## Brain Damage in Climbers

September 26, 2007

A worrying finding, for someone who enjoys both climbing and thinking and wants to be at least moderately accomplished in both. From SciAm Mind Matters:

…neurologists Nicholas Fayed and colleagues at the Clinica Queron and Miguel Servet University Hospital in Zarogoza, Spain, gave MRI brain scans to 35 climbers (12 professionals and 23 amateurs) who had returned from high-altitude expeditions, including 13 who had attempted Everest.

The results on the Everest climbers are the most stark. Of the thirteen climbers, three had made the summit, at 8480 meters, three had reached 8100 meters, and seven topped out between 6500 and 7500 meters. Though the expedition suffered no major mishaps and none of the 12 professional climbers suffered any obvious signs of high-altitude illness, only one of the 13 climbers returned with a normal brain scan. The brain scans showed that all but one climber suffered cortical atrophy and enlargement of the Virchow-Robin spaces. These are spaces surrounding brain blood vessels that drain brain fluid and communicate with the lymph system. Widening of these VR spaces is seen in the elderly, but rarely in young people. The amateur climber’s brain had also suffered subcortical lesions in the frontal lobes.

OK, I don’t intend to attempt Everest even in the distant future, but even relatively low-altitude challenges like Mont Blanc (~4800m) can result in brain damage. The study [1] referred to in the SciAm post included seven amateurs who attempted Mont Blanc. These amateurs lived for most of their lives below 200m and had never ascended higher than 3000m. (Interestingly, there were 8 such amateurs in the study who attempted Aconcagua — brave souls! Unsurprisingly, only 2 of that group made the summit.) Of the 7 Mont Blanc climbers, 1 had cortical atrophy, 2 had enlargement of their Virchow-Robin spaces, and 1 had subcortical lesions. Quite worrying considering that I’ve climbed above 4800m on a couple of occasions. The authors also scanned 7 amateurs who attempted Kilimanjaro (which was one of my >4800m trips), and only 1 of them showed any brain abnormalities, even though Kili is more than 1000m higher than Mont Blanc. This puzzled me until I read the details and found that all the 7 Mont Blanc subjects reached the summit of Mont Blanc, but only three of the Kili subjects summited Kili, 2 having stopped at 4600m, 1 at 5000m, and the other at a lower altitude. So on average the Kili subjects hadn’t climbed 1000m higher than the Mont Blanc subjects.

1. Nicolás Fayed, Pedro J. Modrego, Humberto Morales. Evidence of Brain Damage after High-altitude Climbing by Means of Magnetic Resonance Imaging. The American Journal of Medicine Volume 119, Issue 2, February 2006, Pages 168.e1-168.e6. doi:10.1016/j.amjmed.2005.07.062

## Crises Everywhere

September 21, 2007

A Chronicle of Higher Education article on the ‘crisis’ in American science. Same story as in the non-sciences: there are too many PhDs being generated compared to the number of academic jobs available. Furthermore, the increase in PhDs over the last two decades has not been accompanied by an increase in the number of tenure-track positions, and it’s getting harder for young scientists to win grants. It’s something I think about often because I’ve long been wavering between attempting a career in theoretical physics and attempting one in philosophy (like most philosophers of science, I don’t believe in a clear-cut boundary between the two, but the reality of professionalization of academic disciplines is that there is one for non-trivial bookkeeping purposes). In my final year of undergrad education, I was almost completely convinced that philosophy was the way to go, and am still convinced that my interests have a greater intersection with what people who are thought of as philosophers of physics do than with what people who are thought of as physicists do (the awkward phrasing is to accommodate the fact that what people are thought to be doesn’t always accurately reflect the nature of the work they do). But if the job market is signficantly better in theoretical physics, perhaps I should make do with trying to be one of those theoretical physicists who work on semi-philosophical issues. Unfortunately, since physics PhD-granting institutions are not in the habit of putting their placement records on their websites the way most top philosophy PhD-granting departments do, it’s difficult to compare career records across the two fields. And by talking separately to philosophers of science and to theoretical physicists, all you’ll get from both sides is that the job market is pretty bad in their respective fields. The best comparison I could get was from a philosopher of physics who (naturally) has several friends who are theoretical physicists, and he “wasn’t convinced” that academic job prospects in theoretical physics were better, citing friends who were in their tenth year of postdocs. But then he, of course, is one of the very few philosophy PhDs with a tenure-track position at a prominent research university, a position which might have tinted his lenses a bit. Some figures must be out there somewhere, though.

Then we can throw in extra factors, such as my relative uncertainty about my philosophical capabilities (relative to other wannabe philosophers) versus my relative certainty that I can’t really compete with most theoretically-inclined physics students, both compounded with the large uncertainties associated with my limited experience in high-level philosophy and theoretical physics. Not to mention my skepticism about the value in a lot of theoretical physics that is being done (this has to do with my philosophical inclinations). Which is a strange turnaround from the time when I wondered whether philosophy was a futile pursuit. Increasingly, when reading science papers, I find myself asking meta-questions about the papers: whether the questions they attempt to answer should be answered at all, etc. And I don’t think I’m the only one who finds the sheer number of seemingly pointless, poorly motivated papers that make it onto the arXiV an indication of the crisis-like state of theoretical physics. The PhilSci archive, in stark contrast, seems a lot more sane, but that is possibly just due to better moderation, or a lower volume of papers overall. In other words, there seems to be an intellectual crisis of sort in theoretical physics in addition to the job crisis, whereas philosophy arguably just has the job crisis. Of course, I don’t have submit papers that are that bad, but the worry is that people are submitting bad papers because that is all they have left to say.

Update: Chad Orzel digs up some physics hiring figures from the AIP: 350 tenured or tenure-track hires in 2002 and 2004, with 1300 physics and astronomy PhDs awarded in 2005.

## Proofs Demystified!

September 20, 2007

Via James Cook, I find out that Timothy Gowers is blogging. Amongst other things, he has explanations of two mathematical theorems that proceed by analogy from a lower-dimensional case. The first is on how to discover the formula for solutions to cubic equations by analogy with the formula for quadratic equations. The second is on how to get to the essentially two-dimensional Cauchy integral theorem from the one-dimensional theorem that if $f:\mathbb{R}\rightarrow\mathbb{R}$ and $f$ is everywhere 0, then $f$ is constant. Clear, intuitive explanations in fluent prose — a refreshing change from the usual math-textbook style.

## Robert Pippin on the Analytic-Continental Divide

September 15, 2007

From an interview in the latest issue* of the Yale Philosophy Review, an undergraduate journal:

[...]

You have to get two PhDs in most European countries to be a university professor… that means you’re about forty-four years old, literally, when you’ve finished doing your research. And the Europeans have sort of awakened to the fact that their (basically) thirteenth-century university system isn’t functioning all that well. So, to some extent, the whole issue of Continental and Analytic is an anachronism, because Continental philosophy on the Continent is evaporating. The whole Heidegger movement in France and Italy is on its last legs. It is the last gasp of the whole tradition of philosophy as a kind of avant-garde cultural enterprise connected with literature and poetry and art and architecture, which is some of what people mean by ‘the Continental tradition:’ that it’s not just a disciplinary matter, but it’s taken to be connected with the entire world of culture in a way that, in America, it tends not to be. That may have been true, but it’s also evaporating… And the pressure on modernizing the university is also changing the way that graduate education in philosophy is organized, and, to some extent, Americanizing it. [...]

So whatever this distinction was, firstly I think it’s more accurately understood as modes of organizing knowledge rather than commitment issues in ideology or in philosophy. And secondly, it’s changing so rapidly under the influence of forces that are not themselves purely philosophical that it’s become a kind of anachronism to talk that way, except with respect to a large group of American philosophers who still identify themselves with this other conception of philosophy as an avant-garde cultural humanistic enterprise.

On the ‘values’ that allow him to identify good philosophy:

Well, I would say as a beginning footnote that I am in an extremely privileged position because I teach at the Committee of Social Thought at the University of Chicago. I literally get to teach absolutely anything I want, in any discipline. And Chicago has a kind of ethos where it’s not regarded as ‘poaching’ or as the incompetent trying to parade as experts. Everyone understands the Committee as the attempt to do something different, to break the hold of the traditional way. And if a little amateurism creeps in, or dilettantism, or cafe society philosophy, well, that’s the price for having the Committee on Social Thought and the people at Chicago are willing to pay it. But what I mean is it’s easy for me to say this, because I have an established career, and I went thought a long career of just doing traditional, disciplinary philosophy. So, institutionally I’m in a very unusual position: even people who have similar interests to mine, if they’re in a philosophy department, they have an undergraduate program that has to be staffed, certain courses that have to be filled every year, and somebody has to teach Intro to Ancient, somebody has to teach nineteenth century, somebody has to teach Kant every other year in the graduate program, and if you’re that person, you have to do that. Your research is just determined by the size of the department and what you have to do. So it doesn’t matter, in a way — going back to this institutional question, which I think is a neglected one in discussions of philosophy — what your new paradigm for philosophy is, because you don’t get to do it. And if you’re doing it before you’re tenured, then you’re taking an even huger risk that you won’t be regarded as having done real philosophy.

*The same issue contains my written-in-one-weekend paper on Goethe and Wittgenstein, which I’m not particularly proud of because it doesn’t seem to answer, or to be aimed at answering, any particularly significant question. It was one of those things where I, as usual, found myself with a disgusting buildup of deadlines in finals week, and scrambled to think of something to write about for the final paper for a course. I did actually enjoy the process of writing the paper, but after the fact I had to admit it was more of an interesting, rambling diversion than a focused attempt at tackling a philosophical problem.

## What’s Going On?

September 7, 2007

A derivation in Boltzmann’s Lectures on Gas Theory [1] that seems mathematically suspect:

If we set $f=e^{\varphi(mc^2)}$ and $F=e^{\Phi(m_1c_1^2)}$, then the last of Equations (27) becomes
$\varphi (mc^2) + \Phi (m_1c^2) = \varphi(mc'^2) + \Phi(mc^2 + m_1c_1^2 - mc'^2)$.

Here the two quantities $mc^2$ and $m_1c_1^2$ are clearly completely independent of each other, and also the third quantity $mc'^2$ can take all values from zero to $mc^2 + m_1c_1^2$, independently of the first two. Denoting these three quantities by x, y and z, and differentiating the last equation with respect to x, then with respect to y, and finally with respect to z, we obtain:
$\varphi'(x) = \Phi' (x+y-z)$
$\Phi'(y) = \Phi'(x+y-z)$
$0=\varphi'(z) = \Phi'(x+y-z)$
whence it follows that
$\varphi'(x) = \Phi'(y) = \varphi'(z)$.

Since the first of these expressions does not contain y or z and the second and third must be equal to it, the second may not conatin y and the third may not contain z. They do not contain any other variables; hence they must be constant; since they are equal to each other, the derivatives of the two functions $\varphi$ and $\Phi$ must be equal to the same constant, $-h$, whence it follows that:

(36) $f=ae^{-hmc^2}, F=Ae^{-hm_1c_1^2}$.

The first thing to point out is the typo in the triplet of equations: There’s no reason why $\varphi'(z)$ or $\Phi'(x+y-z)$ should be equal to 0, so the third equation in the triplet should just be $\varphi'(z)=\Phi'(x+y-z)$. In any case, it would make no sense to have $\varphi'(z)=0$, since that would mean that $h=0$, $f=a$ and $F=A$.

But on to what seems to be a mistake. Taking $x=mc^2$, $y=m_1c_1^2$, and $z=mc'^2$, if we differentiate $\varphi (mc^2) + \Phi (m_1c^2) = \varphi(mc'^2) + \Phi(mc^2 + m_1c_1^2 - mc'^2)$ by x, y and z separately (which seems to be what Boltzmann suggests we do), we get the triplet of equations
$\frac{d\varphi\left(x\right)}{dx}=\frac{d\Phi\left(x+y-z\right)}{dx}$
$\frac{d\varphi\left(y\right)}{dy}=\frac{d\Phi\left(x+y-z\right)}{dy}$
$\frac{d\varphi\left(z\right)}{dz}=\frac{d\Phi\left(x+y-z\right)}{dz}$
Boltzmann, however, writes $\frac{d\Phi\left(x+y-z\right)}{dx}$, $\frac{d\Phi\left(x+y-z\right)}{dy}$ and $\frac{d\Phi\left(x+y-z\right)}{dz}$ all as $\Phi'(x+y-z)$. Which seems to be how he gets to equate $\varphi'(x)$, $\Phi'(y)$ and $\varphi'(z)$. But why should it be true in general that $\frac{d\Phi\left(x+y-z\right)}{dx}= \frac{d\Phi\left(x+y-z\right)}{dy}= \frac{d\Phi\left(x+y-z\right)}{dz}$?

[1] Boltzmann, L. Lectures on Gas Theory (trans. Stephen Brush). University of Calfornia Press, 1964.

## High Energy Giraffes

September 5, 2007

Count me unimpressed by this paper by Don Page posted, strangely, in hep-th. The following excerpt might illustrate why:

…one gets that the following estimate for the height of a giraﬀe:
$H \sim \alpha^{4/5} m_e^{2/5} m_p^{-4/5} g^{-3/5} \sim \alpha^{-7/10} m_e^{-19/20} m_p^{-13/20} \sim \beta^{1/20} \gamma^{3/10} a_0 \approx 2.44\, {\mathrm m}$ (23)

Unlike the previous estimates of both Press [1] and Carter [3], this estimate is within a factor of 2–3 of the height of the tallest running animal, the tallest land animal, the giraﬀe.

It is interesting that when one writes the result as the Bohr radius $a_0$ multiplied by the appropriate powers of α, β, and γ, the ﬁne structure constant α drops out, and the multiple of the Bohr radius involves only the ratio of electron and proton masses, β ≡ me /mp and the ratio of the electrical to gravitational forces between two protons, $\gamma \equiv e^2/(Gm_p^2)$ (in units with $4\pi\epsilon_0 = 1$), with Planck’s constant not appearing anywhere beyond its appearance in the Bohr radius $a_0 = 4\pi\epsilon_0\hbar^2/(m_e e^2)$.

It is also interesting that the power of the mass ratio β is so small. Since β 1/20 ≈ 0.6868 is within a factor of 2 of unity, and since I have been cavalierly dropping many other factors of 2, one can drop this factor in Eq. (23) to obtain
a simpliﬁed equation for the height of a giraﬀe that actually works even better empirically (though it is still not quite the maximum observed height of giraﬀes):
$H \sim \gamma^{0.3} a_0 \approx 3.56\, {\mathrm m}$. (24)

Using the fact that he’d been dropping other factors of 2 to justify dropping another factor? And then taking the new result, which is less than a factor of two off the height of giraffes, to be a better empirical result? When you’ve dropped that many factors of two, I don’t think it matters anymore that you’re a factor of 2 rather than a factor of 2.5 off the facts.

After that, Page goes on to estimate the mass of the largest land animal. He gets 165,000 kg and 508,000 kg as two possible estimates. The first is good for blue whales, which are not land animals. The second is off even for blue whales. Elephants go up to 12,000 kg only. Page writes, however, that “it is gratifying that even the mass estimates are within two orders of magnitude of observed values.”

## Musical Reductionism

September 2, 2007

Some thoughts triggered by reading the bust-up at Musical Perceptions and Mathemusicality over whether music should be analysed harmonically. Since I know nothing about Westergaardian theory I won’t comment on whether it can explain everything harmonic theories do and more. But James Cook’s (JC from here on, because I’m lazy) comment at the latter link rang bells in my head — the debate seemed to parallel philosophical debates about reductionism. Scott Spiegelberg (SS from hereon) first takes Cook to be saying that harmony doesn’t exist, and Cook denies that he espouses such a doctrine, although he had led SS down the wrong path in saying ‘I don’t believe there is such a thing as “harmony”’. The philosophical parallel is, of course, with eliminativism. JC further clarifies his non-eliminativist stance thus:

Please note that I did not say harmony was unimportant; I said it was logically superfluous. This should be a signal that I don’t believe this debate is actually about different ways of hearing music; it’s about different choices of theoretical vocabulary used to express one’s hearing of music. The point is that so-called “harmonic” phenomena admit a much better description in terms of Schenkerian/Westergaardian operations on basic tonal structures.

[...]

More generally, it should not be assumed that just because one criticizes a certain theory, one therefore is not interested in the phenomena that the theory purports to address. When I say that harmony doesn’t exist, it’s as if I said that phlogiston doesn’t exist — which doesn’t mean I think there’s no such thing as combustion.

So it would seem that JC thinks the argument should be about whether harmony is a good way to explain music. How exactly does he think Westergaardian theory is a better explanation? One point he mentions is that there are some musical phenomena that can be explained by Westergaardian analysis but not by harmonic analysis. In other words, Westergaardian theory is more complete than its harmonic competitors. Another point that has been mentioned on several occasions is that JC, along with many other composers and listeners, thinks that Westergaardian theory tracks their actual compositional thoughts and intentions more closely — they hear music in Westergaardian, not [traditional] harmonic, terms. This, however, has to be weighed against the fact (attested to by SS and other participants in the debate, and consistent with my limited acquaintances with musicians) that many other composers or listeners take a harmonic perspective to music, so harmonic theories track their musical experiences closely. Should we then abandon harmonic analyses for Westergaardian analyses? After all, at this point they seem pretty much even on the ‘natural perspective’ front, but Westergaardian analysis is purportedly more complete.

To answer (or at least feel my way towards an answer to) that question, I returned to the parallel with reductionism. The Standard Model in physics is more complete than quantum electrodynamics, quantum chromodynamics, or electroweak theory, and is the most complete and accurate physical theory we have today. Nevertheless, it’s not the case that all physical calculations are done using the Standard Model only. We use the Standard Model only when the phenomena in question are at a level where Standard Model-specific effects become important, and that is not the case for most physical phenomena under investigation today. We are happy to use the less complete theories as long as they can adequately account for the phenomena we apply them to. Nobody has suggested completely abandoning the less complete theories for the Standard Model, but it is reasonable to suppose that if Standard Model-specific effects are found to feature significantly in most observable physical phenomena, that the Standard Model will be the theory of choice in most physical calculations. In other words, eliminating the use of a theory requires more than showing that it is incomplete for certain phenomena — old theories that do account for enough phenomena adequately still warrant usage, and one would certainly not condemn these theories as fairy-tales just because they are less complete than some other theory.

Which is why I think there is no call to label harmony as something that ‘belongs instead with gods, witches, phlogiston, and élan vital in the hallowed hall of Bad Theories — those that are such that to retain them after they have been “reduced away” would actually obscure the true explanation for the phenomenon they were invented to explain.’ JC might object that QED, QCD and so on are at least consistent with the Standard Model in their domains of application, whereas harmony is, in some sense, inconsistent with Westergaardian theory, and hence should be completely abandoned. But we do not think Newtonian mechanics has the same theoretical status as ‘gods, witches, phlogiston, and elan vital’, even though it is inconsistent with modern physical theories. This is because Newtonian mechanics explains enough to warrant some respect (and continued use) as a theory. (Phlogiston is an interesting case because it did explain enough as well, but it turned out to be ‘more convenient’, in the light of our other theories about mass and so on, to reject it as an ontological entity. The literature on the phlogiston issue is extremely large and someone like me who has barely read anything about it probably has a view to crude to be worth mentioning, but it is this: I wouldn’t consider it an incapacitating blow to a theory to be compared to phlogiston.) Similarly, the purported greater completeness of Westergaardian theory does not necessarily warrant abandoning harmonic analyses. Incomplete theories can be perfectly usable within certain domains, and complete theories are not necessarily more usable — we wouldn’t describe organic chemistry in terms of the Standard Model because chemical theories are more usable, albeit less complete. If I have been successfully erecting buildings based on Newtonian mechanics, I wouldn’t abandon the theory just because one day physicists told me that some Standard Model thingy is more accurate and complete than Newtonian mechanics — Newtonian mechanics has worked so far for me, so why should I bother? Why can’t we use both theories, according to what the situation demands? For something like music, where listeners’ perceptions count for a lot in deciding which theory is the ‘best’, the continued perception of harmony by a significant group of listeners is strong reason not to be an eliminativist about harmony.

## My Three Biggest Gripes About Maths Textbooks

September 2, 2007

1. Not enough diagrams.

2. Not enough examples.

3. Not enough explanation (as opposed to derivation).

For that reason, I prefer physicists’ explanations of mathematics to mathematicians’ explanation of mathematics — provided that both are actually correct explanations (frequently, physicists distort mathematical truths to cater to their more mathematically naive students, but that’s not the kind of physicist’s explanation I’m looking for).*

The distinction between explaining [the derivation of?] rather than merely deriving mathematical theorems — a distinction that I firmly believe exists — could be an apt illustration of the deficiencies of deductive-nomological ‘explanations’.

*Update: I should note one outstanding exception to the mathematicians’ textbook vs physicist’s textbook distinction: Hermann Weyl’s Space Time Matter, from which I’ve quoted before. Despairing at getting an intuitive grasp of tensors from Theodore Frankel’s The Geometry of Physics, I turned to Weyl, whose long expository passages of prose help prod my intuition into making connections with my prior knowledge of geometry. Frankel, on the other hand, just has the usual mathematician’s terse rigour, which is well and good if you already understand the material and are looking for a proof (not explanation) of something, but not if you’re a beginner seeking understanding.