Re: Rotations - why are they not vectors


<mariano.suarezalvarez@xxxxxxxxx> wrote in message
news:1153025545.663758.95150@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Terry Padden wrote:
I am bothered by the mathematics of rotations. It is I believe
mathematically acceptable for any physical reality to be defined on an
abstract axiomatic basis. Then anything that fulfills a given defining
set
of axioms for a type of mathematical object is a mathematically valid
example of the defined mathematical object.

A set does not make a vector space.

You B***** Fool. Who mentioned sets !!

You need to specify
two operations, addition and multiplication by scalars.

The obvious ones you moron. You can ADD rotations; and you can SCALE
rotations by a suitable Field. Idiot !!

[snip]
NB I am aware that 2-D rotations do-not-commute, but it seems to me that
that has nothing to do with axiomatics or my questions.

Actually, the composition operation on rotations (with a fixed center)
in the plane *is* commutative.

Yes you fool - but that is in 1-D ; and I wrote do-not-commute in 2-D.
Can't
you even read a simple sentence ???


You may want to review Halmos' presentation of what a vector space
is, if you think that commutativity is irrelevant, by the way...

NO ! I want you to go AWAY !!!!!!




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