Part of the series The Frontiers Collection pp 201217
Cognitive Science and the Connection Between Physics and Mathematics
 Anshu Gupta MujumdarAffiliated with Email author
 , Tejinder SinghAffiliated withTata Institute of Fundamental Research
Abstract
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in the brain from these primordial perceptions, using what are known as conceptual metaphors. Known cognitive mechanisms give rise to the extremely precise and logical language of mathematics. Thus all of the vastness of mathematics, with its beautiful theorems, is human mathematics. It resides in the mind, and is not ‘out there’. Physics is an experimental science in which results of experiments are described in terms of concrete concepts—these concepts are also built from our primordial perceptions. The goal of theoretical physics is to describe the experimentally observed regularity of the physical world in an unambiguous, precise and logical manner. To do so, the brain resorts to the welldefined abstract concepts which the mind has metaphored from our primordial perceptions. Since both the concrete and the abstract are derived from the primordial, the connection between physics and mathematics is not mysterious, but natural. This connection is established in the human brain, where a small subset of the vast human mathematics is cognitively fitted to describe the regularity of the universe. Theoretical physics should be thought of as a branch of mathematics, whose axioms are motivated by observations of the physical world. We use the example of quantum theory to demonstrate the all too human nature of the physicsmathematics connection: it is at times frail, and imperfect. Our resistance to take this imperfection sufficiently seriously (since no known experiment violates quantum theory) shows the fundamental importance of experiments in physics. This is unlike in mathematics, the goal there being to search for logical and elegant relations amongst abstract concepts which the mind creates.
 Title
 Cognitive Science and the Connection Between Physics and Mathematics
 Book Title
 Trick or Truth?
 Book Subtitle
 The Mysterious Connection Between Physics and Mathematics
 Pages
 pp 201217
 Copyright
 2016
 DOI
 10.1007/9783319274959_18
 Print ISBN
 9783319274942
 Online ISBN
 9783319274959
 Series Title
 The Frontiers Collection
 Series ISSN
 16123018
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing Switzerland
 Additional Links
 Topics
 eBook Packages
 Editors

 Anthony Aguirre ^{(8)}
 Brendan Foster ^{(9)}
 Zeeya Merali ^{(10)}
 Editor Affiliations

 8. Dept of Physics, UC Santa Cruz
 9. Foundational Questions Institute
 10. Foundational Questions Institute
 Authors

 Anshu Gupta Mujumdar ^{(11)}
 Tejinder Singh ^{(12)}
 Author Affiliations

 11. 706, Bhaskara, TIFR Housing Complex, Homi Bhabha Road, Mumbai, 400005, India
 12. Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India
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