TY - JOUR
ID - 13924
TI - The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Chatelin, Françoise
AD - Universite Toulouse 1 Capitole,
Y1 - 2016
PY - 2016
VL - 1
IS - 1
SP - 199
EP - 228
KW - Relator
KW - noncommutativity
KW - nonassociativity
KW - induced addition
KW - organ
KW - metric cloth
KW - weaving information processing
KW - cloth geometry
KW - hyperbolic geometry
KW - special relativity
KW - liaison
KW - geodesic
KW - organic line
KW - action at a distance
DO - 10.22052/mir.2016.13924
N2 - 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.
UR - http://mir.kashanu.ac.ir/article_13924.html
L1 - http://mir.kashanu.ac.ir/article_13924_66d8c3b9adb9b68702310db250cb14db.pdf
ER -