well, I can tell you right now it falls apart, as one of the assumptions is invalid:<br /><br /><blockquote><font class="small">In reply to:</font><hr /><p>The Physical Universe conforms to the relations of<br />ORDINARY COMMUTATIVE<p><hr /></p></p></blockquote> Rotation doesn't fit that, try it. Rotate a book around all three axis...Lay it flat in front of you, looking at the front cover.<br /><br />Now, rotate it upright (standing up, facing you).<br /><br />next, rotate it 90 degrees counterclockwise about the verticle axis (now standing up and facing to your right).<br /><br />Then rotate it about the horizontal axis pointing away from you (i.e. it down and to the right, laying it on it's face). You have done 3 90 degree rotations about different axis.<br /><br />Do those steps in different orders. If it is truly commutative, you will always end up with the book in the same position, since A*B*C = A*C*B = C*B*A = B*A*C = B*C*A.<br /><br />But it won't work.<br /><br />Heck, you can do it with two steps. Rotate it up around the verticle axis 90 degrees, then around the horizontal axis that runs parrallel to the table edge (i.e. flip it up towards you). Start over with it in the same spot, and instead rotate it up towards you, then around the verticle axis.<br /><br />You don't get the same thing.<br /><br />Rotation is not commutative.<br /> <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>