[Note: This used to be a longer essay (by blog standards), so I've cut it in two. Stay tuned for the second half next week, and may your existential concerns about the inexplicable and irreconcilable be assuaged at some point.]
The most common interpretation of eternal recurrence is flawed in that it assumes that there are a finite number of events within an infinite time. (It is assumed of eternal recurrence that events must recur the same way ad infinitum because there are a finite number of events within infinite time). This is not possible, because infinite time entails infinite events. It is already established that identity of events depends, particularly in cases of the most complex events, almost intrinsically on the time at which the event occurred. The more time there is, the more events there must be. If time is endless, the number of finite events throughout time must also be endless.
There are, I believe, an infinite number of events, objects, non-objects, and object-events housed within infinite space (I know that such a wording implies the finite. Just roll with it). As such, the universe and time as we know them cannot recur in exactly the same way because:
(a) time has no end, and therefore each event, no matter how similar is unique due to its having to have occurred at some point within the infinite;
(b) time’s arrow denies the possibility that events could recur in the same way, because additional variables affect the universe ad infinitum (read: there is no limit to progress);
(c) the universe is in a state of constant flux. For the most part, this is because of (a).
However, as I write this, I can conceive of possible refutes that will need to be explored:
1. Identity of events with reference to placement on a timeline depends on an arbitrary conception of time as having units. Infinite time, as I have stated, is infinitely divisible, but is also an infinite unity. One cannot divide infinite time into two times, there is but one time, in which arbitrary divisions are imposed, but they are not true divisions. This suggests that what would commonly be referenced as time1 cannot be distinguished from time2, because it is part of a unity. As the increments imposed upon time are a man-made conception, the idea of one time following another is also a human conception, and as time is a unity, it is entirely reasonable to assert that all events as we perceive them are simultaneous – that is, one infinite (and infinitely divisible) time, in which one infinite (and infinitely divisible) event occurs. That said, the infinite event is infinitely divisible into finite increments, just as time is, which allows us the illusion of unique events. In all, though, this argument does not fully refute my initial argument, as the infinite nature of both time and the event preclude any definitive start or end point at which events can recur.
2. It is commonly theorized and/or prophesied that earthly (a very limited scope, in terms of universe, by the way) progress has reached - and will on several future occasions – reach points of stagnation and even regression. Arnold J. Toynbee, for example theorized that a human over-focus on the successes of the past will create stagnation by leaving humans unprepared to deal with future problems. The point being both that human progress is limited to the availability of those resources to them, and that past and future projections of technological stagnation are an example of the way in which eternal recurrence can be interpreted more loosely as ‘history repeating itself.’ It is not necessarily the case, however, that progress cannot occur after or even during a period of stagnation, to reach or overcome the level it had been at prior to that period. Likewise, as stated in (a) and noted in (1), identity of events does not allow for history to repeat itself exactly, as eternal recurrence would require. That is to say that eternal recurrence, as it is commonly conceived, cannot be possible if there are an infinite number of unique events.
Next Week: Conclusions on Eternal Recurrence, in which I provide a bit of denouement on this issue, and uneasily put it to bed.
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