In practice you can only make finite observations and recruit finite computational resources. In theory, as soon as you introduce infinity, very ugly things happen to your axiomatic systems. Better stay clear of that stuff if you can avoid it...
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"infinity leads to ugly outcomes" >> this is the heart of where we disagree. Infinity is the perfect elegance (and ugliness etc.) - how i see it.
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Infinity is a wonderful tool if you want to make stuff, a cornucopia: shake it a little, and things fall out of it without limit, but it is also infinitely hard to make by itself. No finite process can create an infinity, but once you have it, you can easily create universes.
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Does the universe you imagine here have discrete time? Infinite time?
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Relativistic time exists only for embedded observers (observed rate of change in an observer's environment, relative to its own rate of change). I don't know how to make global continuous time work without making the universe hypercomputational.
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I intended to refer to the time of the computation, not of the observer (the latter is much later in the understanding of the model). You mentioned a succession of states, step by step, that time I was asking about. Step by step -> discrete. But finite or infinite?
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I do not know how to get evidence for that. If a universe is deterministic and has finite size, it becomes periodic if you let it run for long enough, and an embedded observer cannot find out when it started, if it had a starting point.
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Ok, I‘m fine with that kind of circular time (up to isomorphism).
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A periodic universe might offer some evidence for its periodicity though!
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Might. Btw., do you see arguments for reversible computation? (The less it is reversible, the hidden its past is. Hm. Thats actually a kind of reversibility from inside. Better I take that back, and think about it before :-) )
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A periodic universe is reversible. Our universe appears to be reversible: You cannot delete information. Entropy reflects the increasing cost of observers to keep track of increasing history.( Note that reversible does not have to mean symmetric.)
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I see. I didn‘t think about this implication of periodicity. Doesn‘t really sound like what I mean with reversability, but that‘s not your problem :-)
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The definition of reversible computation is that every state can have only exactly one possible preceding state. This way, you can construct an inverse rule, and derive the past from the present (if you have full information).
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