Re: Interval in a continuum is a fractal
- From: Venkat Reddy <vreddyp@xxxxxxxxx>
- Date: Sun, 2 Dec 2007 07:33:19 -0800 (PST)
On Dec 2, 5:33 pm, LauLuna <laureanol...@xxxxxxxx> wrote:
On Nov 30, 4:07 am, Venkat Reddy <vred...@xxxxxxxxx> wrote:
This is another perspective to explain things when I say you can't
break the conituum interval into points.
An interval in continuum such as time span is bounded by two time
instants, which are modeled as real numbers in mathematics. The
interval also has a non-zero extent or magnitude or span which is
modeled by the "measure" in mathematics.
Any statement that is even remotely related to "such an interval is
made up of certain things", has to deal with division process of such
interval. Simply defining that such interval is made of time instants
is like saying I just said, and you can't question. We need to attempt
a division process to see if it is right.
Such a division process on an interval results in smaller intervals
which has the same properties of the original interval - having bounds
of same type, and having a non-zero measure of extent which is also
same type. This can be continued for ever but the intervals or parts
do not cease to hold the properties of the whole, which qualifies the
partitions as fractals.
Fractals do not collapse to zero extent. It is just forced by our
arrogance at not recognizing the nature and it symmetry. Nature has no
jumps. If the measure has to collapse to zero, there needs to be a
reason such as hitting the "largest number" of divisions.
This is the crux of what I meant in all my recent posts and threads.
- venkat
I grant that Venkat Reddy is not always clear but I don't understand
why all this scandal.
Venkat Reddy is only pointing out what is obvious: the analytical
construction of the continuum and the spatial/temporal continuum are
not isomorphic, and they can indeed hardly be so, since they are
structures of a quite different nature.
When Cantor and Dedekind constructed the reals as an numerical model
of the spatial/temporal continuum they didn't prove any isomorphism;
attempting to do it would have been nonsensical. They just assumed the
model was good enough as to contain no 'numerical error', i.e. no
error that could be rendered as a numerical excess or deficience in
some computed quantity. And they were right, for all we know.
Going further as to claim there exists an isomorphism like the one
existing e.g. between <[0,1], <= > and <[1,2], <= >, is really
audacious.
I think this is all Venkat Reddy is trying to say. Except perhaps for
the resistance here found, it could be labeled as trivial and little
more.
That's an excellent summary of the things. Indeed, it is a trivial
matter except for the resistnace found here, such as saying "Reals are
THE continuum", "Infinite number of zeros produce non-zero quantity",
"A line is composed of points" etc. That's where I continued my fight.
On the other hand, I tried to revive the infinitesimal as the seed of
existence than using zero or non-existence as the seed for the non-
zero extent. However, I could not complete my thought-work on this
yet.
- venkat
.
- References:
- Re: Interval in a continuum is a fractal
- From: LauLuna
- Re: Interval in a continuum is a fractal
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