[extropy-chat] something rather than nothing

A B austriaaugust at yahoo.com
Mon Apr 16 21:02:47 UTC 2007

Hi Stathis,

Stathis wrote:

 "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."

I acknowledge that using the denominator in order to
count upwards is really odd, but I believe it is
ultimately necessary in this case. In this example,
the Universe has a finite age (3 time-units). That
means that either its fundamental time-units are
either infinitely small (in which case it cannot
possibly include an internal observer - since there is
only a finite number of total infinitely small
time-units), or they are of a discrete and finite size
in which case only a finite number of them can "fit"
into the total lifespan of this Universe (3, in this
much simplified case). If we consider the passage of
time to correspond with a change in either the
numerator or denominator, then we cannot "begin" with
the fraction 0/3. The reason is, that as the numerator
counts-up three times in order to create 3/3, the
quotient only becomes 1, and the Universe is already
supposed to have an age of 3 time-units at that point,
not just an age of 1 time-unit. You could try starting
with the fraction 3/3 and counting-down with the
denominator, but as I argued earlier, in order to
reach the final age of 3 time-units, the denominator
would have to go past 1 and become 0, which would mean
that this Universe would also have to become
infinitely old anyway. Another problem is that in this
case, you'd be starting your count at the value of 1
(3/3) and not at the value of zero. You could try
starting with the fraction 3/4 and reducing the
denominator to 1, but this violates the rules that
we've established: the time-units are already
fundamental, and there can only be 3 of them, not 4.
Also, the time value of 3/4 is illegal because it
would be a three-quarters division of a single already
indivisible time-unit. At this point, the only way I
can see that would allow this to "work", is to remove
the lower bound on the time-units, IOW, allow them to
be infinitely small. We also have to start at a value
of zero in order to represent the very beginning of
this Universe (or what is actually infinitely close to
zero - besides if this Universe emerged from
Nothingness, even a fraction cannot exist until
*something* does), and since the numerator cannot
start at zero, the only way to effectively achieve
that is to make the denominator positive infinity to
start with. At this point, it loops back to the
beginning of the argument: If the time-units must be
infinitely small in this example, then a Universe that
consists of only a finite number of time-units is
going to have an infinitely short lifespan, and
therefore could not possibly contain any internal
observers). Only in a Universe that consisted of an
infinite number of infinitely small time-units, could
any internal observer exist. Also, the weird
"indeterminate form" nature of the quotient of
+Infinity/+Infinity allows that the *actual* size of
the time-units does not have to be infinitely small.
It can be any positive real number, between being
infinitely small (but still existent) and arbitrarily
large. One way to illustrate this is to point out that
the "value" of an infinite number of milliseconds is
totally identical to the "value" of an infinite number
of centuries.

Well, I tried to make this a little less nonsensical,
but that doesn't mean it's "good" at this point.  ;-)

Best Wishes,

Jeffrey Herrlich   

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