Chatelin, F. (2016). The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics. Mathematics Interdisciplinary Research, 1(1), 199-228. doi: 10.22052/mir.2016.13924

Françoise Chatelin. "The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics". Mathematics Interdisciplinary Research, 1, 1, 2016, 199-228. doi: 10.22052/mir.2016.13924

Chatelin, F. (2016). 'The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics', Mathematics Interdisciplinary Research, 1(1), pp. 199-228. doi: 10.22052/mir.2016.13924

Chatelin, F. The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics. Mathematics Interdisciplinary Research, 2016; 1(1): 199-228. doi: 10.22052/mir.2016.13924

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

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.