the center of the world

[Nick Perkins]

"Alex Martelli" <aleaxit at yahoo.com> wrote in message
news:9i7tjr11b9o at enews3.newsguy.com...
> "Keith F. Woeltje" <kwoeltje at mail.mcg.edu> wrote in message
> news:3B471BA4.7050306 at mail.mcg.edu...
> > Saw this on slashdot and thought of this thread. Here's what the Debian
> > folks did. My trig is pretty rusty, so I'm not sure the method is
correct.
> >
> > http://people.debian.org/~edward/average/
>
> Thanks for the reference (and I thought I was being original...!), but
> it seems to me the algorithm they're using is exactly the one that has
> been proven wrong on this thread: they compute the 3D center and
> project it back onto the sphere's surface.  Intuitively appealing, but
> just doesn't work right...
>
>
> Alex


So who is going to tell the Debian folks that their next conference should
actually be a bit closer to the north pole?

( which i only suspect to be the proper result,
  from eyeballing the beautiful 3d maps they have.. )

((still no idea how to solve it properly..
  ..(hill-climbing search?) ))


BTW, was thinking again about the thought-experiment with 50 people together
near the north pole, and 51 people together near the south pole...<by Keith
Woeltje>..

I agree that the 'centre of gravity projection to the surface' is probably
wrong, but i think the 'obvious' result, that the centre should be just near
the equator, is flawed:
If the goal is to find the spot which minimizes the total person-distance of
travel for all to meet, then would it not be that the point minimizing this
total would be exactly where the 51 people are?  It would be cheaper than
any point in-between!  So it would seem that the 'projection' method may not
be that far off, and perhaps it is actually quite accurate for large
populations.  I can't decide.  People at Debian seem to think it's right, or
at least close enough.