**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Thu, 10 Jun 1999 10:03:42 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen Paul King: "[time 401] Re: Quantum Particles are Fluids."**Previous message:**Stephen P. King: "[time 399] On the Problem of Information Flow between LSs"**Next in thread:**Stephen P. King: "[time 402] Re: [time 400] On the Problem of Information Flow between LSs"

On Wed, 9 Jun 1999, Stephen P. King wrote:

*> Dear Matti and Friends,
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*>
*

*> In [time 395] Constructing spacetimes, Matti wrote:
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*>
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*> "There is also problem about information flow between different
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*> LS:s. How can one define information current between LS:s if
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*> these systems correspond to 'different spacetimes'?"
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*>
*

*> There is much to be discussed here!
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*>
*

*> If I am correct, "current" is defined as some quantity of change
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*> occurring through a boundary of some sort.
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*> (http://www.whatis.com/current.htm) It is usually assumed that some
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*> particle or fluid is being transferred from one location to another and
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*> a term "density" is associate with "Current per unit cross-sectional
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*> area". So we are thinking of the concepts: "flow", "boundary",
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*> "information", "different space-times", and "particle".
*

Yes. This definition works also in infinite dimensional case.

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

*> using graph theoretic concepts since we can easily generalize them to
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*> continua:
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*>
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*> http://hissa.nist.gov/~black/CRCDict/termsArea.html#search
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*>
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*> Flow: "A measure of the maximum weight along paths in a weighted,
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*> directed graph" We could consider the "weight" as the degree to which a
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*> given edge connects a pair of vertices, e.g. if a pair of vertices are
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*> identical relative to their possible labelings the weight is 1, the
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*> weight is 0 if their respective sets of labels are disjoint. (When
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*> considering spinors as labels of the vertices we use alternative
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*> notions.)
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*>
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*> http://hissa.nist.gov/~black/CRCDict/HTML/flow.html
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*>
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*> Boundary: I can not find a concise definition so I will propose a
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*> tentative one: the boundary of a graph B{G} is the minimum set of
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*> vertices |V_G| that have as incident edges that connect a pair of
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*> points, one of which is an element of ~{G} and the other which is an
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*> element of {G}; where {G} and ~{G} are a graph and its complement.
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*> I am not sure that this notion is appropriate. :( I am thinking of
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*>the
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*> way which traditional set theory defines a boundary of a set: "a point
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*> is in the boundary of a set iff every neighborhood of the point
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*> intersects both the set and its complement". So the boundary of a set of
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*> these points. It looks like the only element involved would be the empty
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*> set {0} in the usual way of thinking of sets in the binary logical
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*> sense, this relates to my discussion of the Hausdorff property...
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*>
*

Does this approach generalize simplicial cohomology? Simplicial complex

defines homology groups. It has simplices up to dimension D if simplicial

complex is D-dimensional. One can consider functions in the set

simplices of given dimension. One can define co-exactness and

co-closedness and cohomology groups. Info current would be a function in

the set of D-1 dimensional simplices. Info current would in general

correspond to an element of cohomology which is not coclosed. This makes

sense only in ordinary topology defined by norm but you are talking about

non-Hausdorff property.

*> Information: Now here is the key problem: How to define "information"!
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*> What is Information? Is is "meaning" as in "the semantic content of a
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*> pattern of matter/energy"? Is it the bits that are recovered when a
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*> string of bits is encoded or compressed by some scheme and then decoded
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*> or decompressed by the scheme's inverse? Is it the value of a quantity
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*> present at some arbitrary point?
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*>
*

Very stimulating questions! While visiting at your homepage I

realized for the first time how many times 'information' appeared

there. For some mysterious reason I have managed to circumvent the

challenge of defining this concept until now. Perhaps my

strong opinions about computationalism explain this(;-).

a) I think that its is meaningful to talk about 'meaning'

only if one talk about *conscious* information. OK?

b) It is certainly impossible to characterize conscious experience

by a bit sequence. This was one of reasons I have been very sceptic

about 'information content of cs experience'.

One could however circumvent this problem! Conscious information could be

defined as *difference* of informations associated with initial and

final states of quantum jump. This would reduce problem to that of

associating information measure to quantum states! Since quantum states

correspond to a well defined geometric objects there are hopes of

associating information measures with them! This looks a clever

trick to me at least!(;-)

c) One can probably define several types of informations associated

with configuration space spinor field and assign

information measures to them. Perhaps one must give up the idea

about single information measure. Perhaps the essential question

is 'About what the information is about' and each question gives

different measure of information.

d) I realized that the information associated with configuration space

spinor field, about which I talked in previous postings,

is essentially *information about position in configuration space*

plus information about spin degrees of freedom relative to the

ground state which corresponds to Fock vacuum and contains no information.

Information is defined as the information gain involved in total

localization of the configurations space

spinor field to single point in Fock vacuum state. Single 3-surface

in configuration space into Fock vacuum state is selected and Shannon

formula defines the information gain. Same works for Schrodinger

amplutitude in nonrelativistic situation.

Critical Question: Does the information of the configuration space

spinor field provided about the position in configuration space

of 3-surfaces provide information about configuration space

and spacetime geometry? There are hopes since spin degrees of freedom

(which correspond to fermionic degrees of freedom in infinite dimensional

context) are involved and entanglement is associated with these degrees of

freedom. Recall that fermions describe 'reflective level of cs' in TGD

approach to cs (Fock state basis has interpretation as Boolean algebra).

e) You mentioned bit counting as a possible manner to define information.

Interesting possibility is that real to p-adic correspondence

could provide measure for the information content of the configuration

space spinor field based on counting of bits, or actually pinary digits.

i) Pinary cutoffs of configuration space spinor field provide a

sequence of more and more accurate discretization of configuration

space spinor field.

ii) The mapping of real configuration space spinor field to its

p-adic counterpart involves *minimal* pinary cutoff for which

continuation to smooth p-adic configuration space spinor

field is possible. Minimal pinary cutoff comes from

the requirement that the canonical image of the pinary cutoff allows

continuation to a *smooth* p-adic configuration space spinor field.

If pinary cutoff of the canonical image is too

detailed, completion is not possible.

iii) There would be thus some number N of pinary digits and

I(X^3) =N(X^3)

would serve as a measure for the information contained by

the value of the configuration space spinor field at given point of

configuration space.

iv) One could define the total information contained by configuration

space spinor field as sum of informations associated with

discretized configuration space.

N= SUM_i N(X^3_i).

This number is infinite as real integer but *finite as p-adic number*!

Real information is obtained as the canonical image of I

and would be finite. Higher pinary digits would

not be be given such importance as for low pinary digits in this

information measure. This is indeed very reasonable: lowest pinary

digits contain the essential and the rest is just details.

Note: the value of p-adic prime associated with entire universe is

very probably infinite so that N is probably infinite as

ordinary integer still. Note that infinities can cancel

in info content of cs experience defined as difference.

v) This information is obviously information about the construction of

the p-adic counterpart of configuration space spinor field from

its real counterpart by canonical identification mapping. Is this

information given by conscious experience? Perhaps! Conscious

experience always involves coarse roughening: higher pinary digits

do not have same importance as lower pinary digits. Conscious experience

forms abstractions. So, perhaps the contents of conscious experience

involve essentially the coarse roughening involved with reals to p-adics

map?

f) All geometric structures of real quantum TGD

are mapped to their p-adic counterparts using phase preserving canonical

identification map with minimal pinary cutoff.

i) This approach might work also at spacetime level

for spinor fields defined on spacetime surface. To each spacetime

time=constant section of spacetime surface one could associated

information I in similar manner and pinary cutoff

would provide the discretion of 3-surface making it possible

to define total information as sum over informations associated

with the points of X^3. CAnonical image would define real

information which would be finite.

ii) The mapping of real spacetime surface to its p-adic

counterpart involves this map and one can assign the real counterpart of

p-adic integer N of pinary digits to each point of real spacetime

surface as its information content. Again also total

information content could be defined as sum for the

minimal pinary cutoff of spacetime surface.

I think I must stop here.

Best,

Matti Pitkanen

*> Different space-times: This statement implies a plurality, a multitude
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*> of configurations of distinguishable particles such that a basis of
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*> three orthogonal directions is definable in conjunction with a dynamic
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*> that alters the configurations in a uniform way.
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*>
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*> Particle: An entity that in a given reference frame or framing is
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*> indivisible. It should not be assumed that an entity that is indivisible
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*> in one framing need be so in another framing. I am thinking of a framing
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*> as a finite context or environment that acts as a "contrast" for the
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*> entity in question.
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*>
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*> The problem I see right away is that information is not a
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*> substance in
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*> the normal sense, since it has the properties of compressibility and,
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*> according to Bart Kosko, irrotability, which are in contrast with those
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*> properties of matter which is, usually incompressible and rotateble....
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*>
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*>
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*> But, I think that Peter's notions are the most relevant to this
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*> conversation of "information flows" between LS, so we need a way of
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*> bridging between the formalism of graph theory and the formalisms used
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*> in Peter's papers.
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*>
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*> We'll take that up after some discussion. :)
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*>
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*> Later,
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*>
*

*> Stephen
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*>
*

**Next message:**Stephen Paul King: "[time 401] Re: Quantum Particles are Fluids."**Previous message:**Stephen P. King: "[time 399] On the Problem of Information Flow between LSs"**Next in thread:**Stephen P. King: "[time 402] Re: [time 400] On the Problem of Information Flow between LSs"

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