This week I submitted my essay to the 2015 FQXi Essay Contest, Trick or Truth?, which is focused on the surprising success of mathematics and its relationship between mathematics and physics.
My essay titled “The Deeper Roles of Mathematics in Physical Laws” demonstrates the deeper relationships between mathematics and physics by considering the concept of consistent quantification applied to the simple case of combining things, which in certain cases leads to additivity. This is an important essay for me since the concept of consistent quantification is central to much of our foundational work.
Our essay can be found here:
Please vote if you feel it.
And read and vote on the other essays too.
Here is the abstract:
The Deeper Roles of Mathematics in Physical Laws
Kevin H. Knuth
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as exemplified by the laws of physics. In this essay, I claim that much of the utility of mathematics arises from our choice of description of the physical world coupled with our desire to quantify it. This will be demonstrated in a practical sense by considering one of the most fundamental concepts of mathematics: additivity. This example will be used to show how many physical laws can be derived as constraint equations enforcing relevant symmetries in a sense that is far more fundamental than commonly appreciated.