Nonuniversality in Computation: Thirteen Misconceptions Rectified

In January 2005 I showed that universality in computation cannot be achieved. Specifically, I exhibited a number of distinct counterexamples, each of which sufficing to demonstrate that no finite and fixed computer can be universal in the sense of being able to simulate successfully any computation that can be executed on any other computer. The number and diversity of the counterexamples attest to the general nature of the nonuniversality result. This not only put to rest the Church-Turing Thesis, by proving it to be a false conjecture, but also was seen to apply, in addition to the Turing Machine, to all computational models, past, present, and future, conventional and unconventional. While over eight years have now passed since nonuniversality in computation was established, the result remains largely misunderstood. There appear to be at least two main reasons for this state of affairs. As often happens to new ideas, the nonuniversality result was confronted with a stubborn entrenchment in a preconceived, deeply held, and quasi-religious belief in the existence of a universal computer. This was exacerbated by a failure to read the literature that demonstrates why such a belief is unfounded. Behavior of this sort, sadly not uncommon in science, explains the enduring mirage of the universal computer. The purpose of this paper is to rectify the most notorious misconceptions associated with nonuniversality in computation. These misconceptions were expressed to the author in personal communications, orally, by email, and in referee reports. Each misconception is quoted verbatim and a detailed response to it is provided. The paper concludes by inviting the reader to take a computational challenge.