Numeric Representation and the Boundary of Pure and Applied Mathematics Abstract: Being so basic to mathematics, numeric representational systems touch many areas of the discipline. Numeric systems could be said to lie on the boundary of pure and applied mathematics, […]

MATH 4.0 REQUIRES A RE-BOOT OF SCIENCE Scientists from both the theoretical and experimental sides of science have, apparently, overlooked the importance of numerical systems in science’s development. The same situation has been true of mathematics, as both math and […]

Abstract: Assumptions about what is a theory and what is a mathematical model are considered related to the question “How can mindless mathematical laws give rise to aims and intentions?”. Theory cannot be reduced to a mathematical model and requires […]

My essay entry to the FQXi 2015 Essay Contest “Trick or Truth: the Mysterious Connection Between Physics and Mathematics”:  Can Mathematics Reasonably Represent Nature?

A comment I made to an essay by Peter Jackson in the FQXi Essay contest: Consider the number of squared quantities in physical theories along with the connection to complex numbers.  If we have a squared value, then the ‘real’ […]

If we consider what is needed to advance science today many responses will list a number of unsolved complex mathematical problems. However these responses would presume the major hindrance to advances in science and engineering is the resolution of known, […]

If scale is a physical continuum, then shouldn’t there be situations we must use a cross-scale approach?  What sorts of problems might require such a cross-scale approach? Consider attempting to determine the combined velocity of a small object (on earth) […]

We do consider scale as part of our reality.  We even consider it to be a continuum of reality, if not part of our 3-D model of space.  However, we experience objects as appearing differently at different scales.  Our bodies […]

To understand how basic this concept of scale is, consider specifying a point in space.  We need a reference system for this, traditionally thought of as a three-dimensional set of axes.  One axis exists for each dimension and locating a […]

The size, or scale, of objects in our world is a commonplace part of our universe.  We experience objects smaller than ourselves, like a pin, and objects larger than ourselves, like a building.  For centuries our reality did not go […]