%0 Journal Article
%T The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics
%J Mathematics Interdisciplinary Research
%I University of Kashan
%Z 2538-3639
%A Chatelin, Françoise
%D 2016
%\ 01/01/2016
%V 1
%N 1
%P 199-228
%! The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics
%K Relator
%K noncommutativity
%K nonassociativity
%K induced addition
%K organ
%K metric cloth
%K weaving information processing
%K cloth geometry
%K hyperbolic geometry
%K special relativity
%K liaison
%K geodesic
%K organic line
%K action at a distance
%R 10.22052/mir.2016.13924
%X This 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.
%U http://mir.kashanu.ac.ir/article_13924_66d8c3b9adb9b68702310db250cb14db.pdf