[extropy-chat] something rather than nothing
Stathis Papaioannou
stathisp at gmail.com
Tue Apr 17 05:21:20 UTC 2007
On 4/17/07, A B <austriaaugust at yahoo.com> wrote:
>
> 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.
I still find your use of fractions confusing: I assumed you are talking
about the fraction of the total age of the universe, but at times you seem
to be talking about fractions of time units as well.
I can see that if time comes in discrete quanta (my understanding is that
physicists are divided as to whether this is the case) you can't really have
a "zero" time, because the first event has to occur in the first unit. So in
the universe you describe, the first event occurs during "1", the second
during "2" and the final during "3". There is time for an observer to
experience 3 states, at most. This would work just as well in a block
universe cosmology (actually, continuous time would work just as well in a
block universe, if you just make the time slices infinitesimally small).
Have I completely misunderstood something?
Stathis Papaioannou
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