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