Yonatan Zunger’s Blog

Incidentally, Cabbala isn’t the biggest thing on my mind tonight. There’s a new paper out on the archive (here) which I suspect is on the tail of something very, very important. I think that Bousso’s approach to holography has something very “right” about it, and this paper may be one of the first hints of exactly which way this needs to go.

J. T. Chang, Recent common ancestors of all present-day individuals. Chang considers a statistical model in which a population of constant size n goes through successive generations, and shows that (under suitable assumptions – infra) for n reasonably large (>~200 based on numerical simulations), there exists a single common ancestor of everyone in the population log₂ n generations in the past – and if one goes approximately 1.77 log₂ n generations back, everyone in the population is either a common ancestor of all people in the present generation, or of nobody. That is, either a given family line has died out completely, or just by statistical diffusion, they’ve become related to everyone living.

Applied to the population of Europe, this threshold seems to happen about 1000 years in the past. So it’s fairly likely that everyone with even a single European ancestor within the past 100 years or so can, in fact, claim descent from Charlemagne.

There are two technical assumptions in this paper. One is constant population size; it seems like it would be straightforward, although a technical pain in the ass, to relax this. The other more interesting one is that it assumes a random mating model; i.e., the probability that someone in generation t is a parent of someone in generation t+1 is uniform. This obviously isn’t correct, but I can think of a good way to model something more realistic – consider a set of k populations of size f_k, each of which has random mating within it, and with a cross-mating probability distribution p_{k k’}. This could model the existence of disjoint social or geographic groups. I’m rather curious about whether this would substantially change the results. One interesting question is, given a total population size and a decomposition into subgroups, whether or not there’s a “critical size” for a subpopulation which will lead in finite time to that population dying out, becoming completely assimilated, or becoming ancestors of everybody.

The following may be a little on the technical side. It deals with some thoughts about physics that have been going through my head lately.
Physics rambling

(Summary: In a previous post, I referred to a statement made by Lee Smolin that “time does exist,” and that I disagree with him. It has been pointed out to me that this sounds like an extremely odd statement and counterstatement without its original context. I offer in my defense that he started it, and he gave no context either. So here’s a summary of what he meant by that, and in very briefly why I don’t feel confident that it’s correct.

Lee, if you’re reading this, please correct me if I’ve misstated your position!
(more…)

(Mostly notes to self)

Two interesting short papers today by Wung-Hong Huang. hep-th/0308094 is a short proof that if SUSY is unbroken at the classical level, then it can’t be broken at any level of perturbation theory, even if all the gauge symmetries are broken. Not an unexpected result, but it’s kinda stark – just more evidence of how powerful a symmetry SUSY really is. Need to think a bit about this issue, and what it means for SUSY breaking in the universe.

hep-th/0308095 is an analysis of the statistical mechanics of systems that allow boson-fermion transmuting processes. I need to think a bit about his result – there’s at least one subtle step there – but if it’s correct, then this would be a nice way to think about the stat mech of a supersymmetric gas. (To do: Figure out what the value to his α parameter would be for a given gas, say shydrogen.) I’m not sure if this is good for anything, but (a) imagining what the universe would look like if it were supersymmetric is fun, and (b) this seems like it might have some unexpected uses later, if nothing else in getting a solid feel for some weird kinds of statistical systems.

(From a problem set my students just handed in…)

The amount of energy it takes to bring water from room temperature to a boil is enough to launch it 34km straight up. The amount of energy it would take to boil it down all the way – until it all evaporated – would launch it 270km.

Compare this to a typical altitude for a 747, about 11km, or for a space shuttle, about 150km.

Damn. Water has a very high heat capacity.

And the idea of launching a liter of water 34km into the air is pretty cool.

Other related ramblings

On Edge, Martin Rees – a noted cosmologist, someone who definitely knows what he’s doing – has an article about multiverse cosmology. (This is a general-public article, BTW, not a technical one)

Now, I’ve got one primary objection to this article, which is that it makes multiverse cosmology sound like something much more agreed upon in the scientific community than it actually is; its current status is more on the lines of “a definite possibility, one whose details haven’t been worked out yet, but has some really good features as a prospective model.”

But that aside, he has some interesting things to say on the subject. One intriguing possibility he brought up, which I hadn’t heard before, was that in an infinite universe, someone has very likely developed extraordinarily powerful computers, ones powerful enough to simulate not just individual life forms but even large sectors of the universe itself, and that for all we know, we may be living in such a simulation.

The philosophical implications of this sort of thought are rather intriguing. On the one hand, we couldn’t necessarily intrinsically tell whether we’re in such a simulation or not, since we don’t have any outside reference points to work by; but it may be possible under such circumstances to communicate with the simulators, by some means or another, and indicate that yes, there’s life inside here.

The good/bad thing with this line of thought is that it seems that one could use it as a basis for virtually any argument; it’s like theology, but even less constricting. Can’t explain some property of the universe? Maybe the simulators programmed it to be that way. (Like the “well, that’s just how God planned it” excuse – a great way to avoid answering any inconvenient questions)

What’s interesting, here, is that this seems to arise naturally as a consequence of certain kinds of cosmology: If the universe really is large enough to contain all things, one must expect such simulations to exist therein. But this gives us no information whatsoever about whether we’re elements of such a simulation.

Anyway, this is just sleep dep and a great deal of physics (from the past few days) talking at this point. There are some interesting issues brought up here, but they’re about on a par with solipsism as far as really arguable points. Perhaps it’s time for bed.