Computer Engineering Commons^™

Designing, Understanding, And Analyzing Unconventional Computation: The Important Role Of Logic And Constructive Mathematics, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we explain why, in our opinion, logic and constructive mathematics are playing -- and should play -- an important role in the design, understanding, and analysis of unconventional computation.

Metrization Theorem For Space-Times: From Urysohn's Problem Towards Physically Useful Constructive Mathematics, Vladik Kreinovich

Departmental Technical Reports (CS)

In the early 1920s, Pavel Urysohn proved his famous lemma (sometimes referred to as "first non-trivial result of point set topology"). Among other applications, this lemma was instrumental in proving that under reasonable conditions, every topological space can be metrized.

A few years before that, in 1919, a complex mathematical theory was experimentally proven to be extremely useful in the description of real world phenomena: namely, during a solar eclipse, General Relativity theory -- that uses pseudo-Riemann spaces to describe space-time -- has been (spectacularly) experimentally confirmed. Motivated by this success, Urysohn started working on an extension of his lemma …