[time 825] Chu spaces, causality, local systems... quantum laws of form? ...

Ben Goertzel (ben@goertzel.org)
Mon, 27 Sep 1999 09:25:38 -0400

> > 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.

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
direction for physics... and remain concerned about how it generalizes to
deal with
weak & strong nuclear forces...

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?

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.

However perhaps one can view Chu spaces as a kind of pre-physics. this
might make sense.

first, out of the void, there burst Chu spaces...

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...

But, I'm not sure I love this "top-down" approach where you start with a
of everything and then whittle down.

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...

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....

Now I will speculate shamelessly, indicating the kind of direction I would
like to go in,
although I have not gone here rigorously yet:

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 { }
a voyager from one local system to another?

Whatever goes on inside a local universe is reversible hence causality does
not exist in there.
the sending of voyagers from one local universe to another is irreversible
and thus creates

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.

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.
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.

-- Ben Goertzel

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