The set of all clock faces a working clock can produce - call this the set of all valid clock faces - has the same topology (and cardinality) as a circle.
Yes.
The set of all possible clock faces has the same topology (and cardinality) as a 2-dimensional torus.
Show me.
John K Clark
Some of the laws of physics could change from universe to universe, but there must be some laws that remain invariant across the entire multiverse because without rules it would behave chaotically and if the multiverse behaved that way so would all the universes in it, including ours. However there is order in our universe, but what is fundamental and what is not? I think we probably all agree that purely mathematical things like pi or e would remain constant in all universes, but consider some of the physical things that might change:
The Planck constant. The speed of light. The gravitational (big G) constant. The mass of the electron, proton, and neutron. The electrical charge on the proton and electron. The inverse square law of gravity and electromagnetism. The conservation of Mass-energy, momentum, angular momentum, spin and electrical charge.The relative strength of the 4 forces of nature. The number of large dimensions in a universe. The Hubble constant. The ratio of baryonic matter to dark matter and dark energy.
It seems to me that the speed of light and Planck's constant may be more fundamental than other "constants" and the basic structure of the laws of physics may be more fundamental than the constants they use. But I could be wrong, perhaps the things that always remain the same are none of the above and we haven't even discovered them yet.
John K Clark
Are atoms real? Whatever the answer to that question is imagine if it were exchanged, that is suppose that magically the reality of atoms became unreal or the reality of atoms became real, would the world be in any way different as a result? I think the clear answer is no, therefore regardless of what the status of atoms may ultimately be, the question "Are atoms real?" is not real because real things make a difference and unreal things do not.
John K Clark
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