The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics

Document Type : Special Issue: AIMC 51


Ceremath, Université Toulouse 1 Capitole, and CERFACS, 42 avenue G. Coriolis 31057, Toulouse Cedex 1, France


‎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.


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