Posted: Sun Oct 25, 2009 8:32 am
Just because we can't conceive it, can we know it doesn't exist? (Interbane already pointed this out.)Robert Tulip wrote:We cannot conceive a real space in which pi does not apply. Pi is part of the structure of space, in so far as circles exist. Pi is an eternal logical condition for the existence of circles.Interbane wrote:You say that pi is the same for all eternity, but you don't support this claim with any reasoning.
However, we *can* conceive it. Pi depends on Euclidean geometry, that is, geometry in a flat plane subject to Euclid's five axioms. Consider a circle inscribed on a sphere C(s). The radius of C(s) will be longer than the radius of the same sized circle on a plane C(p) because the center of C(s) is not in the same plane as the circumference. Thus the ratio of circumference to radius will be different for the two circles, i.e., in geometries on the surface of a sphere, pi has a different value than it does in plane geometry. Actually, on a sphere, pi would not have any fixed value. The ratio of circumference to radius would not be the same for the equator of the sphere as it would be for a much smaller circle inscribed on the sphere.
I don't think nature obeys anything. Nature does what it does. It looks to me like math is a conceptual framework humans invented to describe observed consistencies in nature's behavior over a very short period of time. All we can say is that for the moment or two out of the history of the universe that human brains have been looking, some aspects of nature have been consistent. Cosmologists theorize that the rate of change in the universe has not been constant in the past. I see no reason to expect it to remain constant in the future.Interbane wrote:What is still a grey area for me is why nature obeys mathematical rules. Why does math necessarily apply? These processes and relationships are different than the idealist category of geometric shapes, so if you have insight in this area that is how you'll get through to me.
I would guess that thinking that nature "obeys" mathematics comes from using the "law" metaphor to talk about our descriptions of nature. Humans obey laws (sometimes), so talking about Newton's laws of thermodynamics or Boyle's laws of pressure and volume leads by analogy to thinking of nature "obeying" our descriptions rather than the other way around.
This is the sort of pitfall I believe one is likely to fall into along the Platonic path.
I would say that the temporal thing it depends on for its existence is a consciousness sufficiently developed to form the concept.Robert Tulip wrote:A number such as pi, derived from the ratio between diameter and circumference of a set of planar points equidistant from one point, is indeed the same for all eternity, because it does not depend on anything temporal for its existence.