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

*Wed, 09 Jun 1999 17:07:08 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 400] Re: [time 399] On the Problem of Information Flow between LSs"**Previous message:**Matti Pitkanen: "[time 398] Re: [time 396] Re: [time 391] Re: What are observers"**Next in thread:**Matti Pitkanen: "[time 400] Re: [time 399] On the Problem of Information Flow between LSs"

Dear Matti and Friends,

In [time 395] Constructing spacetimes, Matti wrote:

"There is also problem about information flow between different

LS:s. How can one define information current between LS:s if

these systems correspond to 'different spacetimes'?"

There is much to be discussed here!

If I am correct, "current" is defined as some quantity of change

occurring through a boundary of some sort.

(http://www.whatis.com/current.htm) It is usually assumed that some

particle or fluid is being transferred from one location to another and

a term "density" is associate with "Current per unit cross-sectional

area". So we are thinking of the concepts: "flow", "boundary",

"information", "different space-times", and "particle".

We need definitions that are mutually consistent, I am proposing to

using graph theoretic concepts since we can easily generalize them to

continua:

http://hissa.nist.gov/~black/CRCDict/termsArea.html#search

Flow: "A measure of the maximum weight along paths in a weighted,

directed graph" We could consider the "weight" as the degree to which a

given edge connects a pair of vertices, e.g. if a pair of vertices are

identical relative to their possible labelings the weight is 1, the

weight is 0 if their respective sets of labels are disjoint. (When

considering spinors as labels of the vertices we use alternative

notions.)

http://hissa.nist.gov/~black/CRCDict/HTML/flow.html

Boundary: I can not find a concise definition so I will propose a

tentative one: the boundary of a graph B{G} is the minimum set of

vertices |V_G| that have as incident edges that connect a pair of

points, one of which is an element of ~{G} and the other which is an

element of {G}; where {G} and ~{G} are a graph and its complement.

I am not sure that this notion is appropriate. :( I am thinking of the

way which traditional set theory defines a boundary of a set: "a point

is in the boundary of a set iff every neighborhood of the point

intersects both the set and its complement". So the boundary of a set of

these points. It looks like the only element involved would be the empty

set {0} in the usual way of thinking of sets in the binary logical

sense, this relates to my discussion of the Hausdorff property...

Information: Now here is the key problem: How to define "information"!

What is Information? Is is "meaning" as in "the semantic content of a

pattern of matter/energy"? Is it the bits that are recovered when a

string of bits is encoded or compressed by some scheme and then decoded

or decompressed by the scheme's inverse? Is it the value of a quantity

present at some arbitrary point?

Different space-times: This statement implies a plurality, a multitude

of configurations of distinguishable particles such that a basis of

three orthogonal directions is definable in conjunction with a dynamic

that alters the configurations in a uniform way.

Particle: An entity that in a given reference frame or framing is

indivisible. It should not be assumed that an entity that is indivisible

in one framing need be so in another framing. I am thinking of a framing

as a finite context or environment that acts as a "contrast" for the

entity in question.

The problem I see right away is that information is not a substance in

the normal sense, since it has the properties of compressibility and,

according to Bart Kosko, irrotability, which are in contrast with those

properties of matter which is, usually incompressible and rotateble....

But, I think that Peter's notions are the most relevant to this

conversation of "information flows" between LS, so we need a way of

bridging between the formalism of graph theory and the formalisms used

in Peter's papers.

We'll take that up after some discussion. :)

Later,

Stephen

**Next message:**Matti Pitkanen: "[time 400] Re: [time 399] On the Problem of Information Flow between LSs"**Previous message:**Matti Pitkanen: "[time 398] Re: [time 396] Re: [time 391] Re: What are observers"**Next in thread:**Matti Pitkanen: "[time 400] Re: [time 399] On the Problem of Information Flow between LSs"

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