I Am a Strange Loop

Let me contrast two very different types of answer that someone might give. The first type of answer — myopic to the point of silliness — would be, “Because its predecessor never falls, you dummy!” To be sure, this is correct as far as it goes, but it doesn’t go very far. It just pushes the buck to a different domino, and thus begs the question.

The second type of answer would be, “Because 641 is prime.” Now this answer, while just as correct (indeed, in some sense it is far more on the mark), has the curious property of not talking about anything physical at all. Not only has the focus moved upwards to collective properties of the chainium, but those properties somehow transcend the physical and have to do with pure abstractions, such as primality.

The second answer bypasses all the physics of gravity and domino chains and makes reference only to concepts that belong to a completely different domain of discourse. The domain of prime numbers is as remote from the physics of toppling dominos as is the physics of quarks and gluons from the Cold War’s “domino theory” of how communism would inevitably topple country after neighboring country in Southeast Asia. In both cases, the two domains of discourse are many levels apart, and one is purely local and physical, while the other is global and organizational.

Before passing on to other metaphors, I’d just like to point out that although here, 641’s primality was used as an explanation for why a certain domino did not fall, it could equally well serve as the explanation for why a different domino did fall. In particular, in the domino chainium, there could be a stretch called the “prime stretch” whose dominos all topple when the set of potential divisors has been exhausted, which means that the input has been determined to be prime.

The point of this example is that 641’s primality is the best explanation, perhaps even the only explanation, for why certain dominos did fall and certain other ones did not fall. In a word, 641 is the prime mover. So I ask: Who shoves whom around inside the domino chainium?

The Causal Potency of Collective Phenomena

My next metaphor was dreamt up on an afternoon not long ago when I was caught in a horrendous traffic jam on some freeway out in the countryside, with several lanes of nearly touching cars all sitting stock still. For some reason I was reminded of big-city traffic jams where you often hear people honking angrily at each other, and I imagined myself suddenly starting to honk my horn over and over again at the car in front of me, as if to say, “Get out of my way, lunkhead!”

The thought of myself (or anyone) taking such an outrageously childish action made me smile, but when I considered it a bit longer, I saw that there might be a slim rationale for honking that way. After all, if the next car were magically to poof right out of existence, I could fill the gap and thus make one car-length’s worth of progress. Now a car poofing out of existence is not too terribly likely, and one car-length is not much progress, but somehow, through this image, the idea of honking became just barely comprehensible to me. And then I remembered my domino chainium and the silly superlocal answer, “That domino didn’t fall because its neighbor didn’t fall, you dummy!” This myopic answer and my fleeting thought of honking at the car just ahead of me seemed to be cut from the same cloth.

As I continued to sit in this traffic jam, twiddling my thumbs instead of honking, I let these thoughts continue, in their bully-like fashion, to push my helpless neurons around. I imagined a counterfactual situation in which the highway was shrouded in the densest pea-soup fog imaginable, so that I could barely make out the rear of the car ahead of me. In such a case, honking my horn wouldn’t be quite so blockheaded. For all I know, that car alone might well be the entire cause of my being stuck, and if only it would just get out of the way, I could go sailing down the highway!

If you’re totally fog-bound like that, or if you’re incredibly myopic, then you might think to yourself, “It’s all my neighbor’s fault!”, and there’s at least a small chance that you’re right. But if you have a larger field of view and can see hordes of immobilized cars on all sides, then honking at your immediate predecessor is an absurdity, for it’s obvious that the problem is not local. The root problem lies at some level of discourse other than that of cars. Though you may not know its nature, some higher-level, more abstract reason must lie behind this traffic jam.