It's clear that this mistake was made even before complex numbers were invented, when somebody incorrectly concluded that the real number line was horizontal. Apparently this unsung genius thought that the difference between positive numbers and negative numbers was no more salient than the difference between left and right. On Tue, Jun 21, 2016 at 4:44 PM, 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:
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun