eternal reoccurence

[ObnoxiousCynic]

In mathematics, the Poincaré recurrence theorem states that certain systems will, after a sufficiently long time, return to a state very close to the initial state. The Poincaré recurrence time is the length of time elapsed until the recurrence. The result applies to physical systems in which energy is conserved. The theorem is commonly discussed in the context of ergodic theory, dynamical systems and statistical mechanics.

The theorem is named after Henri Poincaré, who published it in 1890.

en.wikipedia.org/wiki/Poincar%C3 … ce_theorem

Another problem encountered in this particular view is whether time can only exist for one person in the entire universe. Again, there are two different possibilities, one is that there truly is only one person in the universe, which any one person can hypothesize about oneself. If one considers the possibility that this entire “reality” is simply one’s dream, then there is no problem with a conception of time consisting entirely of one’s own experiences, and thus repeating only for the self. [2] If, however, there truly are multiple conscious entities in the universe, the idea of the Eternal Recurrence requires a breaking away from the traditional conception of time as a linear, four-dimensional matrix. As the time line progresses there must be points, namely where each subjects recurrence occurs, where a new time line breaks off from the ongoing time line and loops back on itself. Please see figure 1.1 below for an illustration of this possible time line.

                                                                    Figure 1.1

The time line progresses, but loops back on itself for each subject.

        While this may seem outlandish, modern physicists have been formulating theories that would accommodate a time line as illustrated above. Albert Einstein's groundbreaking work with Relativity showed that time as a straight, consistent linear concept is insufficient to support what actually occurs in the universe, and Stephen Hawking's A Brief History of Time served to revolutionize humanities understanding of the universe and its temporal structure. These works laid the foundation for a more innovative formulating of temporal theories. [u][b]Julian Barbour proposes a conception of time as a collection of eternal instants that are perceived by consciousness as a linear progression from one moment to the next in his book The End of Time. Under this conception, every moment of time is, in itself, an eternal and existent universe that people's consciousness' "visit" one at a time. Under this framework, every conceivable moment would eternally exist and could easily be revisited by one consciousness at a latter point in that subject's experiencing of time. This would make it possible for multiple subjects to return and re-experience the linear progression of their experiences, independent of each other, without any effect on the overall temporal matrix of the universe. [/b][/u]
        These temporal theories draw heavily on modern scientific movements such as quantum mechanics and astrophysics, which where not developed until long after Nietzsche's death, but appear to offer the best and strongest conception of the Doctrine of the Eternal Recurrence as a structure of time. Whether Nietzsche had a conception of the universe similar to this far in advance of the modern movement is not discernible, but given his groundbreaking thought in many other areas, would seem to be a possibility. Even with this possibility in mind, making the Doctrine internally consistent as a temporal structure requires a tremendous amount of speculating about and "restructuring" the physical universe. These speculations may be true in actuality, and indeed, there is increasing evidence for such an abstract view of time, but the other possible interpretation of Nietzsche's meaning behind the doctrine, as a "test" or psychological decision-making mechanism, requires less accommodation to function.