At 16:14 -0700 7/12/1999, Jonathan Coxhead wrote:
> I see CLOCKWISE INTEGRAL and 2 subsequent characters listed in the
>"mirrored" section of the Unicode Standard. I don't know a lot about
>right-to-left writing systems, and less about how mathematics is layed
>out within them, but isn't the notion of "clockwise" based on the
>direction of the sun,
For sundials in the Northern Hemisphere, yes. Presumably cathedral clocks
(which started out with only one hand) mimicked this behavior, thus
producing the much-reviled (on this group, anyway) twice-in-one-day
starting-with-hour-12 clock after a few more cultural permutations.
and so the same in all writing directions?
Yes, but where does it *start* in different writing directions? ;->
> Are these 3 characters there erroneously?
>
> And if there are there correctly, shouldn't COMBINING (ANTI-)
>CLOCKWISE RING OVERLAY and COMBINING (ANTI-) CLOCKWISE ARROW ABOVE be
>present as well?
Indeed, mirroring the conventional direction of integration would cause
havoc in the schools, since it would reverse the sign of the result. No
problem for holomorphic (infinitely differentiable) complex functions, for
which all integrals around a circle come to 0 (stated more precisely, 0+0i,
or 0j0 in Ken Iverson's latest language j) but not so good for meromorphic
functions such as $1/(Z^n)$ (where the integrals are sums of multiples of a
small set of values, starting with $2\pi i$). Integrating around an
essential singularity would not be made hairier by mirror reflection.
> (Maybe it's just the "integral" part that should be mirrored: in
>that case, a note would clarify the intention.)
>
> /|
> o o o (_|/
> /|
> (_/
It is a curiosity of no great significance that if you reverse the
direction of the integrals, and at the same time swap the roles of i and
-i, everything works out correctly. Of course, i and -i are defined to be
the two square roots of -1, with nothing whatsoever in that definition to
distinguish them, so in fact we don't know which one we picked.
Ed Cherlin
"Everything I see reminds me of you, except you. What do you make of that?
(aside) If she can figure that one out, she's good."--Groucho Marx, in A
Night at the Opera
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