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 form 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. In showing that information is conserved in
moving between particle-field or point-wave dualities, etc. then science
demands of representations the ultimately a 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.
If you triples have a in and b out conditioned on r. How
do you put b in and r out conditioned on a?
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.
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.
Paul, I will be following you, but become now completely
over-burdened and quiet.
Good luck
Dick