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 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 Events:

Required reading: Events, Space-time

Okay, last time, i had a look at my giant file of topics, and decided that my "space-time" entry was very short and not very informative. However, today, I found a way to work it into today's subject: events. However, it's still a bit off topic.
So, bear with me. This one's a double-post.

On space-time:

Space has three dimensions: width, length (or height), and depth. The resulting measure for how much space is occupied by something is volume. That measure is simply a way of quantifying what Spinoza called extension. It is the extension of substance into three dimensions. However, an object in space unmodified by time is incomplete. Not only do we need to quantify the spatial dimensions of a substance, but also the temporal dimensions. Not merely depth, width, and height, but also the when of that substance.

This want of a fourth dimension for the description of substance is likely one reason why many physicists believe in an amalgamation of the dimensions known as space-time. All that I have said about infinite space refers specifically to Euclidean and Newtonian absolute space. However, one key feature of space-time (which makes it differ from absolute Euclidean/Newtonian space) is that it appears to be warped by gravitational pulls. It is not clear what implications this has for the occupation of space by matter, but I think it indicates a mapping of objects in space as they are affected by gravity, as opposed to a boundary or a limited shape which space takes. It is the map of the path objects take through space and time (space-time), and not the shape of space-time itself. The normal method of determining spatial boundaries by their relation to other objects makes it all too easy to assume that a lack of objects indicates a lack of space.

On events:

Like the frames of a film, each object exists in space as its own event. Events are less happenings or objects themselves than they are bundles of detailed descriptive data. Events are composed of a what (a thing occupying space), a when (the duration, or point at which it will or did occur), and a how (an adverb and/or adjective) which provides an analytical description. For these purposes, an object is described as ‘the event of object (a)'s existence at location (l) at time (t), with attributes (a1, a2, a3, etc).’ For example, the rocket (what) travelled from the earth to the moon with a duration of Δt (distance over duration = speed), and the rocket was red.

That said, every event has an infinite number of potential (but necessary) descriptors to identify it as a unique event. These descriptors range from the ones I’ve just mentioned to the past, future, and relatively simultaneous events that occur everywhere else. That is to say, every event requires a description that accounts for every other event that is happening, has happened, and will happen in order to be unique. The upshot of a description that must account for every other possible or real event necessitates that every event is the same event, and not unique at all (because any one description describes all events, which all have the same description). There is only one event, in a broad sense, and that event spans the entirety of space-time which is infinite. Therefore, “The Event” is infinite, and inseparable from space-time (the universe), if not synonymous.

Obviously, such vast descriptions are more than what is required and sufficient for the identification of one event, and perceiving it as being different from another. It is as simple as making the arbitrary divisions that are normally made within an infinite medium. We divide finite events from within the infinite event, just as we make finite spaces of infinite space, and finite times of infinite time.

Being able to conceive of a group of finites as parts of one infinite whole requires that we reject, at least on a hypothetical level, the convenient assumption that difference of qualities/attributes is an indicator of individuality. We do not consider a pile of sugar to be something other than sugar. We do not consider one grain of sugar to be something other than sugar. Difference in size, shape, quantity, and– I would argue– even atomic structure, do not necessitate finiteness. Just as a human is made up of bones, blood, flesh, water, etc, the infinite universe is made up of an infinite number of objects and substances with different make-ups and attributes.



Next week: On asymptotes and matter, in which I try to stretch out a short post and hope you understand.

On the identity of the infinite:

Required reading: Identity, infinity, holism, On God as Infinite

No two things can be infinite. That which is infinite is all that there is, by definition. If space is infinite, then God cannot also be infinite. If it is the case that God exists, then God must be infinite in accordance with Anselm’s ontological argument.

So, with those statements in mind, it appears that
a) nothing is infinite
b) only one thing is infinite and all others are not
or
c) that all of the things we believe to be infinite are one and the same thing.

Based on my earlier arguments, it would be counterproductive to choose (a). In selecting (b) we must assume that both time and space are finite, and god does exist, or that either time or space is infinite (but not both) and god does not exist. In selecting (c) we must assume that god, space, and time are all infinite, and the same infinite thing. In fact, given that (c) makes the many into one, we can now also accept (b), which is always true of the infinite by nature.

So, any thing that is infinite is the same thing as whatever else is infinite, and “the thing than which nothing greater can be thought” must be something even greater than what is normally thought of. To clarify: while god is defined as the thing than which nothing greater can be thought, common conceptions of god do not also include the descriptions of space and time. But, here I am claiming that god is space and time; that space and time are god.

Space and time, meanwhile, are the medium in which our physical experiences are built. The greatest physical thing that can be thought of is the universe; a structure encompassing space (which includes matter), time, and also energy. I posit that the universe is synonymous with the infinite thing. Indeed, the word universe means “all in one.” While the universe is typically a physical thing, it extends into the non-physical through time, the laws of physics, thought, and – for the sake of inclusiveness - the spiritual. Each of these affects, and is affected by the physical.



Next Week: On religion and the infinite thing, in which I hypothesize what it means for god to be synonymous with universe.

On infinite time and infinite space:

Required Reading: Absolute time and space, psychological arrow of time

I was thinking about merging these two bits in the first place, but then I changed my mind. Then I got sick last week and didn't bother to update, so I'm merging them again. Besides, this first one is terrible. These two arguments are basically the springboard for next week's ridiculous statement.

Time

Time is infinite, infinitely divisible, and absolute. Even if time is given beginning and end points, its infinite divisibility allows for it to progress eternally, on some small level. Those boundaries would face the same asymptotic relationship that faces measurements, as I’ve described previously.

Besides that, it is impossible to ascribe an endpoint for time. Following the endpoint, were there a mind to perceive it, that mind could easily extend time. The statement “It’s been one hour since time stopped” proves the point through the contradiction. (Indeed, the phrase “following the endpoint” ought to prove the point by inference). In this way, time is endless (infinite). So long as there is a conscious mind to experience time, time will be seen to continue its passing. As such, without a conscious mind to experience time, there is certainly no reason to assume that time would not continue to pass in its absence. Provided that we don’t traipse off into idealism, the object permanence we learn as infants ought to apply.

Space

Space is infinite and absolute. There is no such thing as nothing. All physical things occupy space. Space is an infinite medium in which arbitrary divisions are made, separating it into finite parts. The space between two points is occupied by invisible gases and particles, not nothing.

Every object we perceive occupies a space of the same volume. Our arbitrary measurements of volume allow that space to be reinterpreted in any shape. A sphere which has a volume of 72 cubed metres can be rearranged to take the form of a 72 cubed meter replica of the Taj Mahal.

Physical objects do not “push space aside.” They occupy as much space as is required for such objects to exist and retain their volume and mass. I have encountered the criticism that if space is infinite, and all space is occupied, nothing ought to be able to move (because the combined force of an infinite number of objects would absorb any force made by one object in its attempt to move).

Such a criticism implies nothingness, because it requires that there be “room” for space to displace into in order to make more room for objects to move around. In infinite space, there can be no limitation on the movement of anything, because there is infinite space for things to move within. As objects are merely finite divisions within one infinite space, it is hardly unexpected that space would remain space regardless of whether every part of it moves or is immovable.

Perhaps science has not fully been able to explain the way that objects occupy space. Perhaps objects exchange particles at such a rate that form and structure are retained, but particles no longer occupy the same part of space (again, divisions in space are arbitrary).
“Space” in this instance is not to be confused with Outer Space; a construct which is itself an arbitrary division of absolute space.


Next Week: On God as infinite, in which I bring this whole infinity talk thing to its logical conclusion, and tackle some common ideas about the big guy in the sky.

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.

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.

On the present:

Required Reading: Infinity, Infinite divisibility, Zeno's paradoxes

Prelude - The following propositions and notes are based largely upon extrapolations and inferences I made from the philosophy of Friedrich Nietzsche (and certain of his followers) and the rationalist metaphysics described in the Ethics of Baruch Spinoza. There are elements of this philosophy that seem like science fiction, or don't seem plausible. It is the nature of metaphysics that concrete proof is not likely to exist.

The present is not a single point in time.

This is because time is infinitely divisible into smaller parts. The divisions we make within time are arbitrary, such as 365 days per year, 24 hours per day, 60 minutes per hour, 60 seconds per minute. Seconds divide into centiseconds, milliseconds, nanoseconds, picoseconds, and so on. These divisions are not inherent in time, and could easily have been different.

You could make an infinite number of divisions in time, be they infinitely smaller or infinitely larger. As a result, any attempt to pinpoint the present to an exact point in time is practically impossible. By any human standard, that exact moment has already become the past by the time it is perceived. For that reason, it's convenient for us to think of the present as an approximate value of time; a relative duration.

For example, you might think of today as the present, but one day is a pretty large increment of time by human standards. One day has the capacity to be divided into several smaller parts - but the same is applicable to minutes, and any other measurement. The upshot is that any attempt to describe the present in human terms becomes a clumsy “the present is now, now, now, now, now, now, now, etc.” This is to say that the present is transitory. This moment; this present is already past.

By that same token, if the present is past before we fully perceive it, then the present has a firm grounding in the future, though, admittedly, it does not extend forward very far. To explain: the perception of the present as being a duration of time rather than a specific point means that the duration includes both a moment that has already happened and a moment that is about to happen. Without that anticipatory element, the duration would only be past.

The result, if you can keep up, is that the present is both the past and the future at once, so far as our perception is concerned – it sits on the fence, so to speak.

Obviously our brains can't even conceive of the infinitesimally small increment of time that would be required to actually pinpoint the present. This is made worse by the fact that such an increment would be getting infinitely smaller (because the smaller it is, the more accurate). The result being that a measurement could never actually be made, because the increments we measure with would always be getting smaller and smaller, and never actually reach the point.

Even if humans had the capacity to experience a nanosecond as though it were an hour or a day or a year, that nanosecond itself is infinitely divisible into infinitely smaller increments, such that pinpointing the present cannot be possible. In other words, the present, as anything other than a broad, relative duration (like we normally perceive it), cannot exist.


Next Week: On the paradox of infinite divisibility in which I try to deal with getting from here to there without any idea of where and when here and there actually are...