ABSTRACT

The data analysis framework, that is, the geometry and topology of the data that we are both investigating and making use of, will be considered in this chapter in p-adic number system terms, rather than in real number terms. The chapter describes, with examples, what p-adic numbers are all about. They are an alternative to the real numbers. The leading mathematician and engineer, Alexey Stakhov, gives detailed and far-reaching discussion of the benefits of ternary number theory for computation. The ultrametric topology was introduced by Marc Krasner in 1944, the ultrametric inequality having been formulated by Hausdorff in 1934. An unbounded increase in mass, or other measured quantity, is described in the chapter as leading to zero or negative outcome value. The ultrametric space, with a hierarchical tree representing it, consists of energy basins, that can be embedded. So these energy basins are locally stable states.