THE CALCULATIONS OF CYCLE LENGTHS,
Abstract
A complete set of calculations of cycles of all levels was devised so that comparison with experiment could be made by selection according to special rules from the totality of cycles. The levels of interest are those of increasing descriptive power such as may derive from infinitely proceeding sequences as in the inflow of data into a hierarchial-type information processing system. The algebraic hierarchy generated consists of judgments that can be made about the future development of the sequences expressed in the form of matrix transforms of vectors over the field. Sequences are said to cycle in such a form as V, AV, A squared V . . . A to the jth power V . . . , where the sequence must contain the term A to the kth power V so that A to the kth power V = V. By putting this property of a cycling sequence in terms of the hierarchial concept, there results: To every vector at level K, there corresponds a cycle at level K minus 1. Calculations were made by their multiplication and enumeration, and a standard form for the matrix and initial vector was used which would generate all possible cycles. The spectrum of cycles has been thought of chiefly in connection with the spectrum of masses of the elementary particles.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1964
- Accession Number
- AD0622584
Entities
People
- Michael J. Roy
- Ted Bastin