I think that Hamilton favored left-hand coordinates; does anyone know if he himself was left-handed ?
I'm left handed and I much prefer right hand coordinates. They are quite convenient. A left handed person can hold a pencil and write all while looking at their right hand representation of the coordinate system. They don't have to put the coordinate system down in order to do something else. Very convenient for those of us who work best with visual props. I'd suppose that a left handed system would be similarly attractive to a right handed person. -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Henry Baker Sent: Saturday, November 24, 2007 8:12 AM To: Fred lunnon Cc: math-fun; Dan Asimov Subject: Re: [math-fun] The Axiom of Choice for roots of z^2 + 1 I thought that physics was such that if Pooh chose the wrong paw, time would then go backward... (CPT - invariant only if charge, parity & time are all simultaneously interchanged.) -- Also, in quaternions, x^2+1=0 has an infinity of solutions, as Hamilton points out. I think that Hamilton favored left-hand coordinates; does anyone know if he himself was left-handed ? At 02:27 AM 11/24/2007, Fred lunnon wrote:
On 11/23/07, Dan Asimov <dasimov@earthlink.net> wrote:
I've often wondered if it is somehow a mistake for mathematics to distinguish between i and -i.
There is absolutely no mathematical way to distinguish between the two. Perhaps they should only be referred to as a pair, and never one at a time?
Opinions?
--Dan
"Pooh looked at his paws. He knew that one of them was the right, and he knew that when you had decided which one of them was the right, then
the other one was the left, but he could never remember how to begin." [A.A.Milne (1926); http://www.everfree.ca/2007/01/pooh_on_your_shoe_kid.html]
And, using elementary physics at least, there's also no way to tell the
difference. But the existence of symmetry doesn't (necessarily) imply that it's a good idea to factor out the symmetry group!
One situation where something analogous does routinely occur is classical projective geometry; and it's a significant nuisance when this discipline is applied to computer graphics, etc. [In practice it can be repaired by retaining the sign when normalising homogeneous coordinates --- easily overlooked in a coordinate system based on points, the only subspaces which happen not to be orientable.]
Some authors have attempted to repair the omission --- see e.g. Jorge~Stolfi \sl Oriented Projective Geometry \rm Academic Press (1991); www.dcc.unicamp.br/~stolfi --- but the extra complexity doesn't engender any apparent mathematical
interest, merely engineering practicality.
Fred Lunnon
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