Stephen P. King (stephenk1@home.com)
Mon, 27 Sep 1999 23:00:51 -0400
Dear Ben and Friends,
Hitoshi Kitada wrote:
>
> Dear Ben,
>
> Welcome back!
>
> Ben Goertzel <ben@goertzel.org> wrote:
>
> Subject: [time 825] Chu spaces, causality, local systems... quantum laws of
> form? ...
[SPK]
> > > > Perhaps we need to step back and take stock of that ideas
> > > have led us
> > > > to this point. Lance and I have been talking on the phone about
> > > > causality and clocking, toward, I hope, a way of understanding how it is
> > > > that the "space-times" that are 'observed' by Local Systems are related
> > > > to each other.
[BG]
> > Hi, I have not posted to this list in a while because I decided that I did
> > not have time to truly delve into Matti's mathematics and this seemed to
> > be the dominant topic of conversation. but now I will emerge from my lurking...
> >
> > I have read Hitoshi's papers again and remain convinced that this is a
> > fascinating direction for physics... and remain concerned about how it generalizes to
> > deal with weak & strong nuclear forces...
[HK]
> At the present age when there is no mighty theory/view to nature/ourselves,
> this direction would be fascinating. Or, this direction is necessary for us to
> recover/reconstruct ourselves/world. The strong and weak forces might have to
> be included. But before that, I think, there is a necessity that we get our
> world back to our hands. This is a philosophical need for the present age.
The strange way that the "nuclear" forces have a short ranges may give
us a clue, but we do need to develop the formal framework first. This is
what, I believe, Hitoshi is speaking to here. Hitoshi's vision is
revolutionary and is not subject to unproblematic interpretation and
generalization within the usual ways of thinking in physics. I believe
that the difficulties that Matti and Hitoshi are having is that they are
trying to force each other to think within each other's paradigms, which
are complementary, IMHO, but very different.
[BG]
> > The mention of causality intrigues me here because this is something I've
> > been working on in the context of Webmind. It seems that causality is not possible to
> > assess within a local system, but only globally, amongst local systems. Do you agree with
> > this Hitoshi?
[HK]
> Yes, I agree. As well, I feel it necessary to think about mind/consciousness
> as you are doing, which would give us understanding the locality without
> causality.
The way that MIND is a "whole" even when distributed over many physical
components may be giving us a clue as to the mechanism of "locality
without causality". We see in quantum entangled systems the same type of
"wholeness" which have led thinkers like Bohm and Stapp to consider a
physics model that assumes Ideal Monism. The problem of the discreteness
of matter seems to be considered as mere epiphenomena. This is not an
advance, I my opinion, we need a way to see past the dichotomy of mind
and matter to a complementarity of matter and information...
[BG]
> > At the urging of Youlian Troyanov, I have also been reading some of Pratt's
> > papers, and was particularly intrigued by the Stone Gamut paper. However
> > I have some doubts about the usefulness of the approach. It is just so
> > damn general -- so we can generate every
> > algebra there is; so what? The physical world deals with specific algebras.
[HK]
> The approach would be too general to be useful.
This "generality" is necessary if we consider that the Universe, as the
totality of existence, includes all possible material behaviors and
thus, via the duality, all possible algebras describing them. The
selection of "particular algebras" would thus correspond to the
selection of the properties of the physical (material) world.
[BG]
> > However perhaps one can view Chu spaces as a kind of pre-physics. this
> > might make sense.
If it can be consistently shown that Hilbert spaces and/or the more
general Gelfand spaces can be constructed from Chu spaces, and if
Minkowsky and/or Poincare spaces be generated from the interaction
algebras of Chu spaces, this statement will truly be prophetic! ;-)
> > first, out of the void, there burst Chu spaces...
From the ONE, the undivided Universe, a division came into being. In
graph theory there exists a property called the "splittance" of graphs,
that I beleive can help us understand this notion of Ben's.. ;-) That is
essential to understand is that this "bursting" is an ongoing process,
there is no Absolute Initiality involved!
[BG]
> > Then, a selection phase occurs -- those points in the Stone Gamut that do
> > not lead to viable
> > universes die ... and those points that are algebras supporting viable
> > universes survive.
> > thus we arrive perhaps at the octonion and lorentzian groups, as
> > specifically useful points in
> > the stone gamut coordinatization of algebraic structures...
;-)
[BG]
> > But, I'm not sure I love this "top-down" approach where you start with a
> > coordinatization of everything and then whittle down.
[HK]
> I share your view.
It perhaps would help if we consitered "top down" and "bottom up"
appraches as complementary and neither is complete without the other!
[BG]
> > Rather I am still more attracted to the laws of form approach in which you
> > begin with simple
> > structure and then increment onto it, adding on more and more structure at
> > random, retaining
> > it if it works...
[HK]
> This might be a spirit of the age. We have no unique view that is common to
> everybody. At such an age, one has to construct oneself from one's
> neighborhood (not necessarily a spatial neighborhood), or from form in your
> words.
All we have, as individuals, is our own subjective view. That we have
that is similar, is mistaken to be "external" and independent of the
subjective view. This is why, I believe, that we need to look at GR very
carefully!
[BG]
> > The idea of a local system is nothing but a Laws of Form distinction mark
> > (identical to the "boundary" around an individual conscious element that I posit in my
> > theory of consciousness). Then the laws of physics can perhaps be viewed as
> > additional types of boundary composition operators....
[HK]
> Yes, the world has been destructed, and we can/need-to reconstruct it as if
> the components behave like algebraic objects. Namely there is no criterion
> that gives their behavior. We have freedom to start with objects that have
> arbitrary (but fixed) algebraic properties.
We have, in Non-Well Founded Set theory and Chu spaces, a means to
understand the construction/deconstruction process! I take it as my task
to figure out the key formal notions involved and see if we can figure
this out. The way that Pratt connects MIND and BODY is the key!
[BG]
> > Now I will speculate shamelessly, indicating the kind of direction I would
> > like to go in, although I have not gone here rigorously yet:
Please do so! ;-)
> > Typographically, the universe as a bunch of local systems looks like
> >
> > { [a ] [b ] [c] [d] }
> >
> > where [ a ] denotes a local system containing a and the { } boundary denotes
> > a set,
> > i.e. the universe, containing unordered elements
> >
> > When one local system interacts with another it can perhaps be viewed as
> > sending some kind
> > of "messenger" entity to the other; thus we have a new kind of boundary { }
> > representing
> > a voyager from one local system to another?
Is it really necessary to define a third "entity" when a morphism or,
more general, functor would do the same thing? I am thinking that the
notion of bisimulation used in Peter Wegner and Pratt's work is a better
model of interaction between Local Systems as it does not require them
to have "windows", they merely need to be able to "resonate" with each
other!
[HK]
> { } here is different from the { } above representing the universe? Or do you
> mean many (local) universes exist?
[Cut and pasted from TIME 828]
[BG]
> There just aren't enough parentheses in the world...
>
> yes, my {} voyagers are different from the whole universe. The whole
> universe I'll represent by
>
> [_ _]
If I may comment; I believe that any representation of the "whole
universe" that implies some type of boundary is incomplete in the
Goedelian sense! The Universe, as the totality of Existence, is ALL, any
representation of it, being finite, can not be "it"...
> In other words, this represents a global system rather than a local system
>
> We then have
>
> [_ _] = global system
> [ ] = local system
> { } = messenger (voyager)
> < > = quantum logical form
[HK]
> > So you think three kinds of components for the universe? Local
> > systems, local universes and the voyagers or messengers?
[BG]
> No, sorry -- global systems, local systems, messengers and (quantum) logical
> forms
[BG]
> > > Anyone ever build a "quantum Laws of Form" ? This would seem
> > > to be what we need here.
[HK]
> > Yes, this is necessary to recover the world.
[BG]
> I have some ideas on this, I need to write them down
>
> It's not hard to get quantum logic from a Laws of Form -like formalism.
>
> The trick will be to get quantum dynamics to emerge from a simple
> "re-entrant form" or iteration on this space...
Perhaps the ideas involved with n-categories would help?
http://math.ucr.edu/home/baez/week74.html
[HK]
> > Is quantum boundary < > different from [ ] above?
[BG]
> The boundary [] demarcates a local system, a subjective reality
>
> The quantum boundary <> is an elementary quantum logical operator, which may
> be nested <<>> or put side by side <> <> to yield arbitrary quantum propositions.
> (By analogy to Spencer-Brown's Laws of Form which similarly yields Boolean algebra). I
> need to work out the details, which may of course fail to work ;O
[HK]
> > How are/do these three
> > kinds of boundary defined/work? Or what postulates do you require them to
> > satisfy?
[BG]
> > Whatever goes on inside a local universe is reversible hence causality does
> > not exist in there.
I would disagree on the words but not the spirit of this statement.
There is something else involved that involves more that mere
reversibility! The nature of the "inside" of a local system is very
difference from the usual intuitions about dymanics and motions in our
space-times of experience!
> > the sending of voyagers from one local universe to another is irreversible
> > and thus creates causality???
This statement, taken on its face, implies to me that communications
between Local Systems gives rise to causal orderings, and I completely
agree! But, the metaphor fails when pushed to far...
[HK]
> So you think three kinds of components for the universe? Local systems, local
> universes and the voyagers or messengers?
We could think of the "local universes" as defined by the symmetry
groups of the behaviors of the "vayagers or messagers"; but given what I
said above regarding functors and Chu spaces, the same idea would apply!
:-)
[BG]
> > The dynamics of the elements inside local universes, and the dynamics
> > of messengers between local universes, has got to be expressible
> > algebraically. But all
> > the algebras implicit in chu spaces are not needed for this.
Yes, but they are needed for completeness reasons! We must remember
that the Totality of Exixstence is a potentia, an unbounded well of
possibility. We must allow for the possibility of anything to exist if
we are to be able to discuss or conceptualize anything at all! When we
see that what is "actually" experienced is not All, but merely some
bounded and delimited subset of the All, this makes sense... I hope...
:-)
> > Quantum logic comes to mind here, but it does not seem to give enough
> > information -- it doesn't
> > tell you how to run the dynamics of a local system, it only describes some
> > symmetries of the dynamics of the local system.
> >
> > Anyone ever build a "quantum Laws of Form" ? This would seem to be what we
> > need here.
[HK]
> Yes, this is necessary to recover the world.
> > A quantum boundary <w> , where the properties of interaction of <> entities
> > give quantum
> > dynamics. then the world inside a local system would be represented as a
> > bag of <> enclosed
> > entities, whereas the relativistic world amongst local systems would
> > represented in terms of
> > interactions of {} messengers.
[HK]
> Is quantum boundary < > different from [ ] above? How are/do these three
> kinds of boundary defined/work? Or what postulates do you require them to
> satisfy?
>
> >
> >
> > -- Ben Goertzel
> >
>
> Best wishes,
> Hitoshi
Onward!
Stephen
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