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).
Thursday, June 24, 2010
Friday, June 18, 2010
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.
"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.
Friday, June 4, 2010
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.
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.
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