Open AccessShifts in the Foundation: The Continual Modification and Generalization of Axioms and the Search for the Mathematical Principles that Underlie our Reality
Author(s) -
Indrajit Patra
Publication year - 2021
Publication title -
türk bilgisayar ve matematik eğitimi dergisi
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.218
H-Index - 3
ISSN - 1309-4653
DOI - 10.17762/turcomat.v12i2.1126
Subject(s) - generalization , axiom , abstraction , construct (python library) , foundation (evidence) , quaternion , hypercomplex number , computer science , universe , mathematical structure , epistemology , mathematics , algebra over a field , pure mathematics , mathematics education , philosophy , quantum mechanics , physics , geometry , archaeology , history , programming language
The study shall seek to explore the deep, underlying correspondence between the mathematical world of pure numbers and our physical reality. The study begins by pointing out that while the familiar, one-dimensional real numbers quantify many aspects of our day-to-day reality, complex numbers provide the mathematical foundations of quantum mechanics and also describe the behavior of more complicated quantum networks and multi-party correlations, and quaternions underlie Einsteinian special theory of relativity, and then poses the question whether the octonions could play a similar role in constructing a grander theory of our universe. The study then points out that by increasing the level of abstraction and generalization of axiomatic assumptions, we could construct a more powerful number system based on octonions, the seditions, or even other hypercomplex numbers so that we may more accurately describe the universe in its totality.