@ChrisWhite But I guess Mathematica use deterministic simplification, so it should give the same results regardless it is on your machine, or mine or whoever
While picking up a pair of eye glasses dropped by a friend, you notice that they form an inverted image of the background and that the image is stretched horizontally as well. Your friend suffers form myopia,
hypermetropia, astigmatism or both?
I try to do this question by making an equat...
@DavidZ: Monads are just monoids in the category of endofunctors. But more seriously, you can learn monads in 12 minutes - you just can't make the mistake to learn them from CS people who themselves try to understand the concepts by examples within examples.
@ManishEarth: The first line is from this humorous summary and I wasn't joking, if you know what a functor is then the definition of a monad is as complicated as the definition of a group. However, CS people learn about their implementation, learn 3 example, and then write blogs about it.
... obviously to answer simple questions about everyday life:
Why are dishwasher washed glasses "squeaky clean"?
Not that I wish to be ungrateful, but I put far more effort, and found it far more interesting, to write an answer explaining where the idea that black holes are gateways to other un...
@ManishEarth: There is the List monad, Maybe monad, and those are the most approachable exmaples.. It's called the monad toturial fallacy. It's like knowing Z_5, SO(3) and complex conjugation and then trying to explain "group" to someone else in only those terms. There are many truths and specialication/aspects of groups which can never pop up with just some examples.
@Danu: Not only has the author named the method after herself, in the acknowledgements, the author dedicates 'Tai's mathematical model' to her 'late parents.' lol
The "Related questions" list does a great job in presenting the most upvoted (and whatever other parameters are used) questions related to a subject, and the subgroup of linked questions, when present, is even better. However, given the amount of high quality questions and answers that are presen...
@Phonon No, I haven't. But after the horrible job my string theory lecturer did today when trying to do conformal field theory, I might. It literally can't get worse
@Phonon I'm a bit too...unfocused to listen to them right now, though. The christmas markets here have begun, and that means mulled wine is flowing in the evenings ;)
@JamalS Thinking a central charge is unnecessary. Believing conformal weights must be integer (okay, I kinda guided him into saying that, but still...). "Deriving" OPEs and the state-field correspondence without ever even defining the vacuum. Never demanding unitarity.
@JamalS He's a PhD, and he's a (junior) researcher in "phenomenological string theory". The two really compentent string theorists here are unfortunately unavailable this semester - one has his hand full with being the dean and dealing with bureaucratic stuff, the other is on sabbatical
So the string theory lecture got passed to him
Frustratingly, it's not even the first time he gives it.
@JamalS I'm not attending them always, but on Wednesdays I like to go there in the morning so I'm awake to deal with the homework that's due tomorrow afterwards
@Danu Yes and no. The idea of domains and the rigged Hilbert spaces following from them are important. But if you properly construct this physical Hilbert space, you know from the beginning what kind of functions are allowed as solutions to the SE
The SE is nothing but an equation on the Hilbert space of states, after all
To think that there are "solutions" to it that aren't "physical" has the whole thing backwards, in my view
I don't think one should look into "countries" at all when it comes to such matters, it just has nothing to do, I highly doubt QM teaching e.g. is country dependent, rather teacher dependent....
@Danu But the beauty of theory is to get the maximal predictive power with minimal input. If you rely on experiments to tell you what the "physical" solutions are, you need more input than if you had formulated the proper wa of constructing the Hilbert space
After all, a "theory" that predicts all experimental results correctly could also just be a collection of rules "If you do experiment X, you will measure Y with error Z"
but that's not knowledge, not understanding, just a collection of experimental results
I know I'm quite a hardliner on this stuff, but "understanding things physically, but not mathematically" is, to me, just a paraphrase of "I've convinced myself that it works that way, but I cannot deliver a waterproof argument for it"
Anyhow, I forgot how we even started talking about this. It's come up so many times in my conversations now that I'm pretty sure it's just me wanting to polish my point of view.
@ACuriousMind Exactly! And that's fine, if you have an objective arbiter like experiment to help you out.
guys I think a lot of it boils down to how leaned each one of us is toward theoretical physics and not, there isn't a single way of doing physics, most approaches are really complementary...
@Danu I guess my main complaint is that we have known for decade how to replace the intuitive arguments with rigor, and we still teach it in the way the fathers of quantum mechanics first discovered it
It's certainly interesting and important to know how things developed
But it shouldn't be taught as if it were "state of the art"
@Danu I think just the start is the most fitting analogy: Math is like music, or other arts. Not everyone likes them. Not everyone is good at them. But you don't force everyone to draw stupid notes of music, and stupid applications of composing techniques throughout all of school
Somehow, it is understood that, with art, it is alright if you suck at it. But with math, you must be taught. In an age of calculators and computers.
And so math is broken down into little, "easily" disgested pieces that have nothing at all to do with what math is really about
It's really like teaching painting by letting people "connect the dots" over and over again
@Danu tbh I always enjoy learning mathematical nuances and details Gauge usually hints at (emphasizes) in most of his answers and discussions, and most often find them a very useful addition to what I already may know, or thought have known. At the same time, the point you bring across, has also always been part of my learning in physics, i.e. not need to learn about all details to be able to understand some of the advanced topics, when one luckily can rely on physical thinking.
An essential difference between math and conventional art is that it's a lot harder to enjoy high level mathematics for a layman. It's literally impossible, in fact. A skillfull painting/musical piece however is much more accessible.
@Phonon I've started trying to be more like the stereotypical mathematical physicist. I think there is a lot of value to knowing the hardcore stuff, but being able to see through it.
@ACuriousMind In fact, I find myself quite frustrated because I cannot seem to get the faintest clue of what Grothendieck's work is about, even with my (relative to the average) enormous background in mathematical/logical thinking
@Danu In my view, and in one word: Structure. Modern algebra, all of homotopy and category theory and all of algebraic geometry with its schemes and stacks, is about seeing structures without caring about the particulars. About what is local and what is global in the most general way.
And about making naturalness precise. One of the best Ah, that's why! experiences of my life was when I finally understood why universal properties are so powerful.
I do not understand the details of motives and topos theory. But one of my long-term goals is, for example, to understand what the heck Urs Schreiber is doing in this paper.
I'd really like to understand that stuff. I'm very seriously debating whether it's worth it or not to try to really learn things like algebraic geometry
@Danu If it is held by someone with a faible for abstraction, go for it. If it is held by someone with a fetish for varieties and polynomial stuff, run as fast as you can
@Danu Yes, but...more general
Amazingly, you can do essentially everything you can do on manifolds on these smooth spaces, but you do not have these annoying local definitions with charts to deal with
I started reading Recoltes and Semailles, damn it. That's how bad I wanna learn about him
user54412
11:07 PM
@ACuriousMind You know, I was hoping you'd chime in on this question to assure the OP that yes, entanglement does get more attention than it deserves.
user54412
Especially with everyone's insistence that we only test entanglement by spacelike-separating our measurements, as though spacetime has anything to do with it.
As much as I like getting on my soapbox and telling people that entanglement is really a natural occurence as soon as you think about any composite system at all, I think that doesn't answer the question
Neuneck has the correct answer, for the record. The others all wax about what this experiment may or may not imply, but theirs is the only one to unambiguously state that even if you expect the stone to drop to the floor, you still look if it actually happens.
While picking up a pair of eye glasses dropped by a friend, you notice that they form an inverted image of the background and that the image is stretched horizontally as well. Your friend suffers form myopia,
hypermetropia, astigmatism or both?
I try to do this question by making an equat...
... obviously to answer simple questions about everyday life:
Why are dishwasher washed glasses "squeaky clean"?
Not that I wish to be ungrateful, but I put far more effort, and found it far more interesting, to write an answer explaining where the idea that black holes are gateways to other un...
