Dialogue Concerning The Two Chief World Views

TL;DR

This paper uses Galileo's dialogue format to explore contrasting views on the P vs NP problem through a modern philosophical debate between proponents of each position and a neutral observer.

Contribution

It introduces a novel dialogue-based approach to discussing the P vs NP problem, inspired by Galileo's historical dialogue on cosmological models.

Findings

Clarifies the core arguments for P ≠ NP and P = NP.

Highlights the philosophical and practical implications of each position.

Encourages open-minded discussion on computational complexity.

Abstract

In 1632, Galileo Galilei wrote a book called \textit{Dialogue Concerning the Two Chief World Systems} which compared the new Copernican model of the universe with the old Ptolemaic model. His book took the form of a dialogue between three philosophers, Salviati, a proponent of the Copernican model, Simplicio, a proponent of the Ptolemaic model, and Sagredo, who was initially open-minded and neutral. In this paper, I am going to use Galileo's idea to present a dialogue between three modern philosophers, Mr. Spock, a proponent of the view that $\mathsf{P} \neq \mathsf{NP}$, Professor Simpson, a proponent of the view that $\mathsf{P} = \mathsf{NP}$, and Judge Wapner, who is initially open-minded and neutral.