"Timothy Golden BandTechnology.com" <tttpppggg@yahoo.com> wrote in message
news:1176809176.756188.122610@n76g2000hsh.googlegroups.com...
On Apr 17, 12:03 am, "Dr. V I Plankenstein" <Plankenste...@stle.sci>
wrote:
What you wrote is very brief but I can present a little argument
that
favors your perspective.
When we instantiate a concrete distance we are forced to select a
unit
measure. Until such a reference is chosen there is no measure. This
can
be
taken as bringing the real numbers into question from a physical
perspective
since they make an assumption that such units are already chosen.
This
is in
the geometrical Cartesian representation of space that I mean this
to
apply.
We find that the selection of unit reference is arbitrary in
practical
measurements. There is a thread on this titled "The Unity Problem"
on
sci.math.
I suppose a quantum distance could exist yet shouldn't we accept
that
a
continuous distance greater than it is possible? Far from building a
lattice
space this provides an interesting topology with a sense of
adjacency
that
automatically implies an exclusionary principle.
The universality of this concept is challenged by the photon which
does
not obey that exclusionary principle. There is no maximum photon
density.
Yet we may discover that there is a lower limit on wavelength. That
I
suppose could be a corollary of such a theory.
-Tim
I have been saying that "length is probabilistic", and this can have
multiple meanings.
One possible meaning might be that you have a certain length, and
that
the
endpoints are fuzzy. Fuzzyness is only found at the endpoints fo the
interval.
The other possible meaning is that this fuzzyness is found
everywhere,
and
is associated with each point on the interval. The the points in the
interval are existentially fuzzy, and this would cause an apparent
overall
change in length.
I tend to favor the second usage, but they may be equivalent or
indistinguishable situations.
The wierd thing is that the change of length is a delta, you could
call
it
(delta)L or just dL.
This dL is directly related to the probability which we mentioned,
and
you
can also modulate the probability, call it (delta)Probability or
just
dP.
Somehow this stuff shuold all be possible with the number (a + ~b).
Any ideas ?
What you are about to say makes no sense at all.
If the qualities of
a + ~ b
were to cancel some effects of a rich basis then the consequences
would be of interest. But it seems that you need a structured basis to
get there. Just focusing on this random component is limiting. It may
be of value however it needs to be applicable to something. I do not
believe that it alone has enough to develop any consequences.
I still think this leads to a wavelet style of analysis where your
a + ~ b
becomes something more like
a1 = b1( b0 - a0 )
or some such iterable diminishing concept. Then in this flux instance
the a0 is a zero order flux in its undithered form. It is more static
than a1 and a1 is more static than a2, etc. This is a resolution
concept and the idea that the a's may just keep going becomes
acceptable since they diminish if b is a probabilistic factor 0<b<1.
Ya know Tim, I know that I'm full of *****, but at least everything that
I
talking about really is consistent and not really very outlandish
mathematically. Now - I never made fun of your polysigned reals, because
I
think that imagination is more important than knowledge. But I have to
tell
you something, that it really sounds a little bit like I'm being mocked
here, and I gotta tell ya that I admire your spirit.
You're the only person in the universe who cared enough to make fun of
it,
and this may surprise you but I truly appreciate that.
But, there is an element of disappointment in that your sinicism seems a
little light on the "verve" if you know what I mean. A little
strategically
placed sarcasm would really help things I think.
I'm not being cynical and I'm not making fun of your math. I do
believe there needs to be some basis to work from. The harshest
criticism that I have for you is that declaring
a + ~ b
is not a solution to anything. It is a tool. I am happy to consider
scenarios. You could shorten your symbology to
a ~ b
but I think your long form is more clear to a beginner.
The reason I wrote ( ~b ) is to indicate that this item is being chosen at
random. You would want to use the plus sign to indicate addition as opposed
to multiplication or something else, hence, ( a + ~b ).
It is also useful to think about things like a * (~b ).
This whole approach has many technical difficulties, but I think that it is
so similar to complex analysis that development could follow very much along
the same lines as complex analysis.
At this point we need to understand commutivity, associativity, etc etc. All
of the fundamental stuff needs to be worked out. Then we need to figure out
how to "represent" things, and interpret things geometrically. We need to
understand functions which use such nummbers, etc etc.
THEN we can understand waves. And THEN we can try to construct a cellular
automata. And link the two from first principles, topological indeterminacy
of the number (a + ~b) . At that point, the wave particle duality is
explained algebraically.
.
