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 1.1.1 Turing: Arithmetic Computation “Computing is normally done by writing certain symbols on paper. We may suppose this paper is divided into squares like a child's arithmetic book. In elementary arithmetic the two-dimensional character of the paper is sometimes used. But such a use is always avoidable, and I think that it will be agreed that the two-dimensional character of paper is no essential of computation. I assume then that the computation is carried out on onedimensional paper, i.e. on a tape divided into squares. I shall also suppose that the number of symbols which may be printed is finite. If we were to allow an infinity of symbols, then there would be symbols differing to an arbitrarily small extent. The effect of this restriction of the number of symbols is not very serious. It is always possible to use sequences of symbols in the place of single symbols. Thus an Arabic numeral such as 17 or 999999999999999 is normally treated as a single symbol. ... “The behavior of the computer at any moment is determined by the symbols which he is observing. and his “state of mind” at that moment. We may suppose that there is a bound B to the number of symbols or squares which the computer can observe at one moment. If he wishes to observe more, he must use successive observations. We will also suppose that the number of states of mind which need be taken into account is finite. The reasons for this are of the same character as those which restrict the number of symbols. If we admitted an infinity of states of mind, some of them will be “arbitrarily close” and will be confused. Again, the restriction is not one which seriously affects computation, since the use of more complicated states of mind can be avoided by writing more symbols on the tape. “Let us imagine the operations performed by the computer to be split up into “simple operations” which are so elementary that it is not easy to imagine them further divided. Every such operation consists of some change of the physical system consisting of the computer and his tape. We know the state of the system if we know the sequence of symbols on the tape, which of these are observed by the computer (possibly with a special order), and the state of mind of the computer. We may suppose that in a simple operation not more than one symbol is altered. Any other changes can be set up into simple changes of this kind. The situation in regard to the squares whose symbols may be altered in this way is the same as in regard to the observed squares. We may, therefore, without loss of generality, assume that the squares whose symbols are changed are always “observed” squares. “Besides these changes of symbols, the simple operations must include changes of distribution of observed squares. The new observed squares must be immediately recognizable by the computer. I think it is reasonable to suppose that they can only be squares whose distance from the closest of the immediately previously observed squares does not exceed a certain fixed amount. Let us say that each of the new observed squares is within L squares of an immediately previously observed square. ...” ⎯ Alan Turing, On Computable Numbers, with an application to the Entscheidungsproblem,” Proc. Lond. Math. Soc. (2) 42 pp 230-265 (1936-7); (A link to this paper online can be found at www.turing.org.uk/sources/biblio.html). 1.1.2 von Neumann: Computers “Conceptually we have discussed . . . two different forms of memory: storage of numbers and storage of orders. If, however, the orders to the machine are reduced to a numerical code and if the machine can in some fashion distinguish a number from an order, p. 40
Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker the memory organ can be used to store both numbers and orders.” ⎯ Arthur Burks, Herman Goldstine, and John von Neumann, “Preliminary Discussion of the Logical Design of an Electronic Computing Instrument,” reprinted in John von Neumann, Collected Works, Vol. V, p. 35, Macmillan Company, New York 1963. 1.1.4 Masters of Doom, Physics “...after so many years immersed in the science of graphics, he [John Carmack] had achieved an almost Zen-like understanding of his craft. In the shower, he would see a few bars of light on the wall and think, Hey, that’s a diffuse specular reflection from the overhead lights reflected off the faucet. Rather than detaching him from the natural world, this viewpoint only made him appreciate it more deeply. ‘These are things I find enchanting and miraculous,’ he said, ‘I don’t have to be at the Grand Canyon to appreciate the way the world works. I can see that in reflections of light in my bathroom.’” ⎯ David Kushner, Masters of Doom, (Random House, 2003) p. 295. Kushner is describing the programmer John Carmack, who developed most of the code for the firstperson-shooter computer games Doom and Quake. 1.1.5 Hegel: Organic Growth --- or Society “For the rest it is not difficult to see that our epoch is a birth-time, and a period of transition. ... This gradual crumbling to pieces, which did not alter the general look and aspect of the whole, is interrupted by the sunrise, which, in a flash and at a single stroke, brings to view the form and structure of the new world. “But this new world is perfectly realized just as little as the new-born child; and it is essential to bear this in mind. It comes on the stage to begin with in its immediacy, in its bare generality. A building is not finished when its foundation is laid; and just as little is the attainment of a general notion of a whole the whole itself. When we want to see an oak with all its vigour of trunk, its spreading branches, and mass of foliage, we are not satisfied to be shown an acorn instead. In the same way science, the crowning glory of a spiritual world, is not found complete in its initial stages. The beginning of the new spirit is the outcome of a widespread revolution in manifold forms of spiritual culture; it is the reward which comes after a checkered and devious course of development, and after much struggle and effort.” Georg Hegel, The Phenomenology of Mind (1807), Harper & Row, 1967, p. 75 - 76. Outtakes Short Chapter-by-Chapter Outline (Note that this is an outdated chapter sequence that matches the initial proposal.) 1. Computers have evolved gradually, almost like a new animal species. By looking at how they do some common tasks, we discover a rigorously logical universe. 2. Our machines can simulate the workings of the nature so accurately that some scientists believe the world is fundamentally a set of computations. p. 41
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