University of Kashan Mathematics Interdisciplinary Research 2538-3639 1 1 2016 01 01 The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics 199 228 13924 10.22052/mir.2016.13924 EN Françoise Chatelin Ceremath, Université Toulouse 1 Capitole, and CERFACS, 42 avenue G. Coriolis 31057, Toulouse Cedex 1, France Journal Article 2015 11 19 ‎This paper extends the scope of algebraic computation based on a non standard × to ‎the more basic case of a non standard +‎, ‎where standard means associative ‎and commutative‎. ‎Two physically meaningful examples of a non standard + are ‎provided by the observation of motion in Special Relativity‎, ‎from either ‎outside (3D) or inside (2D or more)‎, ‎We revisit the "gyro"-theory of Ungar to present ‎the multifaceted information processing which is created by a metric cloth W‎, ‎a relating computational construct framed in a normed vector space V‎, ‎and based ‎on a non standard addition denoted ⊕ whose commutativity and associativity ‎are ruled (woven) by a relator‎, ‎that is a map which assigns to each pair of admissible vectors ‎in V an automorphism in Aut(W‎). ‎Special attention is given to the case where the relator is ‎directional‎. Relator‎ ‎noncommutativity‎ ‎nonassociativity‎ Induced addition‎ ‎organ‎ ‎metric‎ ‎cloth‎ ‎weaving information processing‎ ‎cloth geometry‎ ‎hyperbolic geometry‎ special relativity‎ ‎liaison‎ ‎geodesic‎ ‎organic line‎ ‎action at‎ ‎a distance‎ https://mir.kashanu.ac.ir/article_13924_66d8c3b9adb9b68702310db250cb14db.pdf