I'm a bit confused by this Q&A pair:
http://physics.stackexchange.com/questions/253062/dimensional-analysis-problem
(10k on Physics, or dev team.) The question looks like this:
Of note:
The answer was posted 10 minutes after the question.
The answer was upvoted at some point.
The question ...
@EmilioPisanty that's because our homework policy says that full answers to homework questions get temporarily deleted. It wouldn't be a temporary deletion if I never went back and undeleted it. Do note that until just now I had no idea there was an automatic process that deletes answers to deleted questions.
@EmilioPisanty It matters if the question is later edited, reviewed, and undeleted; I think it also makes a different for answer bans. Or at least I thought so.
I don't remember that specific case but I probably knew the question was deleted when I undeleted the answer. There's no special console or shortcut or anything that helps with handling complete homework answers.
@DavidZ Yeah. Really bizarre bug. But I guess that's what happens if you go down to weird corner cases like mods going into the catacumbs and manually undeleting stuff that remains deleted anyway ;-).
Assuming the raw materials stick together with no holes, then volume = weight / density of material
https://threesixty360.wordpress.com/2009/06/18/calculus-demonstration-3d-printing/ Here's another guuy who has the same thought that 3D printing and volme intergrals are related
@JohnRennie Actually, given what you just said, 3D printing will be a nice experiment for a calculus class to illustrate the concepts of a volume integral
as many researches have shown that a hands on experiment on a concept can help retention of the knowledge
I'm a big fan of the podcast Astronomy Cast and a while back I was listening to a Q&A episode they did. A listener sent in a question that I found fascinating and have been wondering about ever since.
From the show transcript:
Arunus Gidgowdusk from Lithuania asks: "If you took a one kilog...
but photons dont have rest mass. it's relativistic momentum which is because of velocity. If photons werent moving nearly as fast, their relativistic mass lowers, no? @0celo7
@Secret ...if you look at the definition of a Riemann (or Lebesgue) integral it is just adding up the "layers" of the line/area/volume covered by the function being integrated.
Alright @0celo7 as an object gains velocity, it gains momentum (both mass and velocity increases, right?) then its gravitational pull is increased. So, velocity directly affects gravitational pull because its increasing the mass? Is that the right reason?
Whenever a theory appears to you as the only possible one, take this as a sign that you have neither understood the theory nor the problem which it was intended to solve. (Karl Popper)
For light $\lambda \nu = c$, which is obviously constant. For de broglie waves $\lambda \nu = v$ where $v$ is the phase velocity, but $v$ is not constant. Offhand I can't remember the expression for the phase velocity.
@0celo7 I think intuitively it's just something that assigns sign to the zeros of a vector field - sources get a +1 and then every other zero gets (-1)^k corresponding to how many directions you have to "invert" to make it a source.
Actually, this case highlight the really key axiom need to be broken:
"You cannot have division by zero unless you violate distributive law"
Counterexample where violate additive identity does not save this algebraic structure
Suppose 0+e=0
Then e(0+e)=e0=e e(0+e)=e0+0=e+0=0 Therefore e=0
Suppose 0+e=a (a is in the set) e(0+e)=ea=e e(0+e)=e0+0=e+0=a Therefore e=a
The above conjecture is supported in that all proposed division by zero numebr system so far, the distributive law is always violated. Hope some day I can prove this rigoriously
@0celo7 It doesn't directly - that the definition of the index as the degree of a map conincides with the assigment of signs to zero according to how far they are from being sources is a non-trivial statement.
@JohnRennie That's true but for example you imagine there could be some other quantities which we are not aware of yet, and can be used to find a new way of describing phenomena. New theories I mean.
@2physics well yes, that was my point. All physicists know that a theory, e.g. GR, is a working apprximation that will (probably) cease to apply in some circumstances.
@2physics well the theories that are made based on the observations we make, are nearly perfectly accurate in predicting what we observe. If we observe something different, then we are no longer describing the same phenomena. So Karl Popper is misunderstanding the purpose of theories.
@2physics That's not what Popper means (I believe). He means that there is never a unique theory to explain a given set of observations (e.g. because you can just add stuff to the theory that predicts things that are as of yet inaccessible to experiments; but it might also be that a totally different theoretical framework gives the exact same predictions, like Bohmian mechanics and standard QM are supposed to). You cannot prove "truth" of theories, that is the core point of his falsificationism.
@2physics You talked about "there could be new quantites we are not yet aware of" - but that need not be the case at all. The exact same observed quantites always have more than one possible theory describing them.
There is no need for something "hidden" or unknown to exist for this to be true
@Obliv lol, you have no idea who Karl Popper is, have you?
I got so sidetracked because of this bullshit energy-momentum description of gravity @0celo7 whereas you could care less about the consequences of GR and decided to learn it simply because you were 'bored' :DDD wat
user116211
Can any operator be self-adjoint but not Hermitian?
@Obliv He was a philosopher who was pretty integral to the development of the philosophy of science and knowledge in the beginning 20th century. You may say many things about his specific views, but that he "is misunderstanding the purpose of theories" is a...bold claim.
user116211
Hmm, I remember @Slereah once mentioned that, damn ;/
@acuriousmind "Whenever a theory appears to you as the only possible one, take this as a sign that you have neither understood the theory nor the problem which it was intended to solve." seems to me like he disagrees that only one theory can predict the phenomena observed. What he classifies as different theories will allow me to judge if he misunderstands theories, I guess it was a bold claim since I don't know what he considers different theories.
@Obliv Of course he disagrees that only one theory can predict the phenomena observed. For instance, that's exactly what standard QM and Bohmian mechanics do. Or, less controversially, Lagrangian and Hamiltonian mechanics as opposed to Newtonian mechanics for (idealized) classical mechanics
@Secret wtf is "a set with distributive law"? Are you talking about a ring (or rng, if it doesn't have an identity, or semi-ring, if it doesn't have additive inverses)?
@acuriousmind Yeah I mean if this quote is meant to address that there can be multiple formulations to predict the same thing at different levels of precision, then sure. I think I misinterpreted "nor the problem which it was intended to solve." as a statement on the accuracy to the 'truth' of a theory, instead of the accuracy to the predictions of a theory.
@ACuriousMind I am not sure, it is clearly a sub<insert suitable word> of magma, since it has elements with a binary operation that is closed. But it does not have additive and multiplicative inverses nor identity
@Secret Yeah, that's a semi-ring without identity elements (which is a structure so useless it doesn't have a name :P) and your conjecture is false for it because it is already false for semi-rings.
@acuriousmind not sure if that made sense. Basically, it came off as an attack on the validity of theories since it seemed like he was proclaiming that the problem to be understood was subjective/dynamic
@acuriousmind to be fair, my first thought was: "I think it's a good quote. Makes sense since there can be many different theories that predict the same thing."
I'm a bit confused by this Q&A pair:
http://physics.stackexchange.com/questions/253062/dimensional-analysis-problem
(10k on Physics, or dev team.) The question looks like this:
Of note:
The answer was posted 10 minutes after the question.
The answer was upvoted at some point.
The question ...
I'm a big fan of the podcast Astronomy Cast and a while back I was listening to a Q&A episode they did. A listener sent in a question that I found fascinating and have been wondering about ever since.
From the show transcript:
Arunus Gidgowdusk from Lithuania asks: "If you took a one kilog...
