My Kind of Textbook

From Hermann Weyl’s Space-Time-Matter (emphases Weyl’s):

It is evident from these arguments that the whole of affine geometry merely teaches us that space is a region of three dimensions in linear quantities (the meaning of this statement will be sufficiently clear without further explanation). All the separate facts of intuition which were mentioned in §1 are simply disguised forms of this one truth. Now, if on the one hand it is very satisfactory to be able to give a common ground in the theory of knowledge for the many varieties of statements concerning space, spatial configurations, and spatial relations which, taken together, constitute geometry, it must on the other hand be emphasised that this demonstrates very clearly with what little right mathematics may claim to expose the intuitional nature of space. Geometry contains no trace of that which makes the space of intuition what it is in virtue of its own entirely distinctive qualities which are not shared by “states of addition-machines” and “gas-mixtures” and “systems of solutions of linear equations”. It is left to metaphysics to make this “comprehensible” or indeed to show why and in what sense it is incomprehensible. We as mathematicians have reason to be proud of the wonderful insight into the knowledge of space which we gain, but, at the same time, we must recognise with humility that our conceptual theories enable us to grasp only one aspect of the nature of space, that which, moreover, is most formal and superficial.

This in the middle of a rigorous axiomization of metric geometry. Beautiful. They just don’t write them like this anymore.

Flabby Particles

In my junk mail folder: spam titled “flabby particle accelerator”.

I have a mental image of two blobs of fat colliding.

Cosmic Entropy

Speaking of messy offices, here’s Alan Guth’s:

The office I saw, though, had even higher stacks.

Found out only last night that both international economy surface mail and international economy M-bag mail had been eliminated by USPS. Panicked and spent a few hours feverishly trawling Google for solutions, before giving up at about 4 am in favour of sleep.

Today, exerted much effort carrying two 15 kg boxes of books to the post office. One at a time. The second using my bike as a (very unstable) pushcart, because my arms had been destroyed by the first. Shipping by M-bag airmail came to $250 in total. It would have been 1/3 that in the past, with the surface M-bag option. The post office clerk said she felt like she was ripping me off. I felt the same too, but that was still by far the cheapest method. There was a family with about 20 boxes in front of me, and they kept apologising to everyone in the long queue for making them wait, and thanked the clerk who dealt with them profusely. There was someone who claimed to have a parcel with more stamps than necessary and wanted to drop it off without having to queue. They wouldn’t let him do it.

Tomorrow: more packing, returning of library books, closing bank account, but not before picking up paycheck, giving my last thanks to the graduate students in my research group, doing laundry,…

Has school ended, then?

My anticipation of enjoying the city while finally free of the clutches of the U of C workload dashed by family visiting, convocation, packing, dumpster diving so that I can pack, and, most of all, writing the summary of my undergraduate research.

The last, ironically, is the one in the list I most want to do. That is, I want the result: that I leave behind a good enough record of my work that whoever takes over the project can start where I left off rather than starting from scratch. I can’t stand the process, though: hours and hours of checking that my numbers are correct, formatting figures in LaTeX, etc. To make things worse I discovered a major error in my previous calculations (yay double-checking!) and had to re-run a large chunk of the analysis. The discrepancy between our simulation-based predictions is still there, but it is no longer as outrageously large as before. Now, very likely there is some other bug in my latest analyses as well, and the latest figures are closer to our expectations through sheer luck.

Eight hours today spent finishing up the new analyses and the draft of the report. Couldn’t believe I was doing it again: sitting in those green sofas on the first floor of the Reg, typing furiously on my laptop. On Sunday afternoon.

The fact is, I will miss that feeling. Perhaps it’s only because of its positive associations.

It’s easy to make myself depressed. Even thinking of a simple, trivial thing like how I will never again peer in at the window of the Reg’s recordings collection looking to hand a grumpy student librarian the slip of paper with my latest CD requests does the trick.

The distinctive smell of the accelerator building. The HEP building doesn’t have a smell, thank god, or I will puke on the last time I leave it. Will probably enter it one more time, on Tuesday, and that’s it.

PAW is one thing I will not be nostalgic about, though. I think I could have saved hours of my life if it had the simple feature that one would expect of a Unix application of allowing one to finish half-completed file names by pressing Tab. The number of times I instinctively pressed Tab only for the cursor to jump several spaces forward and me having to backspace out all those spaces doesn’t bear thinking about.

More Thomas Bernhard

From his Concrete:

But [my sister]’s like that. She’s always turning up with some twit or other who wears shoes made by Nagy, what is more with metal tips which give them a revolting, unnatural gait, claiming that these people are relatives of hers, and consequently of mine. I have no relatives, I always tell her. I have only intellectual kin. The dead philosophers are my relatives. She always responds to this with her sly smile. But you can’t go to bed with philosophy, my little brother, she would often say, to which I would reply, just as often, Of course I can, and at least I don’t defile myself by doing so. This remark of mine once led her to announce, at a party in Muerzzuschlag to which she had dragged me after hours of nonstop nagging, My little brother sleeps with Schopenhauer. He alternates between Schopenhauer and Nietzsche. With this she scored the expected success, as always at my expense.

Previous comments on Bernhard.

How They Lost Me

The U of C physics department, that is.

Following my ecstacy two weeks ago at having been given an unexpectedly early release* from the fetters of the mind-numbing, soul-crushing undergraduate physics curriculum here, I will attempt to summarise my thoughts on the experience, with side remarks on how it ended up pushing me away from mainstream physics.

The first two quarters of freshman year were exhilarating, physics-wise. I loved mechanics, especially the challenging and fun problems from Kleppner and Kolenkow. I didn’t enjoy E&M that much, but still found it an enormously educational experience, with similarly conceptually challenging problems set by the professor. I remember staying up all night puzzling over a special relativity problem set and enjoying every moment of it, up till the final burst of adrenaline at the breakfast dining table, when I finally straightened out all my misconceptions with one crucial perspectival shift.

From then on it was downhill. The conceptually challenging problems disappeared to be replaced by computationally tedious grindwork. Instead of learning new concepts and theories, we were simply learning how to evaluate progressively more complicated equations. The nadir was the two-quarter quantum mechanics course, which I had looked forward to after a year of boredom with physics courses, only to find that it was more computation. Barely a mention of Hilbert space; that had to wait till a special mathematical physics course, about which more later. The only thing keeping me focused on my then goal of becoming a physicist was my highly positive research experience, which is perhaps the aspect of my education here that I consider the most invaluable. More invaluable even than my exposure to philosophy.

In the middle of my second year, I spotted a philosophy of physics course in the catalogue, and enrolled in it with not inconsiderable apprehension. I had struggled for the introductory philosophy courses I took as part of the core curriculum, but the topic — the arrow of time — was intriguing enough that I decided it was worth the risk. I loved that course, and the next quarter, took two more philosophy courses, one of which was a complete writeoff because the professor merely read from his lecture notes. The other was an introduction to analytic philosophy. The first time I read Wittgenstein’s Tractatus, I was so stunned that I read it back-to-back three times over in the same weekend. I promptly decided to try for a minor in philosophy. By the time we were done with the Philosophical Investigations, I decided I wanted more than a minor and applied for a major in “philosophy and allied fields” with the approval of the resident philosopher of physics, which allowed me to include a limited number of relevant physics courses, such as quantum mechanics, as part of the philosophy and allied fields major.

By the middle of the third and final year, I realised that I only had to take two more philosophy courses the next quarter (this quarter, that is) to graduate with a full philosophy major. I promptly did so. By then, my disillusionment with physics coursework had progressed to the point that I couldn’t bring myself to study for my quantum mechanics final at 9 pm the night before, even though I knew I was extremely unprepared (unsurprisingly, I got a B for that course, my first and only in any physics course). There was just one bright spot in my physics coursework experience, but it was a very bright spot indeed, and well worth mentioning. It was “Topics in Mathematical Physics”, taught by this remarkable thinker. I found out that few physicists, even amongst theorists, thought like him about physics.** That he was chums with many philosophers of physics. Meanwhile, I was hearing more and more of the dire state of the theoretical physics job market, and enjoying more philosophy courses. By the end of that quarter I’d pretty much set my mind on a career in philosophy rather than theoretical physics. Experimental physics, too, had been tempting for a while, especially as I was having a particularly positive research experience with an experimental particle physics group. But while I was enjoying the day-to-day challenge of getting around the countless practical obstacles in squeezing useful data out of an enormously complex experiment, I realised that I didn’t want to spend thirty or more years of my life doing this sort of thing any more than I wanted to spend thirty or more years of my life solving crossword puzzles. I would be quite happy to continue plugging at it for two or three more years, but the thought of thirty years of something similar filled me with horror.

The notion of path dependence comes into full relief when I consider how I ended up as an aspiring philosopher. I’d never heard of philosophy of physics and would probably still be ignorant of it if not for the university happening to hire a philosopher of physics in the second year I was here, having been devoid of such people since D. M. left (given how rarely R. G. is on campus, there was no chance that I’d have been introduced to it otherwise). But further factors after that first course combined to tip me decisively over to the dark side. A particularly fortuitous factor being getting to know R. G. in the last course he would teach before retiring. I would also say I was extremely lucky in stumbling into the kind of research experience in experimental physics that I got: I had uncommonly good guidance from the grad students in our group and my supervisor, and learnt a lot about how experimental physics is done that I suspect I wouldn’t have if I’d joined the kind of hands-off group that assigned undergraduates menial labour. Ironically, it was my confidence that I’d done real experimental research that convinced me that that wasn’t my cup of tea, much as I enjoyed and treasured the experience. A negative experience might have led me to hope that when I became a grad student, I might finally get to do real research and things would be better; but as it were, I got a good enough seat in the arena to be able to judge that things would not, in fact, be better. They would probably be worse, if anything, because I realised that I had the uncommon benefit of working on the most physics-intensive side of things (the kinematic and statistical analysis of results) as opposed to the red tape-intensive side (pacifying collaborators and sponsors and such) or the engineering-intensive side (designing the experimental setup).

Another factor, which I once attributed entirely to luck but recently learnt is probably related to a not uncommon phenomenon, was meeting a few philosophers who started out as physics majors and ended up as philosophers for roughly the same reasons I’m putting forward now. These people seem to be not uncommon in theoretical philosophy, and since nearly all my courses were in theoretical philosophy, it is on hindsight no surprise that I ran into so many of them (relative to the total population of philosophers).

So now, on to the job that I will not enjoy, and hopefully philosophy graduate school X years later.

*I stayed up all night to study for the oral exam, only for the professor to inform me, when I stumbled groggily into his office the next day, that he wasn’t going to bother testing me because I was getting an A anyway.

**An anecdote recently related by someone on the committee responsible for this year’s graduate physics qualifying exam: They solicited questions from the faculty, but received only 4 questions out of the 35 people who were eligible to contribute. One question, submitted by a condensed matter theorist, was five pages long and had twenty different parts, at the end of which one was supposed to have derived a significant result in solid state physics. Another question was from R. G., and was rejected immediately because it required students to understand what an observable in quantum mechanics was. Seems a perfectly reasonable demand to me of course, but they thought it’d be unfair to those who only cared about how to calculate things. As obvious a sign of the dominant Shut Up and Calculate mentality*** as you’ll get.

***It does not deserve the term “interpretation”.

Kivy on Music Education

We often think that no student should emerge from college not knowing the great works of Western literature. But does the same apply to the pinnacles of Western music? Should students should be required to know Beethoven’s Eroica symphony the way they are required to know Hamlet? The problem is that while we can argue that knowing the great works of Western literature is essential to understanding humanity, society, and so on, it does not seem possible to make the same argument for musical works that have no programmatic content.

Peter Kivy attempts to connect music to an understanding of humanity by considering music’s social function. Music, he argues, has been a social ritual and a force of social cohesion in every culture we know of. To perform chamber music, or to attend a concert, is to take part in a social ritual. This social ritual increases social cohesion amongst its participants. Kivy takes this as a justification for music education: “Thus, there would seem to be, in this enormous and unique socialising power of music, ample justification for our requiring the educated person not only to be acquainted with the literary totems of his or her tribe, but with the musical ones as well.”¹

It’s not obvious to me why being a tool of social cohesion justifies music as something people should be acquainted with. Sporting competitions, too, are a tool of social cohesion: sports fans of all political stripes unite to support their national teams in international competitions. Yet we would hardly think that a knowledge of the most popular national sports is a necessary part of a great education. Furthermore, the social cohesion argument seems to justify being acquainted with any music that serves the function of social cohesion, and hence does not seem to justify being acquainted with what we consider to be the greatest musical works. Is the Eroica Symphony any greater a force for social cohesion than a simple, inane, but admittedly rousing tune like God Save the Queen? I doubt it.

Kivy had himself earlier recognised the need to distinguish music from other pursuits like sports, and he rightly related it to music’s place in the category of pursuits we call “arts and letters”.² That music falls in that category, and baseball doesn’t, must at least be part of the reason (if there is one) why music should be part of any good general education, while baseball needn’t be. And I think that is because we think of the pinnacles of the arts as different kinds of accomplishments from the victories of a sports team or sportsperson. The amazing feats of physical and mental endurance in sports differ from the creations of artists in that the latter seem to represent, somehow, the potentialities of the human mind. And if this is closer to the essential ingredient (if there’s one) that would make any field of human endeavour an obligatory part of a general education, then it would be more explicable why we should think that students should be acquainted with the musically “great” works rather than the works that can stimulate the most social cohesion, for the great works do seem to present the extremes of the mind’s potential. Kivy, I suspect, might be a little too hasty with his conclusion that “there must be something else about a work of art besides its merely being a great work of art that I think justifies its inclusion in a proper liberal arts education”.³ At least one of his justifications for the above statement is unconvincing. He points out that we tend to feel that “serious” rather than “comic” literary works should be included in the canon of general education, and argues that it’s because “serious” literary works teach us more about “questions of deep and abiding concern” like God, evil, freedom, justice, and so on.⁴ But imagine this: if the only literary works we had were comic works, would we not still feel that some of them should be included in a general education? Isn’t it just that whether a literary works deals with serious issues is a bonus factor that would make it a better candidate for a canonical work in a general education, but what is essential is something else? Here’s another question to pump our intuitions. Do we feel that the masterpieces of so-called abstract art has less of a right to be included in a general education than the masterpieces of representational art? I think not, which is why I think that if there is to be a reason for including art, it is not something reliant on its association with “serious” questions.

I’m also not comfortable with the idea that music that is suited for private consumption would not be justifable inclusions in music education. Now, I’m not entirely sure there is any solo music that really should be played only in private. (Were there any composers who intended some of their solo works not to be performed in public?) But I have an intuition there are pieces that are more suited to public sharing, and others that are more suited to private rumination on the part of the solo performer. We might think here of a distinction between more “intimate” music, like Bach’s cello suites, and something like the Eroica. Are we then going to say that in music education, more “private” music should be passed over in favour of more “public” music? My intuitions rebel strongly against this notion; they want all great music to be included, public or private. Thus we return to the problem of justifying being acquainted with not just any music, but with great music. There is no such problem about the standard justification of including Hamlet in general education, for one could make a plausible argument that the greatness of art works correlates with the lessons they provide about humanity.

Suppose my idea that an important factor is the display of intellectual achievement in great works of art, rather than their social functions or representational content, has a grain of truth in it. Why should we think that people should know about intellectual achievements? Perhaps because these achievements are as much a part of humanity as the supposed “knowledge” that creators of representational art and literature convey to us. And perhaps we focus on intellectual achievements rather than achievements of mental and physical endurance, because it is the mind that is peculiarly human — many animals can doubtless surpass the feats of mental and physical endurance displayed by our greatest mountaineers, but none of them have a chance at surpassing the intellectual feats of our greatest artists.

Another possibility, of course, is that us music-lovers are simply wrong in our intuitions about the value of music education.

——

1. Peter Kivy, “Music and the Liberal Education”, in The Fine Art of Repetition (Cambridge: Cambridge University Press, 1993), 28.
2. Ibid. 13.
3. Ibid. 15.
4. Ibid. 18.