Conclusions on Eternal Recurrence:

Required reading: Eternal recurrence, eternal recurrence vs. infinite events

Obviously, because common interpretations of eternal recurrence don’t consider there to be infinite events, no proponent thereof makes any attempt to reconcile the two. Why should they? There is no empirical evidence that events are infinite (my a priori proofs that space and time, and therefore events are infinite are not empirical, obviously). My best attempt at reconciling the two is to take the expression ‘history repeats itself’ seriously.

While I cannot admit that any event can be the same as another without occurring at the same time, I can admit that some events are so similar as to indicate a loose concept of sameness (but not true identity). For example, the method in which I brush my teeth is generally the same across time. I brush them in a certain way, at a certain time of day, and it takes about the same amount of time every time. There will be deviations in certain circumstances, but it would not be inaccurate to argue that the history of my tooth brushing has repeated itself so often as to produce at least two events that are essentially the same apart from the time at which it occurred (from my human perspective). There is more to eternal recurrence theory that cannot be accounted for in that interpretation, however.

While Nietzsche didn’t believe that explanation, it is believed by Walter Kaufmann - a frequent translator and editor of his work - that eternal recurrence as Nietzsche conceived of it may have been derived from the works of Heinrich Heine, who wrote

“[T]ime is infinite, but the things in time, the concrete bodies, are finite. They may indeed disperse into the smallest particles; but these particles, the atoms, have their determinate numbers, and the numbers of the configurations which, all of themselves, are formed out of them is also determinate. Now, however long a time may pass, according to the eternal laws governing the combinations of this eternal play of repetition, all configurations which have previously existed on this earth must yet meet, attract, repulse, kiss, and corrupt each other again...” [my emphasis]

My reading of this quote seems to cohere well with the ideas I’ve been explaining since the beginning: the infinite has finite parts, and following from that, infinite time yields an infinite number of finite events, or, in a much broader sense, one infinite event.

Heine’s description of repulsion, kissing, and corruption is nice and flexible. It doesn’t say explicitly imply exact repetition, rather, it is a more poetic way of saying “stuff interacts and interrelates, and will continue to do so, in much the same way as it always has,” wherein “stuff” refers to events and event-objects.

Next Week: I don't know. We'll see, huh? I've sort of run out of steam in terms of the logical progression of this philosophy. It looks like the next big topic will be death-related! Exciiiting!

Eternal recurrence vs. Infinite events:

Required Reading: Eternal Recurrence,Time's Arrow

[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.

On Simultaneity:

Required Reading: Simultaneity, Relativity of simultaneity, the present, the paradox of infinite divisibility

I'd like to note, before I get down to business that the wikipedia page for simultaneity has an interesting point, which is that the root of the word "simultaneous" - simult - is indicative of a supernatural or divine coincidence. Understand, as you read the rest of this entry, just how supernatural a coincidence it would have to be for two events to occur simultaneously. Thought for food.

Simultaneity is improbable for the same reasons that pinpointing “the present” is impossible. I say improbable, because it is possible that two events could occur at the exact same time - no matter how infinitely small the increments of time-measurement are.

However, the smaller the measurements are (and remember, the increments of measurement could become infinitely smaller) the more likely it is that you'll discover that two events that appear to be simultaneous are in fact set apart by such and such an infinitely small duration. So, simultaneous events are extremely rare, to the point that it is likely that they have either never occurred or will never occur.

That said it is possible for events in progress to be happening simultaneously, provided that the "happening" of the event is described in a nonspecific way. For example, “burning” refers to the process of being burnt, but does not refer to any specific part of that process. So, two candles can be burning simultaneously, but it can't be determined by any accurate means whether they were lit simultaneously, or burnt out simultaneously, or put out simultaneously, or reached the middle of the candle simultaneously, or began to melt simultaneously, etc.

Because the occurrence of events is asymptotic (approaching zero or infinity), we have to assume (again) that it is either impossible to determine simultaneity, or it must be the case that simultaneity itself is not possible.

Just like we need relative durations in order to talk about the present, we need to think of occurrences relatively in order to assume that some of them happen simultaneously. Without turning a blind eye to the indeterminacy that's packaged in with these concepts, we would lack the ability to experience or comprehend time in a stable and cohesive sort of way.

Meanwhile simultaneity as an objective concept cannot be considered a true possibility - rather, a theoretical concept.

Next week: On the infinite, in which I tackle infinite divisibility a little more directly and try to explain what it really means for something to be infinite.