(This post was originally posted on the NKS Forum.)
The following are some remarks that I made on the Foundations of Math (FOM) mailing list in connection with discussion of the Wolfram 2,3 Turing Machine Prize. Though much of what I say is well understood in the NKS community, I thought it might nevertheless be of interest here.
Several people forwarded me the thread on this mailing list about our 2,3 Turing machine prize.
I’m glad to see that it has stimulated discussion. Perhaps I can make a few general remarks.
What do we learn from simple universal Turing machines?
John McCarthy wrote:
In the 1950s I thought that the smallest possible (symbol-state product) universal Turing machine would tell something about the nature of computation. Unfortunately, it didn’t.
I suspect that what was imagined at that time was that by finding the smallest universal machines one would discover some “spark of computation”—some critical ingredient in the rules necessary to make universal computation possible. (At the time, it probably also still seemed that there might be a “spark of life” or a “spark of intelligence” that could be found in systems.)
I remember that when I first heard about universality in the Game of Life in the early 1970s, I didn’t think it particularly significant; it seemed like just a clever hack.