Maybe it's the extra printer's ink in the minus sign. Try renaming "i" as "+i" , and observe whether the diagrams trun trutle --- er, turn turtle. In the case of Clifford algebra, it's not the sign of a vector itself that signifies (so to speak), but the difference in signs, which --- in some fashion which I do not understand --- seems to be associated with electron spin: rotation of the vector through 2 pi changes its sign, although both vectors represent the same geometric reflection. WFL On 6/21/16, Dan Asimov <dasimov@earthlink.net> wrote:
Jim is right. I always wondered why -i was heavier.
—Dan
On Jun 21, 2016, at 12:19 PM, James Propp <jamespropp@gmail.com> wrote:
Dan is too conservative. The real axis should be vertical, not horizontal. That way, the Galois symmetry between +i and -i would be reflected in the left-right symmetry of macroscopic phenomena in earth's gravitational well.
This convention would work well on blackboards and whiteboards, but I imagine some students would interfere with this crusade for logical consistency by placing their textbooks face-up on a desk or table and reading from them in that position. We'd have to make that illegal, of course.
:-)
Jim Propp
On Tuesday, June 21, 2016, Dan Asimov <asimov@msri.org> wrote:
A somewhat related thing is the naming of the two square roots of -1 in the complex plane. I have long thought that the one in the upper half plane and named i (no reason either of these two things should change, of course) is actually the one that is in the lower half plane and named -i. And vice versa as well.
Correcting these long-held misconceptions would cause profound changes to ripple through mathematics.
—Dan
On Jun 21, 2016, at 9:42 AM, Fred Lunnon <fred.lunnon@gmail.com <javascript:;>> wrote:
For as long as I have known not very much about physics , experts have disagreed over the sign of the Minkowski metric:
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