Some Thoughts on Hypercomputation

TL;DR

This paper explores hypercomputation as a challenge to the Church--Turing Thesis, discussing its implications for the limits of intelligence, information processing, and potential new forms of communication among intelligent entities.

Contribution

It provides a conceptual analysis of hypercomputation's implications for the limits of computation, intelligence, and communication, questioning the universality of the Church--Turing Thesis.

Findings

Hypercomputation challenges the universality of the Church--Turing Thesis.

Physical laws may permit hypercomputational processes in our universe.

Hypercomputation opens new perspectives on communication between intelligent beings.

Abstract

Hypercomputation is a relatively new branch of computer science that emerged from the idea that the Church--Turing Thesis, which is supposed to describe what is computable and what is noncomputable, cannot possible be true. Because of its apparent validity, the Church--Turing Thesis has been used to investigate the possible limits of intelligence of any imaginable life form, and, consequently, the limits of information processing, since living beings are, among others, information processors. However, in the light of hypercomputation, which seems to be feasibly in our universe, one cannot impose arbitrary limits to what intelligence can achieve unless there are specific physical laws that prohibit the realization of something. In addition, hypercomputation allows us to ponder about aspects of communication between intelligent beings that have not been considered before