Eternal recurrence

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I (Lumenos) am creating an experimental dialogMap from re-edited clippings of mine and user:Maratreanism talkpage edits on the topic of eternal recurrence. Bear in mind this does not necessarily represent user:Maratreanism because I don't completely understand them. Others are welcome to edit this dialog map. You may put signed comments on this article page but they may be relocated, deleted, or altered (in this case the signature should be deleted or struck out).

Basic argument for eternal recurrence[edit]

Infinite time or matter + finite possibilities must imply some kind of repetition in reality.

"Agreements": The logic is fine although I would not say space/time is what would need to be infinite but the matter/energy within space/time. You could have infinite "space" beyond the universe or "time" before anything existed. I won't contest eternal causation; that "time is infinite", in other words that something has always existed (and will always exist). I won't contest that there is an infinite amount energy/matter although I see no evidence of this (aside from inner matter).
"Disagreements": I am unconvinced that there are finite possibilities so that is the subject of this "debateMap"/dialogMap.
I should be clear, if you want to claim an infinity of empty space, or an infinity of time in which nothing happened, I'm not going to completely reject that... although I will say it is quite superfluous, and if time and space have nothing in them, we can dispense with them without harm. Maratreanism 05:20, September 11, 2011 (EDT)
Not infinite "empty" space or time, constant novelty at some points resulting in new lifeforms. ~ Lumenos (talk) 16:31, September 12, 2011 (EDT)

Simple argument against finite possibilities[edit]

"Even if there were exceedingly few things in a finite space in an infinite time, they would not have to repeat in the same configurations. Suppose there were three wheels of equal size, rotating on the same axis, one point marked on the circumference of each wheel, and these three points lined up in one straight line. If the second wheel rotated twice as fast as the first, and if the speed of the third wheel was 1/π of the speed of the first, the initial line-up would never recur." (Kaufmann, Walter. Nietzsche: Philosopher, Psychologist, Antichrist. (Fourth Edition) Princeton University Press, 1974. p327)[1]

Assumes reality is continuous[edit]

Counter argument 1: assumes reality is continuous; if reality was discrete instead, you couldn't actually rotate by an irrational amount like 1/π, and rotating by rational amounts they would eventually line up again.
See the 1st-level heading labeled something like "Argument for finite possibilities".

Practically repeating[edit]

Counter argument 2: even if reality is continuous, although the wheels will never ever exactly line up again, they will get arbitrary close to doing so. In the end they will repeat, not precisely, but so close to repeating that it will be repeating for all practical purposes. As time approaches infinity, the wheels will get closer and closer to repeating, so no matter how precise the repetition needs to be, it will happen.
I agree (concede) with this version of the argument. This seems more like an argument for eternal recurrence but it could only have disproven eternal recurrence. It is not clear that the analogy can be applied to the complexity of the universe. Looks more like a bad analogy now. Well done anyway, lumenist. ~ Lumenos (talk) 16:31, September 12, 2011 (EDT)

Argument for finite possibilities[edit]

There are reasons to think the possibilities are finite. Basically, the possibilities are going to be finite if reality has two properties (1) it is somehow bounded in volume, (2) it is somehow discrete (a minimum degree of difference which can occur).

Now, attacking it from the physical viewpoint, let us ask the question "how many Earth-like planets could exist right now?" Assume the universe is infinite in volume, contains an infinite amount of matter, and that matter is at a high-level evenly distributed (which allows "local" clumpiness like galaxies or groups of galaxies), but otherwise obeys the known laws of physics. Now, we'd expect such a universe to contain an infinite number of planets. Of these, some subset would be "Earth-like" (they'd need to be within certain upper and lower bounds of size, in the habitable zone of their star, etc.) The question is, how many distinct Earth-like planets could the universe contain? Well, there is a certain upper bound in volume V, such that every Earth-like volume must be smaller in volume than that. And there is a certain upper bound in energy, E, such that every Earth-like planet must contain less energy than that. If it had more volume, or more energy, or both, it would be a non-Earth like planet (like Jupiter) or a star instead. Now, by the Bekenstein bound, a finite region of space with a finite amount of energy contains a finite amount of information. This means, that any Earth-like planet can contain at most I bits of information. Since information is defined (Shannon information) as the logarithm of the number of distinct states the system can be in, this implies there are at most 2I possible Earth-like planets. So, even though such a universe would contain an infinite number of Earth-like planets, there could only be a finite number of distinct Earth-like planets in such a universe, and hence for at least one such Earth-like planet there must exist an infinite number of identical copies of it.

So, this is basically to give the flavour of my argument for the proposition that "the possibilities are finite". I can produce many variants, using somewhat different assumptions, etc. Basically, infinite time and/or space + finite possibilities must imply some kind of repetition in reality.

More things Lumenos did not understand[edit]

The soul[edit]

(1) the soul has no beginning and no end (2) the set of possibilities is finite. Put the two together, and eventually the soul must endlessly repeat, because by then it would have exhausted all possibilities.

Why would you say the soul has no beginning or end instead of saying that everything has no beginning or end? Aren't the souls just more things repeating along with the physical universe?