Stephen P. King (stephenk1@home.com)
Sat, 02 Oct 1999 11:32:26 -0400
Dear Ben,
Ben Goertzel wrote:
[BG]
> > > I also see that this kind of bisimulation is quite different in detail
> > > from the kind that is defined in math papers. It is only approximate
> > > for one thing. However it may be algebraically capturable, in the
> > > sense that A's simulation of B should be a subalgebra of
> > > the algebra characterizing B...
[SPK]
> > Umm, so would how would the relation between B's (A'S)
> > simulation of A and A (B) be defined algebraically?
[BG]
> Of that I am not sure. One would need to work this out in terms of the mathematics of quantum nonlocality.
Yes! but I think that it is residuation that matters here...
> The question I would ask is this.
>
> Suppose we consider the structure or meaning St(A) of a system A as consisting of the set of patterns that > can be observed in A.
>
> After A and B have interacted, in what sense is B contained in St(A). If some transform Tr(B) of B is > contained in St(A), what is the nature of the transform Tr?
Well, I think that the "set of patterns that can be observed in A" is
an equivalence class. I could be nippy and say "the set of patterns that
can be observer _of_ A" is better... Ok, lets be sure that this is
consistent; with the second statement. [How is the structure or meaning
related? I think that these are duals, but I need to justify this!]
The particular observation by B of St(A) would be similar to that of
some other observer, say C, observing St(A) iff B and C can agree on
some maximum of the members of St(A). I think that if the transform
Tr(B) is contained in St(A) then so would Tr(C) iff Max B of St(A) = Max
C of St(A), this gives the appearance (or really is a restatement of)
the notion that two observers have a "common space-time" to the degree
that they can agree on the behaviors, here that of transformations that
leave St(A) invariant, within such. It looks like these latter
transformations are the fixed points of St(A), this might be the clue
that we are looking for.
Since information is generally defined as "the ability to choose
reliably between alternatives"
[http://www.aip.org/physnews/preview/1997/qinfo/sidebar1.htm], observers
would perceive themselves as having a space-time or "world" in common
iff there motions, given by Tr of the observers that present almost the
same class of alternatives, e.g. St(A) in your writing above.
> This needs to be answered in terms of the mathematics of quantum theory. A more elegant algebraic answer > may be gotten out of answering this question in terms of the full Standard Model (weak + strong + QM) > because this has a richer algebraic structure.
Umm, are not SU(2) and SU(3) the groups that represent the "weak" and
"strong" forces respectively? Are these possibly expressed within Chu_8
and the QM properties as the left and right residuations (inner and
outer products) thereof? We must resist the urge to lump all "objects"
and "morphisms" into one and the same "space"! There are consequences
that must be taken into account when we do so! I think that U(1) and
DIff^4 are external and SU(2) and SU(3) are internal to LSs, but I can't
justify this now...
Later,
Stephen
PS, this essay is perhaps interesting:
http://www.ftech.net/~honeyg/progstone/progstone.html
This archive was generated by hypermail 2.0b3 on Sun Oct 17 1999 - 22:40:46 JST