Re: Letter to the Editor: The truth of ID is self-evident
- From: "rja.carnegie@xxxxxxxxxx" <rja.carnegie@xxxxxxxxxx>
- Date: 11 Feb 2006 15:09:25 -0800
nmp wrote:
On Sat, 11 Feb 2006 11:18:30 -0600, it was decided that Leonard Evens
should write:
The formula Pi R squared, applies not to physical circles but to
circles in Euclidena geometry, which the anceints from Euclid on
understood as an axiomatic system. The derivation of the formula was
based on reasoning from the principles, and didn't depend for
verification on any measurements. Of course, the ancients thought that
Euclidean geometry described the geometry of real objects, and it does
to a high degree of precision in our immediate local environment. But
since einstein, we know that it doesn't describe the geometry of space
exactly in the vicinity of massive objects. This doesn't make much
difference in most practical applications on Earth, but it is a large
enough effect to affect the accuracy of GPS locators. In any case,
Archimedes reasoning was as valid at the time as it is today, and still
applies to circles in Euclidean geometry. No physical proof is
necessary. Indeed physical evidence today shows us that the formula is
not quite correct when applied to circles in the actual universe.
Wait, I don't get it. I already said I am not a mathematician and in
fact I rather sucked at it in high school. So what are you saying here?
That circles "in the wild" are not always real circles? I could
understand that. But if you say that one can have a true circle where
nevertheless Pi*r^2 does not apply, than this is news for me.
A physical circle has an inside and an outside that are separate, for
instance by the thickness of a pencil line. Therefore Pi*r^2 does not
apply exactly.
As for non-Euclidean geometry, consider a curve one mile north of the
equator (or indeed just consider the equator) as the circumference of
the northern hemisphere. However, the surface area enclosed is not
Pi*r^2.
Or look at it this way... if the Egyptians and Babylonians put up with
a defective pi for thousands of years, then it isn't so obviously true
as that.
.
- References:
- Letter to the Editor: The truth of ID is self-evident
- From: Jason Spaceman
- Re: Letter to the Editor: The truth of ID is self-evident
- From: Leonard Evens
- Letter to the Editor: The truth of ID is self-evident
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