A Hypercomputation in Brouwer's Constructivism

TL;DR

This paper introduces a new form of hypercomputation based on Brouwer's constructivist philosophy, extending the concept of computability beyond traditional Turing limits.

Contribution

It proposes persistently evolutionary Turing machines, a novel hypercomputational model grounded in Brouwer's constructivist ideas.

Findings

Defines persistently evolutionary Turing machines

Shows how they extend classical computability

Connects hypercomputation with Brouwer's constructivism

Abstract

In contrast to other constructivist schools, for Brouwer, the notion of "constructive object" is not restricted to be presented as `words' in some finite alphabet of symbols, and choice sequences which are non-predetermined and unfinished objects are legitimate constructive objects. In this way, Brouwer's constructivism goes beyond Turing computability. Further, in 1999, the term hypercomputation was introduced by J. Copeland. Hypercomputation refers to models of computation which go beyond Church-Turing thesis. In this paper, we propose a hypercomputation called persistently evolutionary Turing machines based on Brouwer's notion of being constructive.