Παρασκευή, 26 Δεκεμβρίου 2008

"How to Program an Infinite Abacus"

Joachim Lambek wrote an interesting paper entitled "How to Program an Infinite Abacus" which was published in the Canadian Mathematical Bulletin. Unfortunately, this paper is currently not available in any form. For the benefit of all those people who might like to have a look at this paper, I have prepared a transcription of this paper which is available here.

Δευτέρα, 1 Δεκεμβρίου 2008

A comment on a comment

Recently, "someone" posted a review of my book on hypercomputation on the Brains site. The reviewer argues that

This area is full of problems, some of which are physico/mathematical and some of which are conceptual. Unfortunately, from a quick sample, Syropolous's book does not avoid common mistakes and confusions—some of which I've been trying to correct in my own work.

First of all, I have to admit that back in 2004 I read a paper by this reviewer, but at that time I did not considered it interesting. However, after I read this review of my book, I read The Physical Church-Turing Thesis: Modest or Bold?, the reviewer's latest manuscript, in order to see what he meant by common mistakes and confusions and how he was trying to solve them. In this manuscript, the reviewer puts forth a number of criteria that every machine has to satisfy in order to be ``useful for physical computing.'' These criteria are:

  • Readable Inputs and Outputs
  • Process-Independent Rule
  • Repeatability
  • Resettability
  • Physical Constructability
  • Reliability
Obviously these criteria constitute a description of a feasible computing device. Unfortunately, it is obvious that these criteria are too restrictive or, to put it in another way, these criteria assume that only "modern" computers are useful physical computing devices. In particular, what for one person is readable for someone else is not readable at all (e.g., data on a computer screen are not readable by a blind person). As far it regards physical constructability, the reviewer talks about Malament-Hogarth spacetime computers and tries to prove that they are non-feasible while he ignores two important papers in the field: Non-Turing Computations Via Malament–Hogarth Space-Times and Relativistic computers and the Turing barrier.

All in all, I fail to see how he can correct the problems with such views. In addition, his view is deeply mechanistic and unfortunately too simplistic.

A "Solution" to Riemann Hypothesis

Riemann hypothesi s is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex n...