It appears you had some similarly "awed" views regarding infinity.
Yes, it's very innocent appearing that infinity "stretches" forever or some other linear connotation - very simple, just a line.
But it's most entirely not how it "works" (sort of) - there are many forms of infinities and all of them are in a sense the same thing (if you pick the very largest infinite possible, which in physical terms would seem to be time - we never have more information than is available over time, every other infinite form of construction is smaller and derived from time).
And for an infinity to exist in time, it can't be an identical repetition or everything becomes superimposed as a single identical thing. So then it becomes a bit more significant ... but it goes past this - how do we actual end up perceiving time? Well it comes in terms of distinct types of conscious experiences - I consider it similar to a string of properties that exist in a moment - for example, seeing a tree could be described in various ways as fractal with various textures and colors and contrasts between background and foreground colors etc.
The complete "alphabet" of human perceptions is likely not incredibly large and there may be just a few hundred basic "atoms" in these concepts (I'm just making a rough guess - might be a couple thousand, though it could be 50 ...it's not "huge" - the larger space of experiences over time result from combining these and with memory).
So let's say we tried to count and we had the equivalent of 50 binary valued perceptions (the property either exists or it doesn't) and let's say there are something like 40 of these sets per second.
Now how long would it take to fill all possible conscious experiences with this set?
Well we have 2^50 possible combinations and we divide that by 40 per second and 3600 seconds per hour, 24 hours per day (ignoring night) and 365 days per year gives us close to 900,000 years (this is very rough, it could be billions or trillions of years)
Now there could be a question of whether or not these could stop in some manner before or after death and I personally can't see how that could be possible because it requires that something outside this timeline change to indicate whether or not life is currently occuring - but if such a state could be toggled from "stopped" to "running", then what would stop it from changing back again if it went from "running" to "stopped" - you'd need some other latch to tell the first latch to not toggle anymore and then we end up finding that there would need to be some infinite sequence of such latches and still no guarantee that anything remains latched.
Logic can't contain time - they're actually two entirely separate "elements" - logic describes static forms, but none of them inherently move unless "given" time (which comes from outside the logic) and so logic just really can't touch time, it's dependent upon it to do anything.
So in a sense it seems just unknown whether or not time is infinite, but there appears little reason to believe it's finite because it really isn't even constructed by any form of finite logic.
So in the example, above - you'd need to go past those 50 perceptions to represent times over 900,000 years and so we could add something like a new color of the rainbow - let's just say it's some new funky glow, but then that's just another 900,000 years.
And it gets even more interesting because you can't simply increase the number of perceptions without physical properties to encapsulate them - for example, if there were an infinite number of perceptions, if only finite physical information is available, then if can't "fill" all this with unique forms, so this information needs to become unbounded as well, and then we once again find that finite intelligence couldn't comprehend infinite information and so finite bounds on this are "broken" as well and basically anything that we try to impose a finite restriction on is ultimately surpassed by infinite growth.
Now consider that even the bounds of imaginary for a person are finite because they're only made from a finite set of concepts derived from finite experiences and senses etc.
Actually we already have what could be infinite qualitities in conscious perceptions already - the textures, smells, colors etc. though potentially stimulated via. numeric and finite "external" information are not in themselves easily quantizable - to elaborate, let's say that there is a specific wavelength that is precisely "green" and we can quantize it into the detection of some quantity or number in the environment (this should be possible), now though we could reference this objectively as the discrete symbol for "green", the quality of green consciously perceived could vary from person to person and doesn't appear to have any quantizable trait - what if someone actually saw green similar to turquoise or even as something wildly different and experienced sight similar to a blind person feeling textures? There doesn't appear any way to draw a fine line to these experiences and separate them into any numeric form.
So this could already represent something equivalent to an infinite component of experience, though they still only exist as some finite perceivable collection of them in experiences and so they ultimately would have to differ over time as well.
Basically it appears that a linear view of infinity is a complete misrepresentation of it and infinity does not resemble anything like 1,2,3,... or straight lines. It's an alphabet of so much complexity that it's about impossible to say much of anything specific about its properties except that there can always be things past the lines you draw.
And from your post it appears it "hit you" to an extent also how significant that is, though you may not have recognized the extent of it.
Now none of this appears entirely certain though - logic doesn't seem to work with time very well and so similarly it could be that time is actually irrational (and I mean that in the sense of randomness and insanityand not similar to an irrational number) and yes, despite no logical way to describe how, it still "stops" and/or "starts" and somehow maintains a logic in one respect and not others, but it just seems extremely unlikely (if Occam's Razor applies and its simple then time should be infinite - there's really no other explaination) and was there ever something in "Everything" that implied only a finite quantity of things could exist? Seems highly unlikely - I'm personally willing to accept that time is infinite and it fits in well with so many other things that it's become almost obvious to me (though it appears there may never be certainty, but since when have we had absolute certainty - the existence of time is probably the #1 most significant physical thing around - it's also the most common noun in English http://wwp.greenwichmeantime.com/press/time-noun.htm). And it wouldn't be surprising at all to find the that single largest infinite thing is also the thing/noun most frequently referred to
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