December 94 - THE VETERAN NEOPHYTE
THE VETERAN NEOPHYTE
Nothing Comes From Nothing
Take a good look around at all the different structures you see in the world. Not only the physical
structures, like buildings and mountains and dogs and trees, but the conceptual structures, like
language and government and the Dewey decimal system and the management hierarchy at your
place of work. Some of these structures seem to exist independently of humans, but others seem to be
completely invented, made up from whole cloth, so to speak. But how can that be? Can you really
create something from nothing? I wonder.
I just got back from a sort of educational/recreational summer camp for adults (I'm writing this in
early August). It was the California Coast Music Camp, a week of intensive classes and refreshing
musical single-mindedness. There were no cars, no computers, no worries -- nothing to do but play
and sing and learn (and swim and eat and hike).
The camp itself was classic: squat brown bunkhouses scattered in small groups like big hollow dice;
long low latrines, redolent with that cloyingly sweet chemical peculiar to outdoor bathrooms;
enormous vats of jello and drowned salad at the ends of the long serving tables in the echoing dining
hall; bug bites, bug spray, and bugs -- you get the idea. And even though it was strictly adults, all the
same feelings I remember from my one camp experience as a kid were there in the wide and ragged
spectrum of emotions it generated. I had the same scary and uncertain feelings at the beginning,
wondering if I really should be there at all; the same gradual discovery that it was all OK, and in fact
was fantastic; and, at the end, the same bittersweet longing to start it all over again.
Music really is a lovely thing. One of the classes I took was called "Theory, Scales, and Chord
Construction on the Guitar" and it was on the third day of class, as I was plunking away at yet
another arpeggio, that I began to get my first glimpse of the underlying structure of the notes on the
guitar fretboard. (And I do mean glimpse: it's something that will probably take a year or more to see
clearly, and five or ten years to really feel -- and that's if I practice every day.) I was suddenly struck
by the notion that it's the discontinuities in musical scales that make them both difficult and
interesting, that it's the complications in the structure of music that give it an interesting shape. If
you've ever taken a music theory class, or even a piano class, you might know what I mean: if only
there were a black key between every pair of white keys, things would be much simpler. It's that
damned half step between B and C and between E and F that screws things up. But it also seems that
those discontinuities -- those bumps and dips in an otherwise smooth, even progression -- are what
give rise to all the beauty and complexity and subtlety. It's precisely those "flaws" in the structure
that lend it an interesting texture.
However, the structure itself is artificial. Underneath, the range of musical tones is actually
any slide whistle demonstrates. It's a spectrum, a continuously varying quantity, in this case the
frequency of vibration of a material. So the set of notes we use -- our tuning system -- is externally
applied, a necessarily arbitrary set of discrete slots pasted onto an underlying continuum. It's a sort ofquantization of something inherently smooth that lends it a tractable structure, that gives us a handle
with which to manipulate it and a context in which to make sense of it. By conceptually making the
smoothly varying curve into a step function, by arbitrarily chopping the continuous line into discrete
chunks, we can somehow work with it more manageably and think about it more clearly.
If you look around a little, you'll find examples of this kind of artificial structuring of continuums all
over the place. The computer in front of you (or wherever it is) is an excellent example. Many early
computers were analog; they dealt with smoothly varying quantities (usually voltages in circuits). But
they turned out to be too hard to program -- in effect you had to create a physical circuit that
modeled the problem you wanted to solve. By making the computer purely digital, we abstracted its
operation away from the physical realm into the realm of pure logic, and that really opened up a lot
of doors. Another much simpler example is a radio dial; it actually represents a continuous spread of
frequencies, but we've arbitrarily divided it into bands so that we can parcel it out to those who want
to use pieces of it.
More abstractly, in mathematics one often takes a continuously varying function and "pretends" for a
moment that it's a step function, simply because it makes things easier to deal with. Then, when
you've got a handle on the step function, you can use a nifty trick (called calculus) to sort of
extrapolate what you've discovered about the steps and apply it to the whole curve. Time itself (which
sure feels like a continuum, whatever it is) is conveniently chopped into bits by humans to make it
easier to keep track of and to talk about.
But there are other quantities in our world that seem to come to us already divided up into discrete
chunks, already structured. The periodic table of the elements certainly isn't a continuum. There's no
smooth transition between sodium and magnesium, though they sit next to each other in the table.
The distinction between the phases of matter -- solids, liquids, and gases -- seems pretty clear, too.
(Well, OK, there are some bizarre in-between states you learn about in college, but they're
encountered only in extreme conditions, usually artificially induced in laboratories and definitely
inhospitable to mammals.) Living things appear to be made up of lots of discrete functional blocks --
organs and cells and organelles and protein molecules and such -- and the interactions of these
discrete parts are what makes them "go." DNA itself, the structure that stores the instructions for
building, is just a binary (or rather quaternary) string, with each discrete position capable of storing
only four possible values. Even the seeming continuum of a fluid like water is an illusion. In reality
it's made of discrete particles, and it's their interactions with one another that give rise to "fluidness."
This endless interplay between the continuous and the discrete, between discovering structure and
creating it, seems to be at the heart of many (maybe most) human endeavors. On the one hand, we
often labor mightily to reveal structures that are somehow already there. Many of the sciences, in
particular, are precisely an attempt to make clear the underlying structure of the universe, to peel
away the layers of obfuscation that our senses have piled on. But it's not limited to science:
Michelangelo spoke of sculpting not as inventing the shape of the statue, but rather as freeing it from
the stone in which it was imprisoned.
On the other hand, many human activities are all about applying structure to something formless, or
about creating structure from nothingness. Again, the arts spring to mind. A painting, a poem, a
story, a song -- all these begin from nothing: from a blank canvas, from an empty sheet of paper,
from silence. Computer programs, those awesomely complex logical constructions we devote
ourselves to so slavishly, seem to be created from thin air, and serve as the structure for an otherwise
"formless" machine. Business contracts, sheet metal ventilation ducts, bingo games, steering
committees, and acoustic guitars -- these are all structures that we've created from, essentially,
Ah, but there's the real question: are the structures we build really new? Do we really just invent
them, whole, from nothing? Or do they grow from and reflect other underlying structures that are
already there? The latter seems much more likely to me. If you look closely,
even a structure that at first blush seems really new turns out to be a recombination or an extension
or a reworking of some existing structure. Sometimes I think of evolutionary processes this way, as a
sort of extrapolation, a patient elaboration, of a very few essential, innate principles that lie buried far
beneath the surface, an endless cycle of structure standing on the shoulders of what has gone before.
Perhaps the macroscopic shapes of living things hint at the underlying nature of matter: quantum
reality writ large, for all to see.
So, getting back to music, does the tuning system
that we use reflect some underlying structure, some relationship among the frequencies, or is it truly
arbitrary, decided by some bewigged old coot in the dim and dusty past? To find out, I did a little
snooping around in the local library and on the net. The answer turns out to be complex (no surprise
there), and it
has as much to do with accidents of history, people's personalities, and the practicalities of tuning
instruments as it does with mathematics. There is an underlying structure beneath the western tuning
system and many others (the relationships among the harmonics of a vibrating string or column of
air, first elaborated by -- you guessed it -- the Greeks). But it also turns out that most music has
evolved away from those "ideal" frequencies for a variety of reasons that have little to do with
mathematics or physics. Here's what I think: I think the structure of music is largely determined by
the structure of us.
Sunburst shapes -- mandalas -- appear over and over in pictures drawn by children, no matter what
their culture or language or what part of the world they live in. You could argue that it's simply
because there are lots of radially symmetric things in the world, and that children are simply drawing
what they see. But I prefer to think that mandalas somehow mirror the internal structure of the
human mind, that they are, in a sense, pictures of humanity.
Humans spend enormous amounts of time shaping things, refining things, expressing things,
creating. Where does all the structure come from? I think it's simply an outgrowth, an elaboration, a
reinterpretation and repackaging, of the structure inside ourselves, which in turn reflects the
structure of the universe we live in. Taken all together -- all the songs, all the buildings, all the
stories, all the social groupings and computer programs and bad jokes and trash and art -- the
structures we humans reveal and create form a churning, turbulent, clouded mirror, a mirror that
occasionally, if we look very closely, may afford us a glimpse of who and what we really are.
- Catapult: Harry and I Build a Siege Weapon by Jim Paul (Villard Books, 1991).
- Weetzie Bat by Francesca Lia Block (Harper & Row, 1989).
- Cane Toads: An Unnatural History by Stephanie Lewis (Doubleday, 1989).
DAVE JOHNSON has for years had the same favorite quote, from Albert Einstein: "He . . . who can no longer pause to
wonder and stand rapt in awe is as good as dead; his eyes are closed." But recently he encountered another, in a book
by Primo Levi, that came very close to unseating Einstein's: "It is enough to think of intestinal worms: they feed themselves
at our expense with a food so perfect that, unique in creation, together perhaps with the angels, they have no anus."
Although Dave howled uncontrollably at that one, Einstein still wins in the end. *
Thanks to Lorraine Anderson, Jeff Barbose, Brian Hamlin, Mark "The Red" Harlan, Bo3b Johnson, Lisa Jongewaard, and
Ned van Alstyne for their always enlightening review comments. *
Dave welcomes feedback on his musings. He can be reached at JOHNSON.DK on AppleLink, firstname.lastname@example.org on the
Internet, or 75300,715 on CompuServe.*