**Stephen P. King** (*stephenk1@home.com*)

*Mon, 02 Aug 1999 21:46:05 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 513] Rational mechanics and payoff matrix"**Previous message:**Matti Pitkanen: "[time 511] Re: [time 510] Re: [time 509] Observation models"

Dear Friends,

I have been talking a lot about the work of Vaughan Pratt on the Time

List and it has become evident that I need to write a post on his work

and how it is relevant to our work here. This post is only a rough

sketch that I hope is polished by the interactive discussions to follow.

I will start with a quote from Richard Feynman speaking about the

Principle of Least Action:

"We have lost the idea of causality that the particle feels the pull

and moves in accordance with it. Instead of that, in some grand fashion

it smells all the curves, all possibilities, and decides which one to

take (by choosing that for which our quantity is least)."

[Richard P. Feynman, The Character of Physical Law, The M.I.T. Press,

Cambridge, 1965.]

In the papers of Vaughan Pratt we find an interesting way of thinking

about how a particle could "smell all the curves". He proposes that the

short-lived theory of mind-body dualism of Rene Descartes. Pratt finds

that the formalism of Chu spaces addresses the shortcomings of the

philosophy of mind-body dualism. The causal interaction of mind and body

is defined in terms of Chu spaces and residuation. First we need to set

up some preliminary concepts.

The concept of Linear Logic was used as the framework that lead to this

line of thinking. It is used construct ways to test the behavior of

computer programs in conjunction with hardware implementations of such.

http://www.brics.dk/LS/96/6/BRICS-LS-96-6/BRICS-LS-96-6.html

http://www.csl.sri.com/linear/overview.html

http://www.csl.sri.com/linear/jervell.html

The concepts of Mind and Body speak to the distinct aspects of the

Universe, matter and information. It is proposed that matter (qua

material configurations) and information (qua "meaning") are not

identical, they are complementary or "dual" aspects of finite subsets of

the Universe (which is identified with the totality of existence and is

non-dual in-itself (or "self-dual"?) and tenseless).

Pratt told me in a e-mail today when I asked him about how to define

Mind and Body:

"Perhaps "mental" and "physical" would have been better, illustrated by

such examples as "predicate" ("is red") vs. "subject" ("the ball"), or

"thought" vs. "thing", as instances of mental vs. physical."

A quote from ratmech.ps:

"We interpret interaction as causality. Causality is directional, but

the direction depends on whether we have in mind physical or mental

causality. We interpret $x$ |= $a$ ambiguously as the time elapsed

between the occurrence of the physical a and its impression on the

mental state $x$, and as the truth value of $a$ as a proposition. [The

reader may be understandably concerned at this identification of

physical and ostensible mental propositions. However a Boolean

proposition about events A is of type 2^2^A and $each exponentiation$

dualizes, whence two of them return us to the physical plane. The truly

mental propositions are constituent descriptive clauses of a physical

DNF formula, each describing a possible world.] The former is physical

causality or $impression$, flowing forward in time from events to

states. The latter is mental causality or $inference$, flowing backwards

in time from the thought of $a$ to the inference of $a$'s occurrence. In

this way time flows forward (from the usual point of view) while logic

flows backwards. This is the $primary$ interaction, and it occurs only

$between$ the mental and the physical planes.

We thus see that the seat of casual interaction in Cartesian duality is

not the pineal gland but the identification of impression and inference.

We write $x$ |= $a$ as expressing equally the impression of event $a$ on

subsequent state $x$ and the deduction by state $x$ of the prior

occurrence of event $a$. The Cartesian dictum $cogito, ergo sum$ is the

case of this where $x$ is the thinker's state and $a$ the event of his

or her existence." ... "Examined closely, our analysis shows that

Descartes' dictum properly tensed becomes $cognito, ergo eram$ (I

was)..." ... "We pass now to interaction $within$ each plane, whether

physical or mental, which we derive as $secondary$ interaction from the

primary form with the aid of $residuation$, a pair of operations on

binary relations that constitutes dynamic implications forwards and

backwards in time: For K = 2, =| as a matrix of 0's and 1's is an

ordinary binary relation: the event $a$ either is or is not related to

state $x$. This relation is understood ambiguously as a two-valued

distance in either time-space (a =| x, physical) or information space

(x|= a, mental)." (pg. 8)

Here Pratt discusses how the $direction$ of causality depends on

whether one is considering the physical aspects of a subset of the

Universe (identified by Hitoshi as a Local System) or the informational

aspect of a LS. A LS is considered as a generic model of an observer or

measuring system, capable of registering the dynamical behavior of other

LSs via the mechanism of $ coinductive bisimulation$ between LSs.

Bisimulation is discussed in Peter Wegner & Dana Goldin's paper

(http://www.cs.brown.edu/~pw/papers/math1.ps)

"Symmetry of equivalence gives rise to the terms bisimularity and

bisimulation that captures the if-and-only-iff nature of relations

between equivalent objects. Coinductive bisimulation captures mutual

two-way behavior simulation of each system by the other." (pg. 16,

Mathematical Models of Interactive Computing, By Peter Wegner & Dana

Goldin)

The physical configurations of a LS's observations are ordered via

physical $implication$ and the information of a LS is ordered via the

mechanism of logical $entailment$. Individual physical properties are

called $events$ and individual mental or informative properties are

called $states$ in Pratt's presentation.

Pratt says:

"When we unravel the primitive causal links contributing to secondary

causal interaction we find that two events, or two states, communicate

with each other by interrogating $all$ entities of the opposite type.

Thus event $a$ deduces that it precedes event $b$ not by broaching the

matter with $b$ directly, but instead by consulting the record of every

state to see if there is any state volunteering a counterexample. When

none is found, the precedence is established. Conversely, when a Chu

space is in state $x$ and desires to pass to state $y$, it inquires as

to whether this would undo any event that has already occurred. If not

then the transition is allowed." (pg. 9, ibid.)

Here we are getting closer to our opening remark by Feynman! We must

note that in the preceding quote from Pratt, idealistic conditions are

considered. In the situation of Local Systems, as modeled By Hitoshi, it

is assumed that only a finite number of states (events) can be

"consulted" in a finite amount of time and that the "record" is subject

to falsification unintentionally by noise or intentionally by secondary

"eavesdropping" observers. Going back to Feynman's notion, we must ask

how it that the curve that minimizes the action is selected? We are

considering the transition of events $x$ to $y$ and dually, of states

$a$ to $b$, to be defined by such minimized curves.

Now, in traditional physical thinking we have a clear notion of that

the curves connecting physical events, they are called $geodesics$ and

are considered to be the paths that rays of light take in space-time.

The question of whether space-time is defined by the rays or has a

priori ontological status will not be addressed here. I merely say that

it seems to be enough to consider that a space-time is defined by the

Diff^4 group of a set of light-rays.

We must note that traditional physics also assumes that a single

space-time exists and thus only a single unique set of geodesics, as a

light-cone structure, need to be considered. But as we have seen in

situations that consider the quantum mechanical properties, it is

impossible to define a single unique light-cone structure for all

subsets of the Universe since the definition of such implies that a

single $anti-set$ of curves exists connecting the information states

entailed by the single set of physical events and that this anti-set

exists a priori as a "pre-computed" Boolean lattice of logical

inference.

The a priori existence of such a Boolean lattice must be considered

carefully! If such exists in the same sense that the Universe exists, we

are faced with the question as to how this "object", which would have

the status of a Platonic Form, would be $knowable$ by the infinity of

finite subsets of the Universe or LSs. It is obvious that there is a

deep difference between the existence of something and the ability to

have useful knowledge of it. The ability to gain useful information

about something takes into a discussion of thermodynamics and I wish to

reserve that topic to a latter date.

It might be asked why am I proposing a dualistic model of interactions

instead of a monistic one; to answer this I shall again quote Pratt:

"If one truly believed that the [subsets of the] universe proceeded via

state transitions, this might seem a rather roundabout and inefficient

way of implementing those transitions. However it seems to us ... that

the more likely possibility is that the [subsets of the] universe only

$seems$ to proceed via state transitions, due perhaps to our ancestors

having ill-advisedly chosen monism as the natural world view, perhaps

millennia before the rise of Cartesianism, perhaps only some years after

its decline. What we conjecture actually happens is that events signal

states forward in time, or equivalently that states infer events

backwards in time, and the world we imagine we live in is simply what

that process looks like to its inhabitants when interpreted

monistically.

Why this theory as opposed to any other? Well, certainly no other

theory has satisfactorily explained this causal interaction of real

mental and physical planes as conceived by Descartes."

Next, Quantum Mechanics in the Chu space representation.

Onward,

Stephen

**Next message:**Matti Pitkanen: "[time 513] Rational mechanics and payoff matrix"**Previous message:**Matti Pitkanen: "[time 511] Re: [time 510] Re: [time 509] Observation models"

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