I will probably live to regret this, but…
In response to a request that was put to me on a certain social-networking site that will remain nameless…
Here are 25 propositions that I endorse, but which I expect are capable of provoking argument. They are in no particular order.
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1.There are no deities; all major religions are mistaken.
2.“Atonal” music is no such thing; it is merely highly complex “tonal” music. Schoenberg’s early works are music-theoretically more similar to his middle and later works than to the music of the eighteenth century.
3. Rameau’s theory of “harmony” was wrong from the start; over time it has gotten even wronger.
4. Schenkerian theory, though originally a huge step in the right direction, is now an anachronism; it has been superseded by Westergaardian theory.
5.In exactly the same sense in which there is progress in the sciences, so too is there progress in the arts. The best composers of today know more about music than Beethoven, just as the best mathematicians of today know more about mathematics than Gauss. This doesn’t undermine Beethoven’s greatness any more than it undermines Gauss’s.
6. The role of “natural talent” in the intellectual pursuits is misunderstood and greatly overestimated. You may never learn to paint like Leonardo, but you may indeed come close enough that your previous self couldn’t tell the difference.
7. People who talk about “g factor” with any regularity tend to be jerks.
8. The nature of language has been very poorly understood by philosophers, and only marginally better (on average) by linguists.
9. The error of logical positivism was not the verifiabilty criterion itself, but the fact that it was formulated as a criterion for meaning. What they meant to say was this (and this).
10. The main purpose of studying mathematics is to develop intellectual agility. Mathematicians are (or should be) people who get the same kind of pleasure from manipulating concepts that children do from playing with colored blocks.
11. Intellectuals have a blind spot when it comes to politics. Last year, people who think for a living were capable of arguing that the economy was good under Clinton and bad under Bush, hence you should vote for Obama.
12. Climate science is young and presumably involves some bad-ass partial differential equations; it should not be compared to Darwin’s theory of evolution during policy debates on global warming.
13. Teachers of music theory are perpetually embarrassed by their inability to pinpoint what it is they are trying to teach students. But the test is quite simple: you will know you have done your job when your students can accurately write down music they hear.
14. Most people who wax on about the greatness of Bach’s fugues wouldn’t be able to tell the difference between a fugue by Bach and a fugue by a mediocre contemporary — let alone one by, say, Handel.
15. Richard Dawkins should be knighted.
16. Max Tegmark basically has the right idea with his Level IV Multiverse. (This is my preferred solution to the problem of cosmological fine-tuning.)
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17. Course grades should be abolished, especially in graduate school. Oral exams/interviews, work samples, and recommendations are entirely sufficient for academic evaluation. (In short: follow the Princeton model.)
18. The “many-worlds” interpretation of quantum mechanics is the correct one.
19. Semantic externalism is so, so wrong. (See here.)
20. There’s really no downside to signing up for cryonics. (Assuming you can overcome enough inertia to actually do so, of course.)
21. General topology is an example of what the definitive solution to a time-honored philosophical problem (the nature of space and continuity) looks like. It is an abstract subject that should blow your mind. It is emphatically not a mere vocabulary that is useful for analysis or algebraic topology.
22. The argument about the Axiom of Choice is over. AC won. It’s one of the Official Axioms of Mathematics. If you don’t like its consequences, see a therapist. (Or: study alternative systems. But for God’s sake don’t claim that standard mathematics is “wrong”.)
23. Finitism is not only misguided, it’s philistine. (OK, so there are only a finite number of atoms in the universe. So the @#$% what? We’re talking about math here.)
24. Karl Popper missed the point. We don’t need to philosophically distinguish “science” from “pseudoscience”; it suffices to distinguish good theories from bad.
25. The phrase “classical music” should be banned. The term is “art music”.
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February 16, 2009 at 1:41 am |
Thought-provoking – thanks for that.
I am definitely going to start using the term “art-music” too.
February 19, 2009 at 7:41 am |
#2-5: This is going to frustrate you, but… mu.
#6. The last claim is irrelevant; even if someone with my genes had trained for years as a painter under ideal conditions in the Renaissance, I doubt they could have advanced the art of painting to anything like the degree that Da Vinci did. Ditto with my math aptitude; of course I can re-derive the calculus with ease, but I’d probably never have derived it from scratch if I didn’t know what I was looking for.
#12. From what I hear (from a Martian climatologist friend of mine), climatology seems to be about on-par with the current state of economic theory. Which is to say, not settled, but convincing enough to base policy prescriptions on for now.
#22. Eh, I can’t get so militant about AC. It extends our finite intuitions in an interesting and productive direction, and doesn’t seem to contradict itself, so I like it. Then again, I haven’t really run into militant intuitionists, etc. Ditto for #23.
Come on, James, where are your controversial opinions?
February 19, 2009 at 2:35 pm |
Patrick:
#2-4: That’s OK, I hardly expected you to have an opinion! But as these are indeed some of my most notable controversial beliefs, it would have been near dishonest for me to exclude them from this list.
(#5 is a bit surprising, however. Usually this one provokes instant indignant contradiction similar to that produced by #6. Speaking of which…)
#6: First let me point out that “natural talent” is distinct from “genetic causation”. The latter stands opposed to environmental causation, whereas the former stands opposed to such traits as passion and diligence. For all I know, passion and diligence may be determined by genes; or perhaps “natural talent” as people think of it is caused by being hit on the head in a particular fashion, or drinking Florentine water. In any case the nature/nurture axis is, as I see it, orthogonal to the talent/hard-work axis.
Secondly, when you say:
even if someone with my genes had trained for years as a painter under ideal conditions in the Renaissance, I doubt they could have advanced the art of painting to anything like the degree that Da Vinci did.
is this conclusion the result of your own detailed study of painting, and in particular of Leonardo’s work as compared to others’? Or is it, as is more often the case, the result of having heard the oohs and ahhs of Authoritative-Sounding People?
One must guard against a form of mysterianism that is entirely analogous to, and every bit as pernicious as, mysterianism about consciousness. Namely, that Great Artists and Scientists are Possessed with Inspiration that is Forever Inaccessible to the Mere Mortal. As usual, this is nothing but an excuse to avoid looking at the gears inside.
#12. From what I hear (from a Martian climatologist friend of mine), climatology seems to be about on-par with the current state of economic theory. Which is to say, not settled, but convincing enough to base policy prescriptions on for now.
Well, of course; what else would you base policy prescriptions on? Current climatology is no doubt the best that we can do at the moment, and surely we should base policy on the best information we have; but the best we can do isn’t the same across different fields of knowledge. There’s a difference between Staples of Science and cutting-edge stuff, and I do not think the public understanding of science is well served by blurring the distinction.
(A separate point is that it is probably wise to be more than usually cautious about scientific findings that seem to conveniently lend support to particular political factions — most especially factions toward which one is already inclined. Naturally, this applies to economics just as much as climatology.)
22. I am probably more irritated by intuitionists and finitists than most people. But almost as distressing are the ordinary mathematicians who will tell a class, “You can’t really prove Zorn’s Lemma.” Yes you can! So long as you’re working in standard set theory, Zorn’s Lemma is a perfectly good theorem (or lemma, anyway).
I am all in favor of logical, philosophical, and set theoretic subtleties. In fact, one reason I’m so adamant about stamping out the memes of finitism and intuitionism is that they have a corrupting effect on people’s understanding of the technical situation (as the Zorn’s Lemma comment illustrates).
The next time someone replies to a mathematical statement with “But doesn’t that depend on the Axiom of Choice?”, I’m going to answer “Yes, and also on the Axiom of Extensionality, and several others, too”.
February 20, 2009 at 8:43 am |
#5: I agree in general, but the following troubles me:
Do you then think that a well-educated modern could with practice write a fugue in Bach’s style that surpasses his own work? (Could you do so?) If it’s rather that Bach has near-perfect execution but that his style is obsolete, why do even the best-educated moderns still listen to Bach regularly? In short: What aspect does he offer to the listener and critic that more recent composers don’t, and why don’t they exceed him in that aspect if they can?
#6: Willpower is not something extraneous to your brain. It is my experience that passion and drive are not things one can simply decide to have more of, any more than a depressed person can simply decide to be happy again.
I would be a much better mathematician if I had the work ethic of some people I know, but the strategies of “trying harder”, “trying to try harder”, etc, have repeatedly failed. I find myself better off making the most of the times I find myself motivated, and putting myself in situations where I find myself more likely to get motivated.
All brains are not equal, although a fatalism about this tends to have bad consequences of its own. Of course current decisions can subtly change the brain directly, and greatly influence its future environment; but the extent to which willpower can change character is vastly overestimated.
And of course the painting example is only a guess, because I don’t really know the extent of Leonardo’s advances in Renaissance painting (much less what it would feel like to discover these); but I feel quite confident about the calculus example, based on my own mathematical abilities after years of training and on an appreciation of how far beyond his contemporaries Newton had to abstract in order to invent the calculus.
February 20, 2009 at 8:51 am |
P.S. I don’t believe in Inspiration. I believe that by their genes and histories, the brains of Bach, Leonardo, Newton, etc. were more suited than most to recognizing or manipulating certain patterns relevant to their particular fields, just as some brains are structured to recognize exact pitches. There’s nothing magical about variations in brain structure.
I conclude from my evidence so far that most people’s brains are not built for these tasks in the same way, and that no realistic sequence of decisions will turn an average person’s brain into one with the proper structures to see those patterns. (The structures needed seem to be more subtle and difficult to acquire by practice than those needed to learn perfect pitch.)
February 21, 2009 at 5:29 am |
Do you then think that a well-educated modern could with practice write a fugue in Bach’s style that surpasses his own work?…What aspect does he [Bach] offer to the listener and critic that more recent composers don’t, and why don’t they exceed him in that aspect if they can?
I have no doubt that there are people around today who would be capable of writing Baroque music that would be regarded as equal to or greater than Bach’s. (Imitating Bach personally is of course a different matter.) The reason they don’t do so is the same reason mathematical prodigies don’t usually shut themselves in a room to spend their time rediscovering mathematics from scratch. The most capable people in a field are typically very eager to climb those proverbial shoulders of giants and get on with that field as it is practiced in their time.
One thing that a past composer like Bach offers, that is difficult to reproduce, is a certain naïveté. It’s virtually impossible to deliberately forget musical knowledge and replicate the experience of only having been exposed to the music that Bach was exposed to. Whenever I attempt the exercise of composing a Baroque-style piece, I inevitably find the experience rather artificial, because I can’t use the best ideas that naturally occur to me without violating the authenticity of the style; they’re things you simply wouldn’t think of without having heard later composers such as Mozart or Schoenberg. Obviously, Bach didn’t have this problem; he could use whatever exotic idea he came up with — just as modern composers can in their “real” music.
I conclude from my evidence so far that most people’s brains are not built for these tasks in the same way, and that no realistic sequence of decisions will turn an average person’s brain into one with the proper structures to see those patterns.
This could ultimately be true in some sense; and perhaps you’re currently working at or near your limit. But the catch may be hidden in the word “realistic”. The fact is that most people don’t
even try. (Heck, I know this, and I’m still nowhere near my own limit.)
Besides, we can see the patterns in question — at least in retrospect. From our current vantage point, you or I could rederive calculus; so why can’t we introspect to find out what cognitive mechanisms were stopping us from seeing it in the first place, and then correct the problem?
March 12, 2009 at 1:02 pm |
James, I always wanted to ask you the following question. Although I very much believe Westergaard is on a good path, do you not hear “rootedness” in common practice tonality? And if you do, how do you justify the ability to recognize it if it is artificial?
March 12, 2009 at 3:28 pm |
Greg,
I’m not sure exactly what you mean by “rootedness”…maybe you could elaborate?
Although I am, as you know, a vehement critic of the doctrine of “root progressions” introduced by Rameau, I don’t object to calling C the “root” of a C major triad*; nor do I object, in principle, to the notion that there is a musical difference between a triad in 5-3 position and one in 6-3 or 6-4 position (but caution! the situation is not at all what harmonic theory teaches it is — especially at foreground levels. E.g. quite often a 5-3 is actually an elaboration of the corresponding 6-3 [or even 6-4!], rather than vice-versa.)
*I was about to write that “this much is in Westergaard”; but a check of the relevant section of ITT (3.4) reveals that Westergaard in fact eschews the term “root” in favor of “fundamental pitch class”(!) Although ITT is completely free of any polemic (however merited) against harmonic theory, it should nevertheless tell you something that Westergaard, who is normally scrupulous about preserving traditional musical terminology when it applies, actually goes out of his way to avoid the term “root”.
March 13, 2009 at 11:09 am |
Besides, we can see the patterns in question — at least in retrospect. From our current vantage point, you or I could rederive calculus; so why can’t we introspect to find out what cognitive mechanisms were stopping us from seeing it in the first place, and then correct the problem?
It would be very unlikely, from an evolutionary standpoint, for there to be a universal capacity for mathematical abstraction that is simply blocked in most people; that would be as if there were genes dedicated to preventing our arms from becoming wings, rather than birds having genes that develop wings.
Rather, we seem to have some cognitive modules that can be developed (read: shanghaied) into reflecting the complex processes of mathematical thought. The better mathematicians have indeed spent more time working with these modules, but it seems to me that their brains develop in that direction more easily from the start.
March 13, 2009 at 7:56 pm |
It would be very unlikely, from an evolutionary standpoint, for there to be a universal capacity for mathematical abstraction that is simply blocked in most people
Indeed, because there isn’t such an ontologically primitive thing as a “capacity for mathematical abstraction”. Abilities of this sort are supervenient byproducts of brain structure — where the structure in question is not necessarily the initial state of a person’s brain.
You may as well argue, on the same grounds, that it’s useless to attempt to impart any skill currently possessed by only a small number of individuals. After all, the reasoning would go, those individuals must be biologically distinguished in their ability to acquire the skill in question — since if they weren’t so distinguished, everyone else would be able to acquire the skill too, but for some “block”; and such a “block” is evolutionarily unlikely.
Clearly, that argument can’t be right. The fact that some people don’t possess an ability doesn’t imply that they are biologically “blocked” from developing it. This is why the analogy with bird wings fails: because of the nature of our brains, not all of our abilities are directly controlled by our genes.
May 29, 2009 at 2:48 am |
On #25, I agree that “classical music” is not a good description. But people who use that term usually mean something much closer to “music in the European art-music tradition” than “art-music”; Gamelan and ragas would not be characterized as “classical music”.
What term should be used for “European art music from the time of Hadyn, Mozart, and early Beethoven”? If you ruled the world and no-one used “classical music” to mean “art music” or something similar, “Classical music” (like “Baroque music” to refer to the art music of an earlier time) would do fine. But as long as “Classical music” gets used with other meanings, there seems to be no good term.
September 25, 2009 at 6:24 am |
Wow, I just came across this site and I think that this list is fairly brave. I expected many comments regarding #1 but I don’t see any.
I thought #25 was humorous; I mean when did ‘they’ start calling it ‘classical’ music any way?
Anyway I thought there were going to be some lectures on Mathematics, but maybe you abandoned that idea? Just wondering.
September 27, 2009 at 9:58 am |
Anyway I thought there were going to be some lectures on Mathematics, but maybe you abandoned that idea? Just wondering.
No, I haven’t abandoned the idea — just like I haven’t abandoned the idea (believe it or not) of answering funkhauser’s latest question.
Alas, in thinking that I was going to be able to do these things imminently, I appear to have been a victim of the planning fallacy.
I actually have a rather large number of unfinished drafts for various posts and pages. Some subset of these will be finished over the weeks, months, and years to come.
(Funkhauser won’t have to wait for more than another month or so. The mathematics lectures will take longer, however.)