the center of the world (was Re: Check out O'Reilly's Open Source Convention Highlights)

[Alex Martelli]

"Grant Griffin" <not.this at seebelow.org> wrote in message
news:3B3B2DED.5303198A at seebelow.org...
    ...
> Hey, who said anything about "world"?...

Kernighan and Ritchie did (they were greeting it, I believe).


> But now that you mention it, the US Midwest *is* pretty centrally
> located on a "world" basis.
>
> as-much-as-anything-else-on-this-sphere-<wink>-ly y'rs,

An interesting exercise might be to define a *meaningful*
"central location" -- one based on population distribution
(or other geographical distributions of interest).

After all, since tunas are unlikely to attend a conference
on technical computer issues (given that you can tune a
filesystem, but you can't tuna fish), "weighting" the vast
aquaceous parts of the (approximate) "sphere" equally to
the populated landmass may be a fine exercise in geometry,
but doesn't make much sense otherwise.  As soon as you want
to move from pure geometry to some kind of geography, I
think some demographic issues must arise.  Even without
considering demographics, at least some account could be
taken of land vs ocean and maybe of land with/without
permanent ice covering.

Some data, ordered by-country, can easily be found for free
on the web, http://www.worldbank.org/data/wdi2001/worldview.htm
for example.  Latitudes and longitudes of cities in various
countries are also easily available, e.g. at
http://www.realestate3d.com/gps/world-latlong.htm.  We can
get a first approximation for a distribution of world human
population by assuming a country's population is divided
equally among its major cities.  This will require some work
and supervision because of varying formats etc in the files
being used -- or is there somewhere on the net that already
gives me in a single readable file a lot of data boiled down
to triples (population, latitude, longitude)?  Anyway, once
I do have such a file, I can presumably find the "center of
the world" (approximate) -- the one point on the Earth's surface
that minimizes population-weighted sum of great-circle distances
to 'population centers'.  Of course I could get different
centers by choosing different weighing factors (country GNP
rather than country population, for example).

Hmmm, if the coordinates were on a plane, finding the weighed
center would be trivial, but offhand I can't think of how to
do it on a sphere's surface -- I guess there must be some way
more suitable than just solving a generalized extremization
problem -- can anybody suggest one...?

Of course, there are enough degrees of freedom in the outlined
procedure that it can probably be used for my real purpose, i.e.,
proving that the relevant "center of the world" is within easy
walking distance from my home and thereby convincing the PS^H^H
O'Reilly to hold their next conference somewhere that's highly
convenient for me...


Alex