Nietzsche's eternal recurrence of the same and the paradoxical nature of infinity

[KingCrimson]

Let me share an anecdote with you.

When I was 15, I started reading (Western) philosophy. My first interest was with Nietzsche, as I guess is true for many young people. When I came across his concept of "eternal recurrence of the same", it totally blew my mind. I didn't know what to make of it, though - was something as radical as this actually possible?
So, giving away my authority as one tends to do , I asked my German and philosophy teacher, a great guy, well-read, very intelligent, cared a lot about his students. He had written a few books and taught at University level as well. I owe him a lot.

I told him I had read about Nietzsche's idea of eternal recurrence, and asked him what he thought about it:
"Can you take this seriously? I've read online that many philosophers think he had already been insane when he came up with that idea."
I will never forget his answer. Grinning, he said: "That depends on whether you take infinity seriously or not."
It took me a few seconds to grasp what he had just said. Then it dawned on me. "Oooooooh! Wow!" He smiled.

I realized in that moment, that IF you take infinity seriously, that is, if you believe it "exists", then "eternal recurrence of the same" would be the logical consequence. Infinity implies eternal recurrence of the same. If infinity is real, then eternal recurrence of the same has to be real, too. On the other hand, without infinity, there cannot be any eternal recurrence of the same, because, well, how can something recur eternally if time is limited?

After this, I started contemplating the nature of infinity. That's when I came across a paradox that I still do not have a satisfying answer to. It is this.

If infinity exists, then every possibility exists. Everything that can happen, will happen, in every way possible. So I tried to apply this to my own life. There had to be infinite parallel realities that were all exactly the same, with the difference that, at one moment in time, I did something slightly differently.

Let's imagine a universe where everything is exactly as it is right now, with the only difference being that at one moment in time, let's call it moment X, instead of scratching my head, I scratch my nose. Otherwise, my entire life and the entire world are exactly the same.

BUT the problem is that, logically, such a world cannot exist. In a world governed by the natural laws that we know, it would be impossible for me to do anything other than what I had actually done, that is, scratch my head. If I were to scratch my nose instead, not only would it change the course of my entire life, but of the whole universe. The entire universe would have to operate according to different laws so as to make it possible that I scratch my nose instead of my head at moment X.

But if the entire universe has to operate according to different laws, how can it be exactly the same in every other way? Wouldn't the entire universe have to look completely different from the get go, my entire life included?

BUT, if infinity is real, it would HAVE to be possible, because infinity implies every possibility, every single world in every possible configuration. On the other hand, it seems like there are configurations which are impossible. But if there are impossible configurations, that would contradict infinity. Now there is no escape from the paradox. The cat is chasing its own tail.

You can use any example you like obviously. Imagine a universe where everything is exactly the same as it is right now, except that on October 1st 1977 a singular ant in an Arizona forest walks slightly to the left instead of to the right. You get the idea.

So, my question to you is quite simply - What do you make of this? Is there a way to resolve this, or is this just an instance of the finite human intelligence trying to grasp the nature of infinite using very limited rationality?

Please forgive me if you consider this useless mental masturbation. It probably is that. I guess I enjoy mental masturbation sometimes, and I just figured that in this forum, there might be people who could offer some valuable insight into this problem. I do not suggest that anything can be gained from contemplating this. At the end of the day, infinity has to be realized in one's own direct experience, I understand that. I've had profound mystical experiences on psychedelics myself. I am quite simply curious whether anybody else had come across this paradox - I guess countless people contemplating the nature of infinity would have had to have come across it, I would think that it would have to be a known paradox among philosophers even - and whether you have any thoughts on this. Thank you!

Edited March 18, 2022 by KingCrimson
Grammar

[Reciprocality]

There are mathematical expressions of infinity which patterns necessarily never repeat.

Is three dimensional space just like that? If it is then it would be trivial to say that anything ever repeats.

At the same time, everything must in some sense never go completely away from existence (for elsewise they could never have been experienced at all), which is why if we consider everything in a unity of metatime no repetition is required, just an infinity of manifestations that never begun nor ended. Is it one dimensional? I don't think it makes sense to even ask the question. Everything must in meta time be simultaneous, thus have no dimension.

[Reciprocality]

It is though, unclear to me if it is by means of this meta time I consider my existence inevitable or if I am sensible to meta time because I am conscious period.

[KingCrimson]

@Reciprocality But these mathematical expressions of infinity whose patterns necessarily never repeat are only a very tiny fragment of Absolute Infinity, right? There is an infinite amount of lesser infinities (like the whole numbers, or the mathematical expressions you're talking about) within the Absolute Infinity. Am I missing something?

[Reciprocality]

@KingCrimson The thing I would consider here is why mathematics can be infinite, because this general rule says nothing about physical durations but something about how our minds can make distinctions.

It is simply because we can take two distinct numbers and divide them by a third that infinity occurs, that is actually not true, there is a general rule underlying this example which is its reason for being possible. You have to intuit this general rule for yourself, as you must intuit everything for yourself.

10 divided by 3 is 3.333.. N, but this says nothing about physical infinity, only how our minds make imperfect maps.

[Reciprocality]

Every time we speak of the physical we make imperfect maps, so I am unclear as to whether it is actually possible to make much sense of physical infinity by science.

I guess it must be seen a priori, in fact I know so.

[Breakingthewall]

I would say yes, infinity implies that everything that can happen will happen. but there are things that cannot happen, like scratching your nose instead of your eyebrow without changing a law, and many other things. and those things will not happen in infinity. only what is necessary happens

[Gili Trawangan]

1 hour ago, KingCrimson said:

If infinity exists, then every possibility exists. Everything that can happen, will happen, in every way possible.

Notice that, with this premise, you are limiting infinity.

Infinity doesn't mean that everything that can happen will happen. That would be a limit, and infinity is absolutely free. It doesn't have to be anything, but it can be anything.

[KingCrimson]

@Reciprocality I think I can intuit that general rule you are talking about. I need to mull this over before getting back to you. I am not sure I fully understand yet.

@Gili Trawangan

Hmm. I think I see what you're saying. Here are the thoughts that came up for me:

Aren't you making a distinction between possibility and actuality here? In the last analysis, is it not the case that there is no distinction between possibility and actuality?

But let's keep the distinction and remain in the realm of possibility for now. If infinity CAN be anything, it CAN be a universe in which everything is exactly as it is now, only that instead of writing this comment, I am taking a bath. Logically, even the theoretical possibility of such a world seems impossible, does it not? At the same time, infinity would have to have the freedom to (theoretically, potentially) be anything it damn pleases, which is a contradiction. -> The paradox still stands, does it not?

[michaelcycle00]

1 hour ago, KingCrimson said:

But let's keep the distinction and remain in the realm of possibility for now. If infinity CAN be anything, it CAN be a universe in which everything is exactly as it is now, only that instead of writing this comment, I am taking a bath. Logically, even the theoretical possibility of such a world seems impossible, does it not? At the same time, infinity would have to have the freedom to (theoretically, potentially) be anything it damn pleases, which is a contradiction. -> The paradox still stands, does it not?

Yes, it can be a Universe where you took a bath instead of writing this comment. In fact, if you could free your mind from the usual limitations you could go “back in time” right before writing this comment and take a bath instead. I don’t fully see the contradiction, but then again, everything is happening in no-time, rather than in “infinite time” because there’s neither a beginning nor an end. There’s literally no future or past, your future could literally be going into “the past” and doing something so very slightly different than you remember doing. Also, existence is full of paradoxes so don’t sweat it too much. It’s part of being absolute and unlimited. 

[Adamq8]

Nice post and a serious philosophy, I tend to view infinity as in, unlimited, as in, a point of "view" , for example, imagine God, an Infinite Mind, which means that it is unlimited in configurations of reality, that Mind also set the rules of logic, or more or less that this Mind is logical, as an attribute.

The concept of infinite possibilitys is intriguing but I believe that it is false, certainly our minds can concieve that reality might function that way, but reality is consistent, following logic and reason in many ways, it is like thinking thoughts after Gods thought, we RECOGNIZE, every scientist goes out with the assumption that reality is intelligble, that we can gain knowledge about reality by studying it, in the beginning that kind of mindset arose from a Christian perspective on reality, since God is the creator and is the law giver and the designer of the universe, us as creations, " made in the image of God" can understand and use nature to our advantage.

We are blessed with free will, which is a disputed question if it even exists, but I would say that it does in fact exist, Will exists.

It is sorta like, infinity canceled itself out making a Mind for reality almost, and this Mind is outside of time and can enter into creation by limiting himself, and making himself known both through nature and through revelation.

This is God which has a unlimited Mind but is still not non sensical in its operation, sure it can be that, but it chooses not to be like that, instead it creates an ridiculous balance in nature between chaos and order, it is the Logos of the Father which orders reality in to "being".

I really think that a divine Mind is responsible, the question is just how different this Mind is to its creatures, I see infinity as in infinite possibilitys as a possibility but it is not actual, instead this Mind thinks reality into being and structure out of nothing.

This Mind is ACTUAL, and is actualizing potential, since it is limitless it is infinite possibilitys within this Mind but yet it transcends infinity and has it within itself, imagine that Being, which creates the universe, but the universe can't contain it, because it is creating everything and no creature can grasp the creator