[extropy-chat] something rather than nothing
Stathis Papaioannou
stathisp at gmail.com
Thu Apr 12 03:26:05 UTC 2007
On 4/12/07, A B <austriaaugust at yahoo.com> wrote:
>
> I wrote earlier:
>
> ..."Also, I wonder if it is even possible that a
> Universe
> such as ours (one that includes observers who can
> detect a greater-than-zero but finite history) can
> even become *anything but* infinitely old.
>
> For example, if a hypothetical Universe was destined
> to only become finitely old (eg. 6 Billion years
> old)then dividing that finite history by +Infinity
> would lead to any
> "time-unit"/"observer-moment"/"apparent history" being
> infinitely small. So the only length of history that
> could possibly be observed would be an infinitely
> short one. Or to put it more directly, it seems that
> no observer could possibly exist at all in this
> hypothetical Universe. And I don't yet see any reason
> why the starting denominator could not be +Infinity
> (which would represent the "very beginning" of this
> hypothetical Universe) given that the value of the
> quotient would still be greater-than-zero (and
> positive) although very, very, very tiny."
>
>
>
> I've thought a little more about this, and I have
> another micro-argument in support of this preliminary
> conclusion. Problem is, it's only half-baked because
> it's hard for me to wrap my brain around, and what's
> worse is that it's even harder for me to meaningfully
> present through e-mail. But, what the hell I'll give
> it a try, I hope it may generate some useful input or
> refutations.
>
> First imagine a hypothetical Universe that is
> predetermined to become only finitely old because it's
> destined to end in a Big Crunch. Now convert its
> final, total age into a finite number of individual
> "time-units" (the most fundamental possible units for
> this hypothetical Universe). For simplicity sake,
> assume that it's final total age is only 3
> "time-units" long (this is a very short-lived
> Universe). So I'll use 3 for the numerator (Think of
> the 3 as equaling: three more than zero). The problem
> arises when I try to use 3 as the starting
> denominator. In order for the Universe to successfully
> achieve the age of 3 "time-units", the denominator
> must count-down to the value of 1. But, if the
> denominator counts-down to only 1, then the numerator
> can only achieve the age of 2 "time-units" and
> therefore it could never "reach" its final age.
> (Because there are only units of change between 3 and
> 1. ie. 3 becomes 2, and then 2 becomes 1). This
> Universe could apparently reach it's final age of 3
> "time-units" if and only if it's denominator became 0.
> This quotient is always called "undefined", but that's
> really just a euphemism for equaling positive
> infinity. You might say that a work-around would be to
> start with a denominator of 4, allow that to
> count-down to 1 and allow the numerator to count-up to
> a full 3. The problem with that is, the "time-units"
> we are using are already fundamental, and there can
> only be 3 of them (not 4) in this hypothetical
> Universe. So, apparently in this case, I can't use any
> starting denominator greater than 3, and I certainly
> can't use any starting denominator smaller than 3 that
> would still allow the Universe to reach its final age.
> Yet another problem is that if this Universe were to
> "start" with the fraction 3/3, that would mean
> counting-up from 1, and not from 0 the way it should
> be. The only way this would "work" would be to allow
> that the individual "time-units" for this Universe to
> have no lower bound. In other words, to allow that the
> "time-units" for this hypothetical Universe would be
> infinitely small (but still existent). And if the
> "time-units" have to be infinitely small, then it
> would require an infinite number of them (ie.
> Infinity/Infinity) in order to allow the existence of
> an observer within this hypothetical Universe. The
> passage of 3 infinitely small "time-units" is not
> going to allow the existence of an internal observer.
> So in a terribly, terribly convoluted way, I think
> this supports my contention that: only a Universe that
> will reach an infinite age can include internal
> observers. Therefore, my preliminary conclusion is
> that our Universe will never end in a Big Crunch and
> will continue to exist into the infinite future. Of
> course, I'm willing to change that conclusion
> depending on any convincing evidence or argument.
>
> I realize that this is probably clear as mud. I know I
> wouldn't want to try and interpret it. :-)
>
> In any case, I welcome any comments, even the
> dissenting variety.
>
> Best Wishes,
>
> Jeffrey Herrlich
Could you clarify your usage of numerator and denominator? The denominator
is the number on the bottom, stays fixed and cannot be zero, while the
numerator is the number on top and can take any value, although in this
context it will vary between 0 and the denominator, 3.
Stathis Papaioannou
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