Judging Idealizations

The combination of talking to practicing physicists and reading the literature on the foundations of statistical mechanics has led me to wonder if those of us who are worried by foundational problems are particularly autistic, in the sense that we take literally things that we ‘should not’ be taking literally. Many foundational problems stem from ‘problematic’ idealizations such as the infinite time limit in non-equilibrium statistical mechanics and assuming quasi-ergodicity to be ‘like’ ergodicity. But clearly there are some idealizations which are implicitly taken to be less problematic. For example, even people who are foundations-oriented don’t tend to raise a big fuss over the use of point masses in classical physics, despite the fact that point masses aren’t supposed to exist. The rigid elastic spheres model in statistical mechanics doesn’t bother people as much as the infinite time limit ‘approximation’ does.

The questions I’m interested in are:
1) What kinds of idealizations bother physicists?
2) What kinds of idealizations bother philosophers (or ‘philosophical’ physicists)?
3) What kinds of idealizations should we be bothered by? (Why should we — if you think we should — be more bothered by the infinite time limit idealization than by the point masses idealization?)

1 and 2 are empirical questions; 3 is normative.

The analogy to autistic behaviour is as follows: Throwing a fit over the fact that people don’t mean ‘How are you?’ literally, versus accepting it as a social signal and reserving your indignation for ‘real’ acts of dishonesty.

How Melodies Work

I’d blogged earlier on a particularly satisfying book haul that included a conference volume autographed by Chandrasekhar and Antonio Damasio’s Descartes’ Error, autographed by the author himself. What I didn’t realise was that one of the books in that haul which I’d picked up on the basis of its title and cover alone, Robert Jourdain’s Music, the Brain, and Ecstasy, had once belonged to the late Wayne Booth:

I decided to read it last week as a break from the likes of van Fraassen, wasn’t sure at first that the signature was Booth’s, but quickly became sure when I came across comments in the margins that indicated significant musical knowledge, in particular knowledge of the cellist’s part in the opening of Shostakovich’s 12th String Quartet. I then remembered that Ted Cohen had mentioned that Booth was an amateur cellist.

The book itself lived up to its promise. Lively, picturesque prose, betraying the fact that Jourdain is a writer by profession (after reading a certain amount of philosophy, I tend to be somewhat grateful to read prose that is not only clear, but also flows):

The power of sound cannot be explained merely by the power of music’s structure, for there are plenty of non-musical sounds that cut deeply. The infamous use of chalk squeaking across a blackboard is example enough. The screech of the chalk is not very loud in the scheme of things, so its intensity cannot be the culprit. And while the sheer ugliness of the sound is hard to match, there are plenty of sights that are equally ugly, but somehow do not reach to our core and cause us such pain. For pain it is. Inordinate noise has been used as an instrument of torture for centuries, and is disallowed by the Geneva Convention. On the other hand, it is hard to imagine extracting a spy’s secrets by showing him the collection of the Museum of Contemporary Art.

It will probably not go unnoticed that that’s an unfair (if amusing) attack on contemporary art, since presumably it’d only be fair to compare it to contemporary music rather than chalk-board screeches. And it is not inconceivable that one could extract a spy’s secrets using rather more visceral and upsetting images than those found in the MCA. Nevertheless, I think Jourdain is essentially right on this point: it’s easier to imagine that we could get used to upsetting images than to imagine we can ever find the sound of chalk screeching across a blackboard neutral or pleasant.

In keeping with his art-snobbery, Jourdain inserts negative remarks on modern music throughout the book. On several occasions Jourdain compares contemporary art music unfavorably with that of the old masters, and accuses audiences to such music of subjecting themselves to an unpleasant experience only because they know they are supposed to enjoy it. He paints the old masters as having already explored all the aspects of harmony worth exploring, and claims that present explorations of alternative harmonies and of timbres are inadequate in comparison.

His elevation of harmonic structures above everything else also leads him to dismiss pop music for having inanely simple harmonic structures. To be fair, though, such dissing is only a small proportion of what makes up the book, so it didn’t grate too much with me.

The musically educated would probably find much to disagree with in Jourdain’s cartoon picture of what makes music work, but I still think it is a good book for a preliminary introduction to the psychology of music — I would have liked to read it before I was introduced to formal musical analysis.

Some of Wayne Booth’s remarks in the margins illustrate how the musically educated could too easily find fault with Jourdain. In the section on how melodies work, Jourdain claims that a scale is “boring to listen to”. Booth writes here “Shosta. qt. #12 opening cello”. Indeed, the cello’s opening part in Shostakovich’s 12th String Quartet (listen to an excerpt here) is essentially a drawn-out ascending scale with some oscillation about each note of the scale. It doesn’t sound boring to me though, and no doubt it didn’t sound boring to Booth. But I do think Jourdain is right insofar as most people would find that ‘melody’ boring. I suspect that Booth, like me and most others who enjoy Shostakovich’s music, find in the slowly ascending scale a creeping ominousness and increasing tension, the harmonies used adding to the uncertain, foggy, almost paranoid atmosphere that few composers can bring forth so vividly. But I know several people, even professed classical music lovers, who can’t abide Shostakovich. They are unable to appreciate themes rather than melodies, and blurry atmospheric effects rather than explicit statements. A major reason why I dislike [most] pop music is its lack of the kind of subtle shadings that make the opening to that quartet.

It’s worth noting, though, that Shostakovich’s opening probably relies on our “positive” reactions to full, well-formed, ‘interesting’ melodies. It’s partly because the opening does not form a ‘real’ melody that we get that feeling of uncertainty. So Shostakovich leverages on what makes other melodies work to make his music ‘work’ in a different way.

PRL

I’m pretty bad at reading scientific papers in general, but, by god, PRL papers are the worst. Squeezing a significant scientific result into four pages does not make your exposition any more understandable to the non-specialist. And, given PRL’s stature in the field, one would think papers in PRL should be on average more understandable to the non-specialist.

Concatenationism

It’s not often nowadays that I finish reading a book in two days. Nor am I often largely convinced that I was wrong as a result of reading a book. But Jerrold Levinson’s Music in the Moment has managed to break through both my procrastination and my obstinacy. Clear, graceful prose overcame the former tendency. And I’d like to think my obstinacy collapsed under the weight of good arguments.

Levinson argues against the idea that a theoretical understanding of the large-scale structure of music is central to musical understanding. He claims that the intelligent amateur listener who has no knowledge of formal music theory, he says, can nevertheless be said to essentially understand music. Grasping of architectonic structure is at best peripheral to understanding music, although it may be indispensable in understanding how music works (throughout the book, Levinson is careful to distinguish between these two kinds of understanding). Levinson calls this thesis concatenationism, and outlines it as follows:

1. Musical understanding centrally involves neither aural grasp of a large span of music as a whole, nor intellectual grasp of large-scale connections between parts; understanding music is centrally a matter of apprehending individual bits of music and immediate progressions from bit to bit.
2. Musical enjoyment is had only in the successive parts of a piece of music, and not in the whole as such, or in relationships of parts widely separated in time.
3. Musical form is centrally a matter of cogency of succession, moment to moment and part to part.
4. Musical value rests wholly on the impressiveness of individual parts and the cogency of the successions between them, and not on features of large-scale form per se; the worthwhileness of experience of music relates directly only to the former.

Since I myself had gone through the experience of having what I’d thought to be my considerable musical experience (both playing and listening) shrink to nothingness before the power of the first formal music analysis skills I acquired, my first reaction to that statement of concatenationism was one of ridicule. Statement 2 was possibly acceptable, but Statements 1, 3 and 4 seemed wildly off the map, seeing as how I’d apparently understood so many musical works better after building up my music analysis muscles.

It turns out that Levinson does not subscribe to the extreme form of concatenationism laid out above. Replace the “only”s and “wholly”s with “centrally”, though, and you’ve basically got Levinson’s final, moderated, conclusion. He does not deny that architectonic features of the music have a causal role to play in musical understanding. That would be silly, since recurrences of long-past motifs, for example, can induce strong psychological reactions in the listener. But he does want to distinguish between the causal role that large-scale forms have and the significance of a conscious awareness of them for musical understanding. The amateur listener’s particular emotional reaction to a tonality late in a musical work is often caused by large-scale structure of some sort, even by structural elements that occurred way back in the piece. But if, as is almost always the case, the listener does not need to have a conscious awareness of that structural relationship to have the kind of reaction to the structural element that indicates that he/she does understand the music, then it is true that as far as conscious apprehension goes, music resides only ‘in the moment’.

Levinson does admit that there are musical works for which a conscious understanding of large-scale structure does add considerably to one’s understanding of the musical work. But he thinks that

1. This is not true for most pieces of music (save for recent forms of music like aleatoric music)
2. Although a conscious grasp of large-scale structure adds a non-trivial element to understanding, the core determinant of musical understanding is still that of being able to hear the cogency in short-term musical progressions.
3. A conscious grasp of large-scale structure, no matter how important, is still parasitic on an appreciation of short-term musical cogency. To use one of Levinson’s examples, it is because we are gripped by the short-term cogency of the last movement of Brahms’ 4th Symphony that we get so much intellectual satisfaction from appreciating that it is a passacaglia:
   

   One cannot help but marvel that such a fluid and organic musical embodiment of — let us say — the seriousness and tragedy of human existence in fact breaks down, coda apart, into thirty-one distinguishable units of strictly equal length, each involving the same small-scale harmonic motion.

   But without our perception of its moment-to-moment fluidity and organicity, we would hardly be aesthetically awed by its large-scale structure. After all, anyone can write “thirty-one distinguishable units of strictly equal length, each involving the same small-scale harmonic motion” — the trick is writing something like that which, to put it crudely, sounds good.

I would say I’m largely convinced by his arguments, although there are two aspects that don’t sit entirely well with me. The first is his assertion that musical value is wholly determined by, roughly speaking, the quality of immediate musical experience. The second is the suspiciously clean divide between conscious (‘intellectual’) understanding and unconscious reactions to causal factors deliberately embedded in the large-scale structure of a musical work by composers and performers.

A Frustrating Conversation

I suspect conversations of this type will be not uncommon as long as I continue encountering people who consider themselves to be scientists by profession (the reason for this awkward phrasing will become clear). So this is a gentle reminder to my future self to be prepared for what follows.

I was talking to a purported scientist about my career plans, and explaining my interests in the foundations of physics and so on, and why although I appreciate the importance of measuring this or that quantity (resp., coming up with this or that theory) that overthrows or verifies a certain theory (resp., gives a superior account of existing experimental evidence), I personally do not derive much satisfaction from actually doing those things, and would not psychologically be able to commit myself to them as a long-term intellectual pursuit.

She responded that someone with my limited experience should not judge all of physics that quickly, that I won’t know if there aren’t any areas of physics that I could really be interested in but haven’t encountered, and so on. Fair enough. Given my radical reassessments of my interests in the last two years alone, I would be foolish to discount undiscovered interests. But the mere possibility that I could find something really engaging in conventional physics is not a good reason to apply to physics grad school now, which is what she was trying to get me to do.

I had been trying to keep the philosophy thing under wraps because, from experience, some so-called scientists are allergic to philosophy, but eventually the turn of the argument that ensued led me to reveal that aspect of my interests. Upon which she said, ‘But that’s not research, is it?’

Oh dear.

The thing that you, future self, should remember, is that it’s impossible to try to explain to people like this, at least not in a conversation of reasonable length, why it is that it’s not quite possible to draw a line between what is [scientific] ‘research’ and philosophy without doing philosophy yourself. And it’s impossible because these people don’t even know what philosophy is. Of course, you can go on about the history of philosophy, and the incestuous relationships the history of science has with it, but this will draw only blank looks from them, because the names and developments you mention are, though possibly vaguely familiar, meaningless to them.

Just to vent, it was both amusing and bothersome to have someone tell me that I don’t know enough about physics to know what I’m interested in in physics, and in the next breath make a gargantuan claim about a discipline about which her ignorance pales in comparison to my ignorance about physics. We even got to a point in the conversation where she was lecturing me on how the disciplinary boundaries she said I was drawing within science (between the ‘foundational’ problems I liked and other kinds of problems) were ‘artificial’, and on how a ‘good scientist’ should be willing and able to solve any problem in science. The irony in that kind of argument coming from someone who’s just decapitated philosophy from science should be obvious.

This brought to mind an asymmetry in interdisciplinary perceptions: While many scientists are quite happy to discount philosophy as a legitimate field of inquiry, the vast majority of philosophers have the opposite attitude towards science. That is, one group is relatively ignorant about what the other group does but does not discount it, while the second group (similarly ignorant) does discount what the first group does. The reasons for this asymmetry are left as an exercise for the reader.

Spin Echoes and Thermodynamics

I’ve been reading the original literature on the spin echo experiments. These experiments are significant in statistical mechanics because they allegedly involve ‘preparing’ a system of spins in such a way that they spontaneously evolve from an apparent high-entropy state to an apparent low-entropy state. This is done by changing the sign of the Hamiltonian of the system. The state of the system is described by the Schroedinger equation , so the transformation has the same effect as the transformation . So the spin echo experiments create a dynamical reversal of the system in order to recover an initial low entropy state. This is potentially problematic for the second law of thermodynamics, depending on which version of the second law is your favourite.

Following the trail of citations to and from the original Hahn experiment led me to Rhim, Pines and Waugh, who claim to “dispel any doubts about [the spin echo experiment's] conflict with thermodynamical principles”. In Section C of their paper, they distinguish the spin echo experimenter from the Maxwell demon thus: In order to work its magic, the Maxwell Demon must know the microscopic variables of the system, that is, the momenta and positions of the particles in the system. But the Loschmidt Demon (the experimenter in the spin echo experiment) need only know the values of the “macroscopic variables” (their words) M (the magnetization of the system) and E (the energy of the system). Rhim et al write:

Improv Comedy as a College Admission Essay

Many people are put off applying to the U of C for college because of its infamously odd essay questions. For me, though, the essay questions were a postive indication of the quality of U of C students. After all, those who can be bothered to answer them, or who even enjoy answering them (I did), would be more likely to be people I can get along with. Take this year’s fourth essay question:

Modern improvisational comedy had its start with the Compass Players, a group of University of Chicago students, who later formed the Second City comedy troupe. Here is a chance to play along. Improvise a story, essay, or script that meets all of the following requirements:It must include the line “And yes I said yes I will Yes” (Ulysses, by James Joyce).

* Its characters may not have superpowers.
* Your work has to mention the University of Chicago, but please, no accounts of a high- school student applying to the University—this is fiction, not autobiography.
* Your work must include at least four of the following elements:
* a paper airplane
* a transformation
* a shoe
* the invisible hand
* two doors
* pointillism
* a fanciful explanation of the Pythagorean Theorem
* a ventriloquist or ventriloquis
* the Periodic Table of Elements
* the concept of Jeong
* number two pencils

I know certain people who would find such a question annoying, and they are boring people.

Familiarity and Understanding

I’ve long suspected that much of what I take to “understand” in mathematics or the mathematical sciences is simply familiarity. This is confirmed when I discover that concepts I was previously uncertain about seem to crystallize immediately when I re-read explanations of them. I may completely fail to grasp a concept the first time I read about it. But as I re-read definitions of it, written in myriad forms, I start losing that feeling of unnamable fear I get upon first encountering an abstract definition. Perhaps surrounding a concept with related pictures, which I acquire as I read more widely on the subject, helps me to make connections. But there is also a component due to sheer familiarity — I’ve lost count of the number of times I’ve said to myself ‘oh, it’s just that other thing I read about elsewhere’, and subsequently felt more confident that I understood the concept.

Thus, as I go through the Ehrenfests’ seminal summary of the foundations of statistical mechanics for the second time, I find myself easily skimming through some parts, even though reading it the first time was a torturous process. Parallel experiences can be found in my six-month-long attempt at learning differential geometry — it was only after reading many different approaches to the subject that a picture finally formed in my mind of what a tangent vector really was (that is, a more accurate, abstract picture than that of an arrow tangent to a surface).

My feeling is that this relation between familiarity and understanding is stronger in mathematics than in other disciplines. Perhaps because it is more true in mathematics than anywhere else that knowing how to use a concept is definitive of understanding.