Towards the Mathematics of Intelligence
Soenke Ziesche, Roman V. Yampolskiy · 2025
In this chapter, we aim to contribute further to the still very young field of “intellectology”, which examines the space of possible minds and was introduced by Yampolskiy. We are looking at mathematical properties of sets of minds as well as minds in nested constellations by utilising operations of set theory. More specifically, we study the mathematics of intelligence of set unions and complements as well as subsets with intelligence being an inherent feature of minds. For example, if a mind A with intelligence of 100 is united with a mind B with intelligence of 110 what do we get? As with many aspects of intellectology, this area is largely unexplored. This chapter is structured as follows: in the first section, we describe potential constellations of minds that have been proposed earlier by using set theory, which appears to be a useful instrument for our purposes. This is followed by a section about the definition and evaluation of intelligence, which is a challenging field itself. In the subsequent main section, we investigate the math of intelligence for grouped minds, nested minds and deducted minds.