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This is one formula in AIT that is totally unlike anything in Shannon information theory. That’s all the unfinished business from Day III! Now let’s start Day IV proper by explaining LISP! 5 What Is LISP? LISP = LISt Processing. Lists are arbitrarily long nested tuples, and may have repeated elements. LISP is like a computerized version of set theory! The LISP S-expression ((A bc) 39 x-y-z) denotes the following nested tuples: A, bc , 39, x-y-z Programs and data in LISP are always S-expressions.

That aborts everything! If so, U of p returns out-of-data. So the program for the universal U consists of a high-level language algorithmic part followed by data, raw binary data. The algorithmic part indicates which special-purpose self-delimiting computer C should be simulated, and the raw binary data gives the binary program for C! I believe that I’ve picked a very natural U . 9 Running U on Simple Examples Here’s our first example of a program for U . This program is all LISP prefix with no binary data.

Springer-Verlag, Singapore, 1999. – G. Chaitin, “An invitation to algorithmic information theory,” in D. S. Bridges, C. S. Calude, J. Gibbons, S. Reeves, I. H. , Combinatorics, Complexity & Logic: Proc. of DMTCS ’96, pp. 1–23. Springer-Verlag, Singapore, 1997. – [The above two papers are both chapters in] G. Chaitin, The Limits of Mathematics, Springer-Verlag, Singapore, 1998. html 8th Estonian Winter School in Computer Science, EWSCS’03 Palmse, Estonia, 2–7 March 2003 EWSCS is a series of regional-scope international winter schools held annually in Estonia, organized by the Institute of Cybernetics, Tallinn.

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