A friend today sent me this picture from the Boston Museum of Science. It’s especially funny to me, because I have formal education in both mathematics and philosophy. And anyone who’s read Plato’s Republic is bound to think it odd.

It’s odd because Plato’s good society, the republic, requires its citizens to study mathematics for ten years. So it’s not like Plato takes math lightly. This quotation arises during Socrates’ and Glaucon’s conversation about education (the character of Socrates speaks in the first person).

[Socrates:] Now, when all these studies reach the point of inter-communion and connection with one another, and come to be considered in their mutual affinities, then, I think, but not till then, will the pursuit of them have a value for our objects; otherwise there is no profit in them.

[Glaucon:] I suspect so; but you are speaking, Socrates, of a vast work.

What do you mean? I said; the prelude or what? Do you not know that all this is but the prelude to the actual strain which we have to learn? For you surely would not regard the skilled mathematician as a dialectician?

Assuredly not, he said; I have hardly ever known a mathematician who was capable of reasoning.

But do you imagine that men who are unable to give and take a reason will have the knowledge which we require of them?

Neither can this be supposed.

Source: Republic 531e, translated by B. Jowett

Jowett translated the Republic in the 19th Century, so having entered the public domain it’s well-distributed, if perhaps not as clear as it could be. Here are the same lines from a couple of other translations:

Surely you would not regard experts in mathematics as masters of dialectic.

Certainly not, except a very few of those I have met.

trans. F.M. Cornford

‘The subjects we’ve described are only a prelude to the main theme we have to learn. For you don’t think that people who are good at them are skilled in dialectic, do you?’

‘Heavens, no, though I have come across a few exceptions.’

trans. Desmond Lee

When Jowett’s translation talks about being “capable of reasoning,” it’s referring to “dialectic,” which for Plato is a special way of reasoning, not just reasoning in general. “Dialectic” is the capstone of Plato’s proposed education; after training in it for five years, the leaders of his republic should begin to understand philosophical issues.

So we can let mathematicians off the hook a little bit: Plato’s not saying they’re unreasonable, just that they generally haven’t achieved the heights of thinking made available by dialectic. Why this is so comes out a little bit later in the next book:

The detached studies in which they were educated as children will now be brought together in a comprehensive view of their connexions with one another and with reality.

Certainly that is the only kind of knowledge which takes firm root in the mind.

Yes, and the chief test of a natural gift for Dialectic, which is the same thing as the ability to see the connexions of things.
…
When they reach thirty they will be promoted to still higher privileges and tested by the power of Dialectic, to see which can dispense with sight and the other senses and follow truth into the region of pure reality.

Source: Republic 537, trans. Cornford

In other words, dialectic brings everything together. Referring to his famous allegory of the cave, Plato is saying that dialectic is like the last step, where the former prisoners are no longer seeing shadows or indirect images, but are looking at the “sun” of truth. The problem with mathematics by itself is that it doesn’t provide the big picture; it’s limited to a particular discipline, so it’s merely a shadow of the form of the Good.

I decided to track down this supposed Plato quotation and found the following in A History of Western Music:

Furthermore, the foundations of music once established must not be changed, for lawlessness in art and education inevitably leads to licence in manners and anarchy in society. For Plato the saying “Let me make the songs of a nation and I care not who makes its laws” would have expressed a political maxim; more than that, it would have been a pun, as the word nomos, with the general meaning of “custom” or “law,” was used also to designate the melodic patterns of a certain type of lyric song.

Grout, Donald J. A History of Western Music, 1973. p. 8

Notice the ambiguous “would have”: “For Plato the saying . . . would have expressed a political maxim.” It is possible that Grout could have used “would have” in the sense of “did,” but none of the footnotes near the quotation (there is none for the quotation itself) points to such a passage. In fact, the relevant passages in the footnotes—from Plato’s Laws—actually seem to support the converse: Plato wants law to control the music. But somewhere along the line an ambitious musical-political theorist made it through page eight of A History and decided to resolve the ambiguity in his own favor.

“Suppose a man was in charge of a large and powerful animal, and made a study of its moods and wants; he would learn when to approach and handle it, when and why it was especially savage or gentle, what the different noises it made meant, and what tone of voice to use to soothe or annoy it. All this he might learn by long experience and familiarity, and then call it a science, and reduce it to a system and set up to teach it. But he would not really know which of the creature’s tastes and desires was admirable or shameful, good or bad, right or wrong; he would simply use the terms on the basis of its reactions calling what pleased it good, what annoyed it bad. He would have no rational account to give of them, but would call the inevitable demands of the animal’s nature right and admirable, remaining quite blind to the real nature of and difference between inevitability and goodness, and quite unable to tell anyone else what it was. he would make a queer sort of teacher, wouldn’t he?”

“Very queer.”

“But is there really any difference between him and the man who thinks that the knowledge of the passions and pleasure of the mass of the common people is a science, whether he be painter, musician, or politician? If he keeps such company, and submits his poems or other productions, or his public services, to its judgment, he is going out of this way to make the public his master and to subject himself to the fatal necessity of producing only what it approves.”

Republic 493

Currently, encryption is based largely on complex numerical codes that even the most sophisticated computers would, theoretically, fail to break.

But Lo says these numeric codes could be broken in the future with new mathematical theorems.

As a fundamental law of nature, however, quantum uncertainty will never be changed, and will never become obsolete.

At great risk of arrest, I took this picture on the subway tonight.

But the question is, can it pay the bills?

Some classical music is enjoyable.
Some concertos are not enjoyable.
Therefore, some concertos are not classical music.

This is an invalid syllogism, so it can’t be “sound,” because a “sound” syllogism is one that is valid and has true premises. But that didn’t stop numerous students who went on to evaluate the truth of the premises.

Here’s what surprised me: quite a few concluded that this was an unsound syllogism, because the first premise is false. In other words, they believe that no classical music is enjoyable, and they said so directly in their explanations.

They’ve never enjoyed a piece of classical music? That’s like saying you’ve never been in love or never laughed. It reminded me of a passage from a book that influenced me when I was a freshman in college, written about college students twenty years ago: Allan Bloom’s The Closing of the American Mind.

The power of music in the soul—described to Jessica marvelously by Lorenzo in the Merchant of Venice—has been recovered after a long period of desuetude. And it is rock music alone that has effected this restoration. Classical music is dead among the young. This assertion will, I know, be hotly disputed by many who, unwilling to admit tidal changes, can point to the proliferation on campuses of classes in classical music appreciation and practice, as well as performance groups of all kinds. Their presence is undeniable, but they involve not more than 5 to 10 percent of the students. Classical music is now a special taste, like Greek language or pre-Columbian archeology, not a common culture of reciprocal communication and psychological shorthand. Thirty years ago, most middle-class families made some of the old European music a part of the home, partly because they like it, partly because they thought it was good for the kids. University students usually had some early emotive association with Beethoven, Chopin and Brahms, which was a permanent part of their makeup and to which they were likely to respond throughout their lives. This was probably the only regularly recognizable class distinction between educated and uneducated in America. Many, or even most, of the young people of that generation also swung with Benny Goodman, but with an element of self-consciousness—to be hip, to prove they weren’t snobs, to show solidarity with the democratic ideal of a pop culture out of which would grow a new high culture. So there remained a class distinction between high and low, although private taste was beginning to create doubts about whether one really like the high very much. But all that has changed. Rock music is as unquestioned and unproblematic as the air the students breathe, and very few have any acquaintance at all with classical music. This is a constant surprise to me. And one of the strange aspects of my relations with good students I come to know well is that I frequently introduce them to Mozart. This is a pleasure for me, inasmuch as it is always pleasant to give people gifts that please them. It is interesting to see whether and in what ways their studies are complemented by such music. But this is something utterly new to me as a teacher; formerly my students usually knew much more classical music than I did.

The Closing of the American Mind page 69

Everything

Everything—
a bumptious, stuck-up word.
It should be written in quotes.
It pretends to miss nothing,
to gather, hold, contain, and have.
While all the while it’s just
a shred of a gale.

—Wislawa Szymborska

And Prof. R. had this to say last week: “Habermas is a gasbag, and Derrida was either insane or a charlatan.” Further evidence that R. is the right man to help us navigate Hegel.

They describe it as pretty neat as well as being scientifically interesting, and useful. After listening to some compositions and creating a few random ones myself, I must agree that it is. And anyone who has listen [sic] to the radio the last few years could certainly use some unique music.

Scientifically interesting, maybe. But after playing around with it, the best “compositions” I heard could hardly rival Muzak. Curiously, the site’s FAQ has a comment about “meaning”:

Can WolframTones compositions have meaning?

That’s a complicated philosophical question. There’s some discussion of meaning in the computational universe in A New Kind of Science. It’s probably fair to say that objects in the computational universe–and WolframTones compositions–develop meaning as they get connected to other things. In some ways WolframTones compositions are like objects in nature: their features emerge from specified underlying rules. So if the form of a sunset, a tree, or a mollusc shell is meaningful, then so can a WolframTones composition be.

Right. And that’s why rule-generated music is unlikely to mean much to its listeners–you’ve eliminated half of the human component in the communication process. It’s more like the sound of a babbling brook than a symphony.

While it’s true that human musicians incorporate rules into their compositions, they do so reflexively, so that various parts of the piece respond to other parts of the piece. The composer responds to and adjusts the music according to how it achieves certain criteria (such as beauty), criteria that are difficult to make into algorithms. When the computer is aware of how its composition makes it feel and changes the piece accordingly, then we’ll be getting somewhere.

Now if only I could keep that same excitement into early November, when papers will really start weighing down on me. I guess nothing gold can stay.