@0celo7 I've taken it a few times & got ENTJ twice and INTJ once. So I'm not really sure how intro/extro-verted I am, but I do seem to be Intuitive, Thinking & Judging
How can we do integrals on a manifold? I am reading Bernard Schutz's book on GR and he talks about doing this.
I just don't get how we know we can do integrals on a manifold. Given all the complexities with differentiating on a manifold, why can we integrate like this along one of the coordinate lines?
user54412
1:48 AM
@Sean Which they sometimes deserve no doubt, but I thought even psychology understood that Myers-Briggs with BS.
user54412
It's just something AP psych teachers love, because it involves a worldview that's simple and easy to grasp, yet just complicated enough to make it seem worth studying.
@ChrisWhite My teacher admits that Myers-Briggs is too simplistic. We learn about the Minnesota test, which has ~500 questions and is constantly tweaked, but it costs money so we can't feasibly take it.
@StanShunpike Well, the simple answer is forget there's a manifold at all, since your coordinate chart means you can consider yourself to be on $\mathbb{R}^n$
@0celo7 You didn't check with MS Office support? Why?
user54412
@0celo7 What I really want to take some day is one of the psych tests administered for people in sensitive positions -- the kind that are supposed to stress you out and see if you hold up.
My father was in the military during Nam, but his duties involved training helicopter pilots State-side, so he did not go over with his brother (who flew helicopters over there)
You can definitely express it as a linear combination of tensor products of lower-rank tensors, but that's true of all tensors
If you're asking whether the curvature tensor can itself be expressed as a tensor product of other tensors (or other meaningful tensors), that I'm not sure about. But I'd guess no.
@0celo7 $L_+^\uparrow$ is some restricted Lorentz group? But, anyway, you obtain the algebra homomorphism as the derivative of the group homomorphism. In general, the adjoint group action $BAB^\dagger$ is $ba+ab^\dagger$ (for $a,b$ generators of $A,B$) infinitesimally, it has to do with some version of the BCH formula, I think.
@0celo7 Complexifying the algebra often makes things easier without significantly changing the rep theory, by the way.
I'm always amazed by questions that I figured nobody would look at and might get closed as off-topic and then they get me a ton of rep when I answer them
@0celo7 For such covering maps, it should be an isomorphism, yes. But that doesn't change that the algebra homomorphism is the derivative (or, more precise, "induced map on tangent spaces") of the group homomorphism in general, regardless of whether one of them is an isomorphism or not.
@ChrisWhite I asked a question last year about a long chain of arguments. At least one or two papers have come out this year (which I have not edited into the question). One of the authors of one of the papers answered the question.
I also have read parts of this debate which has been going on for years.
And then there are the more "direct" fights such as this and this
I'm working on a program that has to do with adding sound waves on top of sound waves. Currently what I'm doing is simply an average of the two waves. So if I have wave A, and I want to write wave B 'on top' of it, every sample in the new A is equal to the average of two matching samples in the o...
I'm leaning towards off-topic because, while it is kind of physicsy with adding waves, it's definitely in the realm of audio engineering and there's probably scores of people on another SE that deal with exactly this problem
user54412
I feel like ultimately the person wants to do audio engineering, but since the question is phrased in general, with no reference to file formats or software, I'm inclined to classify it as physics.
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Where can I learn about the functionality of motors and generators, so I can answer questions such as these? I need a good textbook that starts from the basics (eg faradays) then moves up with lots of questions.
Can I also know if this is hard to pick up?
@ChrisWhite in physics, we can simply play the two sounds simultaneously. That will add them together and won't decrease the volume of any individual sound. This question has to be taken in context of combining sounds in a software program, otherwise it is so trivial that it doesn't make sense
The question asks where to find resources to solve the question. Seems on-topic in a sense to me, although I think anything about Newtonian mechanic will suffice, so I'd be a duplicate of the book recommendations
FWIW I think that if a question asking for books showing how to do X is on topic, it also implies the question that directly asks how to do X is also on topic. And vice versa.
@StanShunpike I'm also in the "No" camp, but you win some and you lose some.
The"Yes" people effectively promised to keep them curated and maintained to maximize their value and minimize the basic incompatibility with the SE system. As far as I can tell they're mostly keeping up with the work.
I just got flagged over at History of Science and Mathematics for "welcoming" a user in a way that is standard on PSE. The flag says that I was being too rude :\
@tpg2114 To a non-bitter and non-jaded person, they sort of appear the same
@Danu Your comment wouldn't have been rude if it were properly addressing the question. But given that it didn't, I'd say that added a "rush to judge" quality that increased rudeness above normal levels
Proposal: History of Science and Mathematics
Can we just go ahead and make this site a site for the history of academics, it is much more general and would attract more people to this site.
I'd like to point on the idea of question as a knowledge resource.
It has come to my knowledge that understanding a subject, especially Physics, requires experience with as many questions as possible.
Reading many solutions of expert members of the Physics site may indeed help many students t...
The options for Low Quality posts are
No comment needed
Commentary on another post
A "Thank you" comment
"I'm having this problem too" comment
Different question than posted
Link-only answer (and not spam)
"This is a bad answer" does not appear on the list, so voting to delete such an answer ...
It's not an answer to the question. It's an answer to a totally different question
@KyleKanos If someone else already put the canned comment in, then choosing the appropriate reason only upvotes the comment, it doesn't repeat canned responses
I use No Comment when I add my own comment in. If I can explain why I think it's inappropriate as a posted answer to the question, then I write that comment and select no comment needed, because I provided one already
Depends.
A downvote should be the solution in the case the post is not useful. As in:
It is technically correct, but isn't clear.
It is technically correct, but is only a link or is of some other value.
It is technically incorrect, but is of some value to the original question.
Deletion is r...
If a question is flat-out wrong on top of being exceedingly brief, in poor English, or whatever, by all means vote to recommend deletion.
If it looks beautiful except for being wrong, I'd stick with downvotes and comments.
> If it looks beautiful except for being wrong, I'd stick with downvotes and comments.
@innisfree There is a big overlap (also in terms of expertise of users) and the audiences for each separately are probably too small to justify a site.
If an answer is (a) asking a new question, (b) meant to be a comment on another post, (c) a thank you comment, (d) a "me too!" post or (e) a link only; then by all means flag it as not an answer
A bad or a wrong answer is still technically an answer. Moderators aren't here to judge the correctness of answers. That's what the voting system is for, so the right way to handle those is to downvote, edit, or leave a comment.
The "not an answer" flag is for posts that are either completely un...
Other than off topic flags, there are several different types of flags that one can cast on a question, answer, or comment. What are each of these flags for?
Question and answer flags:
spam
offensive/abusive/hate speech
not an answer
very low quality
other
Comment flags:
rude or offensive
...
@danu there's certainly overlap between maths and physics - as @kyle noted, occasionally revolutionary developments in maths were motivated by physics, and vice versa - but the overlap between the histories maths and e.g. biology is tenuous.
The other point is fair enough... It just turns out that most people interested in either discipline turn out to have at least a mild interest in the other as well.
Let's be perfectly clear here. Are you siding with saying it is incorrect but still an answer, or sufficiently unrelated to the question that it constitutes a non-answer?
We're debating if it is related enough to be an answer but wrong for the question, or not even wrong as it's too unrelated to the question
Well, FWIW, I'm arguing that it does not fit any one of the 5 "Not an answer" reasons ("me too," new question, link-only, comment on another post, saying "thanks") so it shouldn't be deleted as "Not an answer."
And I'm saying that writing a comment that it is unrelated to the question and then selecting "No Comment needed" is a valid option
We clearly established that that is a valid option, since the meta posts all agree it is. But now we need to establish that the answer is sufficiently unrelated
@KyleKanos You aren't disagreeing that totally unrelated answers can be flagged as NAA and deleted, you only argue that this specific answer is not totally unrelated; that it is subject to one of the strings
> The "not an answer" flag is for posts that are either completely unrelated to the question, a "me too" kind of post, a follow-up question asked in an answer, etc.
Most of the books I have been reading in the SR - the first chapter of them - I see no proof for why the $ds^2=c^2dt^2-dx^2-dy^2-dz^2$ why is there a minus sign? Is it related to the geometry of the Minkowski space? I am totally confused.
In physics, a sign convention is a choice of the physical significance of signs (plus or minus) for a set of quantities, in a case where the choice of sign is arbitrary. "Arbitrary" here means that the same physical system can be correctly described using different choices for the signs, as long as one set of definitions is used consistently. The choices made may differ between authors. Disagreement about sign conventions is a frequent source of confusion, frustration, misunderstandings, and even outright errors in scientific work. In general, a sign convention is a special case of a choice of...
You could have $ds^2=-c^2dt^2+dx^2+dy^2+dz^2$
It's somewhat a personal choice for some people to do it one way over another
In addition, why instead of the $t$ in $(t,x,y,z)$ we use $(ct,x,y,z)$? why $ct$? Are my questions rudimentary? If they're, just tell me what's wrong with me?
Another question is, why the Lagrangian is defined $L=T-U$ , $T$ being kinetic energy and $U$ being the potential energy. It is extremely bothering me, since it just came out of air ( At least for me, because I do not know the reason ). That's not the end. Why is the action integral defined that way? Specifically, why we consider the integral to have $\delta S = 0$ . I know it is about the calculus of variation it seems I am stupid enough not to understand such simple fact.
I know that for finding critical point we have to put the derivative of function equal to zero, but why action integral? why is it an integral?
"Why is the sky blue?" "The Sun appears white because we've evolved to perceive that spectrum and intensity of wavelengths as white".... "Great! But you didn't answer my question". "Yes I did".... ::headdesk::
Is there a proof from the first principle that for the Lagrangian $L$,
$$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$
in classical mechanics? Assume that Cartesian coordinates are used. Among the combinations, $L = T - nV$, only $n=1$ works. Is there a fundamental reason for it...
@Jimnosperm The problem is the article has not mentioned anything, I thought $c$ is the speed of light! @KyleKanos Not the wikipedia, article I downloaded from internet.
Yes, $c$ is the speed of light. But one can choose the unit system such that $c=1$ (basically means all your velocities are divided by $c$, though other effects need to be accounted for, such as lengthscales and timescales)
@KyleKanos You know, I am still relying on heuristics and things I learned in past years. When I see a rule or a habit being broken, I get uncomfortable. Now I understand it, thanks. I have not read anything specifically on SR.
@KyleKanos Again, I may seem stupid, but I ask it anyway. Is not the first component of four vector considered to be time quantity? If yes, why $ct$ is considered? $ct$ even if we consider $c=1$ is in $Velocity\times time=length$
A geometrized unit system or geometric unit system is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum, c, and the gravitational constant, G, are set equal to unity.
The geometrized unit system is not a completely defined or unique system: latitude is left to also set other constants to unity. We may, for example, also set Boltzmann's constant, kB, and the Coulomb constant, ke, to unity.
The reduced Planck constant, ħ, is not equal to 1 in this system, in contrast to Planck units.
This system is useful in physics, especially in the special...
@KyleKanos Wikipedia is extremely good resource, but whenever I read it I get headache because I cannot stop the temptation to click on hyperlinks and read the other pages. Finally, I find myself having opened 100 tabs without even understanding what I was looking for!
@Jimnosperm Because the extra component added to it is not time but length, anyway, I don't insist on my thought, it is obvious that it is because of my foolishness :|
@ACuriousMind Wald says something to the effect that...understanding how to parallel transport is equivalent to understanding how to take the derivative...I get the idea that....if I know how to parallel transport, then I know how to compare to vectors. But I don't really see how the affine connection rules help me parallel transport. What does Linearity over R or the product rule have to do with parallel transporting?
Well you can also measure time in meters (though I wouldn't write that in an answer on this site and I wouldn't write it on an exam!) and that's a fun viewpoint to take
2
you know that probably doesn't help. Forget I said it @FreeMind :P
@dmckee it froze again because I didn't know it freezes after one day.. Why don't u wait for me to ask to to unfreeze the room so it won't freeze again before I come back?
I'd like to point on the idea of question as a knowledge resource.
It has come to my knowledge that understanding a subject, especially Physics, requires experience with as many questions as possible.
Reading many solutions of expert members of the Physics site may indeed help many students t...
@KyleKanos I like the recent "I saw a cool simulation and I know how to write some code, so I'm gonna go ahead and solve the universe. Why haven't you guys done it yet? It looks so easy!" questions