't worry about doing exercises.
 
Again, if you think Susskind is a bit wishy washy just remember he is doing fucking renormalization and supersymmetry based on that wishy-washiness, if you get curious about topic X that Susskind mentions check the corresponding theory and problem sections of the books for a direct example, I mean you always want to do one silly $f(x) = x^2$ type example
A good idea is to watch like 3 in a row and take notes in a day, on the same topic, and organize your thoughts then and there, you'll forget a lot but you'll have learned tons of little things and organized your thoughts better, if you still want to learn QFT after you've seen Susskind's ones up to his string theory stuff you can fill in and elaborate on the jigsaw pieces, at least you'll be thinking along better lines knowing some detail on crazy topics!
 
I never thought Susskind was wishy-washy. That dude could pass for the Dos Equis most interesting man in the world.
Its nice he covers so many topics.
I am used to his style and he's very knowledgeable. I used to play Arkham Asylum and watch his GR lectures at the same time. :D
 
10:59 PM
@NeuroFuzzy tough crowd tonight...
 
Nooooooo, daylight saving means I have to wait one hour longer for my votes to refill
Could someone please cast a non-mainstream close vote here?
 
@ACuriousMind done
 
11:40 PM
@AlfredCentauri heheh came out less jokingly than I meant it
 
What's the difference between put on hold and closed?
 
11:57 PM
@StanShunpike Time. I think the status changes from on hold to closed after seven days or so. It's intended to show that reopening can happen if the closing/on-hold reason is addressed.
 

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