Wikipedia:Reference desk/Archives/Mathematics/2012 July 16

= July 16 =

How do you call in statistics when you correct the data?
I mean it in a good way, like social group A has a higher number of criminals than social group B, but also less affluent. When you put data under this perspective, you discover that both were equally criminal, if the same economical status were given. OsmanRF34 (talk) 00:45, 16 July 2012 (UTC)


 * I think you could use "adjusted for..." or "corrected for...", followed by the factor in question (e.g. "adjusted for social group"). (Of course, you need a legitimate method of "adjustment", otherwise you could just make up any old data, heaven forbid...) 86.148.153.100 (talk) 01:34, 16 July 2012 (UTC)


 * Maybe also see regression analysis. Rckrone (talk) 05:10, 16 July 2012 (UTC)


 * The term I've heard statisticians use (not being one myself) is "controlling for ...". — Quondum☏ 06:40, 16 July 2012 (UTC)


 * I think statisticians would not so much "correct" such data as analyse it in such a way as to estimate the sizes of the various effects involved. The techniques of Analysis of variance and Analysis of covariance might be appropriate. Thincat (talk) 10:55, 16 July 2012 (UTC)

"n-body problem" singularities
I was reading the n-body problem article, and in the "Singularities" section it talks of "singularities in which a collapse does not occur, but q(t) does not remain finite". Firstly, does "collapse" mean "collision"? Secondly, does q(t) refer to the position of the particles? Thirdly, if it does, how does the position of the particles ever become infinite? I can see how position could grow without limit if some of the bodies have sufficient velocity to escape the system, but that wouldn't be a singularity, would it? I really don't understand what this is referring to. Can anyone explain? — Preceding unsigned comment added by 86.148.153.100 (talk) 01:42, 16 July 2012 (UTC)
 * This paper is instructive. As far as I can see the answers are:
 * Yes, a collapse is a collision, having 2 bodies at the same place at the same time.
 * Yes, $$q(t)$$ is the position.
 * To be a singularity the position (or velocity) has to become infinite in finite time. I don't really understand it either but apparently this is known to be possible with 5 bodies, and the paper attempts to build an example with 4 bodies.
 * -- Meni Rosenfeld (talk) 04:20, 16 July 2012 (UTC)


 * It may be worth noting that the potential energy of gravitation in the Newtonian model is unlimited as two bodies approach each other, e.g. (intuitively from conservation of energy) potentially allowing infinite velocity via a slingshot effect. — Quondum☏ 07:14, 16 July 2012 (UTC)
 * But infinite velocity would require a collision (of point masses), wouldn't it, which the scenario specifically excludes? I do not see how any finite separation could possibly impart infinite velocity. 86.176.211.101 (talk) 11:38, 16 July 2012 (UTC)
 * Ok, I think I understand where the magic happens, though maybe it's more of a technicality. It's only considered a collision if it happens in some specific point in space. In the construction in the paper, there are two bodies with a distance converging to 0 (thus unbounded kinetic energy), but they both escape to infinity thus there's no point in which they collide. -- Meni Rosenfeld (talk) 12:00, 16 July 2012 (UTC)
 * Escape to infinity in finite time, colliding "at infinity"? 86.176.211.101 (talk) 12:04, 16 July 2012 (UTC)
 * Exactly. -- Meni Rosenfeld (talk) 12:06, 16 July 2012 (UTC)
 * Cool, thanks! 86.176.211.101 (talk) 12:18, 16 July 2012 (UTC)
 * This is somewhat perplexing (but technically I agree) – a "collision at infinity" not being a called collision is such a fine technical point as to be uninteresting. Redefine a collision as the separation of two bodies diminishing to zero in finite time, and this "collision at infinity" would still be called a collision. A far more interesting case would be two objects merging in finite time with zero rate of reduction of separation. — Quondum☏ 19:20, 16 July 2012 (UTC)
 * I suppose it is a moot point, but if you can't point to an actual place where a collision occurs then maybe it's fair to say that it doesn't exist. However, notwithstanding this, it seems to me that this is an interesting and distinct case simply because the bodies can escape to infinity within a finite time (and without the system having already blown up because of a collision). Incidentally, if I may ask another question, I notice that in the paper Meni linked to (which is mostly beyond my ability), it says:
 * "Meanwhile, in 1974, Mather and McGehee showed that if the solution is allowed to be continued through an infinite number of binary collisions, then there exist noncollision singularities with four bodies on the line."
 * Does this imply that there is some mathematically feasible way of continuing the process through a collision? I thought that at a collision everything just blew up to infinity and it was game over as far as the maths was concerned. 86.176.211.101 (talk) 20:57, 16 July 2012 (UTC)
 * Take the case of 2 bodies, for simplicity one of them has infinitesimal mass so the other doesn't move. The motion of the moving particle can be given by $$x=(at+b)^{2/3}$$. What happens after the singularity at $$t=-b/a$$ is underspecified, but it's logical to extend it smoothly as $$x=((at+b)\cdot|at+b|)^{2/3}$$, so the body continues in its path and catapults past the large body in motion that mirrors its approach. The only ways that energy and momentum are conserved is either this or that the velocities are reversed as in a "normal" elastic collision of two bodies. The same can be done with more complicated scenarios. -- Meni Rosenfeld (talk) 14:18, 17 July 2012 (UTC)
 * I see. Thanks for your help. 86.129.16.198 (talk) 22:46, 17 July 2012 (UTC)

(simple) Example of design with non-fixed intersection numbers?
Hello,

I am considering block designs and I had this question: given a fixed block, can I compute how many elements of the design will intersect it in x points? Does it have to be independent of the block I started with? I know that the answer is "yes" for Steiner systems and for symmetric designs but I suspect it isn't true in general. But then the design would have no group acting transitively on its blocks, so it can't be a very well known design. Are there simple counterexamples?

Many thanks,Evilbu (talk) 19:34, 16 July 2012 (UTC)


 * An N by M block intersects at N*M points, or about (((N-1)*M)/2)+N points in the case of triangular blocks. 71.212.249.178 (talk) 22:16, 16 July 2012 (UTC)


 * I'm sorry, what do you mean by N by M block? (I am assuming that the blocks in the design do have the same size)Evilbu (talk) 07:54, 17 July 2012 (UTC)
 * What's the application? 75.166.200.250 (talk) 03:20, 18 July 2012 (UTC)
 * Well, N^2 for square blocks. 75.166.200.250 (talk) 23:06, 18 July 2012 (UTC)