Properties of Infinity

[Magical Realist]

Given enough thought, certain properties or aspects of infinity pertain. Here are some of them:

1) Infinity is never certain. It is contingent and conditional on never reaching an end or limit. But we can never know that for sure. It may at some point turn out to be limited or finite and so cease to exist. Its very existence, by it's own nature, is held in question.

2) Infinity can never be fully defined. To be defined is to have a set and static being that is finite and comprehensible. But since infinity goes on and on, what it contains and is definable as is limitless. Infinity is by its very nature absolutely mysterious and incomprehensible.

3) Infinity is neither present nor remote. It transcends spacetime in terms of not being localizable or "there" in any intelligible sense. It never arrives nor does it recede. It's nature is to forever concentrate and unfold the localized finite towards its own eternal horizon of being.

4) Infinity is neither physical nor mental. It is neither concrete nor abstract. Its being is such that it exhausts all possibilities and yet forever contracts and forever expands at once. It is infinitely miniscule and yet infinitely encompassing. There is iow no floor or ceiling to Infinity. And whatever it provisionally shows itself to be on its surface, it likewise is not, for it is always outside and other than all that is finite and complete.

[confused2]

Until the end of the nineteenth century no mathematician had managed to describe the infinite, beyond the idea that it is an absolutely unattainable value. Georg Cantor was the first to fully address such an abstract concept, and he did it by developing set theory, which led him to the surprising conclusion that there are infinities of different sizes [edit - an infinity of infinities?]. Faced with the rejection of his counterintuitive ideas, Cantor doubted himself and suffered successive nervous breakdowns, until dying interned in a sanatorium. Nowadays, mathematics cannot be understood without his revolutionary insights.

More https://www.bbvaopenmind.com/en/science/...nfinities/

[C C]

Given enough thought, certain properties or aspects of infinity pertain. Here are some of them:

1) Infinity is never certain. It is contingent and conditional on never reaching an end or limit. But we can never know that for sure. It may at some point turn out to be limited or finite and so cease to exist. Its very existence, by it's own nature, is held in question. [...]

Infinity entails unceasing change (either adding more or dividing more), since it can never be a completed, definite magnitude without contradiction of thereby being finite. Even a mind-boggling, vast quantity is still bounded and limited if it is a completed or fixed amount.

For instance, if spacetime is actually infinite -- lacks a state in the distant future where heat death occurs or the co-existing different states do not absolutely end, then it's more akin to a growing block universe (GBU) scenario rather than one that is finished or complete (ordinary block-time).

But that wouldn't necessarily mean we reside in the literal "present" of GBU or where the new changes are being constantly added. We could be located in the remote past of the block, just as can be similarly construed the case (depending) in ordinary block-time.[1]

- - - footnote - - -

[1] The objective unit of time or change that GBU would seem to sport (at its growing "edge") would have to accommodate how fast events happen at the subatomic scale. Which would at least fall in yoctosecond territory if not an outright Planck time-unit. Whereas the rate we experience change comes in irregular millisecond units ("The Movie in Your Head").

The specious passage of time we experience is a product of incremental brain configurations, of the latter discriminating our existence through spacetime into distinct islands of cognition, of which each can only be aware of itself (not the rest all at once). Again, those personal measurements or "moments" are fantastically "slow" or "gigantic" compared to what a hypothetical objective rate of change would necessitate.

So "temporal solipsism" is the misguided belief of projecting our subjective conscious version of change onto a world that (according to materialist dogma) is supposed to be independent of our mental representations. Which accordingly would be a hilarious mismatch (milliseconds versus yocoseconds, or even slimmer yet). An example of how even critical-minded people have severe blind-spots with respect to their combined beliefs being consistent or hanging well together. They don't follow the consequences of a particular _X_ all the way.

[Magical Realist]

Georg Cantor was the first to fully address such an abstract concept, and he did it by developing set theory, which led him to the surprising conclusion that there are infinities of different sizes [edit - an infinity of infinities?].

Infinity is thus a self-containing set of other infinities. Take a piece of a fractal from a fractal and you have another infinite object that spirals and branches out forever. Take any two consecutive numbers from the set of all whole numbers and you have an infinite series of real numbers. Infinity appears to be irreducible to any of its parts. It is a boundless set of innumerably self-containing and superlative magnitudes.