Cat, with all due respect, you know, you are kind of disagreeing with yourself. A universe that is cyclic and something that has been cyclic forever must be infinite. I mean, at least, logic says so.
Well, so, I can consider the definition of the first type of infinity as a "loop" and the second one as an "impossibility." But I can think of another type of infinity, the infinity that goes on forever. For example, a set of all natural numbers. I hope you understand what I mean to sayOK, I worked it out. When we are talking about spacetime, (as we imagine it) as a torus. This is the cyclic part. For whatever 'reason', the torus goes through phases of expansion and contraction, with nexuses (I would have preferred nexi) which I see as BHs and BBs. The Universe so imagined is "infinite" in so far as it is timeless and there is nothing "outside" the torus. That is an "infinite" which is self-contained and goes back on itself. Information (at least on a personal level) is not transferred through nexuses.
Then there is the "infinity" I cannot abide. such as 1/0. This is a mathematical abstraction and, imho, has no relevance in the real world. Similarly the problems of infinity 'outside' the Universe, which quod effuderis is nonsense, (from the definition. These are largely based on anthropocentric inability to conceive of examples such as the first case (above) and they think of a flat "going on forever" because they cannot comprehend a torus of spacetime. Hence you get what comes after the last infinite number, and what is there beyond the last bit of space.
What do you think? Have I solved the question of "two kinds" of infinit(e)(y)?
Cat
Um, actually, no. I mean to say, for example, 1/0 is an impossibility as it is impossible for 1 to come in the table of 0. But, 0/0 is not an impossibility., as you can get 0 everywhere in the table of 0. I hope you can understand what I mean to say.
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Well, Cat, logically speaking, if n is the greatest value that exists, adding 1 to it won't make that value greater. That is just like how asking if something is outside the Universe is a non-question.
That literally means the Universe doesn't exist if we go by that logic."Well, Cat, logically speaking, if n is the greatest value that exists, adding 1 to it won't make that value greater." Absolutely correct.
Hence n = n + 1 is impossible. They are statements of exactly the same thing.
"That is just like how asking if something is outside the Universe is a non-question." Absolutely correct.
Cat
Yes, it reminds me of the time that a tank (Texan for pond), due to winter circumstances, was found to be crystal clear; the bottom was easy to see. It was so inviting, my brother and I (both teenagers) had to jump in!
Yes, and look what happens to the actual equations of physics when it attempts results just after 1 Planck unit of time. Those results, reportedly, shoot off into infinity.
As at least one physicist describes it, "The wheels of the wagon go flying off!" I think we both agree this is where science ends and pseudoscience takes advantage of this for all the fun they think is there.Just remember that you have now gone past the "infinity zone of science", as perhaps we should call it.
[I'm teasing you , of course, given your disdain for infinity. ]
Right, and I'm confident that we have no hard science that can address singularities of any kind. Perhaps the metaphysics that does attempt to address it has merit, but what if it never becomes hard science and never testable?Helio: "There is no physics, IMO, at t=0, only metaphysics, pseudoscience, and lots of word salad and hand-waving. " which, in my view includes t=0 and singularities. We do not know, close to "t = 0) how it works. Cat
P.S. "There is no physics, IMO, at t=0" Well, you said so yourself, and I agree.
Helio, I understand your disdain for pseudoscience. I accept that, most wholeheartedly. BUT don't forget that one of those mad flights of imagination will most probably be the accepted "truth".
Cat
If n = n + 1, and n is an impossibility, then if we apply this logic to the question "what is outside the Universe?", then doesn't the Universe too become an impossibility by this logic?
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