I continuously grapple with this intricate web of thought that intertwines infinity, atomic structure, and consciousness. It's predicated on the assumption that if time truly is infinite, then there isn't just a probability, but an inevitability, that all the matter in the universe will align exactly as they are now.
(I posted this over at c/stonerthoughts, where it will inevitably die without a single interaction, but this is an ongoing pervasive thought I have, and i just wanted to put it out there for more eyes to see.)
This possibility stems from the Poincaré recurrence theorem, a principle in mathematics and physics which suggests that certain systems will, given a sufficiently long but finite time, return to a state almost identical to their initial state. Now, if we consider the universe to be such a system, it implies that given infinite time, every atomic configuration that has ever occurred will inevitably reoccur.
Now, let's venture deeper. If our consciousness is an emergent property of a specific atomic arrangement, then the recurrence of that atomic arrangement implies the recurrence of that conscious experience. Hence, if we're bound to this specific arrangement of matter, and time is infinite, are we not then destined to relive this conscious experience an infinite number of times?
The implications are staggering. It suggests a form of cosmic reincarnation, a cyclic existence governed not by spiritual dogma but by the immutable laws of the universe.
My next step is trying to figure out how this concept could integrate with the theory of an afterlife. Also the infinite nature of the individuals conscience, being the observer and therefore the centre of their own universe.
What's your take on this perspective? How does it change your understanding of consciousness, existence, and our role within this infinite cosmic dance?
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Infinite isn’t synonymous with all-encompassing; the decimal expansion of 1/3 will go on forever (0.3333333…), but it’s never going to contain a 4.
You're correct that infinity isn't necessarily all-encompassing. Your example of the decimal expansion of 1/3 represents a "bounded infinity," where the values can continue indefinitely but are limited in scope - in this case, to repetitions of the number 3.
In contrast, when we consider the potential configurations of the universe over infinite time, we're imagining something more akin to an "uncountable infinity." This is a type of infinity exemplified by the set of all real numbers between two points. For example, between 0 and 1, there's an infinite number of decimal numbers. This infinity is unbounded because there's no limit to the variation within this set - any decimal between 0 and 1 could potentially appear.
So in the context of the universe, the idea is that given infinite time and assuming no constraints, the possible configurations of matter and energy might resemble an uncountable infinity, with infinite potential arrangements. That means, given enough time, even highly improbable configurations could occur.