Re: elementary but precise definition of clockwise.

In article
<1546fae5-80f9-42eb-af74-9c656385759f@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
pauldepstein@xxxxxxx wrote:

....
Is there an elementary but rigorous way of capturing the distinction
between such paths being "clockwise" or "anti-clockwise"?


Not by pure mathematics.


One way is
to look at the winding number as defined in homotopy theory and seeing
whether the winding number is positive or negative....


If you look far enough back in that theory you'll find a
right/left convention somewhere.

There is absolutely no _mathematical_ way to specify "right" and
"left", or equivalently "clockwise" and "anticlockwise". Mathematics
will tell you (for example by using positive and negative determinants)
that there are two sides/orientations, but it treats them both alike.
Because of that symmetry, the only way to define "right" or "left" is by
means of something _physical_.

When you were a small child, somebody may have touched one of your
hands and told you whether it was right or left. It can also be
specified by using the Earth's rotation, or by the direction in which
certain nuclear processes spit out particles; but it always needs
something physical.

Our usual Cartesian axes have x values positive on the right and y
values positive at the top. That's a physical description of what we
draw on paper, but there's no purely mathematical way to say it on an
abstractly defined Euclidean plane. Try!

Ken Pledger.
.