Musings on the Nietzschean concept of "eternal recurrence"

So what's really going on?

Moderators: AMod, iMod

User avatar
MustaphaTheMond
Posts: 25
Joined: Wed Aug 17, 2016 6:28 pm

Musings on the Nietzschean concept of "eternal recurrence"

Post by MustaphaTheMond »

I've been reading a lot of Nietzsche lately, and what particularly struck me were his writings about the "eternal return", "amor fati" or "eternal recurrence" of things. This concept that, given time is infinite whereas the number of possible states are finite, events will recur again and again infinitely (such as me typing this very sentence) seems to be almost eerily echoed by some theories in physics and mathematics.

In mathematics, the Poincare recurrence theorem states that "a system whose dynamics are volume-preserving and which is confined to a finite spatial volume will, after a sufficiently long time, return to an arbitrarily small neighbourhood of its initial state". Indeed, such a mathematical truth supports Nietzsche's belief that "in an infinite period of time, every possible combination would at some time be attained".

Equally, the oscillating universe theory, originally supported by Einstein, speculates that that the known universe ends in a "big crunch" which is followed by another big bang and another crunch etc. etc. in a process which continues indefinitely. If quantum theory is true such that there is only a finite amount of configurations within a finite volume possible, then identical states of the Hubble volume should reoccur, due to chance alone.

Having examined these ideas, Nietzsche's words seem almost prophetic. The idea that everything that has been, has already been, and will indeed occur again due to the infinity of time is extraordinary. Surely such a proposition completely and utterly obliterates the existence of man and every one of our lives into utter insignificant and meaningless nothingness?
User avatar
Immanuel Can
Posts: 22257
Joined: Wed Sep 25, 2013 4:42 pm

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Immanuel Can »

MustaphaTheMond wrote:I've been reading a lot of Nietzsche lately, and what particularly struck me were his writings about the "eternal return", "amor fati" or "eternal recurrence" of things. This concept that, given time is infinite whereas the number of possible states are finite, events will recur again and again infinitely (such as me typing this very sentence) seems to be almost eerily echoed by some theories in physics and mathematics.
That's a fallacy.

"Recurrence" can be expected only if two conditions are met:

1. An infinite span of time, plus

2. A finite set of possible variables.

It's like a die. A die will periodically roll a "six"; but it won't do so reliably the first time or even within six rolls. It will only reliably turn up a "six" if the number of rolls significantly exceeds the number of sides on the die. Then you can practically "guarantee" a six, at some point.

But what if the die did not have six sides, but had infinite sides? Then there is an infinitely great chance that no matter how long you rolled the die, no "six" would ever turn up. There would, in fact, always be an infinite set of other possibilities for any number of rolls you happened to take. You could NEVER guarantee even one recurrence of a six...or any other number.

Well, the mathematics of "eternal recurrence" presuppose that our universe is infinite (it needs to, for purposes of guaranteeing the "recurrence": you need a lot of "rolls of the die). And Nietzsche thinks that this means that sooner or later your "six" has to turn up -- and in fact, it must "recur" an infinite number of times, he thinks.

But he forgot the variables. How many variables (i.e. sides of the die) are available in an infinite universe? By definition, they are themselves infinite. (To put this another way, criterion 1 above is met, but criterion 2 is not.) So no matter how many times he "rolls," Nietzsche never be guaranteed his "six." In fact, there is an infinite chance he will NEVER see his "six." No matter how many recursions there are, there will be no "return" to any particular arrangement of the variables, except by a chance so rare as to be incalculable. And there will most certainly never be an infinite set of "returns" to a singular set of conditions.

What the maths tell us is that our universe will never repeat. Nietzsche's idea is therefore founded on a colossal blunder in mathematical calculation. He was just wrong, and didn't have the clarity of thought to realize it.

But that was pretty much Nietzsche.
Impenitent
Posts: 4330
Joined: Wed Feb 10, 2010 2:04 pm

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Impenitent »

it was not an ontological or physical theory

it was ethics.

he didn't say your existence would recur

he said to live your life (and accept it) as if it would eternally recur(although there was a tinge of determinism in his amor fati)

that's why one has to imagine Sisyphus happy...

-Imp
User avatar
Arising_uk
Posts: 12314
Joined: Wed Oct 17, 2007 2:31 am

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Arising_uk »

Aye.

An individualists approach to Kant's categorical imperative.
User avatar
Arising_uk
Posts: 12314
Joined: Wed Oct 17, 2007 2:31 am

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Arising_uk »

Immanuel Can wrote:... Nietzsche's idea is therefore founded on a colossal blunder in mathematical calculation. ...
Er! No it wasn't as it wasn't based upon such thoughts.
He was just wrong, and didn't have the clarity of thought to realize it.
You'd like to think so but then he did say your bastard of a 'God' was dead, so I can see why you wish your strawman to be true.
But that was pretty much Nietzsche.
Says you. Ever tried his ER in the way it was meant?
User avatar
Immanuel Can
Posts: 22257
Joined: Wed Sep 25, 2013 4:42 pm

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Immanuel Can »

Impenitent wrote:it was not an ontological or physical theory

it was ethics.

he didn't say your existence would recur

he said to live your life (and accept it) as if it would eternally recur(although there was a tinge of determinism in his amor fati)

that's why one has to imagine Sisyphus happy...

-Imp
You've got him mixed up with Camus.
sthitapragya
Posts: 1105
Joined: Sat Oct 18, 2014 2:55 pm

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by sthitapragya »

MustaphaTheMond wrote:I've been reading a lot of Nietzsche lately, and what particularly struck me were his writings about the "eternal return", "amor fati" or "eternal recurrence" of things. This concept that, given time is infinite whereas the number of possible states are finite, events will recur again and again infinitely (such as me typing this very sentence) seems to be almost eerily echoed by some theories in physics and mathematics.

In mathematics, the Poincare recurrence theorem states that "a system whose dynamics are volume-preserving and which is confined to a finite spatial volume will, after a sufficiently long time, return to an arbitrarily small neighbourhood of its initial state". Indeed, such a mathematical truth supports Nietzsche's belief that "in an infinite period of time, every possible combination would at some time be attained".

Equally, the oscillating universe theory, originally supported by Einstein, speculates that that the known universe ends in a "big crunch" which is followed by another big bang and another crunch etc. etc. in a process which continues indefinitely. If quantum theory is true such that there is only a finite amount of configurations within a finite volume possible, then identical states of the Hubble volume should reoccur, due to chance alone.

Having examined these ideas, Nietzsche's words seem almost prophetic. The idea that everything that has been, has already been, and will indeed occur again due to the infinity of time is extraordinary. Surely such a proposition completely and utterly obliterates the existence of man and every one of our lives into utter insignificant and meaningless nothingness?
Time could not possibly be infinite. If it were, it would never reach the present and existence would be impossible. It could be non-linear and unbound but not infinite. And that's it. That is all the math I know. :D
User avatar
Dontaskme
Posts: 16940
Joined: Sat Mar 12, 2016 2:07 pm
Location: Nowhere

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Dontaskme »

sthitapragya wrote: Time could not possibly be infinite. If it were, it would never reach the present and existence would be impossible. It could be non-linear and unbound but not infinite. And that's it. That is all the math I know. :D
Your knowledge of math is below par. Time is not what you think it is.


Life exists only at this very moment, and in this moment it is infinite and eternal, for the present moment is infinitely small; before we can measure it, it has gone, and yet it exists forever...Alan Watts.


Time, if observed carefully, exists only if man thinks of it. Man knows time only when it is thought of and not otherwise. Time is, therefore, a thought and not made up of substance.
User avatar
Hobbes' Choice
Posts: 8364
Joined: Fri Oct 25, 2013 11:45 am

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Hobbes' Choice »

Arising_uk wrote:Aye.

An individualists approach to Kant's categorical imperative.
Individualism does not mandate a specific moral stance. It is easy enough to argue that the best interests of the individual are to comply with moral law. It would depend on the particular society in which that individual finds himself.
User avatar
Hobbes' Choice
Posts: 8364
Joined: Fri Oct 25, 2013 11:45 am

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Hobbes' Choice »

MustaphaTheMond wrote:I've been reading a lot of Nietzsche lately, and what particularly struck me were his writings about the "eternal return", "amor fati" or "eternal recurrence" of things. This concept that, given time is infinite whereas the number of possible states are finite, events will recur again and again infinitely (such as me typing this very sentence) seems to be almost eerily echoed by some theories in physics and mathematics.

In mathematics, the Poincare recurrence theorem states that "a system whose dynamics are volume-preserving and which is confined to a finite spatial volume will, after a sufficiently long time, return to an arbitrarily small neighbourhood of its initial state". Indeed, such a mathematical truth supports Nietzsche's belief that "in an infinite period of time, every possible combination would at some time be attained".

Equally, the oscillating universe theory, originally supported by Einstein, speculates that that the known universe ends in a "big crunch" which is followed by another big bang and another crunch etc. etc. in a process which continues indefinitely. If quantum theory is true such that there is only a finite amount of configurations within a finite volume possible, then identical states of the Hubble volume should reoccur, due to chance alone.

Having examined these ideas, Nietzsche's words seem almost prophetic. The idea that everything that has been, has already been, and will indeed occur again due to the infinity of time is extraordinary. Surely such a proposition completely and utterly obliterates the existence of man and every one of our lives into utter insignificant and meaningless nothingness?
Nietzsche would br slapping his head is despair. His idea was not intended to have any relationship to a scientific/mathematical idea; especially not one which offers an empty theoretical position, so irrelevant.
ER was a musing on ancient philosophical thoughts which he mobilises for the purpose of offering moral advice on how to live your life.
All this science stuff is not relevant.

Nietzsche is asking that were you to believe in the ER then this would be the best way to live your life. I do not even think he meant it literally.

Nietzsche is simply saying you have one life and should live it as if you had to live it again and again, witnessing every part without being able to change it once it has been lived.
By this means your life would be the most authentic, the most fully lived and without regret
User avatar
Arising_uk
Posts: 12314
Joined: Wed Oct 17, 2007 2:31 am

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Arising_uk »

Hobbes' Choice wrote:Individualism does not mandate a specific moral stance. It is easy enough to argue that the best interests of the individual are to comply with moral law. It would depend on the particular society in which that individual finds himself.
Probably but I was just making the point that Nietzsche's approach is about the individual with respect to his moral method as against Kant's universalism for others.
User avatar
Hobbes' Choice
Posts: 8364
Joined: Fri Oct 25, 2013 11:45 am

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Hobbes' Choice »

Arising_uk wrote:
Hobbes' Choice wrote:Individualism does not mandate a specific moral stance. It is easy enough to argue that the best interests of the individual are to comply with moral law. It would depend on the particular society in which that individual finds himself.
Probably but I was just making the point that Nietzsche's approach is about the individual with respect to his moral method as against Kant's universalism for others.
That is a caricature of difference between the two yes. I think Kant might be inclined to say that self interest is best served by collective interest though.
Dalek Prime
Posts: 4922
Joined: Tue Apr 14, 2015 4:48 am
Location: Living in a tree with Polly.

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by Dalek Prime »

Just made me think of determinism again. If your a determinist, even the first time through is hopeless. Everything is planned for you. So the rest is just pointless gravy. How funny is that?
User avatar
MustaphaTheMond
Posts: 25
Joined: Wed Aug 17, 2016 6:28 pm

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by MustaphaTheMond »

Hobbes' Choice wrote: Nietzsche would br slapping his head is despair. His idea was not intended to have any relationship to a scientific/mathematical idea; especially not one which offers an empty theoretical position, so irrelevant.
ER was a musing on ancient philosophical thoughts which he mobilises for the purpose of offering moral advice on how to live your life.
All this science stuff is not relevant.

Nietzsche is asking that were you to believe in the ER then this would be the best way to live your life. I do not even think he meant it literally.

Nietzsche is simply saying you have one life and should live it as if you had to live it again and again, witnessing every part without being able to change it once it has been lived.
By this means your life would be the most authentic, the most fully lived and without regret

I'm not concerned as to what Nietzsche's intention was in this post, I was simply musing and extrapolating on his ideas and linking them to other concepts I have read about because it is profoundly interesting to me.

I think we can agree that Nietzsche would be in despair regardless. :shock:
User avatar
MustaphaTheMond
Posts: 25
Joined: Wed Aug 17, 2016 6:28 pm

Re: Musings on the Nietzschean concept of "eternal recurrence"

Post by MustaphaTheMond »

Dalek Prime wrote:Just made me think of determinism again. If your a determinist, even the first time through is hopeless. Everything is planned for you. So the rest is just pointless gravy. How funny is that?
You could indeed argue that everything is hopeless and pointless, or you could take the view that your choices, actions, intentions are still very real causal states themselves (which have also been caused); which lead to real outcomes in the universe. To realise the truth of determinism does not equate falling into fatalism.
Post Reply