Yes, Paul, what I am saying is that the abstract number Pi only exists in the brains or computational devices that are capable of "thinking" about it. Yet I have to concede that Pi and other abstract numbers are somehow implicit in the structure of the universe, waiting to be discovered by information-processing devices of sufficient complexity, such as our brains.

Robert Kaplan, in his book "The Nothing That Is: A Natural History of Zero", makes a useful distinction between mathematics as discovery and mathematics as invention. It's an interesting read.

According to that distinction, Pi is a very useful discovery, but our notations for it and theories about it are inventions, represented in our brains and communicated mostly in writing, Like zero it doesn't exist as a number except in our brains.

That would seem to make Pi and other quantities similar to gravity or black holes, for example, but more abstract -- a second-order phenomenon -- harder to observe directly than those but, like those, subject to invented explanations after they are discovered. Does that make sense?