I Am a Strange Loop

Perhaps a very critical baseball game just finished three miles up the road. Perhaps it’s 7:30 on a weekday morning and you’re heading towards Silicon Valley. Perhaps there’s a huge blizzard ten miles ahead. Or it may be something else, but it’s surely some social or natural event of the type that induces large numbers of people all to do the same thing as one another. No amount of expertise in car mechanics will help you to grasp the essence of such a situation; what is needed is knowledge of the abstract forces that can act on freeways and traffic. Cars are just pawns in the bigger game and, aside from the fact that they can’t pass through each other and emerge intact post-crossing (as do ripples and other waves), their physical nature plays no significant role in traffic jams. We are in a situation analogous to that in which the global, abstract, math-level answer “641 is prime” is far superior to a local, physical, domino-level answer.

Neurons and Dominos

The foregoing down-to-earth images provide us with helpful metaphors for talking about the many levels of causality inside a human brain. Suppose it were possible to monitor any selected neuron in my brain. In that case, someone might ask, as I listened to some piece of music, “How come neuron #45826493842 never seems to fire?” A local, myopic answer might be, “Because the neurons that feed into it never fire jointly”, and this answer would be just as correct but also just as useless and uninformative as the myopic answers in the other situations. On the other hand, the global, organizational answer “Because Doug Hofstadter doesn’t care for the style of Fats Domino” would be much more on target.

Of course we should not fall into the trap of thinking that neuron #45826493842 is the sole neuron designated to fire whenever I resonate to some piece of music I’m listening to. It’s just one of many neurons that participate in the high-level process, like voters in a national election. Just as no special voter makes the decision, so no special neuron is privileged. As long as we avoid simplistic notions such as a privileged “grand-music neuron”, we can use the domino-chainium metaphor to think about brains, and especially to remind ourselves of how, for a given phenomenon in a brain, there can be vastly different explanations belonging to vastly different domains of discourse at vastly different levels of abstraction.

Patterns as Causes

I hope that in light of these images, Roger Sperry’s comments about “the population of causal forces” and “overall organizational forces and dynamic properties” in a complex system like the brain or the chainium have become clearer. For instance, let us try to answer the question, “Can the primality of 641 really play a causal role in a physical system?” Although 641’s primality is obviously not a physical force, the answer nonetheless has to be, “Yes, it does play a causal role, because the most efficient and most insight-affording explanation of the chainium’s behavior depends crucially on that notion.” Deep understanding of causality sometimes requires the understanding of very large patterns and their abstract relationships and interactions, not just the understanding of microscopic objects interacting in microscopic time intervals.

I have to emphasize that there’s no “extra” physical (or extra-physical) force here; the local, myopic laws of physics take care of everything on their own, but the global arrangement of the dominos is what determines what happens, and if you notice (and understand) that arrangement, then an insight-giving shortcut to the answer of the non-falling domino in the divisor stretch (as well as the falling domino in the prime stretch) is served to you on a silver platter. On the other hand, if you don’t pay attention to that arrangement, then you are doomed to taking the long way around, to understanding things only locally and without insight. In short, considering 641’s primality as a physical cause in our domino chainium is analogous to considering a gas’s temperature as a physical cause (e.g., of the amount of pressure it exerts against the walls of its container).

Indeed, let us think for a moment about such a gas — a gas in a cylinder with a movable piston. If the gas suddenly heats up (as occurs in any cylinder in your car engine when its spark plug fires), then its pressure suddenly increases and therefore (note the causal word) the piston is suddenly shoved outwards. Thus combustion engines can be built.