Topical Guide 86
Paradoxes; Endless Tasks; Work and Play
Guppa’s work on the receiving set since January had, little by little, step by step—some steps forward and some steps backward and some off on dead-end side streets—transformed a couple of bags of electrical gadgets into something that was now very nearly a radio, but that would not cross the threshold to radio-ness until this last difficult coil was complete. Until it was successfully wound, all the effort throughout the year would only be effort expended in an attempt to build a radio; but with the completion of this coil, the effort would become effort expended in the building of a radio.
Little Follies, “The Static of the Spheres”
The right thing and the time it takes are connected by a mysterious force, just like a piece of sculpture and the space it fills.
He who aims at progress, should aim at an infinite, not at a special benefit. …
The imaginative faculty of the soul must be fed with objects immense and eternal.
Your end should be one inapprehensible to the senses: then it will be a good always approached,—never touched; always giving health.
A supertask is a task that consists in infinitely many component steps, but which in some sense is completed in a finite amount of time. Supertasks were studied by the pre-Socratics and continue to be objects of interest to modern philosophers, logicians and physicists. The term “super-task” itself was coined by J.F. Thomson (1954). …
Supertasks often lack a final or initial step. A famous example is the first of Zeno’s Paradoxes, the Paradox of the Dichotomy. The runner Achilles begins at the starting line of a track and runs ½ of the distance to the finish line. He then runs half of the remaining distance, or ¼ of the total. He then runs half the remaining distance again, or ⅛ of the total. And he continues in this way ad infinitum, getting ever-closer to the finish line (Figure 1.1.1). But there is no final step in this task.
This could be one of the coils that Guppa was struggling to wind. It is not one of the coils that Guppa was struggling to wind, but it could be.
I can’t leave this entry in the Topical Guide without a word or two about my own experience of an unfinished task, and my experience in deliberately setting myself a task like that recommended by Emerson, an objective “always approached,—never touched.” It has not been a good experience; and it is not now a good experience. If you ever get it into your head to begin compiling a topical autobiography, something so comprehensive that there is no distinction between momentous topics and trivial ones, give yourself a smack on the side of the head, take a cold shower, go for a long walk, and watch a movie instead.
[Note to self: Be sure to include Paradoxes, Endless Tasks, and Work and Play in the Topical Autobiography of Mark Dorset.]
[more to come on Friday, September 10, 2021]
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