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.

-Maria Bamford

 

(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.)

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.

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).

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…

* 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).

** 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.

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)

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 Earth^TM… or at least it will be once the legal conflicts with Disney are settled.)

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…

You may have heard that Gene Roddenberry wrote lyrics for the theme to the original Star Trek. You may have also heard they're bad—really bad—and hence were never used. Until tonight, that's all I knew about 'em myself. But tonight, in the course of flipping through a "fake book" (that is, a compilation of abbreviated musical scores that just have the melodies and the chord changes and not some sort of false book), I saw the lyrics, and wow! They're mind-boggingly bad. Stupendously bad. Theodicy-necessitating bad. Really bad. Behold, but don't say I didn't warn you.

Beyond the rim of the starlight,

my love is wandering in star flight.

I know he'll find in star clustered reaches love,

strange love a starwoman teaches.

I know his journey ends never;

His star trek will go on forever.

But tell him while he wanders his starry sea

remember, remember me.

(NB: This blog has a free comments policy. But anyone who dares claim the theme to Firefly is nearly this bad will be banned!)

After about 9 months of not posting, I doubt I still have any regular readers.   But for those of you who know me from

http://williamkaminsky.typepad.com

welcome to the new WordPress version.   Since the frequency of my posts over the last year (i.e., near zero) doesn't really warrant a paid subscription blog service like TypePad, I imagine I'll be closing the old TypePad version relatively soon and moving exclusively to this WordPress site.   Thus, for all you who've been kind enough to link to me in the past, please update the link to:

http://williamkaminsky.wordpress.com

[Belated Thoughts on the 60th Anniversary of the Atomic Bombings of Hiroshima and Nagasaki]

[Sunday, Sept. 4, 2005  The portion of this post appearing below in boldface has been revised.  Please see endnote for details.]

There’s a couple of reasons why I’m a theoretical physicist.  For tonight, the pertinent one is this:  I can feel numbers.  To me, they’re not symbols long since divorced from the consequences they were meant to quantify.  Instead, in my imagination, their consequences are palpable, sometimes vividly so.   Thus, while I can intellectually understand the truth behind those now immortal cynical sayings of good ol’ Senator Dirksen ("A million here and a million there, and pretty soon you’re talking about real money.") and mean ol’ General Secretary Stalin ("The death of one man is a tragedy.  The death of millions is a statistic."), I don’t personally feel their truth.    Rather, I personally feel a million dollars as the accumulation of a lifetime or two of paychecks, and a million deaths as an utterly satisfactory reason to emulate Job and blaspheme God to His Face should He ever take the time out of His very, very busy eternity to grant me the ultimate honor of some individualized revelation. 

Now, as you can see from the above examples, my natural knack for internalizing numerical knowledge doesn’t so much have to do with any mathematical facility per se, but rather an ability to imagine something personally poignant in place of the numbers.  And so, gentle reader, if in recent days you have pondered the morality of dropping atomic weapons on Japan and have found yourself confounded by all the cold counteractuals it entails, and if–more importantly–you’re now willing to partake in some moderate emotional masochism, then let me commend to you the following excerpt of Errol Morris’s stunning 2003 documentary on Robert McNamara, The Fog of War.  Better than anything I’ve ever seen, it conveys the brutal emotional truth behind the cold, hard statistic that in the five months leading up to the atomic bombings of Hiroshima and Nagasaki, US firebombing campaigns on 67 Japanese cities directly killed at least 175,000 civilians and burnt to the ground the homes of at least 8,000,000.

The excerpt is entitled Lesson 5: Proportionality should be a guideline in war.  In it, McNamara’s words alone do a good job of conveying the magnitude of the devestation wrought on the civilian population of Japan in the months leading up to the atomic bombings for McNamara conceives of a chilling set of analogies between Japanese and American cities.

MORRIS: The choice of incendiary bombs—where did that come from?

McNAMARA: I think the issue is not so much incendiary bombs. I think the issue is: In order to win a war, should you kill 100,000 people in one night, by firebombing or any other way? LeMay’s answer would be, clearly, “Yes.”

[Speaking rhetorically] McNamara, do you mean to say that instead of killing 100,000—burning to death 100,000—Japanese civilians in that one night we should have burned to death a lesser number or none and then had our soldiers cross the beaches in Tokyo and been slaughtered in the tens of thousands? Is that what you’re proposing? Is that moral? Is that wise? Why was it necessary to drop the nuclear bomb if LeMay was burning up Japan?

And he went on from Tokyo to firebomb other cities. 58% of Yokohama. Yokohama’s roughly the size of Cleveland. 58% of Cleveland destroyed. Tokyo is roughly the size of New York. 51% of New York destroyed. 99% of the equivalent of Chattanooga, which was Toyama. 40% of the equivalent of Los Angeles, which was Nagoya. This was all done before the dropping of the nuclear bomb, which, by the way, was dropped by LeMay’s command.

However, the true genius of Morris’s film in this excerpt is that he breaks away from his characteristic close-ups of his subject’s face to extend McNamara’s analogy of Japanese and American cities to all 67 cities that were the targets of LeMay’s firebombing campaign.   Morris shows a series of bomb damage photographs at speeds that eventually become subliminally fast.  He first captions these with titles in red letters that give the name of the Japanese city bombed and the fraction of its area that was thus burned to the ground, and he then switches to a caption in black letters giving the name of an equivalent US city.  If one is neurotic and masochistic enough to watch in slow motion, one can catch all 67.  As I don’t wish for you, gentle reader, to partake in that much emotional masochism, I transcribe them here in the order shown

When Morris returns to McNamara’s face after this devestating montage, McNamara’s words are absolutely chilling:

McNAMARA: Proportionality should be a guideline in war. Killing 50 to 90% of the people in 67 Japanese cities and then bombing them with two nuclear bombs is not proportional in the minds of some people to the objectives we were trying to achieve.  [Bill's Note: This 50-90% figure is not to be taken literally.  See endnote for context.]  I don’t fault Truman for dropping the nuclear bomb. The U.S.-Japanese War was one of the most brutal wars in all of human history. Kamikaze pilots, suicide, unbelievable. What one can criticize, is that the human race prior to that time and today has not really grappled with what I’ll call “the rules of war”. Was there a rule then that said you shouldn’t bomb, shouldn’t kill, shouldn’t burn to death 100,000 civilians in a night? LeMay said, “If we’d lost the war, we’d all have been prosecuted as war criminals.” And I think he’s right. He’d, and I’d say I, were behaving as war criminals. LeMay recognized that what he was doing would be thought immoral if his side had lost. But what makes it immoral if you lose and not immoral if you win?

Endnote (Sept 4, 2005):  In the original version of this post, which appeared on August 10, 2005 at 2:22 AM—and thus, like most every other post on this blog, was a post written in a state of aggravated sleep deprivation—the "cold, hard statistic" that appears above in boldface

…in the five months leading up to the atomic bombings of Hiroshima and Nagasaki, US firebombing campaigns on 67 Japanese cities directly killed at least 175,000 civilians and burnt to the ground the homes of at least 8,000,000.

instead read

…in the five months leading up to the atomic bombings of Hiroshima and Nagasaki, US bombing campaigns killed over 50% of the populations of 67 separate Japanese cities.

In my sleep deprived state, having just rewatched The Fog of War, I had misunderstood McNamara’s quote to be a statement of the actual results of the firebombing campaign.  Later that day, when it finally dawned on my sleep-reinvigorated mind that if McNamara’s statement were literally true then the US firebombing campaign in 1945 would have killed roughly 10,000,000 (!!) Japanese civilians, I placed the following notice atop the post:

UPDATE IN PROGRESS: Aug 10, 1:22 PM.  I believe there is some sort of major misstatement in this post’s key statistic (found in boldface below) regarding civilian casualties due to the non-nuclear component of the US bombing campaign against major Japanese cities in 1945.  Please note, however, that the misstatement is not my own.  The statistic is an accurate quote of Robert McNamara’s own words describing his World War II service doing statistical analysis in General Curtis Lemay’s Pacific Bombing Command as recorded in the Errol Moris documentary The Fog of War. (For the full quotation see the very bottom of this post.)    I am currently trying to figure out how exactly McNamara misspoke, for example, perhaps confusing civilian fatalities with total civilian casualties and/or the number of civilians rendered homeless.

I must say that I was rather embarassed, given how I’d prefaced the post with all that purple prose about how I’m a theoretical physicist since I have such a keen intuitive and emotional grasp of numbers.   Sleep deprivation is no excuse to be off by 2 orders of magnitude…one maybe… any physicist can be off at first by one order of magnitude… but two!, that’s ghastly.

Anyway, after quite a bit of reading, including the companion book to The Fog of War and several portions of the comprehensive, official US Strategic Bombing Survey, I must honestly say I still don’t know precisely what Messrs. McNamara and Morris were thinking.    However, I think the most likely explanation is that McNamara was speaking of the potential worst-case effects of the bombing, which certainly would be relevant to any ethical discussion about proportionality.   For example, US estimates of the potential effects of the first spate of firebombings on Japan’s 6 largest cities (Tokyo, Osaka, Nagoya, Yokohama, Kobe, and Kawasaki) were the burning down of 70% of the civilian housing [1]. Granted, overall deaths in these estimates were much lower than 70% of the civilian population, being around 500,000 civilians [1], which would have been about 4% of the population in these 6 cities [2]. And of course, the actual results of these raids were even lower: 124,362 deaths and the burning down of the homes of 5,578,000 Japanese, which are 0.94% and 42.5% of these cities’ 1944 populations respectively [2].  But there’s no doubt that the firebombings were planned with knowledge that they well could burn down the vast majority of these cities’ residential areas, and the bombings weren’t going to wait for guarantees that the Imperial Japanese government would implement effective firefighting and evacuation plans. 

References

[1] Schaffer, Ronald.  Wings of Judgment: American Bombing in World War II,  (Oxford University Press, 1985), page 116

[2] Table 30 of the "United States Strategic Bombing Survey — The Effects of Air Attack on Japanese Urban Economy (Pacific Report #55): Summary Report (Urban Affairs Division, March 1947)" as reprinted in MacIssac, David, ed., The United States Strategic Bombing Survey, Volume IX,(Garland Publishing, 1976).

As a most fitting afterword to this blog’s long exegesis of Anthony Cordesman’s June 24th speech at CSIS (audio, video) on what has happened and what needs to happen in Iraq…

Part 1: The Stakes and the Odds

Part 2: The Progress and the Problems to Date

Part 3: Where We Should Go from Here

…I point you to Dr. Cordesman’s response to President Bush’s speech at Fort Bragg last night. 

[Hat Tip: Justin Logan]

P.S. This blog will now return to its regular schedule of non-Anthony-Cordesman-inspired posts.