Re: Epistemology 201: The Science of Science

mmeron_at_cars3.uchicago.edu
Date: 02/11/05 

Date: Fri, 11 Feb 2005 20:50:57 GMT

In article <373kamF57llg0U2@individual.net>, "robert j. kolker" <nowhere@nowhere.net> writes:
>
>
>Albert wrote:
>>
>> Don't spheres exist in Euclidean geometry?
>
>As do spherical surfaces. On a spherical survace "straight lines" are
>great circles.

Nope. Geodesic lines are great circles. A geodesic line within an
imbedded (in higher dimensional space) surface is *not* a straight
line, in general.

And yes, spheres do exist in Euclidean geometry and spherical angles
were already researched by the Greeks. There is *nothing*
non-Euclidean about spheres. The claim that spherical surfaces prove
that space is non-Euclidean comes form cheap coffee table
popularizations and is not only wrong but downright ***idiotic***.

What is ture is that if you take a spherical surface and consider it
to be a plane, *then* it is a plane with non-euclidean geometry. But
that's a different story.

Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"

Relevant Pages