Recent content by JesseM

Can anyone recommend a good book that would cover this, along with other aspects of variance and other measures of correlation like Pearson's and Spearman's that might be helpful in building conceptual intuitions about how to interpret them? (for example, this comment uses a simple example to...

Doesn't the term "independent variables" normally mean they are statistically independent of one another, i.e. uncorrelated? mfb already mentioned that the variances only add to 1 "if the Xn are independent", that's what I took "independent" to mean there.

Thanks--is this answer specific to the case I mentioned where the value of V is a linear sum of the values of the Xn, or is it general? If it's general, could V be any sort of deterministic function of several independent Xn (including things like arbitrary computational algorithms), or are...

Often in empirical studies you see statements that factor X explains some fraction of the variance in some other variable V, and thinking about what this means intuitively made me curious about the following question. Suppose you have a model where the values of some set of factors X1, X2, ...

Looking over the book again, I think the approximation he used to get 55% rather than 50% may have been a very simple one: in chapter 17 he writes that "Einstein's laws dictate that, as seen from afar, for example, from Mann's planet, Miller's planet travels around Gargantua's...

At the start of Chapter 7 Thorne mentions that the Endurance is orbiting at ten Gargantua radii, and given a mass of 100 million Suns and a radius that differs by only a tiny factor from the extremal radius of GM/c^2, Gargantua's radius would be around 492.7 light-seconds. So, ten radii would be...

The problem with talking about how "light cones behave" is that it often ends up just being an artifact of the coordinate system you're using (unless you're talking about some purely issue, like which physical events lie in the light cone and which don't). For example, in the case of a...

Technically, if they haven't solved the two-body problem I suppose that means they can't even know that planetary orbits can be stable (around black holes or even around stars like our Sun), only those of test particles with infinitesimal mass. But I would think the test particle approximation...

I think Kip Thorne would agree with you, it seems like his self-imposed rule was that the movie not slip into total fantasy by depicting things that explicitly violate basic physical laws (like true faster-than-light travel), but that for dramatic purposes it could be unrealistic in other ways...

Kip Thorne explained in ch. 7 of The Science of Interstellar that in order to explain how they could get from one orbit to another despite the major differences in velocities, he was imagining that there were plenty of "intermediate mass black holes" orbiting Gargantua which were large enough...

They didn't actually say the orbiter was orbiting the planet, rather the diagram they drew showed it in a higher orbit around Gargantua.

It's a misconception under the modern definition of the distinction between GR and SR, which revolves around whether spacetime has inherent curvature or not. But it seems to be a historical fact that Einstein and other physicists didn't always define the distinction that way. And while defining...

Are you talking specifically about a spacetime containing closed timelike curves? A spacetime with a single warp bubble doesn't contain any (I think Alcubierre showed this in his original paper, though with multiple bubbles moving in different directions there are CTCs), so in that case can't...

This question was asked before on this thread, the earliest example anyone knew of was the 1909 book The Principle of Relativity, and Non-Newtonian Mechanics by Gilbert Newton Lewis and Richard Chace Tolman, see p. 714 online here.

Thanks again for your help. I used your equations, combined with the equation for the radius of the ISCO given in section 2.5 http://relativity.livingreviews.org/Articles/lrr-2013-1/articlese2.html , and found that the black hole would need to have a rotation rate of about (1 - (1.33266 *...