Wednesday, January 04, 2006
New
discussion about signal pathways
and complex ontology
This is part of a discussion that will be moved to a Wiki page soon.
Communication from Dr
Richard Ballard, founder Knowledge Foundations Inc.
Paul:
Sorry to have to drop out again. The Holidays are a
special time and I wanted to reassert my support for you and your moving
forward constructively. There are invitations there too in my letters, but I
know your fascination with biological particulars so carry on.
The issue of n-aries goes to the issue of can your chosen representation reproduce all the patterns of reasoning found or needed by well established scientific theories.
I have shown that information is conserved in moving between
particle-field or point-wave dualities. A corollary to this is that science demands of representations the
ultimate capacity for reversible mappings. Information conservation implies that information content in
equals information out and a generalized capacity to exchange the roles of independent
and dependent degrees of freedom almost arbitrarily.
In your triples have a in and b
out conditioned on r. How do you put b in and r out conditioned on
a? [1]
N-ary bundles create a generalized linear constraint
system in which any degree of freedom can be forced independently to a selected
value (made an independent variable), removing from the bundle every n-ary with
that degree freedom having a not-selected value.
Each such constrained degree of freedom impacts those
other dependent degrees of freedom (not yet made independent by explicit value
assignment). Given n degrees of freedom, constraints can be applied to m
(independent) in any choice or order, the remaining n-m are (dependently
constrained). If n = 2m, then we are capable of explicitly constraining any m
(independently) and thereby dependently constraining the remaining m. This does
not automatically guarantee conservation, but a conserved mapping is among the possible
representations.
N-ary representations have greater expressive potential
than any real science is using. [2]
Triples are left over representations from the conditional
sentence constructions, applying conditions in if-then chains (one degree of
freedom at a time) in a fixed (irreversible) decision flow. [3]
Paul, I will be following you, but become now completely
over-burdened and quiet.
Good luck
Dick
[1] Note from Paul: In my
work, the a, r, and b are structural in nature; all the result of a measurement
of structure. There is no inference and
no implied meaning. There is also no
logical apparatus defined at this point.
A logical apparatus can be
developed later. Meaning can be
assigned later on.
[2] Note from Paul: We agree
here completely. The n-ary
representation of information, and the associated constraints imposed by your
theory creates a new “mathematics”. The
nature of this new mathematics is not yet understood. I feel that stratification is also necessary so that nested
contextualization find a home.
[3] Note from Paul: You have always misunderstood my intended use here. The triple for me is a result of measurement, a measurement that places “a” and “b” in the same frame. This measurement does not fix the “r” as having a meaning. “r’ is “non-specific”. If bags of < a, r, b >, called syntagmatic units by Pospelov, are aggregated together, then we have n-aries. Do these n-aries meet the constraints that the Mark 3 will place on knowledge representation, well that depends on if you and I can figure out how to do this.