csr:
I have sometimes thought that it must be so with a balloon–and yet is there not a center of a balloon?
The equivalence of perception must, like all things, be guided by faith.
An expanding balloon analogy can be used to illustrate what oat soda has said in post # 16.
Imagine that the surface of a balloon is a universe for some pac-man type creatures. The position of these pac-men in their universe can be described by two spatial dimensions. If we add a third dimension, time, the pac-men can move about on the surface of their balloon universe, and their universe can be modeled as a three dimensional space-time continuum (two space dimensions and one time dimension). Since the pac-men can only dwell on the surface of their balloon universe, their “natural” frames of references will always be fixed on the surface of the balloon.
Now imagine that all the pac-men are arbitrarily darting here and there on the surface of the balloon, and that they are evenly distributed on the surface of the balloon. Imagine that the balloon that they dwell on is also expanding, so that the pac-men are living in an expanding universe. Any single pac-man can imagine that he is fixed in his universe, and that, as a whole, the rest of the pac-men are moving away from him in an expanding universe. No pac-man really has a privileged frame of reference that is more “real” than any other pac-man. Each pac-man perceives his universe the same way, that he is fixed, and that the rest of the universe is epanding away from him.
Let’s go back to the idea that the balloon universe of the pac-man universe has a “real” center from which all pac-men are equally moving away from with equal velocity. If you say that the center of the balloon is that place, then you are saying that the “real” center of the pac-man universe is in a frame of reference that exists
outside the universe of the pac-men, since the universe of the pac-men is only on the surface of the balloon.
That wouldn’t have to be an insurmountable problem to the pac-men. We can imagine that the pac-men are intelligent beings, and that a pac-man genius could develop a higher mathematics that describes the pac-man universe with more than the two spatial dimensions that seem real to pac-men. Pac-men cosmologists could develop a geometry of space-time that describes their universe using three spatial dimensions (and even more than three). Such higher dimensional mathematical models might be useful to the pac-man cosmologists, and let them make scientifically verifiable predictions about their universe. They could even see that this model is so useful, that they come to prefer using the geometry with the “extra” dimensions for solving problems of cosmology.
A Robert Sungenis pac-man could exist in the pac-man universe too. He could argue with the pac-man cosmologists that they are being silly, and that they should accept as absolute truth a model of the pac man universe that has only the two spatial dimensions, since that is what all religious pac-man with common sense believe. A religious pac-man cosmologists could point out to pac-man Bob that God created the universe out of nothing, and that God can see his creation from a frame of reference that is outside the universe perceived by pac-man common sense.