@article {
author = {Chatelin, Françoise},
title = {The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics},
journal = {Mathematics Interdisciplinary Research},
volume = {1},
number = {1},
pages = {199-228},
year = {2016},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2016.13924},
abstract = {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.},
keywords = {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},
url = {http://mir.kashanu.ac.ir/article_13924.html},
eprint = {http://mir.kashanu.ac.ir/article_13924_66d8c3b9adb9b68702310db250cb14db.pdf}
}