Archive for the ‘Philosophy’ Category

Aristoxenus

Tue 5th Jul 11

I read this in the Smog Blog: “But the fact is, if you go to blogs like WattsUpWithThat or Climate Audit, you certainly don’t find scientific and mathematical illiterates doubting climate change. Rather, you find scientific and mathematical sophisticates itching to blow holes in each new study.”

A bell rang in my head. This is the same treatment that Aristoxenus got.

Aristoxenus was the earliest proponent of the theory of equal temperament in music. He was a pupil of Aristotle and the son of a professional musician. He was a competent musician himself, and his musical theory was endorsed by J. S. Bach and has been the standard ever since. All electronic tuners give equal temperament by default, and 99% (say, probably more) of bands, orchestras and solo performers in the western world use it.

The theory divides the musical octave into twelve pitches by equal steps: the seven white and five black notes on the piano keyboard, that repeat the same pattern from bass to treble. Indian, Turkish, and other traditions use more, smaller steps. We needn’t go into the small details here, but if you are intrigued then look at my article on temperament in h2g2.

The odd thing is that between Aristoxenus proposing the theory and Bach accepting it was a gap of two thousand years, during which the system was rejected by musical theorists on mathematical grounds. That’s a long time in the wilderness.

The trouble is that the maths doesn’t quite add up: equal temperament is an approximation. Pythagoras had famously established the physical relation between sound-producing bodies (strings, pipes, bells) and their size, weight, and tension. To sound an octave lower, one string must be twice as long as another of the same material, thickness and tension. To sound a perfect fifth lower, it must be 1.5 times as long, and to sound a major third lower it must be 1.25 times as long.

A compromise must be reached, or else a discord must be tolerated, when you tune a harp to the notes A, B, C, D, E, F, G. If your A is a major third above your F, and your F is a perfect fifth below your C, and your C and G and D are also tuned to perfect fifths, then your D will not be a perfect fifth from your A. You have enough figures above to work out by how much, if you are handy with a calculator (though a pen and paper is all you need). To keep the figures manageable you will have to multiply or divide by two here and there: this keeps the notes unaltered, since twice C or half C gives an octave, still C.

This compromise is simply achieved: spread out the discrepancy throughout all the intervals, so that none but the octaves are pure fractions, but all are bearably close. The brain decoding the vibrations in the air categorises something close to a major third so that we ‘hear it as’ a major third. This ‘hearing-as’ is the miracle of perception; not a simple thing, as brain-circuit diagrams show us, but a capacity we inherit at birth and without which we could not live.

Aristoxenus was the first to challenge the mathematical theory of Pythagoras: while Pythagoras claimed that the perfection of music was its mathematical purity, Aristoxenus claimed that the ear, not the measuring tape, is the proper judge of musical excellence.

What’s wrong with that?

He gave a lecture, which has been transcribed, demonstrating his theory. Having gone through a number of transpositions, he arrived at an outlandish interval, what we might call in modern notation E-flat to G-sharp. Then he said: “Is this a perfect interval? We should let our ear decide.”

To let the ear decide, he must have been tuning things—strings, probably, as they are easiest—as he went along. And to arrive at a perfect interval (tuning his G-sharp the same as A-flat) he must have been tempering the intervals all along. The point of the demonstration was that his listeners couldn’t tell that each perfect fifth he tuned was a tiny bit defective. They ‘heard them as’ perfect fifths.

For two millennia Aristoxenus was disrespected and his theory rejected. A century before Bach, the organist and composer Frescobaldi recommended equal temperament, but, apart from the theoreticians’ distaste for compromise, it was found awkward to tune keyboards in equal steps; they hadn’t hit on the system that organ and piano tuners now use, counting the beats. In the meantime (it seems) lutes and other fretted instruments had been tuned to equal temperament for centuries, since it is actually quite easy to set frets proportionately by eye.

The ancient and medieval theorists rejected equal temperament because their calculations showed (rightly) that it was not a hundred per cent accurate in placing the intervals. It took two thousand years for theorists (led by Rameau) to admit that the discrepancies in the maths were not really so significant in perception; human judgement is satisfied with ninety-nine per cent, and often very much less.

Cavillers. Hair splitters. Look at the big picture.

Dan Dennett

Fri 18th Mar 11


I met Dan Dennett in January. He came to Dublin to speak on the theme ‘Taking the place of religion’. A crowd of maybe four hundred turned up at some expense, and he had a warm reception. He spoke for an hour and took questions for another hour. At the question time only one speaker introduced himself as ‘a believer’, and he then admitted he hadn’t heard the talk, he had come in late just to put his question. I can’t remember what it was, but he must have been disappointed by the mild answer he got.

I like Dennett’s writing, particularly his books ‘Darwin’s Dangerous Idea’ and ‘Freedom Evolves’. Although he is a professor of philosophy he refuses to write in jargon.

I wrote him an email last year thanking him for his elegant unravelling of the free-will problem. The puzzle is this:

Do we have free will, or is everything that happens completely determined?

An example of determinism is the rubber balls bouncing around in a lotto machine. Each ball can only go where physics dictates, according to its individual elasticity and the forces it meets. None of this is random; quantum indeterminacy (or any spontaneous quirk at all) is irrelevant; all that is required is that the bouncing is sufficiently complex to make the order the balls will end up in unpredictable in practice.

So the answer? Yes, we have free will in the sense that we can and do choose things with great discrimination, but also yes, everything that happens (including our choices!) is completely determined by what went before.

It’s a false dichotomy; we are freer than rubber balls because we have greatly superior elasticity, and respond to subtler forces. If you don’t find my description convincing, read the book.

Or just read this, which puts it more succinctly:

(An illustration I stumbled upon)

He replied to my email, thanking me for my poem, and also to another one I sent after booking for his Dublin event. Michael and I arrived very early for the talk, to get the best seats, and there was Dan having his cup of tea, so I sat next to him and we discussed Nabokov, an author we both admire. Very approachable and benign, he is a dead ringer for Santa Claus, even more than I am myself.

The talk was interesting and very well presented, though virtually all of the content was familiar from his books, particularly ‘Breaking the Spell’. His new book comes out this month, dealing with humour. Not sure how I’ll like that; it’s OK to go dissecting religion, but humour? We’ll see.

If there was a slightly anodyne feeling by the end, perhaps it is accounted for by Dennett’s own self-description. “Religious people prefer dealing with Dawkins” he said. “I approach them with Marquess of Queensberry rules and [mimics dodging and sparring] while Dawkins just goes [piledriver punch] and they like that better!”

It seems to me that the question of what will replace religion if (as he hopes) it is indeed on its way out is hardly one that a single person or group can have within their competence; they can only hope the butterfly-wing effect picks them up and amplifies their movement. It seems likely that religion will go on being replaced by more religion; as Wittgenstein said,

All that philosophy can do is to destroy idols. And that means not making any new ones—say out of the ‘absence of idols’

—but it seems to be a strong instinct in humans to replace rather than simply ditch such things. Religions have very strong anti-trampling routines built in; they seem to thrive well under oppression. Pruning toughens them up. One ploy the defenders of religions use is to assert that atheism is a religion. I took part in a discussion on h2g2 that invited endings to the sentence “If atheism is a religion then . . .” My best ending was “vegetarians just eat different animals”.

Meditation is fine without belief, as an exercise in aligning yourself—tuning to the music of what happens. Prayer is like a bicycle helmet: it’s OK to wear one, but not a good idea to believe it will save you. But Dennett specifically does not address revisions of religion; his beef is with those who revise while pretending that they are preserving the original model, such as Pastor Rick Warren.

Anyway, despite its excellence, I’m sure Dennett would be the first to admit that his idea—that TED could provide a focus for some of the good bits of religious practice, the parts that are worth preserving—is a wee bit, how should I put it, aspirational.

The grammar of lying

Thu 29th Jul 10

If you have promised to do something while never intending to do it at all, but then in fact you do it, were you lying or not when you gave the promise?

I read a newspaper article many years ago, recounting a job interview. The writer had answered ‘yes’ to the question

Would you be prepared to bend the truth for the sake of the Corporation?

while keeping a mental reservation to the effect that, in the event, he would not lie, even if the company asked him to.

He wasn’t hired, but some time later he realised that although he thought he had given a deliberately false answer in the interview, in fact he had told the truth. He was prepared to lie, in order to get the job.

Epicurus

Wed 30th Dec 09

Malachy gave me a perfect holiday book: The QI Book of the Dead, a collection of facts and scandal about historical persons. I love the portrait of Epicurus, and the big-minded Ben Franklin.

Epicurus, the book tells us, has the reputation ‘as the high priest of high living and sensuous pleasure, the philosopher of the debauchee and the gourmand. Except that he wasn’t. So far from indulging in orgies and banquets, Epicurus lived on barley bread and fruit, with cheese as a special treat only on feast days. … But Epicurus had the misfortune to live in the highly competitive golden age of Greek philosophy, where he found himself up against the Academy founded by Plato, and the porch (stoa) of the Stoics: both articulate and well-organised opponents. The mud they slung at him over two millennia ago has stuck firm.’

Which deserves to be preserved in an epigram:

To have a bad reputation is to have influential enemies.

A Christmas thought: if the Magi saw and followed ‘a star in the east’ then they came from the west. They may have been from a sect of Platonists disenchanted with the way the Academy’s teaching had descended into nihilism—

I went to university
Studied Greek philosophy
And all that it taught me was there’s nothing to know
But that knowing you know nothing, well that’s knowing something too.

In my fantasy these wise men came east looking for a newborn child to take on the mantle of Socrates, a moral model and innocent victim condemned to death by the state he sought to reform. Socrates (as reported by Plato) had improved on previous moral teachers by urging kindness to enemies simply because treating everyone positively is the right thing to do—something Jesus certainly passed on. The Proverbs of Solomon had said that doing good to your enemy will ‘heap coals of fire upon his head’, and this vengeful prospect was reiterated some centuries after Socrates by a professed Christian (Romans 12:20). Perhaps St Paul didn’t quite get the message.

Hence my take on Christianity and Christmas:

He doesn’t really go with Christmas trees,
This younger, more attractive Socrates—
A sobering memento hung on wood:
See, children, what you get for being good.

I had what may best be called an Epicurean thought (I saw it then as more like Diogenes, another philosopher with influential enemies who have given his school, the Cynics, an even worse name than the Epicureans) on one of my long cycles with Michael. I was approaching the age of sixty and wanted to prepare myself for old age: what should my priorities be? I came up with:

Be less
Do less
Have less
Get out more

My new year’s resolution.


Homan Potterton

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