Hilbert’s Hotel paradox seems to reveal that time has finite attributes even if infinitely extended, because it assumes a discrete occurrence can be observed: adding one room by shifting occupants.

One insight I have into the nature of the mathematically infinite/finite (what the HH paradox explores) is that when we posit the infinite, it exists as wholly unchanging, because it’s the same complete set every time we look at it. By contrast, the finite is unique because it’s distinct information at any given point. Thus, it’s as though the infinite is rendered finite (always the same) and the finite is rendered everlasting (never the same). This paradox explores the interplay between the two based on observation, which goes back to my point that the infinite has finite attributes.

To demonstrate, imagine the universe of reality as something knowable to an omniscient God. It is infinitely complex and impossible for us to grasp. This is how we see NP: being impossibly knowable.

Alternatively, imagine all of reality as the incarnation of infinite potential, such that reality is a discrete occurrence, like the will of God. To demonstrate this, imagine a man under an awning smoking a cigarette in the rain. A breeze passes and a drop of water lands on the end of his cigarette, putting it out. This observation causes him to imagine an alternate universe in which the drop of water merely passed closely, but didn’t connect. If there are parallel universes for every conceivable potential, there would exist a universe for every potential path of the raindrop, or for any drop(s) of water throughout the universe. Therefore, reality itself feels very small by contrast, or by definition, bounded/finite. This is how we see P: being easily knowable.

If reality can be thought of as both infinitely complex & finitely discrete, and even mathematical infinity can be seen as finite, P equals NP because depending on POV they are swappable, or symmetric.

>thoughts?