Rinse and Repeat

The “rinse and repeat” instruction line on shampoo bottles is a beautiful illustration of the tight interconnection of self-inclusion paradoxes, time, quotation marks, levels of abstraction, consciousness, and the evolution of the universe.

Very few people are found dead in showers, their heads rotted away by infinitely iterated applications of shampoo. But the instruction line on the bottle would if followed literally lead to this deplorable result. Idiots, we know, don’t know when to stop. Computers are brilliant idiots; every time one freezes, it is because it has run across the equivalent of the instruction line and gotten itself into an infinite feedback loop.

In fact it is difficult to see how the line could be amended to avoid the error. If one added “Stop” to the end of the line, the idiot (acting as a Turing Machine) might go on repeating forever and never get to the “Stop” instruction. Or if one added before the repeat command “stop after two repetitions”, the idiot might take the injunction to repeat as applying to the reading of the instructions as well as the lathering process, and on returning to the instructions would read, again, “Stop after two repetitions”, and reset its counter obediently to two. If it had a counter. And if it didn’t simply crash as a result of getting two contradictory commands.

A counter is one level up in abstraction; it implies an overview of the process, a summing-up rather than just the execution of the process. But even a simple counter won’t work in this case, as we have seen. Another level is required, to recognize and solve the self-inclusion paradox. The paradox is similar to Russell’s famous paradox of the village barber who shaves everybody in the village who doesn’t shave himself. Who shaves the barber? The issue is whether the command “repeat” applies to itself or not, and whether, if it does, its efficacy somehow ceases after the first iteration. Gödel’s even more intractable paradox, “This statement is unprovable”, contains the same implication, of a self-nested logic that goes on unendingly: “This statement: ‘This statement: “This statement: ‘….’ is unprovable” is unprovable’ is unprovable.”

The simplest components of the physical universe, quantum events, don’t seem to have a “repeat” command, which is what you need to have any kind of coherent time. But the moment enough of them reach a consensus to repeat, classical matter is born, and with it time as we know it. In the competition for survival in time between repeaters and non-repeaters, repeaters of course win, but they do so by idiotically repeating themselves into the future, rinsing and repeating, generating the next moment’s version of themselves as fast as time will allow as described by Planck’s constant.

It was only when higher forms of computational difficulty arose, from whose perspective mere repetition could be recognized and put a stop to when system survival dictated it, that higher forms of matter, especially living matter, and quintessentially conscious living matter, could begin to appear.

Which is why, except when we default to the old logic of OCD, we don’t go on lathering up.