Friday, October 26, 2012

A Turing Machine is a Nightingale

The medieval streets of Cambridge are haunted by the ghosts of all the great minds who’ve called the town home over the centuries—and so are the poems of Göran Printz-Påhlson.  He, too, called Cambridge home, and met many of the luminaries (most notably the titular character of the poem “My Interview with I.A. Richards”).  Some of the early innovators of what became computer technology were Cambridge men, and Printz-Påhlson has a particular fondness for them: Charles Babbage, for example, strides through a Printz-Påhlson poem, as does Alan Turing.  In fact, Printz-Påhlson has a poem called “Turing Machine,” after the hypothetical tape-driven, algorithm-crunching machines Turning dreamed up in the 1930s.

The poem begins with what may seem like the most un-Romantic of subjects: the algorithms that inhabit Turing’s machines.  But by the end of the poem, we’ve twisted around until we’re in the same territory as that quintessential Romantic lyric, Keats’ “Ode to a Nightingale.”  Here’s how Printz-Påhlson’s poem begins:

It’s their humility we can never imitate,
obsequious servants of more durable material:
they live in complex relays of electric circuits.

Rapidity, docility is their advantage.
You may ask: “What is 2 times 2?”  Or “Are you a machine?”
   They answer or
refuse to answer, all according to demand.

From here, we move to more complex types of machines, and more complex operations—including recursive functions, which reference and replicate themselves:

It is, however, true that other kinds of machines exist,
more abstract automata, stolidly intrepid and
eating their tape in mathematical formulae.

They imitate within the language. In infinite
paragraph loops, further and further back in their retreat
    towards more subtle
algorithms, in pursuit of more recursive functions.

So far, it’s all very reminiscent of math class, and unless you’re the type who sees the beauty in mathematical formulae, you’re probably not jumping out of your seat in excitement.  You’re certainly not anticipating a turn toward anything John Keats may have found interesting.  But then there’s this:

They appear consistent and yet auto-descriptive.
As when a man, pressing a hand-mirror straight to his nose,
    facing the mirror,
sees in due succession the same picture repeated

in a sad, shrinking, darkening corridor of glass.
That’s a Gödel-theorem fully as good as any.
    Looking at infinity,
but never getting to see his own face.

The reference is to Gödel’s incompleteness theorems, which tell us that no system of axioms that can be listed by a computer is capable of demonstrating its own consistency.  That is: the system, no matter how elaborate or recursive, no matter how much such a system can reveal, no matter how far it can take us, it can’t turn around and show us itself in its own consistent nature.  It’s terribly abstract, of course, especially to those of us who haven’t done any math more complicated than that which a tax form requires for many years.  But then we get something the poem’s been daringly light on so far: an image.  The image of a mirror, held close to another mirror and aimed at just the right angle, reflecting itself forever in a kind of trippy, curving infinity of recursion.  I remember when, as a kid, I discovered that I could line my mother’s hand mirror up against the bathroom mirror like this, and how I’d try to like the mirror up so I could see all the way to forever, which, it turns out, you can’t quite do.  Printz-Påhlson juxtaposes this image with that of a mirror in which we gaze on our own face, and notes that we can only have one or the other—an image of infinity, or an image of ourselves.

Here, at last, is where we tread on very Romantic ground: this business of infinity and the self comes straight out of the playbook of Romanticism, and is embodied most powerfully in Keats’ great “Ode to a Nightingale.”  The ode begins with a speaker—let’s just call him Keats—listening to the song of a nightingale hidden in the woods, and drifting off into a kind of narcoleptic state as he listens.  He begins to lose himself, hovering between wakefulness and sleep, until he senses himself disappearing as an individual, and merging into an unconscious state much like death (the ultimate end of the division between the self and the other):

Darkling I listen; and, for many a time

  I have been half in love with easeful Death,

Call'd him soft names in many a musèd rhyme,

  To take into the air my quiet breath;

Now more than ever seems it rich to die,
  To cease upon the midnight with no pain,

    While thou art pouring forth thy soul abroad

          In such an ecstasy!

  Still wouldst thou sing, and I have ears in vain—

    To thy high requiem become a sod.

The next stanza tells us how the individuality of the bird is lost in the timelessness of its song, which is the same for all nightingales everywhere and always. An ornithologist pal once told me that this is, in fact, false: that birds have regional accents, and that their songs evolve over time, so we might have to file “Ode to a Nightingale” with Keats’ “On First Looking into Chapman’s Homer,” where he gets his explorers wrong and Cortez when he means Balboa, as a Keatsian fact-blunder.  But who cares?  In the context of the poem, the point is clear enough:

Thou wast not born for death, immortal Bird!

  No hungry generations tread thee down;

The voice I hear this passing night was heard

  In ancient days by emperor and clown:

Perhaps the self-same song that found a path

  Through the sad heart of Ruth, when, sick for home,

    She stood in tears amid the alien corn;

          The same that ofttimes hath

  Charm'd magic casements, opening on the foam

    Of perilous seas, in faery lands forlorn.

But this drawing away from selfhood toward the infinite doesn’t last: that word “forlorn” reminds Keats of his own little selfhood, and he recoils from identification with the infinite:

Forlorn! the very word is like a bell

  To toll me back from thee to my sole self!

Adieu! the fancy cannot cheat so well

  As she is famed to do, deceiving elf.

Adieu! adieu! thy plaintive anthem fades

  Past the near meadows, over the still stream,

    Up the hill-side; and now 'tis buried deep

          In the next valley-glades:

The final two lines of the poem are really wonderful, leaving us in a state where we can’t decide what is real and what is a dream:

  Was it a vision, or a waking dream?

    Fled is that music:—do I wake or sleep?

Are we little individuals who only dream we can vanish and become one with something infinite?  Or is our sense of identity illusory, a brief dream between the infinities of non-selfhood that precede and follow our deaths?  Keats leaves it there, with no searching after certainty.  We can have our sense of identity, or we can have the mystical union with the infinite, but we can’t have them both at the same time.

And this is the same place Printz-Påhlson leaves us in his much more austere, cerebral poem: with the mirror reflecting itself forever, without us; or with the mirror reflecting us, whole, with no infinite recursion of reflections.  A Turing machine is many things: a grand thought experiment, a model for computer technology, a meditation on the limits of mechanical computation and, in this particular case, a nightingale.