Monday, 12 March 2012


The spacecraft Pioneer 10 and Pioneer 11 were launched in the early 1970s and are drifting silently away from earth to this day. On the side of each probe is a small gold-anodised, aluminium plaque, six inches by nine depicting representations of the species - Homo sapiens - that built and launched them. The wonderful, whimsical idea, conceived by Carl Sagan, was that an alien intelligence discovering the probe in the far future could decipher the inscriptions and learn something of what we had been and hoped to become. What do you say to a hypothetical alien species using no more than 52 square inches of aluminium plate and how do you express yourself? A great question surely for A-level students of critical thinking. NASA's answer was to use the language of mathematics, which seems to be universal, and to provide a sort of Rosetta Stone in the form of depictions of the hydrogen atom (hydrogen is the commonest element in the universe) and a pulsar map. It also included drawings of a man and a woman, naked, provoking the utterly delicious criticism that NASA was using taxpayers' dollars to 'send smut to the stars' (note the censorship of the woman's genitalia).

Voyager I, launched in 1977 - later than the Pioneer craft - is further from earth than any other human artefact. It is currently approaching interstellar space, 120 times further from earth than earth is from the sun (that's 180, 000, 000, 000 kilometers or 4.28 kilometers for every dollar of net worth of Carlos Slim Helu, the richest man in the Solar System), and in 2014 will cross the heliopause, the theoretical boundary where the solar wind is balanced by whispers from elsewhere in the galaxy. Building on the Pioneer plaque, NASA included in each Voyager spaceship a disc encoding a few images of typical earth scenes (e.g. multicultural groups of well-fed children playing happily together) and a diverse selection of music from recent earth history. There's a lovely story (also attributed to Sagan) told about the late Douglas Adams. When he heard that a snatch of Bach's music had been considered for inclusion (and rejected) he said something like: 'don't you think that would have been showing off?'

The story may be apocryphal. It doesn't matter. It's trademark Douglas Adams in that it puts an explosive bullet through the center of parochialism's underdeveloped frontal lobes. The very finest Adams riff was a spontaneously delivered demolition of the hard anthropic principle, the vainest and most absurd of all our species's many parochial fantasies.

'... imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in, an interesting hole I find myself in, fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!' This is such a powerful idea that as the sun rises in the sky and the air heats up and as, gradually, the puddle gets smaller and smaller, it's still frantically hanging on to the notion that everything's going to be all right, because this world was meant to have him in it, was built to have him in it; so the moment he disappears catches him rather by surprise. I think this may be something we need to be on the watch out for.'

Douglas Adams is a hero of mine because he made me simultaneously acutely aware of my own insignificance and glad to be a relatively well-educated human being. The Hitchhiker's Guide to the Galaxy, I think it is fair to say, provides a sounder assessment of our species' importance ('mostly harmless') than all the creation stories of all our holy books combined. There's no point in rehearsing here the statistics that demonstrate our ephemerality (Sagan's 'Cosmos' does an unimpeachable job on this score but Monty Python makes the same point just as well, with added humour here).

Imagine you're a passenger on Voyager I, gazing back at Earth which is long-since irresolvable by your human eyes. Even the Sun is just a bright speck against the glorious galactic skyscape, like Venus viewed at dawn from the Atacama Desert back home. You've subscribed to a news digest service from Earth, just to keep in touch, and today's edition (a few hours out of date, for reasons that Einstein could probably have explained) contains an op-ed piece about this guy Rorty, who says that science and technology are just 'narratives', indistinguishable from other narratives about gods that make the sun rise each morning or devils who whisk away the souls of unbaptised children to an eternity of suffering in a hell beyond human imagining. Your eyebrows, frostbitten in the chill of interstellar space, rise a fraction of an inch (or should that be millimeter? it doesn't seem to matter out here) and you think 'but here I am, a few billion miles from home, thanks to the narrative that put me on top of a ten minute controlled explosion and launched me into space on a trajectory that took me via four gas giants and a few big rocks to this slightly lonely and very dark place. Could Huitzilopochtli really have brought me all this way? Or Jesus? He had some serious powers. Surely the Faculty of Social Studies at the Sorbonne could have designed a semiotic hermeneutics engine that could have propelled me at least this far on the crest of an immense wave of fart gas?

Sagan understood perfectly that the chances of an alien intelligence - if such exist - intercepting one of the Pioneer or Voyager probes is vanishingly small and that the messages were intended for human not alien audiences. Even if near-Earth interstellar space were littered with curious aliens, which it ain't, the chances of one of them noticing our toy rockets are miniscule. But let's just say that, in this, or a virtually identical parallel universe the unthinkable happened and the little green men happened upon Voyager I and decided to haul it into the cargo bay. What are the chances they'd be able to decipher and 'listen' to the recordings? What are the chances they'd appreciate Beethoven and Chuck Berry, both of whom made it onto the recordings, unlike Bach?

In the forgettable Monty Python movie 'Erik the Viking', Erik and his crew arrive at Hy-Brasil and are astonished to find it occupied by welcoming but musically incompetent people. This is funny because such a place could never exist, at least not on Earth. Why not? Because musicality is universally present in normal humans and hospitality to strangers is, if not universally absent, certainly not conspicuous by its presence in the tales and legends that have filtered down to us from prehistory. 

Human musicality is a genuine puzzle for evolutionary biologists. New born human babies have it; almost all adults (even those, like me, with a tin ear) have it; other primates appear not to; some birds might. Steven Pinker described music as 'auditory cheesecake', a super-stimulus that tickles pleasure centers that evolved for other reasons. He came in for a lot of criticism from people with a fine grasp of music but limited appreciation of the gaping holes in their own education (see here)1. The Dutch psychologist Henkjan Honing is also sceptical of Pinker's theory and has done some brilliant and fascinating research, which he summarises here, 16 minutes of unadulterated pleasure.

Music of course has an underlying mathematical structure. Sounds lacking rhythm are noise. An octave is the interval between two musical pitches that harmonise and it so happens that the ratio between the frequencies of corresponding pitches in successive octaves is 2:1. This pattern was discovered independently by many musical traditions long before the mathematical relationships were quantified. But the mathematics of music runs much deeper than this. In this article for example, Dmitri Tymoczko is quoted as claiming that 'When you are sitting at a piano, you are interacting with a very complicated geometry...In fact, composers in the early nineteenth century were already implicitly exploring such geometries through music that could not have been understood using the mathematics of the time...Just as a mountaineer will find that only a small number of all the possible routes between two points are actually negotiable, so musicians will have discovered empirically that their options are limited by the underlying shapes and structures of musical possibilities.'

The narrator of Jorge Luis Borges' novel The Library of Babel is a librarian in a vast hive of interlocking hexagonal rooms, each lined with bookshelves packed with books, each 410 pages long. The books appear to be randomly arranged on the shelves but the librarians have inferred that the library contains every permutation of a limited set of symbols, spaces and punctuation marks. Of course, almost all the books are gibberish or religious tracts but somewhere in the library there must exist improved versions of Shakespeare's plays, perfect predictions of the future and succinct, lucid explanations of true scientific theories not yet discovered. There are vastly many of these literary gems randomly scattered through the library but, because they represent a vanishingly small proportion of all the books, they cannot in practice be located. The librarians, unsurprisingly, go nuts.

There is a musical equivalent of the Library of Babel, a library containing all possible musical scores, of a certain length written with a small, finite number of symbols representing a restricted number of octaves, each divided into an arbitrary number of pitches, say twelve. Most of these scores, when played would be noise. A handful, however, would render Bach's sonatas banal by comparison. Unlike Borges' library, the 'musical' as opposed to noisy scores would run together like veins of ore in a lump of conglomerate. This is not just to say that these rivulets of music are the only scores in the library that could in principle be appreciated but that everything else isn't music, it's noise.

I do not begin to understand either the music or the mathematics underlying Tymoczko's analysis - so feel free to shoot me down - but it suggests the fascinating possibility that music might be a property of nature that humans in the course of our evolutionary history have not so much invented as discovered. Just as flying machines built by other civilisations on planets with gaseous atmospheres will operate using the same laws of aerodynamics that permit heavier-than-air flight on Earth, it is conceivable that intelligent denizens of another reasonably similar world (who will certainly have sense organs capable of interpreting sound waves) might have discovered some of the same pathways through the 'complicated geometry' of musical space. In other words, it is vanishingly improbable but just conceivable, that Chuck Berry could have another hit with 'Johnny B. Goode' on a different planet in another solar system in the far, far future. How cool is that?

1. As an aside, the following sentences from a review of The Music Instinct by Philip Ball, are as fine an example as you could wish for of complete gibberish I've read outside a holy book: 'We do not love music because it exercises our brains or makes us more attractive to members of the opposite sex, but because we have lived with it since we came into being: it is entwined in our common and individual consciousness to the extent that, simply put, we would not be ourselves without it. In contemplating the mysteries of music we are also thereby contemplating the mystery of ourselves.' This half-wit wants so badly that music be mysterious, he is prepared to bury all evidence to the contrary, while his audience watches him dig his own intellectual grave.

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