I Am a Strange Loop

The pressures of daily life require us, force us, to talk about events at the level on which we directly perceive them. Access at that level is what our sensory organs, our language, and our culture provide us with. From earliest childhood on, we are handed concepts such as “milk”, “finger”, “wall”, “mosquito”, “sting”, “itch”, “swat”, and so on, on a silver platter. We perceive the world in terms of such notions, not in terms of microscopic notions like “proboscis” and “hair follicle”, let alone “cytoplasm”, “ribosome”, “peptide bond”, or “carbon atom”. We can of course acquire such notions later, and some of us master them profoundly, but they can never replace the silver-platter ones we grew up with. In sum, then, we are victims of our macroscopicness, and cannot escape from the trap of using everyday words to describe the events that we witness, and perceive as real.

This is why it is much more natural for us to say that a war was triggered for religious or economic reasons than to try to imagine a war as a vast pattern of interacting elementary particles and to think of what triggered it in similar terms — even though physicists may insist that that is the only “true” level of explanation for it, in the sense that no information would be thrown away if we were to speak at that level. But having such phenomenal accuracy is, alas (or rather, “Thank God!”), not our fate.

We mortals are condemned not to speak at that level of no information loss. We necessarily simplify, and indeed, vastly so. But that sacrifice is also our glory. Drastic simplification is what allows us to reduce situations to their bare bones, to discover abstract essences, to put our fingers on what matters, to understand phenomena at amazingly high levels, to survive reliably in this world, and to formulate literature, art, music, and science.

CHAPTER 3

The Causal Potency of Patterns

The Prime Mover

AS THE rest of this book depends on having a clear sense for the interrelationships between different levels of description of entities that think, I would like to introduce here a few concrete metaphors that have helped me a great deal in developing my intuitions on this elusive subject.

My first example involves the familiar notion of a chain of falling dominos. However, I’ll j azz up the standard image a bit by stipulating that each domino is spring-loaded in a clever fashion (details do not concern us) so that whenever it gets knocked down by its neighbor, after a short “refractory” period it flips back up to its vertical state, all set to be knocked down once more. With such a system, we can implement a mechanical computer that works by sending signals down stretches of dominos that can bifurcate or join together; thus signals can propagate in loops, jointly trigger other signals, and so forth. Relative timing, of course, will be of the essence, but once again, details do not concern us. The basic idea is just that we can imagine a network of precisely timed domino chains that amounts to a computer program for carrying out a particular computation, such as determining if a given input is a prime number or not. (John Searle, so fond of unusual substrates for computation, should like this “domino chainium” thought experiment!)

Let us thus imagine that we can give a specific numerical “input” to the chainium by taking any positive integer we are interested in — 641, say — and placing exactly that many dominos end to end in a “reserved” stretch of the network. Now, when we tip over the chainium’s first domino, a Rube Goldberg–type series of events will take place in which domino after domino will fall, including, shortly after the outset, all 641 of the dominos constituting our input stretch, and as a consequence various loops will be triggered, with some loop presumably testing the input number for divisibility by 2, another for divisibility by 3, and so forth. If ever a divisor is found, then a signal will be sent down one particular stretch — let’s call it the “divisor stretch” — and when we see that stretch falling, we will know that the input number has some divisor and thus is not prime. By contrast, if the input has no divisor, then the divisor stretch will never be triggered and we will know the input is prime.

Suppose an observer is standing by when the domino chainium is given 641 as input. The observer, who has not been told what the chainium was made for, watches keenly for while, then points at one of the dominos in the divisor stretch and asks with curiosity, “How come that domino there is never falling?”