Science a GoGo's Home Page Forums General Discussion Physics Forum Hitch-hikers' Guide to Infinity

BS,you regard yourself as a hitchhiker, and I am just a layman interested in physics. We agree on many things, and that is very interesting.

You said, "Mathematics is the language of nature".

I think you have slightly exaggerated the role. Language is used to describe. So you are suggesting that mathematics can describe the physical world. I would suggest a lesser role; it is just a tool to extract results. The physical world should be explained physically, and for that verbal explanation will be enough. However, all physical laws should be mathematically valid. Thus, mathematics has a role in proving whether the physical model is correct or not. The role of mathematics as a vehicle for 'speaking, thinking and discovering' is minimal. The line of thought should be like this: visualize a physical model, then verify whether it is mathematically feasible; if not feasible try another physical model and so on. It should not be in the reverse order: that is, you should not impose a mathematical model (even if it agrees with the observations) on the physical world. The reason is that all mathematically valid explanations are not valid physically, whereas all physical models should be mathematically valid.

So there is a need to distinguish between mathematical and physical infinities as suggested by you. I agree that infinity is not an end. However, zero may be an end or a beginning. Negative infinity is a mathematical concept. It can have some role in philosophy. I think philosophy is linked to other branches like this: philosophy - mathematics - science - philosophy, thus forming a cycle. Mathematics is conceptual, science is real, and philosophy, both conceptual and real.

You said, "Infinity, on the other hand, needs to be understood if we are to have any real grasp of the origin and nature of the Universe."

As you said initially, 'something cannot come out of nothing'. So there is no origin; or, origin will always remain a mystery. In explaining the nature of the universe, infinity has no real role. That is, if a physical theory leads to infinity (other than the basic assumptions that space and time are infinite, and for which there are no explanations), the theory is wrong; there should not be any re-normalizations.