February 17, 2007
Once upon a time, comics didn’t make jokes about their own neuroses. I honestly don’t know how they survived. [Numerous authoritative accounts point to booze, drugs, and sex as their preferred coping mechanisms. -ed.] Luckily, those dark ages are over. And thus now, not only do comics get a more direct way to channel their deep-seated pain into their art, but also we in the audience get a cheaper source of mental health advice. For example, I think the following’s pretty good advice:
I prefer not to think of myself as depressed. I prefer to think of myself as paralyzed by hope.
(For those who were amused by this joke and are tickled by mental health humor generally, note that Maria’s new half-hour special on Comedy Central should be repeating umpteen times over the course of the next month.)
February 14, 2007
So, after an utterly unplanned 8 month hiatus, I’ve decided to resume blogging. I plan to start slowly in order to make sure I don’t pull a blogging muscle or sprain my brain. So, don’t expect any long original essays for a while… just some links and quotes. Along these lines, given that today’s Valentine’s Day, it’s pretty obvious what to do: find some pithy poems about love, quote ’em, and call it a day. But this is in fact pretty tough, especially as I feel one should somehow not only pay tribute to the intoxicating ideal of pure, eternal love, but also pay heed to the bittersweet reality of conflicted, transitory love. After some thought, I’ve come to the conclusion that the middle verses of Regina Spektor’s song “On the Radio” best fit the bill:
This is how it works
You’re young until you’re not
You love until you don’t
You try until you can’t
You laugh until you cry
You cry until you laugh
And everyone must breathe
Until their dying breath
No, this is how it works
You peer inside yourself
You take the things you like
And try to love the things you took
And then you take that love you made
And stick it into some
Someone else’s heart
Pumping someone else’s blood
And walking arm in arm
You hope it don’t get harmed
But even if it does
You’ll just do it all again
While the lyrics are quite swell all by themselves, the song really deserves to be heard. On the off chance that you don’t immediately want to part with your hard earned cash and buy Regina’s album Begin to Hope just on my say-so, you can hear the song free via the radio player on Regina’s website. The more-or-less direct link is http://www.reginaspektor.com/radio/begtohope/radio.html. Click through to the 4th track.
June 2, 2006
Long overdue update 2/14/2007: The quantum computing result described below remains unproven (though not disproven). It is true that homogeneous mean field spin models (i.e., ones where every spin is coupled to every other and every coupling has the same strength) are characterized at criticality by an entanglement entropy that increases only logarithmically with the number of spins [see, for example, this article by Latorre, et al.] It is also true that systems whose entanglement entropy is O(log N) should be efficiently simulable classically [the seminal paper is this one by Vidal]. However, it remains unclear whether inhomogeneous mean-field models (i.e., ones where every spin is connected to every other, and the coupling strengths have some nonzero mean, but they are not all the same) also have logarithmic entanglement entropy scaling. Most pertinently, the method described below can’t resolve the issue. That is, showing that the ground state energy of an inhomogeneous mean-field model can be given exactly in the thermodynamic limit by a separable Ansatz does not mean that the model’s true ground state is separable. Silly me. 😦 On the bright side, the calculation about the probability a pair of people in a room with N people share a birthday is definitely correct. 🙂
This whiteboard reflects the two things about which I was thinking today.
[Click the picture for a full-size 1600 x 1200 JPEG.]
[The left hand side] Writing up a talk I gave at the Quantum Computation and Many-Body Systems (QCMBS) conference in Key West, FL in early February. (The conference website can be found here. The conference program page has downloadable PDFs of the presentations that were given. Mine is here.) What you see on the board is a formal power series expansion of the Gibbs free energy of a general, pairwise coupled quantum spin system around the noninteracting case. The notable aspects are that if there’s C nonzero couplings in the system, then at every order in the expansion there’s just C nonzero terms and they are such that you can say the magnitude of the nth order correction scales as CJn, where J is the typical coupling constant. For systems where, as the number of spins N goes to infinity,
(1) every spin is still connected to a finite fraction of all the other spins and
(2) the ratio of the mean coupling between any 2 spins to the standard deviation of the coupling between any 2 spins does not vanish,
J must be of order 1/N so as to have a finite free energy per spin. In such a case, only the first 2 terms in the expansion are extensive, and thus spin-spin correlations (be they classical or quantum) do not matter for the Gibbs free energy per spin at any temperature (and thus the Helmholtz free energy per spin at any temperature and thus the ground state energy per spin at zero temperature). This asymptotic lack of quantum entanglement in the ground state implies that a wide class of adiabatic quantum algorithms cannot provide any speedup over classical algorithms for NP-complete graph theory problems on graphs where each vertex is connected to a finite fraction of all the others.
[The right hand side] Recalling, after being embarassingly confused with two of my friends, how to do that old problem “In a room with N people, what’s the probability that at least 2 of them have the same birthday?”, and thus explain why there’s a large chance even in a room of, say, 30 people (much larger than the woefully naive estimate of 30/365).
May 30, 2006
This blog is too infrequent to have many traditions. The following is my only annual one. It's the third time I've had to update it.
I must study politics and war that my sons may have liberty to study mathematics and philosophy.
— John Adams (1735-1826)
As a theoretical physicist with major metaphysical leanings, I've long felt the above quote by President Adams to be especially pertinent to me personally. Therefore, to the many who have made the sacrifice to study the ugly side of life so that others may study the beautiful side, I offer my humblest thanks.
And there have been so many…
|War/Conflict||Personnel Served||Battle Deaths||Other Deaths||Wounds Not Mortal|
|World War I
|World War II
|Persian Gulf War
* See reference notes below for sources of these figures. Note that World War I "Wounds Not Mortal" as well as the Marine Corps contribution to WWII "Wounds Not Mortal" (68,207 of the 671,846) are actually "Wounded In Action" (i.e., number of soldiers wounded) and technically not "Wounds Not Mortal" (of which one soldier could receive multiple ones during his tour of duty, of course).
|Operation||Killed in Action||Nonhostile Deaths||Wounded In Action|
** This year's figures current as of May 30, 2006, 10 AM EDT. See reference notes below.
Notes and References for the Tables:
For 1st Table:
Source: U.S. Department of Defense, Directorate for Information Operations and Reports, Statistical Information and Analysis Division. "DoD Principal Wars – US Military Personnel Serving and Casualties"
All names used (notably, "Vietnam Conflict" and "Persian Gulf War") as well as all years chosen for tabulation (notably, including 1946 casualties in "World War II" and including only 1964-1973 casualties in the "Vietnam Conflict") are those used by the Department of Defense in the above source.
For 2nd Table:
Source: The most recent (which, in this case, was May 30, 2006 10 AM EST) "Casualty Reports" link of www.defenselink.mil, the official web portal to all of the public US Department of Defense websites. Note that the Casualty Reports link is regularly updated and the most current one can always be found at the bottom of the "Press Resources" linklist in the right column of www.defenselink.mil.
NB: A useful general source for all military casualties from all US military engangements is the "Military Casualty Information" webpage of U.S. Department of Defense, Directorate for Information Operations and Reports, Statistical Information and Analysis Division. The “DoD Personnel & Procurement Statistics” page of the Statistical Information and Analysis Division has a wealth of information on many other topics too.
May 23, 2006
Lately, I've been loathe to blog out of fear that it'll lead too much procrastination (which would be especially bad since I think the "just right" level of procrastination is roughly a 40 hour a week job in and of itself).
So, in an effort to make sure this blog promotes rather than detracts from my research efficiency, I'm instituting the following feature seen elsewhere around the web, The Whiteboard of the Week. Not only will it me encourage me to produce at least one tangible piece of evidence a week that I've done work, but also it will encourage me to clean up my messy whiteboard writing.
This week I'm focusing on TAing MIT's introductory solid state physics course for first-year electrical engineering grad students, and thus my office whiteboard today looked like this.
(Click picture for full 1024 x 768 JPEG)
May 9, 2006
Somehow I forgot this bon mot from The Simpsons:
BART: Look at me, I'm a grad student! I'm 30, and I made $600 last year.
MARGE: Bart, don't make fun of grad students. They just made a terrible life choice.
(I'm just kidding. MIT is the Happiest Place on EarthTM… or at least it will be once the legal conflicts with Disney are settled.)
May 4, 2006
So now that this blog's been reincarnated, I suppose I should post something. My normal bloggy habits were to read or see something horrible, become obsessively aggravated by it, procrastinate tremendously on my real work by doing an absurd amount on research on it, and then finally write a post that usually included just a teeny-tiny fraction of all that obsessive work. (Did ya check out the references on the bottom of my Hiroshima and Nagasaki post? I really went out and looked for just the right table in the US Strategic Bombing Survey. I have Excel analysis of it—cross-referenced against Morris's Fog of War documentary to boot—that I didn't include since, well, that'd just make y'all think I'm clinically obsessive. 🙂 )
Thus, I think this time around I should actively try to check this habit or, failing that, at least try to keep it to manageable proportions. So this post is about a teeny-tiny horrible thing, rather than a world-historical horrible thing. But, man, it's horrible in its own special way…