27 December 2005

Male privilege

It makes me sick that this (Boston Globe) is still news. Or even still an issue. But the article doesn't really help. Sure, it mentions that "the responsibility for this lab-vs.-life conflict lies with institutions" and that "[t]he primary barrier, they say, is the conflict between lab and family under the grueling demands of today's academic culture." And, sure, it pays lip service to what I won't deny are extremely important initiatives and programs like "paid maternity leave and child-care scholarships for doctoral students." But the article doesn't come close to addressing root causes.

Why is it graduate student Debrah Rud who is featured in the article? Is there a Mr. Rud? (or, for all I know, another Ms.?) If not, then the university and the government should do everything they can to support the Rud family. If so, then make him take care of the kid.

No, that's too strong. In today's society, most families need two incomes to support their children. And it's a crime that Harvard childcare is too expensive — Harvard should provide free childcare for its grad students (well, for their children, natch) if it really wants to be the most competitive research institution in the world. But why is this article about a woman? Is there really no male grad student at Harvard, who recently had a child, and who is struggling ballancing time with his family and time at work?

No, probably not. Because we don't expect men to make that time. Balancing work and family has always been a job for women. Sure, it's great that women are entering the workforce, but heaven forbid they give up their seminal role as primary caregiver. Thing is, articles like this only normalize that dichotomy.

Lord knows I'll be thinking hard about whether to have kids, because I fully intend to have a career. But if I'm in a reasonable position, say with a tenure-track job that looks like it might make me a full professor, then, yeah, I'd love to have a family, and I'd even plan on scaling back my time at work to take care of my children. I plan to work carefully with my partner to make sure that we both have the time we need with the kids, and that neither is shouldering either burden — as primary caregiver or primary breadwinner — unfairly. If it really is the case that one of us is honestly much more interested in one of those roles than the other, then it's not unreasonable for us to go that way, although I'm guessing that the lifestyle I will end up leading is a two-salary one. But all too often both members of heterosexual couples want to have kids, and both wish they could spend more time at home, and it's the woman who ends up doing so. And in so doing she threatens her career, and he doesn't have to.

The studies comparing successful women and successful men are extraordinary. Look at the rates of who has spouses who basically stay at home to support them. Look at the rates of who has children. Men can have families and jobs without worrying; women cannot. And that's a problem in our society that needs fixing.

And it's the men who need to fix it.

25 December 2005

Relativistic Invariance

The basic equation of motion of a Newtonian particle in one dimension acting under a potential energy $V(x)$ is

$$ \frac{\d^2}{\d t^2}q(t) = \frac{1}{m}\frac{\d}{\d x}V(x) $$

where $q(t)$ is the position (measured in $x$) of the particle at time $t$, and the left hand side is evaluated at $x=q$. (I tend to write $\d$ for $\partial$ --- my TeX files always start with \def\d\partial.) This equation can be written more succinctly as $a = F/m$.

This equation is symmetric under what I will call the common relativistic (or Galileo; "common" as an antonym to "special", "relativitistic" because this is a kind of "relativity") transformation
$$ x \mapsto x + ut $$
describing the (Newtonian) coordinate change between inertial frames at relative constant velocity $u$ to each other (the coordinate $t$ remains unchanged). To wit: Under such a transformation, the derivative in the left-hand-side remains untouched, and is now evaluated at $x = q(t) - ut$; the right hand side sees a replacement of $q(t) \mapsto q(t) - ut$ and the $ut$ drops out in the second derivative, so any motion satisfying Newton's equation in one (inertial) frame will satisfy it in all (inertial) frames. In general, such a transformation may introduce a $t$-dependence in $V$; this doesn't bother us though, except for raising the specter that energy might no longer be conserved. If $V$ is a constant in $x$, this doesn't happen, of course, and solutions $q(t) = vt$$ remain solutions, albeit with different $v$. For my purposes, all I actually care about is the equation of motion in the absence of forces (when $\d V / \d x = 0$).

Einstein (most likely working in close consultation with Maric) is, of course, famous for modifying Newton's equation to instead remain invariant under the special relativistic (or Lorentz) transform:

$$ x \mapsto \frac{x + ut}{\sqrt{1 - u^2/c^2}} $$
$$ t \mapsto \frac{t + ux/c^2}{\sqrt{1 - u^2/c^2}} $$

What I'm wondering about in this entry, however, is a different equation of one-dimensional motion, this one written down by Schrodinger:

$$ i\hbar \frac{\d}{\d t} \Psi(t,x) = \frac{-\hbar}{2m} \frac{\d^2}{\d x^2} \Psi(t,x) + V(x)\Psi(t,x) $$

where now we must reinterpret particles. No longer is $q(t)$ "the location of our particle at time $t$"; instead, $|\Psi(t,x)|^2$ is the "probability of measuring our particle as having position $x$ at time $t$". (I retain the quotes only because really such a probability is the infinitesimal $\Psi dx$, and the probability of measuring the particle to be between $x = a$ and $x = b$ is the appropriate integral. In this discussion, I'm going to ignore the problems of normalization.)

In the case when $V(x)$ is the constant $V_0$, we can easily solve this equation:
$$ \Psi(t,x) = \sum a_j e^{i(w_j t + k_j x)} $$
where $-\hbar w_j = E_j = \frac{\hbar^2 k^2}{2m} + V_0$. ($E_j$ is the "eigenenergy" for the $j$th summand; $w_j$ and $k_j$ are the corresponding frequency and wave number, respectively.) The universal constant $V_0$ cannot be measured; changing it corresponds to multiplying the entire wave function by some $e^{i\theta}$. I.e. the physical system has this one real degree of degeneracy.

Consider one particular eigenstate $e^{i(wt+kx)}$, and transform it a la "common" relativity. We'd get an adjusted state $e^{i((w+ku)t+kx)}$. Does this satisfy Schrodinger's equation for a constant potential? Well, yes. The wave we get is red-shifted, and we now need
$$ -\hbar(w+ku) = \frac{\hbar^2 k^2}{2m} + V_0 $$
$$ V_0 = -\hbar(w+ku) - \frac{\hbar^2 k^2}{2m} = -\hbar k u $$
But the transformed $V_0$ depends on $k$, so a superposition of eigenstates does not transform to a state satisfying Schrodinger's equation.

This is not, actually, surprising: Replacing $\Psi(t,x)$ with $\Psi(t,x+ut)$ in Schrodinger's equation affects the time derivative as well as the space derivative: Writing $\Phi(t,x) = \Psi(t,x+ut)$ gives $\d\Phi/\d t = \d\Psi/\d t + u\d\Psi/\d x$. On the other hand, the right-hand side $\d^2/\d x^2$ does not pick up such an extra term. Only in the high-energy ($k\to 0$) limit does the extra $-ku\hbar$ term vanish, but never before the $w ~ k^2$ term does.

(Incidentally, lest ye think Schrodinger's equation is actually special-relativisticly invariant: checking the relationship between $k$ and $w$ after a Lorentz transform gives a fourth-power in $k$ on the right and only a squared $k$ on the left. And the high-energy limit is equally bad.)

So what's up? Why do we tout Schrodinger's equation when it can't even give the right formulas under the patently classical common-relativistic transform? And what's the popper formula? I take it on good authority that the Dirac Equation is special-relativistically invariant (interestingly, and unlike Einstein's special relativity equations of motion, Dirac's wave function does not transform as a vector under rotations in 3-space, but as a mystical object called a "spinor"). But I'd expect there to be a common-relativistic equation of motion spit out by various more basic Quantum-Mechanics axioms. Or is it that Schrodinger actually correct and I'm just being daft?

20 December 2005


John Jones, over at the USDCMDP, recently posted a stinging critique of Intelligent Design, as well as a thorough recap of the events leading to the Dover, PA, creationism trial. No, Jones is not a liberal blogger. John E. Jones III is the U.S. District Judge for the Middle District of Pennsylvania, a Republican nominated by George W. Bush and confirmed unanimously by the Senate, and he presided over the trial. His ruling (pdf) is fascinating, and long (over a hundred pages). I suggest you skim it in its entirety — I did.

I'd like to highlight the conclusion of his ruling, both for its cogency and for its acerbity (I was going to use "piquancy", but The American Heritage Dictionary tells me that such use is archaic, and I'm anything if not with the times):
The proper application of both the endorsement and Lemon tests to the facts of this case makes it abundantly clear that the Board’s ID Policy violates the Establishment Clause. In making this determination, we have addressed the seminal question of whether ID is science. We have concluded that it is not, and moreover that ID cannot uncouple itself from its creationist, and thus religious, antecedents.

Both Defendants and many of the leading proponents of ID make a bedrock assumption which is utterly false. Their presupposition is that evolutionary theory is antithetical to a belief in the existence of a supreme being and to religion in general. Repeatedly in this trial, Plaintiffs’ scientific experts testified that the theory of evolution represents good science, is overwhelmingly accepted by the scientific community, and that it in no way conflicts with, nor does it deny, the existence of a divine creator.

To be sure, Darwin’s theory of evolution is imperfect. However, the fact that a scientific theory cannot yet render an explanation on every point should not be used as a pretext to thrust an untestable alternative hypothesis grounded in religion into the science classroom or to misrepresent well-established scientific propositions.
(Underlined citations in original; emphasis added.)

I've only read the beginning of On Pandas and People; its introduction, at least, allows that microevolution and divine creation are consistent. Indeed, microevolution has been observed and measured, and most IDers/Creationists endorse it, but they reject macroevolutionary theories of the origins of life. When Jones describes "evolutionary theory", however, he means it in the same sense as the IDers do (a la his Finding of Facts): the idea that modern species evolved over millions of years from nothing. What is elucidated in the ruling is not whether this claim is consistent with ID (and the Court is careful to make no ruling on the truth of the claims of the Theory of Intelligent Design proper), but that ID proponents misinterpret and misidentify scientific disagreements about the details of evolution's mechanisms as evidence against evolution, and moreover they misinterpret and misidentify evidence against evolution as evidence for intelligent design.

Jones goes on, getting more and more astringent as he approaches the end:
The citizens of the Dover area were poorly served by the members of the Board who voted for the ID Policy. It is ironic that several of these individuals, who so staunchly and proudly touted their religious convictions in public, would time and again lie to cover their tracks and disguise the real purpose behind the ID Policy.

With that said, we do not question that many of the leading advocates of ID have bona fide and deeply held beliefs which drive their scholarly endeavors. Nor do we controvert that ID should continue to be studied, debated, and discussed. As stated, our conclusion today is that it is unconstitutional to teach ID as an alternative to evolution in a public school science classroom.

Those who disagree with our holding will likely mark it as the product of an activist judge. If so, they will have erred as this is manifestly not an activist Court. Rather, this case came to us as the result of the activism of an ill-informed faction on a school board, aided by a national public interest law firm eager to find a constitutional test case on ID, who in combination drove the Board to adopt an imprudent and ultimately unconstitutional policy. The breathtaking inanity of the Board’s decision is evident when considered against the factual backdrop which has now been fully revealed through this trial. The students, parents, and teachers of the Dover Area School District deserved better than to be dragged into this legal maelstrom, with its resulting utter waste of monetary and personal resources.

To preserve the separation of church and state mandated by the Establishment Clause of the First Amendment to the United States Constitution, and Art. I, § 3 of the Pennsylvania Constitution, we will enter an order permanently enjoining Defendants from maintaining the ID Policy in any school within the Dover Area School District, from requiring teachers to denigrate or disparage the scientific theory of evolution, and from requiring teachers to refer to a religious, alternative theory known as ID. We will also issue a declaratory judgment that Plaintiffs’ rights under the Constitutions of the United States and the Commonwealth of Pennsylvania have been violated by Defendants’ actions. Defendants’ actions in violation of Plaintiffs’ civil rights as guaranteed to them by the Constitution of the United States and 42 U.S.C. § 1983 subject Defendants to liability with respect to injunctive and declaratory relief, but also for nominal damages and the reasonable value of Plaintiffs’ attorneys’ services and costs incurred in vindicating Plaintiffs’ constitutional rights.

Jones' ruling is, of course, a win for the Left and a major rebuff for the Right. But let's be careful before partying too hard. Liberals ought to support teaching Intelligent Design in schools. Students should read (excerpts from) this ruling, and learn about the history of the Evolution/Creation controversy in the U.S. They should have assignments that involve critically examining claims and evidence, comparing various versions of so-called evolutionism with various versions of creationism, and understanding how much of the dichotomy is false. Pedagogical studies have shown how best to convince kids of evolution's power as an empirical fact: respect them enough to teach them everything. When you hold something back, the kids know it, like refusing to discuss birth control or homosexuality in a sex-ed class.

The Dover ID Policy was a bad one, supported by religion and poorly instigated, and "Defendants are permanently enjoined from maintaining the ID Policy in any school within the Dover Area School District." But I hope that high-school biology teachers don't interpret this and other rulings as totally barring mention of ID in science classrooms (indeed, in Edwards (landmark 1987 case against Creationism), the Supreme Court found that "teaching a variety of scientific theories about the origins of humankind to school children might be validly done with the clear secular intent of enhancing the effectiveness of science instruction"). Of course, an already overloaded science curriculum does not need such extra material, so teachers who decide not to broach the subject in favor of other more worthwhile material are not shirking their duty. Still, a nice extra-credit assignment or option for a term paper would be such a compare-contrast exposition.

On this and other major national issues, Liberals are becoming stodgy and entrenched, giving up the role of social-change activists to the Radical Religious Right. We should be out there, empowering students to research and criticize lots of ideas (because such empowerment is a value in its own right, and incidentally those students will be more likely to decide that Conservatives' religious beliefs are wrong). As soon as IDers can claim that their policies are "for the secular purposes of improving science education and encouraging students to exercise critical thinking skills" (even though the Court found in this case that "Defendants’ previously referenced flagrant and insulting falsehoods to the Court provide sufficient and compelling evidence for us to deduce that any allegedly secular purposes that have been offered in support of the ID Policy are equally insincere.") — as soon as IDers can claim to support critical thinking and academic freedom, we have lost the moral high ground.

But it doesn't stop there. We're reduced to defending Choice by pointing to the power of precedent, when there are many precedents (e.g. Plessy) requiring reversal. There are valid and strong arguments for why precedent should be respected, but that's not what we need — instead, we must effect a radical change in the understanding of life and rights of creatures like fetuses (I have no doubt that a neonatal fetus is a feeling mammal, and a person as much as my cat is; the point isn't life per se, because I would hold a private funeral for a fetus who undergoes late-term abortion, but rather who should make decisions over whether a woman remains pregnant). We should present reasoned, impassioned arguments for the Equal Rights Amendment, for a more progressive tax system, for Medicaid and Social Security overhauls (resulting in more tax-funded healthcare for everyone, especially members of the lower classes, and in a standard retirement age closer to 80) and for a new understanding of environmental rights. And don't get me started on foreign policy, where the "conservatives" and "liberals" switch sides every few administrations.

Instead, the disquieted left is putting much of its formidable creativity into ultimately unhelpful (if not down-right hindering) negative personal attacks.

At least we can still advocate for gender-neutral marriage.

18 December 2005

One Lion to rule them all

It's been, oh, probably ten years since I last read C.S. Lewis' The Chronicles of Narnia — I did read all of them, some more than once, and enjoyed about half — more recently, I've read many reviews and discussions of the new film and the old books. I'd like to respond to a few published thoughts, and record a few of my own (with the caveat that my memory for the original texts is patchy at best, so take my claims with a pinch of salt thrown over your shoulder). Which is to say, to the extent that it's possible to post spoilers to a film like this, I will try to the utmost to do so.

Andrew Adamson's new film is not the first time Narnia has been on screen. The low-budget made-for-TV 1988 production is really quite wonderful, and clearly motivated the current rendition. I've never seen the 1979 cartoon — is it any good? Hopefully, Adamson and WETA will also produce remakes of Prince Caspian and the Voyage of the Dawn Treader (presumably as two separate movies this time) and The Silver Chair, as well as my favorite book of the series, The Horse and His Boy. Adamson has masterfully updated the 1988 movie, replacing its motley mix of live action, animatronics, and animation with a variegated blend of live action, animatronics, and (now computer-) animation.

Part of me had hoped for some new and radical reading of Lewis' original fable. Such hopes, of course, could only be realized by a small independent film company — Disney is much too conservative, and American audiences cling to their literal interpretations of original texts. Besides, Aslan's Passion is already a radical rethinking of an original fable. C.S. Lewis used The Lion, the Witch, and the Wardrobe to come to terms with his own burgeoning Christianity (J.R.R. Tolkien, a devout Catholic since his mother converted when he was eight, takes the credit for helping his friend and colleague see the light). Part of me would also like to read a book report comparing Lewis' Narnia with the His Dark Materials trilogy by atheist and church-critic Philip Pullman: Lion is infinitely more magical than Compass, and differences in writing quality can be attributed to the age ranges of the intended audiences; but the extremely rushed Amber Spyglass is infinitely better than the sorry excuse that was The Last Battle.

After Peter Jackson's epic experiment in condensing and editing more than a thousand pages into ten hours, the generally positive reviews have applauded Adamson's faithful translation of two hundred thin pages. Eric at Speaking Natalie correctly writes that "they didn't change anything ..., but they did add things": Adamson's decision to start with the 1940 London air raids, which Lewis mercifully omitted, has been much-discussed (I found it emotionally moving, and at the same time of inferior animation quality). The Rings-inspired battle sequences are also new — I enjoyed some of it, thought that most was boring, felt the air-raid reprise lacked panache, and found Aragorn extremely out-of-place.

Eric raises the issue of Peter's character, and to his comments I'll agree: Adamson improved upon the book by allowing Peter to be flawed as an older brother. It's now much more meaningful when he admits that "[Edmund's betrayal] was partly my fault, Aslan. I was angry with him and I think that helped him to go wrong." What Adamson leaves out is Lewis' dislike, and Peter's revulsion, of battle. Only a split-second of screen-time allows Peter to look disgusted after killing Maugrim, and he's too steely (and adroit) in battle — I'd much rather this description of one-on-one fighting:
Then came a horrible, confused moment like something in a nightmare. He was tugging and pulling and the Wolf seemed neither alive nor dead, and its bared teeth knocked against his forehead, and everything was blood and heat and hair. A moment later he found that the monster lay dead and he had drawn his sword out of it and was straightening his back and rubbing the sweat off his face and out of his eyes. He felt tired all over.
Michael Nelson, writing in The Chronicle of Higher Education in the review I linked to, defends Lewis against Pullman's claim of the former's "sadomasochistic relish for violence" by arguing that Lewis, who fought in the trenches in World War I, understood violence as "nothing romantic," and that children who read Narnia encounter "their first unglamorous act of violence, the first to make them doubt that killing, even when it has to be done, is something to celebrate." I'd ask only that Adamson live up to that tradition.

To the other Pullman critiques that Nelson counters, I say only that Rings is infinitely worse. Lewis may have allowed the good, Christian Narnia to be light-skinned and the generally evil, heathen Calormen to strongly remind readers of northern Africa (Adamson thankfully left out all other humans); Tolkien describes all those dark-skinned southerners as evil and characterless. Just as insidiously, Tolkien's races fight primarily as races — orks and urukai and hobbits each pick sides, and few have character development — whereas if memory serves me correctly Lewis allows his motley crew of animals and mythical creatures from varius mythologies to fight on both sides (as in all wars, dwarves fight dwarves and cheetahs, cheetahs). The number of women characters, even minor ones, that appear in the entire Lord of the Rings you can count on one hand; in Narnia, girls are brave instigators of geopolitical upheaval, even if they are bound by early twentieth-century norms. In short, Nelson has picked himself a straw punching bag.

The new Chronicles of Narnia provides nothing new, except a chance to go to the movies and discuss Narnian lore (for a detailed introduction, see the Wikipedia entry), and ponder questions like "In a land where animals can talk, why would the good Kings and Queens go stag-hunting?". I think I will reread The Horse and His Boy, and wait for a big-budget epic film adaptation of The Golden Compass. I'd also like to see Dealing with Dragons done big-budget, but that may have to wait, for all that it would adapt well.