Ok, but before we turn everything upside down, can we think a little about why academia ended up being the way it is? Hanson had some good status-based explanations about the academic career trajectory.

If you haven't done cutting edge stuff, the worry is you don't know what you are talking about yet, and shouldn't be a public-facing part of science.

Also there are well-known popularizers who aren't significant academics, e.g. Bill Nye. Bill Nye did some engineering stuff, though.

LW, Eliezer, etc, can't stay on the "crank" level, not playing by the rules, publishing books and no papers.

Why not? What's stopping them?

One of the rules is that beginning academics must not publish work like this. They have to publish cutting edge research for a long time before they are allowed to synthesize or popularize.

If I'm following, you're suggesting that the distinction being introduced here is between two different set of cognitive processes, one of which (call it A) is understood as somehow more natural or innate or intrinsic to the human mind than the other (call it B), and creative thinking is part of B.

No, I'm not suggesting that. That may be what Okeymaker is suggesting; I'm not quite clear on his/her distinction either. What I was originally addressing, however, was komponisto's assertion that "high IQ" is merely "high processing speed and copious amounts of RAM", which I denied, pointing out that "high processing speed and copious amounts of RAM" alone would surely not have been enough to invent calculus, and that "creative thinking" (whatever that means) is required as well. In essence, I was arguing that "high IQ" should be defined as more than simply "high processing speed and copious amounts of RAM", but should include some tertiary or possibly even quaternary component to account for thinking of the sort Newton must have performed to invent calculus. This suggested definition of IQ seems more reasonable to me; after all, if IQ were simply defined as "high processing speeed and copious amounts of RAM", I doubt researchers would have had so much trouble testing for it. Furthermore, it's difficult to imagine tests like Raven's Progressive Matrices (which are often used in IQ testing) being completed by dint of sheer processing speed and RAM.

Note that the above paragraph contains no mention of the words "natural", "innate", or any synonyms. The distinction between "natural" thinking and "synthetic" (I guess that would be the word? I was trying to find a good antonym for "natural") thinking was not what I was trying to get at with my original comment; indeed, I suspect that the concept of such a distinction may not even be coherent. Furthermore, conditional on such a distinction existing, I would not sort "creative thinking" into the "synthetic" category of thinking; as I noted in my original comment, no one taught Newton the algorithm he used to invent calculus. It was probably opaque even to his own conscious introspection, probably taking the form of a brilliant flash of insight or something like that, after which he just "knew" the answer, without knowing how he "knew". This sort of thinking, I would say, is so obviously spontaneous and untaught that I would not hesitate to classify it as "natural"--if, that is, the concept is indeed coherent.

It sounds as though you may be confused because you have been considering Okeymaker's and my positions to be one and the same. In light of this, I think I should clarify that I simply offered my comment as a potential explanation of what Okeymaker meant by "creative thinking"; no insight was meant to be offered on his/her distinction between "natural" thinking and "synthetic" thinking.

There's all sorts of complicated details that are completely missing from the US coverage of the trials, which make the prosecution's position much more understandable. Perhaps the prosecution did not have sufficient evidence, but neither did the prosecution come up with some batshit insane theory out of the blue for no reason when they had everything explained with Guede.

Komponisto is Italian and translated documents from the prosecution for the benefit of the community.

I think it's worth reading this if you think it's some variety of a clear cut case.

.. The thing that puzzles me here is why Knox was ever prosecuted at all. The prosecution had Guede. Who left his fingerprints all over the scene, fled the country, had a history of burglary and knives and changed his story repeatedly. That's a pretty simple and very solid case. Why the heck the prosecution insisted on trying to pin the crime on two more people who could have no plausible reason at all for conspiring with him is just inexplicable to me. I mean, traces of dna from people who lived in the apartment? Wtf? All that proves is that they indeed, lived there.

We're heading into the last few hours to make predictions on the outcome of the latest round of the Amanda Knox/Raffaele Sollecito case. I've made mine. See also here (and, for that matter, the post and other comments).

The main sources of uncertainty are the general unpredictability of Italian Supreme Court decisions (as demonstrated in the nigh-inexplicable -- at least on naïve theories of how the system should work -- overturning of the acquittal by the Supreme Court two years ago), the fact that the panel that hears the case tomorrow won't actually be the same one as the one that heard it the first time, the fact that a juror in last year's retrial has come out expressing doubts about the case in the Italian press recently, and the fact that Knox and Sollecito do, in fact, have a pretty good case (even if their case was better at the previous levels of trial).

Of course, these factors aren't independent by any means, and I think they are dominated by the inertia of the previous verdicts. But, I don't dare put my confidence at more than about 60%.

I didn't have anything really radical in mind. I think it's pretty clear that there's a long-term trend toward high-level music-making relying on notation to a decreasing extent. I have a number of friends who are professional composers, and some of them use notation to write for instruments, while others use electronics and largely don't use notation at all. (The latter group, who compose for video games, movies, etc., are the ones who actually make money at it, so I'm by no means just talking about avant-garde electronic music.) A lot of commercial composers who would have been using paper and pencil 30 years ago are using Logic or Digital Performer today.

The other factor, of course, is that notated genres of music ("classical" music and its descendants, and some others) are increasingly marginal in Western culture. This trend is often way overblown, but is clearly visible at the timescale of decades or longer.

What I certainly don't mean to suggest is that individuals who use notation in our musical lives, like you or me, will stop using it. It'll be a cohort replacement effect, and no doubt a very gradual one. Nor do I think that music notation will entirely go away at some foreseeable point in the future. But reading and using it will slowly become a more specialized skill. My impression, though I don't have a reference for this and could be completely wrong, that the ability of American adults (not pro musicians) to read music notation with some fluency has hugely declined over the last half-century.

All this is very much the framing argument of Taruskin's Oxford History of Western Music, with its much-criticized focus on what he calls the "literate [his needlessly inflammatory term for 'notated'] traditions" of music. Within that frame, he casts the present day as essentially an "end-of-history" moment.

Correct me where I'm wrong here! I'm not a specialist in these issues.

Let me add that, like you, I absolutely love music notation, borderline fetishize it, and say all this with more than a trace of a Luddite's sadness.

Good post and I'll chime in if you don't mind. I teach this stuff for a living and even highly skilled musicians struggle with it in various ways (myself emphatically included).

The main thing I want to say is that there's a reason why essentially all music education consists of many years of rote learning. Obviously, that rote learning works better if it's guided in appropriate directions, but I really don't know of any alternative to what you describe when you say "an orders-of-magnitude-less-efficient mechanism for memorizing note-to-note mappings for every note and every pair of keys." I hate to say it, but ... yep. [EDIT: eh, let me qualify that a bit. See point (A) below.]

Sight-transposition (i.e. sight-reading plus on-the-fly transposition) is a ninja-level skill. Some instrumentalists (usually those who play non-concert-pitch instruments) can do it reasonably well for at least some transposition intervals, and a few people like professional vocal accompanists and church organists need to be able to do it fluently as an expected part of their job. But outside of those folks, even professional musicians rarely have that facility.

Here's something that directly supports your point at (D). As you know, pitch intervals in tonal theory are given names that break arithmetic—a second plus a fourth is a fifth, even though 2+4≠5. A certain well-known music theorist often expresses the view that this blatantly illogical convention is almost entirely responsible for the popular perception that music theory is a really, really difficult subject. I think this exaggerates things, but he's got a point. However, most musicians know those interval names really well and have never thought much about how stupid they are, and so then high-level music theory becomes opaque to skilled musicians because we start by renaming intervals correctly (i.e. a second is diatonic interval 1, and you can add them like normal numbers).

In the case of the frustrating conventions of staff notation, there are historical reasons going back a millennium why we write pitches like that. Various reforms have been proposed, but path-dependency basically makes it impossible that any of them would ever be adopted. Far more likely (and well underway for decades now) is that musicians will stop using notation altogether.

Just to briefly answer your other questions with my personal views:

(A) Personally yes, I have all the note-to-note mappings memorized. I do this completely via thinking in scale degrees. I can name any scale degree in any key, so questions like the one you mentioned just revolve around thinking "B-flat is scale-degree 4 in F major. What's scale-degree 4 in C or A-flat?"

(B) Yes, I do think this is plausible, and underappreciated in the specific case of music, since most musicians don't think much about the ways in which notation isn't an optimized system.

(C) Maybe this is too glib, but ... social interaction? "Overthinking it" isn't a path to doing well in social settings. For that matter, natural language might be another. In many respects it's best learned by rote (along with some theory—just like music) but I've certainly had classmates in language courses who get too hung up on the illogic of grammar to progress well in basic skills like speaking and listening comprehension.

komponisto has an explanation for that, saying that what is being played is not chords, but temporal sequences moving between chords.

What? I don't understand what that means, which suggests that it isn't something I said.

Here are some points to consider:

• Sight-reading is nice to be able to do, but it's far from essential. Reading music is the fundamental skill. There's nothing wrong with learning a work of music layer by layer, component by component. Indeed, complex contemporary music is often too difficult to sightread, even for the world's most skilled performers; they have to practice it bit by bit, just like you do for the music you play.

• If you're reading music properly, you don't see

.

What you see instead is

or

,

or, since we're talking about piano music,

or

.

These are visually distinct stimuli that happen to share some features; you seem to want the shared features to have more significance than they do, which is a form of misunderstanding the notation.

Are you aware of the concept of the grand staff? The upper and lower staffs of piano music can be conceived together as a single entity, with middle C lying in between them. This wouldn't be possible if, for example, the lower staff used the sub-bass clef, which has the same note pattern as the treble. (Now, admittedly, a lot of piano music doesn't treat the grand staff this way -- often putting the bass clef in the upper staff and the treble in the lower, sometimes both at the same time -- and I'm not much of a fan of it myself, generally preferring to regard the each staff as autonomous. Still, I have to admit to finding the notation in e.g. the second movement of Webern's Piano Variations, which has both upper and lower parts frequently changing clefs, somewhat awkward and confusing -- even though it's done for a specific purpose.)

You should, in any case, be able to play

with the right hand or

with the left.

• I suspect you simply don't read enough music to get in the habit of seeing the notation the way it's meant to be seen (and automatically knowing such things as how notes map under transposition). I also have a "highly trained" mind, and I don't have the difficulties you do, so the thesis of your post seems obviously false to me. In particular, I don't think you've made a convincing case that music is more difficult for amateurs who happen to be scientists than for other kinds of amateurs. If anything, I would (continue to) expect the musical literacy of scientists to be higher than that of the general population, on IQ/having-an-interesting-mind grounds alone.

• On enharmonically equivalent notes (e.g. E# and F), you say:

Yes, I know they're not really equal in most historical intonations, blah blah etc.

but it's not (primarily) a question of historical intonations. Being acoustically distinct is not a necessary condition for being musically distinct. It's a question of the "same" entity being conceived differently in different contexts. Homophones in language (two/to/too) are a close analogue: they might actually be pronounced differently in some dialects or some contexts, but even if they're pronounced the same, they're still different words. (I don't think this actually falls within the scope of your "blah blah etc.")