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

*Sat, 11 Sep 1999 15:54:17 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Hitoshi Kitada: "[time 751] Re: [time 747] Re: [time 744] My Paradigm Shift"**Previous message:**Hitoshi Kitada: "[time 749] Re: [time 748] About L_0: reply to Hitoshi"**In reply to:**Matti Pitkanen: "[time 748] About L_0: reply to Hitoshi"**Next in thread:**Hitoshi Kitada: "[time 751] Re: [time 747] Re: [time 744] My Paradigm Shift"

Dear Bill et al,

If I could add my $.02 to this discussion. :-)

WDEshleman@aol.com wrote:

*>
*

*> Hitoshi,
*

*>
*

*> [WDE]
*

*> objective:
*

*> The nature or structure of an object independent
*

*> of observation.
*

Would this not make the objective "nature or structure" of an object

indeterminate or probabilistic in-itself? I think that this is necessary

since we must allow for any consistent sequence of observations of the

object at the a priori level, e.g., independent of observation.

BTW, an observation is a measurement when we are using a mapping into

the reals, from what I have read. I think that an observation of general

would be best defined as a category theoretical morphism (an

"informorphism" to be specific) between objects which are to be

considered as members of equivalence classes prior to the particular

observation. These in turn give a natural meaning to the concept of

"Many-Worlds". :-)

*> subjective:
*

*> The nature or structure of an object as it appears to an
*

*> observer.
*

Here we have the results of the mapping after the selection process has

occurred. It seems to be the consensus of experts looking into this type

of notion that the "nature or structure" is always tensed "after" the

act of mapping. Thus Pratt says "I think, therefore I was". BTW, I am

trying to define a generic example of Lance's "clocking" with the notion

of a mapping or "informorphism" between equivalence classes.

It is my belief that the commutativity of the informorphism diagram is

the best formal way of understanding this. This is discussed in Peter's

Section 9 in http://www.cs.brown.edu/~pw/papers/math1.ps, pg. 19-21.

*> Light speed would then be subjective, and
*

*> FTL (and/or infinite speed) an objective property?
*

I think so. If we consider the "objective property" as containing "all

possible" velocities, then to characterize it as "infinite speed" as an

average over these would be correct.

*> [HK]
*

*> Yes. In your definition of objective and subjective, I agree.
*

*>
*

*> [WDE]
*

*> Yes, something is lacking in those statements; e.g.:
*

*>
*

*> 1) Where does objective end and subjective begin?
*

We must examine how it is possible to put a "cut" between the two

properties. What is the "mechanism" by which a specific subjective

property is selected from the equivalence class of all possible? I

propose that the mechanism of a Chu transform in general or the

informorphism specifically is the best candidate...

*> 2) Can an objective mathematical model have both
*

*> objective and subjective properties?
*

To be "objective" a model required that it can be encoded into a

"kickable" object. We can think of a stone sun dial as encoding the

various theorems of trigonometry and geometry, but note that without an

observer that can decode this information the "mathematical model"

concept is mute. Meaning is not inherent in objects, it is given only

within the context of interaction. We say that the meaning is "in our

minds not in the object itself", but actually it is in the interaction

between the two!

*> 3) Mathematics doesn't "kick back" like objects do,
*

*> so is there really no hope of obtaining a mathematical
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*> model that describes real phenomena? Does the ability
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*> to write it down with symbols demand that it is therefore
*

*> objective?
*

This question reminds me of the problem of making a "true and complete

map" of a town. If we are going to encode in some kickable object

(matter or energy) the information that gives us a means of answering

any question about the town we must first ask if the town itself can

encode the information. There does seem to be a limit of how much

information (in bits) can be encoded in matter!

(http://pespmc1.vub.ac.be/ASC/Bremer_limit.html)

*> 4) What is the degree of "distortion" experienced by
*

*> an observer? Could the "distortion" sometimes be
*

*> negligible? Or, always be zero?
*

We could think of this "distortion" as a measure of the noise inherent

in the interaction between object and observer. Frieden quantifies this

in his paper: Langrangians of Physics and the game of Fisher-Information

transfer. (Frieden & Soffer, Phys. Rev. E 52, Sept. 1995)

We could think of the distortion as a parameter \theta that we are

trying to estimate. This follow from the "imperfect observation", e.g.,

distorted experience of the object in question, y = \theta + x of

\theta, given the distortion x.

"The system comprising quantities y, \theta, and x is a closed one. No

other inputs effects are assumed present. It becomes apparent that the

closed nature of the measurement system implies an isolated physical

system as well."

"Consider the class of "unbiased" estimates, obeying <|theta^hat(y)> =

0; these are correct "on average". Then the "mean-square error e^2" in

the estimate \theta^hat obeys a relation e^2*I >/= 1 (1), where I is the

Fisher information: I = \integral dx p'^2(x)/p(x) (2).

The prime in "p'" denotes a derivative d/dx and the integration limits

are infinite. The quantity p(x) denotes the probability density function

for x and x is the noise [or in the case of your posed question, the

distortion]. We call equation (1) the Cramer-Rao inequality. "It

expresses the reciprocity between the error e^2 and the Fisher

Information I. The quantity I is therefore a quality metric of the

estimation procedure [or in the context of our discussion, the degree of

distortion in a given observation]. Since the quality increases (e

decreases) as I increases, I is called an "information"."

quotes from ibid. pg. 2274-5

If we try to imagine the conditions under which the "distortion" is

negligible or zero we would be constructing a model were infinite

computational resources would be required and an infinite amount of free

energy is available to be consumed by the computational process. Here I

am considering the act of observation as a computation of \theta.

This is similar "in spirit" to Matti's concept of NMP. :-)

*> 5) Can the mind imagine a unique correct objective structure?
*

*> Or will the mind always be restricted to contemplating
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*> multiple consistent objective structures? Optimistically,
*

*> the unique correct objective structure, is the simplest
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*> model with the best explanation, is it not?
*

If we were to be able to affirm that a mind could imagine a "unique

objective structure", we would have be be able to defend it against all

possible contrafactuals, e.g., observations that imply a different

objective structure! How can we say that "the mind always be restricted

to contemplating multiple consistent objective structures", when where

is more than "one" mind in existence? A given mind can only contemplate

a structure that is "objective" (kickable) given its own standard of

"kickability" or \theta. (Umm, I had previously referred to this

quantity as \epsilon!

*> 6) Would not an objective structure that allows instantaneous
*

*> communication between its parts, be composed of rigid and
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*> incompressible objects that transmit displacements due to
*

*> the direct contact between all of the objects?
*

Well, that would be the case if it were possible to construct such a

structure within the \theta of some observer! Such an observer would be

"omnipotent" and "omniscient", but completely lacking of the ability to

"change its mind", since its space of possible descriptions is a

singleton! Umm, this is exactly the situation that Matti is requiring

for the "Category of infinite-dimensional geometries"!

Onward,

Stephen

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