University of KashanMathematics Interdisciplinary Research2538-36391120160101The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics1992281392410.22052/mir.2016.13924ENFrançoiseChatelinUniversite Toulouse 1 Capitole,Journal Article20151119This paper extends the scope of algebraic computation based on a non standard $times$ 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 $pluscirc$ 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.http://mir.kashanu.ac.ir/article_13924_66d8c3b9adb9b68702310db250cb14db.pdf