Notes for the Lifebox, the Seashell, and the Soul - Rudy Rucker

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Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker Figure: Two Ways to Slice It. (Hiker + Stick) feeling (Shoe). (Hiker ) feeling (Stick + Shoe). (System Software + Application Software) acting on (Input). (System Software) acting on (Application Software + Input) Suppose I’m in a cold, pitch-dark room in the mountains and I want to arrange my shoes so I can step right into them as soon as I get out of bed. Without getting up, I feel around with my hand on the floor beside the bed. I don’t feel the shoes, but my hand happens to light upon the handle of a light-weight walking stick. Good. Now I reach out into the darkness with the cane hoping to contact the shoes. On the left, my stick touches the leg of a chair, I trace around for the opening under the chair, poke in there, still no shoes. I reach over to the right, and come across something soft: my coat. And beyond that I find something firm but not stiff: one of my shoes. As I’m feeling around with the stick, I almost forget that the stick isn’t part of my body. It’s as if my nerves grow out into the stick. I become sensitive even to the roughness and smoothness of the things my stick touches. Is the stick part of me, or part of the world? A little of both. The point is that the boundary between me and the non-me is somewhat fluid. Application software is a “stick” that the system software wields in order to do things. Is the application part of the data or part of the computing device? A little of both. Repeated Definition of Computation With all these considerations in mind, I can restate my definition of a computation one more time. • Definition. A computation P is a process governed by a finitely describable set of rules called the software. • The process takes place on a physical system called a computer, which can also be called the computation’s hardware. We think of the physical computer’s rules of behavior as a part of the software. p. 48
Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker • The computer is thought of as embedded in linear time. The states of the computer can be called inputs or outputs, with earlier states being inputs relative to the later states, and the later states being outputs relative to the earlier states. • The computational process that results from starting P on input In is called P(In), and if the process is in the output state Out at time t, we write P(In, t) = Out. The output state Out is completely determined by the software of P, the input In, and the amount of elapsed time t. • In general, if P(In, t) = Out for any time t, we say P(In) produces Out. In other words, the computation P given input In is thought of as a process P(In) which produces a steady flow of outputs. • If P(In) enters the state Out and stops changing, we say that P(In) returns Out. In this situation we also write P(In) = Out. • Some computations P are accompanied by a target detector IsPDone which is a helper computation that allows us to distinguish certain target states as being states in which P has produced an answer. We require that for any state Out, the target detector IsPDone(Out) returns either True or False. In the case where P(In) produces Out and IsPDone(Out) returns True, we can say that P(In) halts relative to IsPDone. Predictability Yes, if I multiply 318 times 478 with pencil and paper, the process is deterministic, but I don’t know the answer till I carry out the calculation, so in that sense the answer wasn’t predictable. Of course if you have a pocket calculator, you can figure out my answer faster than me. But, until you push those buttons, you don’t know the answer either. *** All four abstractly possible combinations of feasibility and predictability can arise, as suggested in the figure below. I made the picture messy to indicate that its not so easy to decide whether a computation is predictable or not. [Author’s note: Bull. I made it messy because I screwed the drawing up.] (The meaning of the “Class” numbers will be explained in a few paragraphs.) p. 49
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Notes for the Lifebox, the Seashell, and the Soul - Rudy Rucker

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