Re: The logic of atheism

Ron Peterson wrote:

> prabbit1@xxxxxxxxxxxxxxx wrote:
>
>> Just happened to think of something that shows how infinities
>> don't "follow the rules." Any infinity of order 1 (forget the
>> proper term) is "equal in size" to any other infinity of order
>> 1 (so that they can be matched in a 1-to-1 manner.) I.e. the
>> set of all whole numbers is "as large as" the set of even whole
>> numbers. So a square with infinitely long sides would have
>> infinitely long diagonals (here, diagonal will refer to any
>> line that crosses the side and the middle, even if it's not
>> corner-to-corner. Don't know if there's a more correct term
>> than "diagonal" but it'll work for us.) So all the diagonals
>> would be of equal length in the segment of them that's wholy
>> contained in the square and and half of each diagonal woult be
>> equal to half of every other diagonal (since half of infinity
>> is infinity), thus it would satisfy the "every point on the
>> figure [edge] is equidistant from a central point" part of
>> being a circle at the same time it's a square (or ANY
>> infinitely large 2-D, singlying connected shape, for that
>> matter.)
>
>> Strange but apparently true (or can someone find a flaw that I
>> overlooked somewhere?)
>
> You're trying to define a square which in the infinite case
> would coincide with a circle. I don't know if you can do that
> since a square needs four distinct vertices and lines joining
> them.
>
> A better approach would be to define a different metric on the
> plane so that the coordinates of the lines describing a square
> would be equidistant from the center of the square.

But that wouldn't mean the construction of a square circle at
all. It'd just mean altering your ruler in such a way that it
reports the results you want, not what actually exists. The points
on the square wouldn't really be equidistant from the center;
you'd just be making up a convenient lie to describe them that
way.

Cheers,

b&

--
EAC Memographer
BAAWA Knight of Blasphemy
``All but God can prove this sentence true.''

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