To What Extent Do We See With Mathematics?

Joselle Kehoe:

When I first became fascinated with mathematics’ tightly knit abstract structures, its prominence in physics and engineering reassured me. Mathematics’ indisputable value in science made it clear that my preoccupation with its intangible expressions was not pathological. The captivating creative activity of doing mathematics has real consequences.

During my graduate school years, I began to consider that the appearance of reality actually depended on the kind of mathematics we use to see it. Was it possible that the use of mathematical ideas, like a lens, could bring some aspects of the world into sharp focus while blurring others to the point of invisibility? A new mathematics, whose development is being led by author and theoretical physicist David Deutsch, may actually highlight what mathematics can do to help us “see” our reality, and maybe even tell us something about how the process works. Deutsch is best known for his pioneering work on the quantum theory of computation, where some of the more mysterious quantum phenomena are harnessed to dramatically enhance computation. While his new mathematics is related to the quantum theory of computation, it is also distinct from it. He calls the new mathematics constructor theory: a theory designed to tell us, in the most general sense, what is and is not possible in the physical world.

Deutsch has discussed constructor theory before. An unexpected early success of the theory, he has said, has provided a new foundation for information theory. Information theory involves the quantification of information. But perhaps most relevant to this discussion is that information theory equates abstract things such as words, coded data and algorithms with physical things such as like electric signals, chemical exchanges and molecular coding. Since they are all information, the employment of information theory is transdisciplinary. Just a few of the disciplines included in its range of application are physics, electrical engineering, linguistics and neurobiology. The processing of information, expressed in the formalism of mathematics, captures the action of many kinds of systems.