Re: elementary but precise definition of clockwise.

K. E. Pledger wrote:

In article
<1546fae5-80f9-42eb-af74-9c656385759f@xxxxxxxxxxxxxxxx
egroups.com>,
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.

[...]

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
y have touched one of your
hands and told you whether it was right or left.

Your point is very clear and very interesting (as well as the whole discussion). Thinking out loud, one-asymmetry -> direction, two-asymmetry -> orientation...?

Anyway, the most interesting point, to me, is the potential connection between "mathematics", "physics", and "memory" (and the potential connection to "intelligence", in a positive or negative way, that to be ascertained).

BTW, I wander if L-functions could have any bearing on this problem of "orientation". As far as I get it, they provide some intrinsic asymmetry, although I cannot understand if that is enough to connect the two worlds of maths and physics.

OTOH, I wander about the potential connections with the concept of Entropy, which seems cyclical (at least in some self-similar way), though asymmetrical (directed, or rather "oriented").

Thanks.

Julio
.