Uncertainty

The essay following was written as it appears: it rapidly became clear to me not long after writing it that that the foundation of this essay was a wholly false premise, which will be clear to anyone familiar with the book I'm discussing. This will be discussed in a subsequent essay tentatively titled "The Liar".

rules
u may be added to any string ending in i
for any x the string mx may be transformed to mxx
iii may be replaced with u
uu may be dropped from the string

exercise: from the starting string mi derive the string mu

So runs, more or less, the first formal exercise in Hofstadter’s Gödel, Escher, Bach, which brings my progress in the book to a standstill this morning. It’s one of those deceptively simple puzzles, trivial at first glance, impossible on closer inspection, requiring the application of insight outside the proverbial box to crack, and to my consternation, which in an hour has worked a fair way towards frustrated anger, I can’t seem to shift it. The issue is easy enough to grasp... To solve it you have to eliminate i. The only way to eliminate i is to work to a string with some multiple of 3i in it. But the only way to increase i is by the second rule transformation, and this "doubling" transformation can’t produce an (n)i where n is divisible by 3. Fiddling on paper produces series after absurd series of strings that keep collapsing to the same dead ends. My creaking, derelict faculties of math and formal logic offer vague insights about factors, primes, 2 is the only even prime, doesn’t that have something to do with it?


It isn’t the puzzle itself or even my failure with it that is getting to me. It is a familiar sort of frustration, knowing you are overlooking some obvious simplicity you are blinded to by some equally simple yet false assumption. I have in recent memory spent more than a few good hours purposely cultivating a similar state playing puzzle games like Braid or Portal.

What’s getting to me is that I know for a damn fact that I already solved this, in no more than 20 or 30 minutes, a decade, maybe 12 years ago, the first time I attempted to read the book.

Maybe I didn’t even figure it out last time, I think. Maybe I just wandered into the right territory noodling around with the transformations. Far from impossible: just the other day I solved all the levels of a tile-flipping flash puzzle game on the internet without ever really grasping the rules, just a lot of clicking and blindly following intuition.

Even so this explanation smells of bargaining to me. As someone still rather freshly exposed to the experience of grief I know that bargaining comes on the heels of denial and I wonder what it is I am trying to deny.

No choice but to give it up for the time being and get things done. In the middle of laundry half an hour later it occurs to me that I may just end up having to accept that I simply no longer possess the class of mind that allowed me to make short work of the puzzle at 28 or 30 years old. And that this is what is really bothering me.

Hofstadter advises the reader not to worry about whether they solve the puzzle: the intent is only to get the “flavor” of it. Oh, and to “Have fun!”

Fucking geniuses.

-=-

Briefly, nearly twenty years ago, I understood Heisenberg’s Uncertainty Principle. By this I don’t mean that I was acquainted with a more or less narrative, prose explanation of the origins and significance of it - something I suppose I still possess to a degree and which I could beef up and give a quick spit shine with an hour or two on the internet.

But during the quantum mechanics section of a tough physical chemistry course series, in the latter half of earning my bachelor’s degree, I was led through the derivation of the actual mathematical expression of the principle, and I understood it. You can talk about the principle but I understood, in that class, that the talking only gets you within a certain vicinity of this level of thought. You can only get to its real meaning through the math. And it was a beautiful thing.

Looking back I suspect that it was also an experience that did away with any lingering ideas I might have been harboring that there was a chance of my personally adding anything really important to science. I was capable of hanging on for the ride as a better intellect than mine illuminated for me the product of mind that had operated on a level that much higher again. But it was immediately evident to me that there wasn’t the slightest inkling of a possibility that I could ever produce original thought like that.

-=-

I have to wonder if I could even work up to the point of being able to follow the derivation of Heisenberg’s principle now. I try to keep up on the science news and indeed still work in the field, but I’m very far from such rarefied stuff. I guess it could hardly be a more moot point at this stage of the game. I will take Hofstadter’s advice and try not to worry, to focus on making the most of what I can manage in the midst of my ordinary human uncertainty.