From the Closed Classical Algorithmic Universe to an Open World of Algorithmic Constellations

TL;DR

This paper explores the transition from a closed classical algorithmic universe to an open, flexible world of algorithmic constellations, highlighting implications for mathematical cognition and computational expressiveness.

Contribution

It introduces the concept of algorithmic constellations as a new model that expands the classical universe, supporting greater flexibility and creativity in computation.

Findings

Classical algorithmic universe is closed and restrictive.

Open algorithmic universe enables higher expressiveness.

Algorithmic constellations support constructivism and creativity.

Abstract

In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the conventional approach to computation. Then we explain how new models of algorithms turned the classical closed algorithmic universe into the open world of algorithmic constellations, allowing higher flexibility and expressive power, supporting constructivism and creativity in mathematical modeling. As Goedels undecidability theorems demonstrate, the closed algorithmic universe restricts essential forms of mathematical cognition. In contrast, the open algorithmic universe, and even more the open world of algorithmic constellations, remove such restrictions and enable new, richer understanding of computation.