Relation between Observers and Effects of Number Valuation in Science

Year
2018
Volume 19
Issue 2
Pages
229-251
Authors
Paul Benioff
Abstract
This paper is a small step towards the goal of constructing a coherent theory of
physic and mathematics together. It is based on two ideas, the localization of
mathematical systems in space or space time, and the separation of the concepts
of number from number value. The separation of number from number value
along with the freedom of choice of number values at different points of space or
space time enables the introduction of a space or space time dependent number
valuation field. The presence of a location dependent number value field affects
theoretical descriptions of many physical and geometric quantities. A simple
geometric example is worked out in detail, that of the length of a path.
The localization of mathematical systems and the separation of number from
number value or meaning both emphasize the role of observers. The separation of
number from number value shows the role of observers in that value or meaning
are conscious observer related concepts. Nothing, including numbers, has value
or meaning to an unconscious observer. The localization of mathematical systems
also shows the role of observers in that the mathematics that is potentially
available to an observer is that at the same position as is the observer. This
represents the mathematical knowledge that can reside in an observers brain. As
an observer moves in space or space time, the mathematical knowledge
potentially available to the observer is the collection of mathematical systems at
the same location as the observer. It is hoped that this work, which was begun in
2010, will lead to a better understanding of the relation between the foundations
of mathematics and physics, and the role that observers play in this relation.

Keywords: choice freedom of number values; local mathematical systems;
observers, number values, and local systems