[extropy-chat] something rather than nothing

[A B]

Hi Stathis,

Yep. You're right. The weak-spot of this question is
the quotient of Infinity divided by Infinity. I had
incorrectly assumed that this quotient could only be
Infinity itself. But, I was wrong. Apparently this is
one of the "indeterminate forms" of mathematics -
where the quotient of +Infinity/+Infinity can be any
positive real number, including positive Infinity. The
quotient seems to "behave" in a dynamically variable
fashion where any two (or more) consecutive
calculations do not have to yield the same result.
Weird. As you pointed out, from a certain perspective,
this also makes sense intuitively. For example,
Infinity/2 is not a use-able calculation in this
example because an observer can never "reach" any
point in time other than an infinitely small fraction
of an infinitely long history (ie. Infinity/Infinity).


So this would indeed allow that a Universe
that was predetermined to become infinitely old could
include observers with subjective experience who
could "see" a greater-than-zero yet finite history of
their Universe, even though their Universe could still
potentially become infinitely old. So it looks like
our Universe could potentially become infinitely old,
as you said, and that our own Big Bang could also
potentially have coincided with "the very beginning".
All of this in spite of the fact that our Universe is
only 15 Billion years old. That's just plain crazy...
but really fascinating, in my opinion.

A lingering question I still have is: if the
+Infinity/+Infinity quotient can yield any positive
real number, then why in this example, does it appear
that the quotient is continually gaining positive
value only? Instead of for example, yielding an
apparent value of +4528, and then subsequently
yielding an apparent value of +326. IOW, *why* are
these seemingly arbitrary calculations completely
consistent with the apparent "arrow of time"? ...???
...? ... Perhaps because "subsequent" calculations
themselves require the passage of time? I wonder if
there is more to be seen here.

Stathis wrote:

..."if the probability of
> observers arising or surviving
> decreases as time increases, it can turn out that
> there is a high
> probability that an observer would find himself in
> the first n years of the
> universe's existence."

True. Or the potential decrease could be the result of
a voluntary aggregation/assimilation of individuals
into a smaller number of "discrete" consciousnesses,
which is what I hope that the Doomsday Argument is
indicating, above any of the alternatives.

Best Wishes,

Jeffrey Herrlich  


--- Stathis Papaioannou <stathisp at gmail.com> wrote:

> On 3/24/07, A B <austriaaugust at yahoo.com> wrote:
> 
> If a Universe was predetermined to have a positively
> > infinite lifespan, then an observer from any
> > "time-location" should be able to look backwards
> and
> > see an infinitely long history of their own
> Universe,
> > back to the "beginning". If we take positive
> infinity
> > (which would represent the total lifespan of this
> > hypothetical Universe) and divide it by any finite
> > number (which would represent a randomly selected
> > "time-location" for an observer) the quotient is
> still
> > infinity which would correspond with the apparent
> > "age" of the Universe from this observer's
> > perspective.
> 
> 
> Not really: if you stand at any finite number you
> can always look backward
> to zero, but you are only at an infinitesimal
> proportion of infinity if you
> look forward. You might say it is surprising that we
> find ourselves at such
> a low number as 15 billion, but it would be equally
> surprising for us to
> find ourselves at any other finite number, however
> large. And that's if the
> distribution of observers is uniform over the
> infinite span of the
> universe's existence: if the probability of
> observers arising or surviving
> decreases as time increases, it can turn out that
> there is a high
> probability that an observer would find himself in
> the first n years of the
> universe's existence.
> 
> Stathis Papaioannou
> > _______________________________________________
> extropy-chat mailing list
> extropy-chat at lists.extropy.org
>
http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
> 




 
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