Sixty-four Puny Bits

Imagine a grid, eight squares across and eight squares high. To the human eye, this is a relatively small number of squares; we've all played crosswords and word-searches with much larger dimensions and never found ourselves whelmed 'neath their vastness, so this eight by eight array is really very modest. It's only sixty-four squares.

Now imagine you have a whole bunch of Post-It® notes that have been pre-printed with that eight-by-eight grid, and you've been assigned the simple task of using a marker to fill-in the squares of the grid, a different combination of squares on each note, in every unique combination of filled and unfilled squares that exists. You might just start with filling in a single square on the first note; the first square, perhaps. Then, on the next note you might just fill the second square. On the third note you might do the first and second square together, and on the fourth note the third square by itself. On and on like that, you fill in a different combination of squares on each sticky note — sometimes you get something that looks like a pattern, or a shape, or a row of eight squares in a straight line, and that makes it more interesting — and the stack grows and grows. It's only sixty-four squares; how long can it take?

Unfortunately for you, it will take a very long time. To be frank, I'm quite sure you'll be dead before you finish. You see, you'll have to do over eighteen billion-billion notes to exhaust all the combinations of those sixty-four squares. The stack of sticky notes, were you to somehow get a tremendously long extension on your life and complete the task, would be over a trillion miles tall — and if you were at the top of that stack, way out in interstellar space, when you finally filled-in the last note and sent-back your triumphant radio message saying, "I'M DONE!", it would take two months for the signal to reach Earth.

The staggering variety of states that can come from such modest sets never ceases to delight me. The squares on a chessboard, the notes of the equally-tempered musical scale, the pixels in a tiny 8x8 character cell — it's within our human capacity to comprehend the bounds and definitions of these sets of data, and to instantly recognize and ascribe meaning to a huge variety of states of that data — the Queen's Gambit, a G-flat minor 7th, a capital A in all its stylistic variations — yet it is utterly outside our power to, in any practical time-frame, iterate and apply logic to every single possible state.

This is, of course, what computers are good at. And the fact that they're so very good at what we're so very bad at is exactly why they're instrumental in our advancement as a species. But there's an enormous gulf between what the brain and sensory organs of a human can do, and what the sequential logic (however deeply parallelized) and I/O devices of even a very large and expensive supercomputer can do. It is, has been, and will for some time be the unenviable task of thousands of exceptionally bright men and women to find a way of giving computers the same ability to see and make sense of signals in noise and patterns in chaos, to close the gulf between the exalted mind and the ignoble machine.

I hope they do it in this century, and I hope I get to see it.

—L.
CCS