It’s common for Americans to discuss where we were when we heard the news on the morning of September 11th, 2001. It’s a question you’re expected to be able to answer: it was the defining moment of our age. None of us would be expected to know someone else’s whereabouts too (unless you’re the sort of person who “checks in” with their family), but there is one significant exception.

On the morning of September 11th, 2001, George W. Bush was in Florida. Presidents travel a lot, and I don’t know the reason was for this trip. But I know that he visited an elementary school and read a particular children’s book.

What a moment for W, who did not graduate at the top of his class, and was planning on clearing brush for the rest of term, to have the eyes of the world upon him: with his derrier crammed into a tiny plastic chair. Not cutting a ribbon on a bridge, or speaking to a crowd at a college football stadium, or deep in consultation with captains of industry, as he might well have done the day before. No, when the cosmic bell rang, and the shutters of the cameras of immortality began recording his every move, W was toddling with tykes.

While I enjoy a bit of parapolitics from time to time, any suggestion of an intentional connection between the two events is clearly absurd. It is pure coincidence, beyond his or his adversaries’ control. The only remarkable feature the two events share is their synchronicity: they co-incided, their incidents occurred together.

Except one of the events happened to be 9/11.

9/11 is such a powerful date, it makes one’s actions important simply by association. People ask each other about 9/11 because coincidence is significant and meaningful. Where were you? If the answer is “in bed with two stewardesses”, chances are you’re a quite different sort of fellow than the one who answers “in bed”. And while he did rally initally, speaking at Ground Zero, as his presidency wore on, we learned that coincidence was in fact a precedent: the decider choked on a pretzel, fell off a segway, and most unkindly, was tricked into prosecuting a war under false pretenses.

You might still want to have a beer with him – that’s what won him a second term and kind(er) feelings on the way out. But despite Karl Rove’s career trying to turn him into “Maverick” from Top Gun, god bless him, he just comes off as kinda dopey. And it runs in the family too – remember his dad, despite being a distinguished WWII vet, was perceived as a wimp (and whined about having to eat broccoli and threw up on the Japanese Prime Minister).

This is fate. In the age of mass communication we call it “public image”, but there is no difference. You are cursed to be a buffoon on the eternal stage? Then there is no avoiding it, it is your destiny. The camera may add twenty pounds, but synchronicity never lies.

Staff notation, the Western system of writing music, was developed in Medieval Europe. In those early days of literacy, music still had no common language. Musicians primarily learned their local style of music from… local musicians, and only the chants in church needed to be noted.

But the notes were imprecise, and limited by ethnic and regional differences. Staff was developed as a proto-scientific way to describe music. And it succeeded brilliantly, blossoming into the whole symphonic culture of Modern Europe. But it also reflects the limitations of the time.

Tuning could be established independently using a metallic fork, but there would be no accurate metronomes for hundreds of years. Without an absolute measure to go by, the creators of the system were forced to use relative measurements, specifying tempos somewhere on a scale between ‘very very fast’ and ‘very very slow’.

Without an absolute measure like pitch, rhythm in staff had to be relative as well, and so it gains precision in fractionally smaller units. An eighth note (one tail) is twice as long as a sixteenth note (two tails). The duration that falls halfway between those, which would be equivalent to a twelfth note, can be indicated by adding a dot to the eighth note. Any level of precision desired can be achieved simply by using a higher fraction.

But there is no such thing as a twelfth note. Even if your rhythm repeats over three or five or six beats, those beats are either “half” or “quarter” or “eighth” notes. It’s a symmetrical, binary, dichotomous way of describing music.

This is not just a semantic difference. The Afro-Cuban tradition that blues (and its children, jazz, rock, and pop) draws its rhythmic complexity from can’t easily be flattened this way. These polyrhythmic types of music often share repetition points at seemingly arbitrary ratios, like 3:4, 5:4 or 7:8. Following the rules to notate rhythms like these results in forests of dots and slashes.

The first time I saw Tinariwen, at the Museum Of Fine Arts here in Boston, their hype man started exhorting the crowd to clap along at the beginning of “Ahimana”. I was sure we were in for a participatory trainwreck. That song has one of the nastiest 3/4 polyrhythms I’ve ever heard, and the crowd – equal parts blue-hair museum members and blue-hair rock dudes – was going to come profoundly unglued in the interference pattern at the first turnaround.

But once he had the crowd’s attention, his dance changed. Three claps and a slow gesture – four beats in total – extending the arm in front of the chest and then drifting out to the side. His arm and fingertips had that unmistakably Arabic pose, but the meaning was clear as when The Temptations did it: it means “wait”, “hang on this beat”.

Musically, this rest had the effect of relieving the crowd from handling the subtle, asymmetrical fraction left over where his four-beat and other musicians’ three-beat rhythms overlapped. The 4/4 pattern implied by making one beat into a rest reduces the complexity – beyond accessible, or even intuitive, to primitive. A child could learn that rhythm.

The gesture is a shibboleth, secret knowledge that one obtains only by spending time in a community. If you spent hours listening to and learning to play Malian music, you’d slowly absorb these rhythms until they were in your bones. But with that secret key, even non-musicians can learn the rhythm instantly, and pass it on to others.

It’s a social, pre-literate, casual way of describing music, but no less accurate.

I played the Malian band Tinariwen for a friend of mine who has the gift of pith. After listening to a few songs, he commented that the tension established by the overlapping rhythms was like the banging of the pots and pans on a donkey’s back as it sways up a mountain pass.

The Malians are desert nomads, so the description might not be factually accurate. But it represents a truth about swing music: it is a shibboleth, a secret sign of occult knowledge. The complexity of the rhythms was honed on long journeys, and long camp nights. It has a generosity of time; time has been lavished upon it, because only hundreds of years of cumulative human persistence can produce something that beautiful.

Learning how to play Malian or Jamaican or Italian rhythms takes time, simply because it took time to write them. The history of the people is encoded inside the music. To understand it, you have to undertake a journey yourself.

One of the benefits of living in Boston is access to frequent (free!) lectures at the colleges. A few years ago I caught a lecture – conveniently timed to coincide with the Marathon – by a professor of kinesthesiology on the evolution of running.

Turns out running is a uniquely human gait; in the way our legs store energy in the Achilles tendon, the closest equivalent is probably the kangaroo. Combined with another human innovation, sweating, no other animal can cover large amounts of distance at a constant pace like a human being.

I’ve always wondered how humans became such successful predators, given the astounding strength and speed and armament of the rest of the animal kingdom, and the professor’s exaltation of humans’ dominance in slow and moist travel wasn’t doing a lot to convince me, until he got onto persistence hunting.

Every animal in the world can beat a human in a foot race – over their distance of choice. But on the flat grass plains of Africa where our ancestors evolved, daytime temperatures often exceed 110 degrees. Hunters would jog – at what today would be considered an amateur rate – in pursuit of a much larger animal as it sprinted away from them. But soon the animal, with its thick fur coat, would have to stop to cool down. The hunters jog, and the prey flees and rests and flees. Finally, it can’t flee again, and they easily dispatch it.

I loved the phrase as soon as I heard it. Persistence fed us in a hostile environment, and shaped our bodies into their modern form. It literally made us who we are.

Open every link on this page, and open every link on those pages, and the pages after that.

This is recursion. Our minds boggle at both the scale and also the speed with which it is generated.

The vertigo isn’t cosmic though, it’s physical: the sensation of some specialized piece of hardware in your mind consuming all available resources, the conscious equivalent of your laptop’s fan blasting on.

It’s a familiar sensation. We understand recursion intuitively in the branching of a tree, or the infinity captured in two mirrors.

“All technology is an extension of the body.” Marshall McLuhan

Recursion is the extension of our persistent restlessness, the obsession of cataloging and exploration.