TY - JOUR
ID - 40434
TI - Everyday physics of extended bodies or why functionals need analyzing
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Lawvere, F. William
AD - Professor Emeritus, Department of Mathematics, University at Buffalo, Buffalo, New York 14260-2900, United States of America.
Y1 - 2017
PY - 2017
VL - 6
IS - Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)
SP - 9
EP - 19
KW - Functionals
KW - physics
DO -
N2 - Functionals were discovered and used by Volterra over a century ago in his study of the motions of viscous elastic materials and electromagnetic fields. The need to precisely account for the qualitative effects of the cohesion and shape of the domains of these functionals was the major impetus to the development of the branch of mathematics known as topology, and today large numbers of mathematicians still devote their work to a detailed technical analysis of functionals. Yet the concept needs to be understood by all people who want to fully participate in 21st century society. Through some explicit use of mathematical categories and their transformations, functionals can be treated in a way which is non-technical and yet permits considerable reliable development of thought. We show how a deformable body such as a storm cloud can be viewed as a kind of space in its own right, as can an interval of time such as an afternoon; the infinite-dimensional spaces of configurations of the body and of its states of motion are constructed, and the role of the infinitesimal law of its motion revealed. We take nilpotent infinitesimals as given, and follow Euler in defining real numbers as ratios of infinitesimals.
UR - https://cgasa.sbu.ac.ir/article_40434.html
L1 - https://cgasa.sbu.ac.ir/article_40434_9767cf7e5bb1b3e6e8b6cb442625ee0f.pdf
ER -