I have a lot of work to do, but I thought I'd check in to see what's up.
If you look on the room info, it shows Bill D as having 350 points. I thought that maybe something had happened. However, I looked at his profile and it still says 1.
I noticed this morning that Bill's answer to the question had three downvotes. I asked why, since the hint seemed very good. Of course, no one has responded.
I am official not connected with my advisor now....and also i am on academic leave for one year....hence looking for some job or internship position...i need to see how things go
My gravater seems to have made an impression on the mods. Bill D says that they are going to force him to wear my "mean square" avatar for a year. I came back to see if it was active now, but perhaps it won't happen until he comes off of suspension.
@Srivatsan hello
Glad to see you before I head off for a walk with the dog.
Hi, all. This is particularly non-stackexchange-question-guide-friendly, so I would like to pose a query to anyone interested here: How does mathematics relate to Physics? Is it a tool for Physics, the interpretation of Physics in mathematical language, the laws that govern Physics, or something else? (None of those are mutually exclusive.) My instructor and I discussed this today and it was a very fruitful discussion.
@mixedmath, when I first started this class in August, I was very weary of the lack of mathematics in it. (I'm a more mathematically-minded person than anything else.) I excelled on the math aspect, but not so much on the conceptual aspect. (I have a hard time visualizing things, sometimes.) So I was torn between the view that the physics guides the math and the math guides the physics (it may be neither). I like the idea that my instructor proposed: [. . .]
mathematics is the queen and servant of Physics. However, I don't know if that's so true. A nuclear engineer I know tells me that physics majors tend to idealize it and the truth is that physics is all applied math. I'm really favoring that position.
So, if we were only considering modern math, I would say that it is impossible to declare that math is purely a servant of physics. I do research now that, as far as I know, is not at all around to support or advance physics. (why it's around is also not so clear, but that is the way of pure math).
But this trend was perhaps not as true in the past.
I respect pure math. :) I have to agree that the idea that mathematics is a servant of Physics is very one-sided because mathematics is so much more vast than Physics.
I try to distinguish between the ideas of 'math' and 'arithmetic.' By arithmetic, I don't just mean sums, differences, quotients, products, and roots. I mean any sort of manipulation of numbers (or functions, etc) that requires no innovative gaps.
In this sense, I would say that there is much physics that relies only on 'arithmetic,' and that this arithmetic is very subservient to the goals of the physicists
similarly, I would say that there are mathematicians that do physics. My first research in differential geometry (forever poisoning me against dif geo, I think, though I'm starting to warm up to it again) was on fluid dynamics
I like that distinction, @mixedmath. I have trouble, for instance, seeing areas such as (I hope no one pounces, lol) category theory being applied to Physics.
Was that a pun, by the way? Fluid dynamics and warming up to differential geometry? :P
I imagine that it has a lot to do with mental temperament, too. There is a mental intimidation in mathematics that most people never get past: The sheer vastness. It's like being in an infinite dimensional room with no floor. I'd say some people are just more comfortable with 3-dimensional (or 11, if you like M-theory) rooms.
(I'm not meaning to imply that this has to do with a difference in intelligence, either.)
that's a good point. theoretical physicists depend on the results of experimental physicists in maybe the same sort of way that mathematicians depend on other mathematicians.
I don't understand ZFC very well, nor the notion of consistency in mathematics. So it is not easy for me to make an intelligent comment about the falsifiability in that regard.
@DanBrumleve Hm, I am not very sure about this. What if someone falsifies quantum mechanics tomorrow? Then, in a sense, all of physics is falsified, which seems entirely analogous to your situation.
@DanBrumleve Would it? I don't worry about this too much but I always heard the slogan, "Maybe ZFC is inconsistent but something which exhibited that is probably impossibly long, so all extant proofs would be fine in some sense."
I can hear it on the radio tomorrow morning now, "Annnnnddd maybeee ZFC is inconsistent, but somethingwhichexhibitedthatisprobabyimpossibly long, SOOOO all extantproofs would be fine!!!!"
inconsistency of zfc means that there is a contradiction in the axioms. so we'd have to invent new axioms and rebuild all of mathematics on that basis. that is not expected. on the other hand, it is expected that the standard model will continue to evolve. but that doesn't make today's standard model useless in the future anymore than newton's laws are useless today. and if course mathematics is still just as useful whether or not there is an extremely long proof of ~Con(ZFC)
I don't think that's... precisely as devastating as the inconsistency of ZFC sounds. Of course, I have no basis for this opinion, given my ignorance. What says yee?
(Speaking of which, the most important thing that Godel killed was Hillbert's dream, I think.)
anyway be sure to check out empslocal.ex.ac.uk/people/staff/mrwatkin/isoc/index.htm ... i spent a lot of time reading here some five years ago but then i forgot the site and i finally succeeded in googling it again just now
@DanBrumleve I logged in at 4:11 for 30 days consec. but boy oh boy... turned out silver badge wasn't poppin. Utterly depressed I refreshed my page...and suddenly voila! I saw the notice. (Ah the feeling...)
1. Let's say I leave such a comment (as I did in the meta post). And a subsequent user who also wants to not-close the post -- should they leave an explicit comment as well? That is, instead of (or, addition to) upvoting my comment.
@MarianoSuárezAlvarez Or maybe they agree with something else in the comment (for example, I also asked for the voter-to-close to leave an explanation; it's likely that many felt similarly).
Ok, I get this. Another question: In the meta post and in some earlier posts (from my memory; I cannot really back it up right now), it seems that the vote not to close gets ignored by the subsequent voters. Does this happen at MO?
@MarianoSuárezAlvarez I don't think many are aware of the convention that "new don't-close votes should be separate comments, not upvotes" either. For instance, I would have considered it unnecessary to add a separate comment for each such vote. I find it likely that maybe 1 or 2 of those 14 upvotes in that meta post were actually new don't-close votes. Of course, we would never know, and nothing can (or, should) be done about this. But I thinking of making people more aware of the protocol.
@anon Well, you leave a comment saying that the post should not be closed. The understanding is that the next person who wishes to close should leave a comment negating this vote.
Someone might post a question on meta about the convention, to make people aware of it. But... it is a little byzantine, and since math.se has way more diversity than MO, I am not quite sure it'd work much.
(At least a majority of the people here belong to (or, are from) an academic background, so despite the diversity, we could hope for some common ground.)
@Mariano : a general advice....I am not able to get enough attention or generate interest/curiosity from people for this questoin : What do you think could be the reason ?
My personal view on the question is that your class of functions is very weird
it does not seem natural in any sense, and it is not related to anything people actually use in mathematical work.
This does not mean it is not interesting—it is interesting for you, for example!
That there way exist a function which is exactly differentiable exactly 3 times on the rational numbers and exactly 7 times on the irrational numbers is a fun fact (I don't know if they do exist :) )
How does one know one is not dreaming? How could one logically demonstrate to a skeptic that one is "really" there, awake and not just dreaming the entire situation/world around him?
Specifically what I'm asking is: which if any philosophers have addressed this problem of how one knows one is or...
I wonder whether iyengar's post at meta got the downvotes because it is incomprehensible or because the person who posted the question. (No explanation for downvotes.)
To me it seems he asks for some possibility of immediate notification from MSE.
Although I am no sure if he is speaking about getting the same notification as in SE inbox via email, too; or whether he wants to follow all posts at MSE.
BTW occasionally I would appreciate the possibility of immediate notification; e.g. if I gave a hint on homework question, I have to check the site repeatedly to see whether the OP has made some progress or whether he needs a new hint.
Let $\{ A_i \}$ be a countable collection of pairwise disjoint sets. Then $$ \nu (\bigcup_i A_i) = \int_{\bigcup_i A_i} f d \mu = \sum_i \int_{A_i} f d \mu = \sum_i \nu(A_i)$$
I think that reputation 1 is way for the software to make certain features inaccessible to the user without starting to add extra checks if someone is banned or not.
