SysteMATHics

"Systemathics" is a temporary title for this collection of information. It relates to Systematics, a discipline started by John G. Bennett. The material here is a re-working and extension of the ideas expressed in a document I wrote in the years 1997-1999, most recently titled Foundations of Number, Structure & Pattern. You can download this as a PDF file (readable with the Adobe Acrobat Reader).

Systematics is (my interpretation) an attempt to understand the meaning implicit in number. Systems of a given size have properties that can be applied in a variety of domains. N-Gram patterns form one part of Systematics. They might be called mathematical organizing thoughts. Archetypes play a similar role in the unconscious, and dreams. A systematician's approach to number may be similar to the approach of a psychoanalyst or shaman to archetypes.

Numbers as we know them are a sort of fractal, in the sense that as we change scale, the patterns formed remain similar, if not identical, to those observed at other scales. Two added to three is five, singly or by the millions. A million divided by 7 is 142,857-with one left over to begin the fraction formed from the same pattern of digits , repeated for as far as one wants to extend the calculation.

There are three areas of mathematical exploration covered in the web pages connected with this one.

Tridaic Numbers - The base N number system usually uses digits 0 to N-1 (e.g., our everyday base ten uses digits 0-9, binary numbers - base 2 - use digits 0 and 1). A number system can also be constructed using digits -1, 0, and 1. A similar number system can be created for any odd number base, with 0 as the middle value for the digits. Such number systems have some interesting properties, for instance, truncation and rounding are the same operation.

N-Grams - This is an exploration into number patterns expressed graphically using the "rules" implicit in the Enneagram.

Dimensionalities - Coordinate systems other than the X-Y-Z first delineated by Descartes are possible for describing the relationships of objects. This exploration of other coordinate systems (found in the Platonic solids and other such shapes) could be a start at extending Systematics past number into geometric structure.

Contacting the Author

If you wish to write to me, send e-mail to sigurdvt@gmail.com - Sigurd Andersen