Previously, AIT had an abstract mathematical quality. Now it is possible to write down executable programs that embody the constructions in the proofs of theorems. This new self-delimiting UTM is implemented via software written in a new version of LISP that I invented especially for this purpose.
Most people believe that anything that is true is true for a reason.
These theorems show that some things are true for no reason at all, i.e., accidentally, or at random. As is shown in this course, the algorithms considered in the proofs of these two theorems are now easy to program and run, and by looking at the size in bits of these programs one can actually, for the first time, determine exact values for the constants c and c' . I used this approach and software in an intensive short course on the limits of mathematics that I gave at the University of Maine in Orono in the summer of 1994. I also lectured on this material during a stay at the Santa Fe Institute in the spring of 1995, and at a meeting at the Black Sea University in Romania in the summer of 1995. After presenting this material at these three different places, it became obvious to me that it is extremely difficult to understand it in its original form.