@0celo7 Yes, one can show that in a compact space, non-emptiness of all finite intersections $I_{i_1}\cap \dots \cap I_{i_n}$ implies non-emptiness of the total intersection.
@ACuriousMind You don't need compactness (Hausdorff suffices)---but the sets $I_n$ should be compact. Of course if you assume compactness then closed sets will do
@Danu The prpblem is that the Zariski topology is so weak that Hausdorffness is a very strong requirement for it (only fulfilled if the spectrum is finite and discrete, I think)
@0celo7 The intersection of a descending sequence of compact subsets of a Hausdorff space is non-empty.
If you assume compactness of the full space then you just need closedness because closed subsets of a compact space are compact, so it's "easier"
But, as I said, in a geometrical sense I think it's fair to say that Hausdorff is "kind of weaker", so I think the former* statement is slightly neater :)
But the two are very closely related. If you can prove one, you should be able to prove the other with barely any modification.
@Danu Ok, take the largest compact set to be the "space" and then apply finite intersection in a compact space $\Rightarrow$ intersection of the entire collection is nonempty
@0celo7 There's a weaker statement about general metric spaces. A subset is compact iff it is complete and totally bounded. The axiom of completeness gives you that complete = closed in the reals, but totally bounded = bounded needs some other property of the reals.
@Danu Let $X$ be a compact space and $\{S_\alpha\}, S_\alpha\subset X$ be a sequence of sets such that any finite number of them have a nonempty intersection.
Then $\bigcap_\alpha S_\alpha$ is nonempty. Do you agree with this?
No, I'm pretty sure that total boundedness = boundedness has to show that there's always a larger ball that contains a finite number of small balls, and that has less to do with completeness and more with the Archimedean property.
If LIGO have made a detection so soon after restarting with the higher sensitivity, simple probability suggests there should be many more detections to come in next year or two.
@Danu Yeah, but it's not like we really do anything "formally" around here. I think it's a good idea to do this to bring attention to the announcement.
I like what they do on Space Exploration, making chat events for all the major launches and the like
We could preemptively post some canonical questions, if people are inclined. (like that one) Or we could go through past questions on the topic and clean them up.
OK I'm an old time (since the early 80s) C the C++ programmer, and I love the efficiency and strong typing, but it can be such a lot of hassle getting stuff done.
Everything seems to require twice as many lines of code as you think.
C# is astonishingly compact. I'm finding C# programs are half the length of the sort of thing I'd write in C++.
And not having to worry about freeing malloced memory is enormously liberating.
And possibly it's just my C heritage, but C# seems very elegant while Python has always seemed rather scrappy to me.
Oh, I'd complain about C++ just as much as you do. I have no shortage of reasons to be frustrated with it, despite having worked with it for many years.
Well, about 5, maybe not "many"
But I have the opposite impression of C# vs Python, at least from what little C# I've seen in code samples. If nothing else, Python seems the opposite of scrappy.
I notice a lot of homework questions come from students with Indian names, though I suspect this just means Indian students are more willing to study Physics than we indolent westerners.
Hi! For many reasons I am very uncertain whether I should agree to a particular topic for my PhD thesis. Since I have a hard time to figure out if this is the right topic for me, I would love to hear your thoughts on this!
Sure! :-) Here you go: This is the literature on which my thesis would be based: https://www.dropbox.com/s/msw6duhh43syxn0/literature.pdf?dl=0.
The thesis topic would be mainly about "Photon Surfaces" - and apparently it is connected to the field of "gravitational lensing"
There are two main concerns:
i) My passion in General Relativity is the question about time and causality. I like any type of problems related to causality, such as the concept of iso-causality. I believe that the proposed thesis topic doesn't have anything to do with any of the problems I am interested in. Is there an…
I do not have a good feeling about this PhD project.... But I also do not have a lot of experience to judge it from a professional standpoint
Remember that the supervisor wants eager and successful students who will make him/her look good. So they will be as keen as you that it's a good match to what you want.
@eigenvalue that's a really, really bad way to start
You will need to trust your supervisor to do the best for you, and if you don't feel that trust exists you need to think long and hard about this, regardless of what the subject is.
With most PhDs, especially in a subject as well worn as relativity, only a few people will have a really authoritative knowledge of the field. Your adviser is (should be) one of them.
All academics started out without tenure, and working with a young ambitious supervisor can be better than working with some prof who has a million other things to occupy his mind.
But if you don't feel you can sit down and have a discussion with this about your (prospective) supervisor that's a problem.
@JohnRennie That's true, but on the other hand working with someone who has connections to the top researchers in the field is way better than working with someone who doesn't
@JohnRennie He is not young anymore... he will retire without tenure. Although he is very nice, friendly and helpful - and the topic is in GR... I feel there are too many flaws that could hurt any further career
The problem with the topic is: I cannot talk about it with him because its his "baby" and he is totally convinced about the topic and idea behind it. But it seems that nobody else in the world seems to care about this particulat topic...
@0celo7 Yes, his baby gets ignored for many years already. In my case, this potential supervisor is in Europe and he is not even a Professor, but a scientific researcher . In Europe this is OK, in general. But in the USA this could be a problem later on
@0celo7 usually, you can tell by their title. Pre-tenure professors have a title like "assistant professor" whereas tenured faculty are "associate professor" or "professor". But the specific titles in use and their meanings can vary by country, and even from one university to another within the same country.
@JohnRennie Yes, I did. On the one hand, I like it because I could stay in General Relativity. But on the other hand, it doesn't seem to involve causality (time) questions.... which is what I am most interested in ... So I have mixed feelings
@eigenvalue Not necessarily. As someone who's never left the US, I'm well aware that most permanent researchers in Europe are not tenured and not even professors.
user54412
Expecting all Europeans to be supervised by tenured profs would be like expecting all Americans to be supervised by Nobel laureates.
The key, as mentioned above, is trusting the adviser, having him trust you, both being enthusiastic about the project, and doing something that someone else at least sort of cares about.
You received many steel balls of the same diameter d and container of known volume V. All dimensions of the container are much greater than balls diameter. How many balls can be placed in a container?
Could it be a correct solution?
To place balls in a container we should arrange this container...
(Also note that posting your question to chat directly after you asked it is not necessary)
@ChrisWhite Kind of...there are those strange users with (unregistered) behind their names on their profile, but their username is usually clickable, not like this one
@hubot Please read the posts I linked, especially the homework policy. It doesn't matter whether or not the question is actual homework, you should ask about a physics concept instead of asking for the solution to a specific problem or about the correctness of your solution
Well Thank you folks. This is wonderful site. I got on to it recently and think should have found it long back. Answers here helped me to get rid of the mystery surrounding my mind in context of quantum entanglement. Now the observed behavior makes complete sense, which is a big relief for me.
I...
@eigenvalue : I get a 404 when I follow your link. So there's not much to go on, and it occurs to me that you might upset/annoy some people in your department if you ask pointed questions. Why don't you ask a few tangential questions on the stack exchange?
Why you have to jump on disagreement. It is not taking anything away from you or anybody else in terms of what you already got on the site? — kpv14 mins ago
Huh?
user54412
well clearly any of your resources I choose to appropriate for myself are not lost to you, because the world revolves around me
@hubot It leads to another correct framework for doing physics so it must have some value.
@ChrisWhite There are (at least) two ways for a post to have a non-clickable user.
(a) Migration from another site where the OP on teh original site does not have a linked account on the destination. But I think you can tell those because they say they've been migrated.
(b) The user who asked it was later deleted or dissociated from the post. I presume that this is the situation in this case.
@ACuriousMind Uhm .... I didn't look at that. Now I don't know what to think. It's possible there is a third channel for creating such posts, but I can't think of one right now.
@SirCumference Now the key question: why does the electromagnetic force seem to get less important relative gravity as the scale increases, given that they both have infinite range and E&M is undoubtable stronger?
Bingo. The really important fact here is the E&M includes 2 signs of charge that can cancel out. So those big pieces of matter are approximately neutral.
@dmckee It never really made sense to call gravity the "weakest force", since 1) Well, it's not a force 2) It can be extremely effective at certain scales, in comparison to the other force
@SirCumference On the contrary, it makes perfect sense to call gravity the "weakest force". For the particles that make up matter, if you take just a few of them, the electromagnetic force between them is far larger than the gravitational force between them.
Just spent the last hour trying to find one, but to now avail. Has anyone ever seen such a thing?
I know that electricity in AC flows both ways but I do not know what happens when it flows both ways. Whats the difference
You received many steel balls of the same diameter d and container of known volume V. All dimensions of the container are much greater than balls diameter. How many balls can be placed in a container?
Could it be a correct solution?
To place balls in a container we should arrange this container...
