>I disagree. The universe only contains real things. Some of these
>real things have imaginary ideas (some of which are representations of
>imaginary objects), but the universe doesn't contain those imaginary
>objects -- only the *representations*. And those representations are
>embedded in a frame of reference defined by the beings possessing the
>The universe does not contain *real* circles.
ahhh aesthetics... when i (as a wise ass) asked what use the imaginary set of numbers had to my math teacher, she promptly responded: "imaginary numbers help us explain the relationships between real numbers"
the concept of a circle: the locus of point equidistant from a central point, gives us a universal notion of what we are trying to create when we attempt to make a circle. and while there is an indefinite margin of error between the ideal cirlce and the circle we created, we can come so close that this margin of error is imperceptible. although we can never create the truth we can get close enough to the truth to be able to perceive within our minds what the truth is.
didnt plato come to the same conclusion?
~the great tinkerer