**Benjamin Nathaniel Goertzel** (*ben@goertzel.org*)

*Sat, 10 Apr 1999 22:23:16 -0400*

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[time 216] Message for time

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At 10:49 PM 4/10/99 +0900, Hitoshi Kitada wrote:

*>Dear Ben,
*

*>
*

*>I hope you don't mind my posting this mail to time list and to Lance... (I sent
*

*>the former message from a Linux machine whose simple mailer seems not to know
*

*>restricting the address to one....)
*

*>
*

*>Let me begin with technical points:
*

*>
*

*>I found by your response that the "intimacy parameter" q does not range over
*

*>the
*

*>interval [0,1], but over the set
*

*>
*

*>Q={b | b is a decomposition of L into disjoint subsets of L},
*

*>
*

*>in the observation of a local system L={1,2,...,N}. Namely Q is the set of
*

*>cluster decompositions b of L. This notion is used in scattering theory for
*

*>many-body problem as is explained in my time_IV.tex, e.g.
*

*>
*

*>The way to define the reference frame associated to a general b belonging to Q
*

*>and the observation corresponding to b are treated in time_IV.tex, I.3,
*

*>(although the calculation of physical values there is an approximation).
*

*>
*

*>The special case q=0 (I-It case) is identified with the case b={ {1}, {2}, ...,
*

*>{N} }. In this case the observer sees the object L as decomposed completely
*

*>into
*

*>single particles, thus observes it classically.
*

*>
*

*>Another special case q=1 (I-Thou case) is the one with b={ L }. The observer
*

*>sees the object L as one whole, thus sees it quantum-mechanically.
*

*>
*

*>So the idea of introducing parameter q is not new. It is just a
*

*>reinterpretation
*

*>or adaptation of known ideas to our problem of observation.
*

*>
*

*>
*

*>Your "strategy" that you confine your comments mainly to this point thus worked
*

*>successfully! resulting in the discovery of a correct set Q.
*

*>
*

*>
*

*>Another point of the principle of observation:
*

*>
*

*>What one sees when observing an LS depends on
*

*>which frame of reference one takes in the observation.
*

*>
*

*>is the "object of observation." Namely this principle implies what one sees is
*

*>different according to which object one sees, which would be a natural axiom.
*

*>Your interesting problems are understood together with Wheeler's case, firstly,
*

*>in terms of this difference of objects that the observer sees, and secondly by
*

*>the difference of q, i.e. on which parts of the object the observer concentrate
*

*>his concern or attention.
*

*>
*

*>
*

*>
*

*>----- Original Message -----
*

*>From: Ben Goertzel <ben@goertzel.org>
*

*>To: Hitoshi Kitada <hitoshi@kitada.com>
*

*>Sent: Saturday, April 10, 1999 1:10 PM
*

*>Subject: Re: [time 198] local systems, measurement, etc.
*

*>
*

*>
*

*>>
*

*>> Hi Hitoshi,
*

*>>
*

*>> I am still thinking about your message and the ideas in it, and have been
*

*>> very busy with other
*

*>> things,
*

*>
*

*>Thank you very much for sharing your time with me. I appreciate!
*

*>
*

*>
*

*>but here is a partial reply just to keep the dialogue going
*

*>>
*

*>>
*

*>> >Then I could understand your proof. It is in my thought one tautology:
*

*>> >
*

*>> >(1') <-> (4').
*

*>> >
*

*>> >Thus correct.
*

*>> >
*

*>> >
*

*>> >Your paraphrasing is quite subtle and clever. I have never thought of
*

*>> >such a paraphrasing. My Japanese and poor English did not give me such.
*

*>>
*

*>> It wasn't meant to be subtle and clever; it was the most direct and natural
*

*>> way for me
*

*>> to think about it. How fascinating! To me it is your way of phrasing it
*

*>> that seems subtle
*

*>> and clever --
*

*>>
*

*>> >I next proceeded to the problems you raised. At first, they looked fatal,
*

*>> > but one day after, they have clear meaning that can be understood. In
*

*>> >doing so, I found one simple principle of observation:
*

*>> >
*

*>> >What one sees when observing an LS depends on
*

*>> >which frame of reference one takes in the observation.
*

*>>
*

*>> I really like your idea philosophically, but am not 100% clear on its
*

*>technical
*

*>> solidity.
*

*>
*

*>As far as I remain at the present stage of my theory, the revision of the range
*

*>of q mentioned above would be the last clarification (hopefully :) ).
*

*>
*

*> More and more I feel the need for some kind of logical or algebraic
*

*>> formulation of the whole theory (and I'm sure you agree with me; as we both
*

*>> know however,
*

*>> the creation of such a formulation takes time and care...)
*

*>>
*

*>
*

*>As we saw above, the basic formulation is already in time_IV.tex. If we could
*

*>proceed to a new area, as you say below we need to clarify the strong forces
*

*>and
*

*>quarks. Maybe I need to study them...
*

*>
*

*>> The observer's "attitude" then plays a role in the results of
*

*>observation....
*

*>>
*

*>
*

*>The "attitude" could be rephrased as "what one sees is what he sees." This is a
*

*>tautological explanation of the word "observation," thus correct.
*

*>
*

*>> Observing with an I-It attitude (q=0) means that the observed system is
*

*>> seen as
*

*>> something definite and solid, i.e. a classical system. The observer's
*

*>> reference frame is used.
*

*>>
*

*>> Observing with an I-You attitude (q=1) means that the observed system is
*

*>seen
*

*>> as something similar to one's own internal world, nebulous and
*

*>> multifarious, i.e.
*

*>> a quantum system. The observed's reference frame is used.
*

*>>
*

*>> The reason this is a new an interesting principle is that you are
*

*>> correlating two
*

*>> different things. You are aligning the dichotomies
*

*>>
*

*>> Classical/Quantum
*

*>>
*

*>> and
*

*>>
*

*>> Observer's ref. frame/ Observed's ref. frame
*

*>>
*

*>> This alignment as far as I can see has not been proposed anywhere before; I
*

*>> do not see it
*

*>> in any of your previous papers (or is it there in a different form, which I
*

*>> did not understand?).
*

*>>
*

*>
*

*>I did not notice the point until you pointed it out here, although I wrote my
*

*>previous response on the basis of time_IV.tex. The formulation converges to
*

*>that
*

*>paper if the notion of intimacy parameter q with range Q is added (with the
*

*>range Q revised as above).
*

*>
*

*>>
*

*>> >Single particle does not have internal space
*

*>> >coordinate because it is 0 (zero) after the separation of its center of
*

*>> >mass.
*

*>>
*

*>> This raises some technical points that I am not quite competent to address.
*

*>> Like, what about quarks? I'm no expert on chromodynamics. Does the fact
*

*>that
*

*>> quarks are not separable from particles mean that the quarks inside particles
*

*>> have no independent positions and momentums? I guess that's right: quarks
*

*>> have charm, color and flavor but no position and momentum independent of
*

*>> the position
*

*>> and momentum of the particles they're in. So I ~guess~ it's OK.
*

*>>
*

*>
*

*>I am not familiar with quark physics at all. I just know quarks could not be
*

*>separated off the particles inside which quarks are. This, as you see, would
*

*>not
*

*>pose any problems to my description, if quarks could be regarded elementary
*

*>particles.
*

*>
*

*>> >Thus it has no internal time and space, and there is only one
*

*>> >space-time coordinate (observer O's coordinate) that is available for
*

*>> >the observation.
*

*>>
*

*>> There is no You, there is only I. A particle is a true It, an inanimate,
*

*>> non-subjective object.
*

*>>
*

*>> The possession of an internal, subjective reality is equated with the
*

*>> possession of
*

*>> internal position/momentum coordinates that are different from the center
*

*>> of mass.
*

*>>
*

*>> Very interesting!
*

*>>
*

*>> >Thus observations are classified by the value q in the interval [0,1].
*

*>> >To q with 0<q<1 there correspond observations intermediate between
*

*>> >Classical and QM observations.
*

*>>
*

*>> So q=.5 means you take the average of the two reference frames?
*

*>
*

*>As revised above, the value q=.5 is not realistic.
*

*>
*

*>> I understand how to average two reference frames, if these are just
*

*>considered
*

*>> as coordinate tuples in 4-space (or tangent bundles to a 4-manifold at
*

*>> different
*

*>> locations, etc. ... then one moves halfway along the geodesic between the
*

*>> points
*

*>> to which the two reference frames are tangent?).
*

*>>
*

*>> But, how do you average the classical view of a system with the quantum
*

*>> view of a
*

*>> system? At first, this seems to go against the spirit of your Local System
*

*>> approach, in which
*

*>> classical and quantum reality are said to operate on different levels.
*

*>>
*

*>> But, I suppose that if the classical and quantum perspectives are talking
*

*>> about the same
*

*>> entities (e.g. particles), then it's OK. The classical view gives precise
*

*>> values for position
*

*>> and momentum of particle X, whereas the quantum view gives probability
*

*>> distributions for
*

*>> this position and momentum. We average these together by considering the
*

*>> classical view
*

*>> as giving a probability distribution described by Dirac delta functions,
*

*>> perhaps?
*

*>>
*

*>> Or am I going in the wrong direction entirely? Now maybe ~I'm~ just
*

*>> dreaming ;)
*

*>> I could write equations for this but won't bother if the ideas aren't right
*

*>> -- I suspect you can
*

*>> fill in the equations I'm thinking of all by yourself...
*

*>>
*

*>
*

*>Your comments led me to notice that [0,1] is not the right range of q. Thanks!
*

*>
*

*>> And it gets trickier when the quantum view leads to the existence of
*

*>> particles (say, Higgs
*

*>> particles or W-particles) that don't even exist in the classical view.
*

*>> Then the existence of these
*

*>> particles is given a probability of q, I suppose, where q is the "intimacy
*

*>> level" telling how close
*

*>> we are to an I-You as opposed to I-It relationship.
*

*>>
*

*>
*

*>I need to study these particles in order to answer your questions, (if they
*

*>exited actually...)
*

*>
*

*>> I have more thoughts about the Wheeler experiments and your comments on
*

*>> them, but can't
*

*>> seem to crystallize them into words, and so will save them for later ;)
*

*>>
*

*>> >For me or general Japanese, strong nuclear force is the one that
*

*>> >realized the atom bomb, and as the people who has ever experienced it
*

*>> >whatever the reason or justice is, we dislike the bomb. We do not or
*

*>> >never use the word "hate" usually, although we have Japanese
*

*>> >correspondent. But our mind seems to "hate" it unconsciously. This might
*

*>> > be one of my reasons that I did not try to study the strong force. But
*

*>> >if the time comes, it might be included in my schedule.
*

*>>
*

*>> This is an interesting point; I hadn't thought of it that way. I was
*

*>> raised as a pacifist
*

*>> and despise the use of nuclear weapons, but don't associate the strong
*

*>> force particularly
*

*>> with these weapons; I associate it more with holding the nuclei of atoms
*

*>> together and hence
*

*>> holding ~me~ together!
*

*>>
*

*>> I think that the basic theory needs to be clarified a bit more before
*

*>> getting into the strong
*

*>> force. But, if the theory is really going to be a grand unification of
*

*>> physics, it obviously needs
*

*>> to take account of quarks.
*

*>>
*

*>
*

*>My purpose or intention when I found the notion of local time was not to make a
*

*>unified theory. Just I thought it could be used to unify QM and GR, although
*

*>Lance afterwards seemed to have regarded it as an attempt to unify physics.
*

*>
*

*>I have to begin with studying strong and other forces if I try to incorporate
*

*>those forces into my context. I.e. I need references. Could you or anyone list
*

*>up the papers that seem to be appropriate to begin the study?
*

*>
*

*>> >> 2) it would make clearer the mapping between your theory and my
*

*>> >> psychological theory of perception and consciousness
*

*>> >
*

*>> >
*

*>> >Your description of Wheeler's quantum eraser seems to indicate that "
*

*>> >consciousness" has its own power. It is the power of grouping objects.
*

*>> >We have here a clear correspondence between your theory and mine. This
*

*>> >would be the core of the mapping.
*

*>>
*

*>> Yes. And your idea of an "intimacy parameter" q that varies from I-It to
*

*>I-You
*

*>> (to put my bizarre psychological terminology on your idea ;) is a part of
*

*>> this mapping,
*

*>> I suppose
*

*>>
*

*>
*

*>I think to put I-It and I-Thou relations is not "bizarre" at all. It is quite a
*

*>natural expression when we think about things. Just "physics" has been
*

*>pretending that the objects physicists see take one particular value of q,
*

*>which
*

*>is all the causes of their contradictions in my opinion.
*

*>
*

*>> >English is quite a different language than Japanese, and the cultures
*

*>> >behind them are too. I have been thinking time is the core of your
*

*>> >culture. I feel I see this in your paraphrasing of the axiom of
*

*>> >independence. You think in chronological order, while we think
*

*>> >everything is at present. Maybe this is why you think the universe began
*

*>> > by Big Bang, while I think it is stationary. This might be just a
*

*>> >difference in custom of thinking. As you say below, it seems better for
*

*>> >us to proceed to the direction that does not relate with this point.
*

*>>
*

*>> I see what you mean. We are possibly better off to skip words and proceed
*

*>> straight to logic,
*

*>> which is more culture-independent. Although I suspect Stephen would like
*

*>> the words
*

*>> better ;)
*

*>>
*

*>> Also, the differences in phrasing may not just be Japan vs. US, but may
*

*>> also be partly
*

*>> "normal physics language" vs. "Ben" ;) I seem to have my own peculiar
*

*>> view of the world,
*

*>> which involves among other things viewing the universe as a mind and
*

*>> imposing psychological
*

*>> terminology on it!
*

*>>
*

*>
*

*>I got the same idea as your view to see the universe as a mind when I found the
*

*>notion of time. Or rather this idea may be imbedded in the eastern way of
*

*>thinking, just without having been expressed explicitly. Or this may not be
*

*>restricted to the eastern, I expect in the western there may be a correspondent
*

*>idea. In fact, I feel I find it in Matti's writings, if my reading the
*

*>introduction of his book is not wrong. (Matti, am I correct?) Even if there
*

*>might be difference between yours and mine on the "universe as a mind" at small
*

*>points, I believe the coincidence between your idea and mine is not just a
*

*>coincidence but an inevitable process of human beings' thoughts.
*

*>
*

*>> About the Big Bang, I have no particular attachment to it. I think it is
*

*>> mostly a modern version of
*

*>> traditional creation myths. However, I think that the empirical
*

*>> observation of ripples in the cosmic
*

*>> background radiation is very strong evidence for the big bang or something
*

*>> like it, and I cannot see
*

*>> any way for a steady state theory to explain these ripples, except by
*

*>> making ad-hoc excuses.
*

*>> E.g., one could explain it by positing a special distribution of iron bars
*

*>> floating throughout space and
*

*>> obscured by nebulae, but this is analogous to explaining the precession of
*

*>> Mercury's orbit in terms of classical mechanics by assuming the sun has a
*

*>> distorted internal mass distribution, instead of
*

*>> appealing to general relativity ;)
*

*>>
*

*>
*

*>You might be right as concerns the background radiation. And my theory could
*

*>explain it because the theory admits to see the universe as rather a classical
*

*>one with some value q=q1 belonging to Q (but not completely classical). The
*

*>problem here is why one adopts that value q1 (or decomposition of the
*

*>universe) when one observes the universe by their astronomical apparatus. Or it
*

*>might be rephrased: why do physicists take the same value q1 when they consider
*

*>and argue the universe? There is no inevitability for them to take that value
*

*>q1: When you see the universe as a mind, you take the value q={ U }, where U is
*

*>the universe system (with, maybe, some abuse of the terminology "q"), while
*

*>when
*

*>you argue Big Bang, you take the value q1. The same person can take two
*

*>different values of q, q={ U } and q=q1, when arguing the same universe. This
*

*>indicates that the problem of the observation of the universe should be
*

*>formulated as follows:
*

*>
*

*>What does the universe looks, at the observer,
*

*>when he takes a particular value of q in his consideration of the universe?
*

*>
*

*>To put it in another way,
*

*>
*

*>What one finds in the universe depends on the way he decomposes the universe.
*

*>
*

*>
*

*>
*

*>
*

*>Best wishes,
*

*>Hitoshi
*

*>
*

*>
*

*>
*

*>>
*

*>> ben
*

*>>
*

*>
*

X-Sender: ben@goertzel.org

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Date: Sat, 10 Apr 1999 22:20:21 -0400

To: "Hitoshi Kitada" <hitoshi@kitada.com>,"Time List" <time@kitada.com>

From: Ben Goertzel <ben@goertzel.org>

Subject: multiboundary algebra

Cc: "Lancelot R. Fletcher" <lance.fletcher@freelance-academy.org>

In-Reply-To: <002501be8358$ee98bae0$9450a3d2@kitada.com>

References: <4.1.19990409234045.00bef210@goertzel.org>

Mime-Version: 1.0

Content-Type: text/plain; charset="iso-8859-1"

Content-Transfer-Encoding: quoted-printable

Just a half-baked thought that will be more fully baked later...

I was thinking about how to make a good formal algebraic formulation of

Hitoshi's theory

of physics and my theory of consciousness, and my mind traveled back to an

unfinished

mathematical exploration that is on the Web in the form of some rough notes

http://goertzel.org/ben/Multi.html

(this is not a research paper, it is notes on about the level of rigor of=

our

e-mails ;)

A brief excerpt, describing the notion of multiboundary algebra, is=

extracted

here, preceded by

some brief comments on how it might be relevant

The basic idea is that you can have different types of parentheses, and

different algebraic

laws applying to entities depending on the kinds of parentheses they live

between.

I was using this idea to explain how you get the algebraic structures of the

Standard Model

(quaternions, octonions, clifford algebras) out of nothingness. I.e.

pregeometry.

But this seems to capture Hitoshi's theory too, in a slightly different way.=

=20

He is saying that

different algebraic rules apply inside the boundary of the LS, than outside.=

=20

I.e. he is introducing

a boundarizing operator that defines an LS. Inside the LS, calculations are

done with amplitudes;

outside they are done with probabilities.

What the best formal way to capture this is, I'm not sure. I'm thinking=

that

the LS-parenthese

is possibly representable formally as an operator that transforms amplitudes

into probabilities...

But this doesn't work in the crudest sense, I need to think about it more...

Still this is very exciting to me. I see the vague possibility of building=

a

unified physics in terms of

a hierarchy of boundary operators, each one associated with an algebra. The

lowest level

boundaries give the emergence of quantum structures from the void; then the

highest level boundary

gives the emergence of classical reality from quantum structures via

observation.

(Finally there is a boundary operator that takes a the quantum state of a

classical structure,

and makes it impenetrable, thus rendering it a basic indecomposable=

particle,

and closing the

loop? -- dreaming again ;)

ben

***

snip from rough paper on multiboundary algebra

****

The development here will remain within the framework of boundaries that

interact in two different ways; the Laws of Form algebra will be enriched,

however, by the addition of more types of boundaries. This development is

eccentric with regard to conventional mathematics, which contains only one=

type

of parenthese for grouping entities, but numerous operations for combining

groups and ungrouped entities. However, introducing several types of=

boundary

is a perfectly viable alternative to introducing several types of operator,=

and

is in some ways, we shall see, a more powerful alternative.

Notation for multiple boundaries is fairly difficult to come by, though the

typewriter keyboard provides a number of alternatives, e.g. ( ) , [ ], { },=

< >

. For talking about multi-boundary algebra in the abstract I will use the

notation (k k) to refer to a boundary of type k, but this notation is not=

good

for working out concrete examples.

The interior of a boundary will be called a "space," and the operator

(k k) * b

will be understood to mean that the entity b is placed in the space=

demarcated

by the boundary (k k). Multi-boundary algebra envisions a universe in which

various simple and composite entities coexist and interpenetrate within=

various

spaces, and in which the results of coexistence and interpenetration depend=

on

the composition of the entities involved, and the space in which the=

entities

exist.

Formally, a general multi-boundary algebra consists of=20

=B7 A collection of boundary types, (k k), k=3D1,=85,n; a "boundary"=

is an

instance of a boundary type=20

=B7 A collection of operators * i, which are used to build composite

entities called "forms" out of boundaries=20

=B7 A rule set R which determines the interaction of boundary forms=

via the

* i operators=20

=B7 A collection of "local" rule sets Rk ,k=3D1,=85,n; where Rk=

determines the

interaction of boundary forms (via the * i operators) which lie within the

boundary (k k)=20

=B7 A function r which maps the set of boundaries into the set of rule

sets;

i.e., it assigns individual rule sets to specific boundaries

The local rule sets must be consistent with the global rule set R. The

individual rule sets must be consistent with the global rule set and with=

the

local rule sets. The local rule set applying to the interaction of two=

boundary

forms is determined by the the boundary that they most locally belong to;=

e.g.

if we have [ < a + b> ] then the meaning of the operation + is determined by

the rule set for < > and not the rule set for [ ].=20

Multiboundary algebra, in general, is an extremely general framework, much=

like

Universal Algebra (but more general). The specific multiboundary algebras to=

be

discussed here will involve the standard two operators, + and *, plus an

additional operator ^ dealing with temporality. Furthermore, in all the

specific

algebras to be discussed here, the + operator will be commutative, and will=

be

associative in regard to the ordinary parenthese ( ), meaning that + can be

commuted across an arbitrary number of arguments, e.g. a + b =3D b + a, a +=

b + c

+ d =3D d + c + b + a =3D d + b + a + c, etc. In more formal language, we=

will be

dealing with +-polycommutative (+,*,^) multiboundary algebras (where "*i

-polycommutative means, in general, that all rule sets in the multiboundary

algebra hold the operator * i to be commutative and associative with regard

to (

) ).

From the definition of multiboundary algebra, we see exactly what the

difference is between the standard mathematical technique of having one

boundary (the parenthese) and numerous operators, and the present=

alternative

of having few operators and multiple boundaries. The notion of=

space-dependent

rule sets has no parallel in standard mathematics, and breaks down the=

barrier

between algebraic rules and algebraic formulas in a very interesting way,=

which

is only explored here very partially.=20

******

ben

**Next message:**Stephen P. King: "[time 217] Re: [time 215] How to define length using LSs"**Previous message:**Hitoshi Kitada: "[time 215] Re: [time 211] How to define length using LSs"**Next in thread:**Hitoshi Kitada: "[time 231] Re:"

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