Ahhhh......(said he), the smell of dinner and a satisfying meal.
MOOOHHOOOHUUAAAAaaaaaahhhhh.....

"n...@bid.ness" <Alien8...@gmail.com> wrote in message

news:1175989313.747877.239460@w1g2000hsg.googlegroups.com...

On Apr 7, 12:40 pm, "Dr. V I Plankenstein" <Plankenste...@stle.sci>
wrote:

The following approach, if valid, would explain wave-particle duality
analytically. The algebra would make perfect sense if this notion of
number is truly sensible and valid.
Heck - when is an apple an orange ? When you have zero of each. So -
when is a particle also a wave ?

Implication is that when there are neither waves nor particles,
they're identical? Fine, but that's a simultaneously limiting and
unlimited case; zero apples are also identical to zero 1964 pink
Cadillacs.

Well, zero particles being the same as zero waves would make sense, but it
is much more sensible to think in terms of these things as being trivial at
Planck scale.

Nonzero real electron waves are empirically identical to nonzero
real electron particles _until_ they are characterized as either wave
or particle by detection. They are generated by identical processes so
may be assumed to have identical propagation-related characteristics
on the way from their place of origin to their place of detection (and
characterization); particle-property-based detection technology
produces results that are distinguishable from wave-property-based
detection technology results.

Very well stated, but if one combines particle counting along with wave
recording into a single device, then your example has no merit. In fact,
this is what the double slit experiment actually does. Heh heh.....

Consider a + ~b, where a is some known nonrandom real, and ~b is some
unknown random real. By definition, ~b is indeterminately chosen from
either continuous or discrete sets, and is expected to be morphic to the
solution set of 0 = 0*a = 0*x = 0, a is a conatsnt, x is a variable as discussed
elsewhere on sci.math.

I think you're trying to apply a distinction before it's necessary
to do so; you've already characterized ~b as "some unknown real", then
go on to describe its possible origin as _either_ from continuous or
discrete sets. In the case of particle physics we do not make that
distinction until we get to the detector; the thing-in-itself's nature
up until that point does not require characterization, and in fact any
attempt to do so directly influences what is detected.

The number a + ~b is interesting because the term ~b is topologically
indeterminate. This number connects two distinct branches of complex-like
analysis, one discrete, and the other continuous. Both branches should
be equivalent to each other under some suitable transformation.

Only if that transformation excludes some members of each set; there
are members of the continuum that are not directly expressible in
terms of _single_ members of the discrete set (irrational numbers
frinst). Conversely there are properties of the discrete that do not
correspond to those of the continuum (quantized spin frinst).

However if you assume a third set which contains both the discrete
and continuum, you have a chance. This is analogous to the "wavicle"
interpretation of particle physics.

Here's another analogy; while you're deciding which set to choose a
value of ~b from, imagine a table on which lie two sheets of paper,
each containing one of the sets. You are waving a pencil in the air
over the table. Both sets exist independently, but as long as you hold
the pencil in the air, ~b is indeterminate; the superset that contains
the papers and the space your pencil can occupy contains all possible
values of ~b _including_ the many functionally identically
indeterminate values up in the air. They are all discrete in one sense
and are members of a continuum in another, but they are equally
indistinguishable _until you choose one_ by putting the pencil to one
of the sheets. Now you may quibble that the values represented by the
pencil being in the air are "imaginary", but are you quite certain
they're not "real" in the sense that they correspond to valid
solutions (physically realizable states)?

Also I refer you to the concept of eigenstates in particle physics.
A while ago it was fashionable to talk about certain composite heavy
fermions as "baryons" which had a quantum number (isospin) that
differed for each particle but was conserved in interactions. Protons,
neutrons, and some other short-lived particles were considered to be
eigenstates of something that only existed in an unphysical,
indistinguished state but was nonetheless "real".

I suggest you consider the concept of "eigennumber" for ~b, and what
sorts of selection rules you may have to invent to resolve your
questions.

What we are attempting to construct is a mathematical framework which is
arbitrarily either continuous or discrete. You have two parallel
mathematical models. One is continuous and the other is discrete. Both are
similar to complex analysis, but the number system is different. We use a +
~b, where ~b is chosen from continuous or discretized sets.

Because ~b is "at the bottom", it will behave like the solution set to 0 = 0
* a = 0 * x = 0 which was discussed on sci.math earlier. Where a is a
constant and x is a variable, hence solution set is simultaneously
continuous discrete and nonexistent all at once.

My claim is that any quantum process can be modelled as being either
discrete or continuous, because that is the nature of spacetime itself. And
further, that we now have a number a + ~b which may be regarded as being
arbitrarily discrete or continuous as well. Hence, the impetus for "
parallel calculi ". A discretized analysis, and a continuous version, and
the result of any experiment will depend SOLELY upon
_how_the_question_was_asked_ .

You will give me a random number a + ~b.

I ask "how many", and I get a discretized answer.
I ask "how long" and my answer will be continuous.

AH HAH !!!!!!

EUREKA !!!!!!!!!!

And this is justifiable because ~b is morphic to the solution set of 0 = 0 *
a = 0 * x = 0 (unproven).

AH HAH !!!!!!

The topological indeterminacy of the term ~b most likely also suggests
existential indeterminacy of ~b, because this term is expected to
morphic to the solution set of 0 = 0*a = 0*x = 0. (needs proof)

You do appear to have a case of topological indeterminacy but only
in more dimensions than you originally considered. Have you ever read
_Godel Escher Bach, The Eternal Golden Braid_?

I did thumb through GEB. Three great names in my opinion - MCEscher - gotta
love that man.