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 time and eternal recurrence:

Required Reading: Eternal Recurrence, Linear and Cyclical Time

Eternal recurrence is a concept derived from Nietzsche. It was unfortunately underdeveloped because the most complete description of it is found in a collection of notes titled The Will to Power, which was released (and liberally edited) posthumously by his sister. As such, followers of Nietzsche have attempted to interpret and disentangle the concept in a faithful way, based on prototypical appearances in earlier works and the fragments found in the notes – an effort made difficult by the vagueness and sometimes contradictory nature of those mentions.

The premise of the theory is that all events (and the objects and beings involved), recur in exactly the same way an infinite number of times. In eternal recurrence time is cyclical rather than linear. All bodies and events will occur again in exactly the same way an infinite number of times because the past and future are practically the same as the present, due to the uniformity of the cycle.

Because it is the most familiar analogue, many seek to liken eternal recurrence with reincarnation. This is not the case in any familiar way. In Nietzsche’s eternal recurrence, it is not a new life lived and there is no retention of prior consciousness (though, there is little information provided, with respect to that angle of approach).

Nietzsche used eternal recurrence as a way of showing that life-acceptance was important, in contrast with looking toward some future reward in a promised afterlife at the expense of putting any value into this life. He called this self-acceptance amor fati, or ‘love of fate.’ The problem, however, is that the frame of reference for what is past and what is future is always based in the present – which I have shown to be elusive and asymptotic.

While both Nietzsche and I assume infinite time, his cyclic time incorrectly assumes a finite number of events - an assumption that makes it difficult to reconcile eternal recurrence with the idea of the infinite thing. Despite the admission that all things are finite divisions within the infinite, forgetting that the number of finite divisions is infinite causes many problems.



Next Week: Eternal recurrence vs. Infinite events, in which I make a rather lengthy attempt to address the issues involved in reconciling the one with the other. (It may end up being a two-parter).

On Asymptotes and Matter:

Required reading: Asymptotes, On Events, On the paradox of infinite divisibility

"Approaching zero" refers to a mathematical concept involving parabolas and curves. An asymptote is a theoretical line which the curve always approaches, but never intersects with, such that if the line were to have a value of zero*, the curve would always approach, but never reach it. Similarly, nearly every quality or attribute has the capacity to “approach zero,” but never reach it.

Asymptotes in parabolic mathematics are examples of how infinite divisibility is a universal trait in a real-world context. The curve never reaches zero because it is dividing the space between the two infinitely. Metaphorically speaking, human experience is the curve, while exact time or exact location is the asymptote. Our curve of experience naturally approaches an exact time or an exact space, but never meets it.

The asymptotic nature of matter (and time) in conjunction with infinite divisibility necessitates that no one particle of matter (or time) can be truly pinpointed. The problem is that it appears as though experience approaches empirical (or objective) reality, but never reaches it. The evidence of reality is made so transitory by its divisibility. The result is that existence and infinite divisibility seem to imply non-existence by the impossibility of making true “this object exists at location x at time t.” This is to say that events/objects cannot be said to exist, because they lack modifiers.

All matter in the universe appears to be on the threshold of being real. Could this be the scientific application of idealism or immaterialism? We're angling dangerously toward hippie talk, here.

*In this case, "zero" refers to the distance of the parabola from the asymptote (or of the curve of existence from reality), and not an absence of value or substance.



Next time: On time and eternal recurrence, in which I try to espouse one of the most important Nietzschean concepts that I don't actually believe.

On the paradox of infinite divisibility:

Required Reading: Asymptotes, Zeno's Paradoxes, Infinite Divisibility, On the Present


Preface: Last week, I went on about how there was no way of pinpointing any moment in time accurately, because accurate measurements require infinitely smaller increments. It is a dynamic relationship which means that truly accurate measurement of anything at all is impossible.


While it seems obvious that events do happen, and must have begun to happen at some point; any attempt to figure out at which point an event actually occurs only tells us the times when the event was or wasn't happening.

The starting point for an event is always a moment that we get close to, but never meet; a sort of asymptote (remember calculus, kids?). For convenience sake, I'm applying the concept of asymptotes to any thing that gets close to, but never reaches a given measure (anything that approaches zero or infinity). Asymptotes imply infinity in that no matter how close a curve gets to an axis, it will never intersect with it because of the infinite divisibility of the space between them.

The fact that accurate measurements for beginning and end points are asymptotic (see what I did there?) suggests that each event has either always been occurring, never occurred, or is actually one event that has no beginning or end; an infinite event. The best guess of anyone as to the starting point of an event is defined by when it did not commence, as opposed to the moment that it did - because we'll never figure out what that moment is.

It’s important to note that here, as in Zeno’s original Arrow and Dichotomy paradoxes (remember the required reading?); the infinite divisibility of both space and time seems to preclude movement (or in this case, commencement of events). However, as in all of Zeno’s paradoxes, we know from experience that despite the fact that from one moment to the next, there is no way of knowing exactly when something started moving and where it moved to, the fact is that it does start moving, and does move somewhere.

Here is a possible explanation for this problem: Just as objects in space do not displace space by existing in it (they are the space they occupy - more on this in a few weeks), objects and events in time do not displace time. Basically, what I'm saying is that space and time are absolute - not relational (these are fancy philosophy terms). We estimate when the beginning and end of events happen, in terms of time. The unity and identity of each event is maintained no matter how many divisions are made in the duration between those beginning and end points - just as objects maintain their form from one point in space to another. No matter how many arbitrary divisions we make in time, an event maintains its duration, just as an object maintains its size no matter how small the increments that we measure it with are.

So, the interpretation of the present as being a relative estimate rather than an exact point is a useful fiction, which allows us to distinguish between relative (and inaccurate) starting points and relative end points in time or space.

Are relative time and space a valid substitute for knowing exact values? My position is that, technically, we can't tell the difference in our every day life, and the problem doesn't really have any noticeable effect on us as it is.

On the other hand, the indeterminacy of one of the fundamental elements of human perception is at once puzzling and intriguing. What does it mean, on a subconscious level, that events never actually start happening?


Next Week: On Simultaneity in which I dance around the idea of whether or not two things can happen at the same time, when one thing can barely seem to happen in the first place.