??so consider .... ????.... random jump operator on circle where .... ???probability density of destination is given by inner product with origin ... ??? .... ???then ... from this construct random jump operators on space of "ordered orthonormal basises of euclidean n-space" in hopefully sort of obvious way .... ????then whether these satisfy some sort of braid relation ??? ...

??hmm, maybe not ... ??pretty unclear to me at the moment ...

??? archimedes's method for picking random point on surface of sphere ... random longitude and random ... ?? inner product with north pole ... ????? ....

?? gauss ... -ian ... ??? ....

?? idea that it's no good if both choices are by longitude or both by inner product with north pole; you need one one way and the other the other; and that screws things up ?? ... ??? ....

?? sas vs asa ... ????

a,b,c

(a.b)(aXb . bXc)(b.c) ???

??? vs ... ???

(aXb . aXc)(a.c)(aXc . bXc) ???

????? .....

(a.b)(c'.a')(b.c) =?= (c'.b')(a.c)(b'.a') ???


???or ... ??? maybe some reciprocals somewhere ... ??? ... ????....


1 a b
a 1 c
b c 1

1 ? ?
? 1 ?
? ? 1