----------------------

Book I:

Patterns In Contexts

----------------------

8/25/2005 Stuff that occurred to me while going through some of my

old journal entries (about eight pages worth).

8/22/2005 Numbers & Patterns Across Contexts

5/1/2005 Property grouping axioms in cross-domain relations

8/24/2005 Properties

8/24/2005 Patterns In Contexts: Neural Nets As Priority Systems

10/8/1999 Patterns In Contexts: a computational model for representing

information metaphorically through abductive reasoning

8/5/2005 Augmenting Ideas: Generating New Perspectives on Information

8/6/2005 Epistemology Systems

5/23/2005 Some definitions for Patterns In Contexts Theory

8/2/2005 Cliff Partitions

5/23/2005 Object-oriented processing

5/27/2005 Simulated Models and Utility Axioms

5/22/2005 Operation Spaces continued - Tomographic Data Structures

5/21/2005 Operation Spaces: Grids V.S. Networks

5/14/2005 Key axioms and branch axioms in pattern collections

11/7/2004 Hypothetical Relation Highlighting in Undefined Data Sets

9/23/2004 Am I reinventing the wheel?

8/20/2004 Programming

8/4/2005 Programming Languages

9/22/2004 Patterns In Contexts Cognition Kernel

6/13/2004 Complexity

6/5/2004 Linker Patterns

5/31/2004 Patterns In Contexts Cognition

9/7/2000 Knowledge Mining

7/13/2005 Pattern Occurances

7/5/2005 ePIC Goal Representation

6/3/2005 Cross-Domain Relations in Analogical Relations

6/3/2005 Patterns In Context and Question Asking Systems for

Object-Oriented Programming

5/30/2005 Complexity Progressions

9/7/2004 Metaphoric Operations on Patterns Across Contexts

8/23/2004 Information Theory Quotes

12/25/2004 Metaphoric Operations

1/9/2005 Visual Dictionaries and Axiomatic Abductive Simulation

8/7/2005 Patterns In Contexts: 3D Engine

1/9/2005 Graphical Representation and Visual Heuristics

7/20/2005 Creativity & Understanding

7/17/2005 Concepts

7/8/2005 Measurement Systems

7/2/2005 Re-contextualized Patterns

6/25/2005 Observing patterns and differences

6/24/2005 Patterns Matching

6/20/2005 Remote-Controlled Contexts Via Pre-Processor Switchboards

6/12/2005 Definitions

6/5/2005 Geometric Abstractions

6/4/2005 Index of Topics

6/4/2005 Abstraction

6/3/2005 Analogical Recursions

5/25/2005 Implicit V.S. Explicit Knowledge

5/16/2005 Analogy, Metaphor, and Examples

5/4/2005 Sight

4/25/2003 Computer Vision

5/6/2005 Rules Are Behavioral Expectations

1/7/2005 Categories: Part 1

11/7/2004 Hypothetical Relation Highlighting in Undefined Data Sets

9/12/2004 Some Thoughts on Information Theory

10/22/2004 Some Methods of Proof

8/12/2004 Axiom Notes

6/8/2004 Contexts

6/5/2004 Perception

8/10/2005 Perception -- continued from 6/5/2004....

5/17/2003 A.I. Notes

10/20/2004 Mission Statement

----------------------

Book I:

Patterns In Contexts

----------------------

Copyright 8/25/2005 Justin Coslor

Stuff that occurred to me while going through some of my old journal entries

(about eight pages worth).

Analogies mimic patterns across contexts via cross-domain relations.

That's the basis of Analogical Reasoning. Every pattern in every context

is unique to the properties and axioms of the contexts they exist in.

I've written this book without doing a lick of research or reading

(except where indicated on a few entries), as an experiment to see if I

could generate some new foundations of knowledge and understanding. Some

experts say I succeeded.

A symmetry is an example of an internal algebra. Unique symmetries are

atomic repetitions, and are the simplest form of patterns, distinct from

perceptually apparently random chaos. (I don't believe in ultimate

randomness).

Analogical mimicing results in similar, yet distinctly different patterns.

All truth is but an approximation of a deeper truth. Understanding is

subject to computational complexity of the perceiver and the data forms and

content perceived.

Knowledge is the quest of discovery, and understanding is the growth of

the perceiver. It's how possibilities happen through careful navigation.

There are no dead ends.

Mark fundamental landmark differences in analogically mimiced patterns,

for possible classification category augmentations (for navigation and

data retrieval purposes). Beware of oversimplification of data streams

in order to fit a pattern into a perceptual mold.

Even if my ideas overlap with existing knowledge, they provide a new way

of understanding that knowledge, and that is valuable because my ideas

are not based on mimicry since I haven't studied topics related to them

much (except a college philosophy course and K-13 math). These ideas

exist for the most part in their own context. They can be no doubt eventually

be linked to ideas in other contexts though. Lexicons can often be linked to

external contexts.

Copyright 8/22/2005 Justin Coslor

Numbers & Patterns Across Contexts

Metaphorically speaking, prime numbers are injective and composite numbers

are surjective, when translating functions from one context to another.

Similarly, single-repetition patterns are injective and composite

patterns are surjective, when translating relations from one context to

another. This is an essential part of analogical reasoning.

Copyright 5/1/2005 Justin Coslor

Property grouping axioms in cross-domain relations.

(See diagram.)

1. All variables have properties.

2. All properties are independent of their variable's context(s).

3. All properties have some combination of qualitative relations,

quantitative relations, existential locations, and existential

conditions.

4. Every variable exists within a context and can vary

from context to context.

5. Contexts are composed of networks of patterns, patterns are composed of

networks of variables, and variables are composed of networks of properties.

6. Information can be represented as patterns in contexts, and in that way it

can be represented metaphorically through analogical reasoning and abductive

reasoning. Relations of various kinds, location(s), and condition(s) (apon and

of) exist at all of the various levels, and those are the data access

points.

As writer and owner of this piece of intellectual property I hereby declare it

universally free for use and modification, except I don't condone it's

use in weapon systems or for deception of any kind. This legal agreement

cannot be modified ever, and all modifications of this logic and/or data are

bound by this same agreement. You may sell applications and/or services that

use this logic (or its modifications) but you may not sell the logic itself

and you may not try to prevent others from understanding or using the

logic in any way except if they try to use it for deception or military

weapon applications. Sincerely, Justin Coslor. May 1st, 2005.

Copyright 8/24/2005 Justin Coslor

Properties

These are first-level definitions of some useful kinds of properties, any of

which can be networked together to create relations and variables and

patterns and contexts that may exist in physical and/or platonic reality:

----------------------------------

* qualitative identifiers: Categorical names and cross-references.

* qualitative factors: Qualitative pieces of composite patterns.

* quantitative identifiers: Cardinalities (orderings), scalers, and surjective

equalities.

* quantitative factors: Representational methods of measurement of dimension

sets.

* states: Observable distinct configurations that mark and increment step

counts.

* conditions: Dependencies that distinctly configure each state.

* cycle counts: A tally that is increased with each repetition of a process.

* recursions: A self-defined process or network (an internal algebra), or a

function that calls itself.

* repetitions: An algebra, atomic elements that repeat, composite patterns

that repeat, or symmetries.

* activity level: The number of cycles per step (positive, negative, random,

or null).

* step counts: A tally that is increased as conditions of each state

transition is reached.

* location: A place in a memory grid where identifiable data is stored.

* positions: The sequence coordinates of variable in N-dimensional orderings.

* orientations: The perspective that data maps are observed from: This may be

contextual, or spatially framed position maps, and perspectives may even

have translation conditions of their own.

------------------------

As you can see, activity level is just one kind of property, and priority

systems such as neural nets can be based on that property. Other kinds

of systems can be based on other properties.

------------------------

* Relations are the juxtaposition of infrastructures, which result in an

output.

Copyright 8/24/2005 Justin Coslor

Patterns In Contexts: Neural Nets As Priority Systems

Neural nets are essentially priority systems for allocating and

de-allocating priorities of networked elements such as variables on a grid.

Each network can be considered a context, and can be said to be a network of

patterns composed of variables and relations. If the patterns are

functions, then the priority of each pattern determines the level of activity

(cycles per step) of each pattern's function(s).

Some priority level results in a random level of activity, and the other

priority levels result in either positive levels of activity, negative

(reverse) levels of activity, and an undefined priority setting results

in no activity.

Example:

Context: ABCDEFG * R1R2R3R4R5R6R7R8 == a network of patterns (see diagram).

Where each pattern == (a variable)(a relation Rn), and the level of activity

of each pattern is:

(undefined, -3, -2, -1, random, 1, 2. 3)(a variable)(a relation Rn),

and the activity level determines how many cycles per step that the

relation Rn operates on the variable, and the pattern it is linked

to. These values could be anything, this is just an example.

Activity level is one type of property of the variable.

***Variables are composed of networks of properties.

***Patterns are composed of networks of variables and relations.

***Contexts are composed of networks of patterns and relations to other

contexts. Properties can be things like qualitative and quantitative

identifiers and factors, states, conditions, cycle counts, recursions

and repetitions, activity level (cycles per step), step counts, locations,

positions, orientations, etc.

Patterns in Contexts:

a computational model for representing information metaphorically

through abductive reasoning.

All ideas herein are Copyright by Justin Coslor on their respective dates.

These notes are a progression of the concepts in the order they occured to me.

10/8/99 Invent a digital method or circuit (fast physical algorithm) for

mimicking a pattern. Do it by modeling the pattern's relationships

metaphorically (as a metaphor of existing memory or experience).

If circular reasoning is involved, what is the least experience or innate

memory required to start the circular reasoning engine?

Topic: Circular reasoning engines (in logic and computation).

11/19/1999 The definitive nature of knowledge. This occured to me as a

pseudo-sophomore at Carnegie Mellon University in Pittsburgh, PA USA.

(It's a first draft so please forgive it's sketchyness.)

All knowledge=information, which can be represented as metaphors. Metaphors

are applied to specific contexts and general contexts=multiple contexts.

A. All knowledge is metaphors applied to >= 1 context.

B. A metaphor is a set of associations (links, patterns) that can or is

applied to a context.

A single context...A single specific context...general/nonspecific contexts.

C. A context is a set of restrictions (restrictions on information,

associations, links, patterns, sometimes even contexts).

Therefore the statement A is equivalent to this statement:

"Each piece of knowledge is a set of associations that can be applied to >= 1

set(s) of restrictions."

The use of this I had in mind is to make a computer software that could

understand and manipulate (and maybe even apply) metaphors. Many other ideas

occurred to me today too, possibly due to doing yogi breathing and meditation

exercises and taking vitamins since my health had been suffering.

10/31/2003 Epistemology Framework for Artificial Intelligence "Patterns in

Contexts" continued...

* A pattern is a collection of symmetries, where each partition section of

data of every symmetry in the collection corresponds to another partition

section of data in that collection, or sometimes corresponds to a piece

or pieces of data in another collection (or other collections) which may or

may not be part of a similar symmetry in that other collection.

If data has recognizable features, it is a pattern. Repetition is what

makes a symmetry, and is what makes a pattern's features recognizable.

Unique partition sections of data are the atomic elements that a pattern's

features are composed of. A symmetry is a type of repetition,

but a repetition isn't always a symmetry (see metaphor definition below).

* A context is a map of patterns within (thus bounded by) either a set or

stream of data in which other patterns are ignored or are not apparent.

Or a context bounded by a larger pattern than the map itself

(which itself is a pattern that may or may not be part of the larger pattern),

such as the ordinal of the map or a pattern larger than the boundaries

of the scope. There can be many parallel streams, waves, or sets of data

in, traveling through, across, or around the self-updating mapping of

patterns which is chosen to be the context.

Sometimes the corrresponding partitions of data that make up a repetition

are translated by some pattern with each iteration, such as in a methaphor.

Yet similarity remains apparent (identifyable by some means).

Again, I believe that information is patterns in contexts, and that

information is metaphoric in nature. Tip: If confused by this write-up

of my premise, try reading the sentence in reverse order then back through

again.

11/24/2003

Information is a symphony of symbolism and symmetry.

12/23/2003

Information, by it's very nature, is a division. Yet it strives to become

whole again, and at the very least, to become balanced.

4/7/2004 Category Theory: Abductive context changing using identified

metaphoric patterns. Some dimension additions for alternating or specializing

the application of a pattern or set of patterns:

- Location

- Relative rate, relative timeline framework

- Newly recognized relations found under sequential and parallelly recursive

brute force and intuitively adaptive experimental logic search strategies --

Yields hypothetical considerations which can be temporally prioritized and

recursively checked and updated from state to state and organized

intelligently by current 1. depth, 2. branch size, 3. branch cardinality

(alpha-numeric, etc), 4. task growth rate, and 5. average task completion rate

(for scaling computability).

When you figure out why a variable is a variable in a particular way, that

understanding becomes a new relation to consider, which in effect and affect

either increases or decreases the dimensionality of the variable's context.

Some dimensions that are added usually increase task completion rate (such as

specialization) other dimensions that ar added usually increase task growth

rate (such as broadening the context or broadening the number of class

categories to consider). Generalization can in some cases merge categories,

classes, and/or contexts, or blur them for simplicity, and can increase or

decrease completion rate.

Generalization is useful for experimentation.

All truth is but an approximation of a deeper truth.

A pattern is like a function, and a context is like a field.

Each has relations, variables (when thought of metaphorically),

and often the potential for variations and unconsidered variables of

dimensionality.

5/15/2004

A working definition of the mystery of consciousness might be ascribed to the

interplay between 1. perspective, 2. priorities, 3. intentions, and

4. awareness; all of which depend on the flexibility, state, and mechanisms of

belief held by the subject.

5/16/2004

My data symmetry section analysis technique for perception through patterns in

contexts may be able to play a key role in automating axiom and theorem

discovery for any given context (i.e. contexts such as the integers, the

reals, wavefield analysis, map data, behavioral intention charts,

language/speech modeling and representation, transform sequences, etc.).

Any pattern discovered within a particular context can be applied to any of

the known axioms and theorems of that context, and patterns that are

discovered can sometimes be related to undiscovered axioms in that context.

Anytime an axiom or theorem is discovered in a context, the entire context is

redefined (as well as its subcontexts), and in doing so, its scope is

narrowed. Choose -> Search -> Experiment -> Classify -> Test -> Prove.

Choose/define context -> search for patterns -> searchfor patterns that relate

discovered patterns -> postulate a classification for each discovered

relation.

For each relation, if a classification category does not exist that

closely matches the relation, then further experimentation, context choosing

(add and/or subtract context dimensions), and pattern searching must be done,

starting with the characteristics of all partially matched categories, until

an accurate or exact classification or category definition can be derived.

After the relation's category is realized, search for more examples of that

relation and derrive a proof of it. If the relation can be proven to be

applicable to all patterns in a given context and all subsets of that context,

it can be said to be an axiom of that context.

8/3/2004

Context can be thought of as a network as well as a shell that encompasses

abstract nodes. The context of a set is merely its powerset, that is, until

relations ar applied. I don't believe in randomness, but I do believe that

some contexts are larger or deeper than the scope of our perceptions.

8/4/2004

A context can also be thought of as a network of patterns, or even the network

of relations that tlinks patterns. But when relations are applied to a

context, it becomes an organism. An organism that is capable of translation

(metaphoric operations), modification (adaptationn), division

(duplication/reproduction/partitioning, and/or growth and association with

other contexts.

8/5/2004

There are patterns, and they exist within and between/across contexts, and

there are relations that act as reasoning engines that operate on the systems

of patterns and contexts.

Patterns can have analogue distortion, digital distortion, or metaphoric

distortion. Contexts can be approximations of larger contexts, and

elaborations or extensions of smaller contets or extensions of other contexts

in general There can be relatively unique (somewhat unique, minimal

commonality) patterns and contexts. Note: the word "commonality" is based on

the greek root "monality", which is the "commonality" of the prime numbers.

Each prime number is a "co-monality." This can be visualized in terms of

geometry, to some extent. Every prime number is balanced, and is symmetrical,

and contains a unique number of dimensions, which are also unique kinds

of dimensions. Patterns and contexts and relations can also be symmetry pieces

of other patterns and contexts and relations, regardless of whether or not

they are distorted in any given state or piece or part or linkage.

8/30/2004

Every context is founded on its own set of axioms and theorems, and adding an

axiom to or from a context's foundation fundamentally changes the context

profoundly, yet some structures may remain un-affected.

(*Note many of these notes may become invalid or ridiculous as you read more,

so mental filtering may be necessary.)

8/23/2004

This is a quote from my journal.

""Metaphor" is a relational model of recursion, where the circular

reasoning (in recursive definitions & recursive functions) cross-relates

the elements of definitions & functions from multiple (or different)

contexts. That is why cross-domain relations are so crucial to the metaphoric

representation of knowledge and knowledge systems (logics)."

8/26/2004

"I also believe that information is metaphoric in nature (has algebraic

interconnectivity), and that it can be represented as a composition of

patterns in contexts, where the contexts themselves can be patterns, and the

atomic elements of each pattern are composed of symmetry sections

(partitiopns of data, where each partition is part of a local or dislocated

repetition (a symmetry, and algebra)). And it is only through the repetition

of a data section that part of a pattern can become recognizable from

apparently random white noise. Randomness and white noise are probably

patterns that are larger than the scope of our perceptions, so the data

appears random.

And I say that metaphors can be represented geometrically because all of

the prime numbers (the balance points in the universe) are symmetrical when

represented geometrically, and it is likely through primarily symmetrical

sensory and cognitive structures that our minds can interpret information.

And I think of metaphors not as A=B, but more like the similarity of the

juxtaposition of A's elements in the context of B, and B's elements in

the context of A, in terms of general systems theory.

I equate truth with workable patterns that become more and more refined

and defined as they get used. I believe that all truth that we are capable

of perceiving is but a small approximation of the whole truth. And that

the truth/patterns that we are capable of using is often subject to perception

within varying contexts. But there seem to exist connections between

information none-the-less, through whatever means. Possibly since (in my

opinion) everything came from oneness)."

9/13/2004

Scope & Context -> Boundaries and Restrictions/Limitations

Class -> Purpose

Type -> Syntax

Pattern Definitions -> Semantics

Data Element Groups -> Configurations (Data Maps & Dependencies)

9/22/2004 Patterns in Contexts Cognition Kernal

Database -> Metabase -> Context Rotator -> Experiment Application Field

Expandable

Adaptable

Translatable

Summarizable subjectively/objectively

======>

Metaphoric Linkers

Patterns Toolkit

Augmentation Socket Parameters

Analysis Scope Dimensionality

of (Input/Internal perspective "eyes")

Geometry & quantitative & qualitative properties of simultaneous interrupts

and their instantaneous functional interrelations and interactions

across multivariate sequence states (such as time & symmetry equivalencies).

*Every set state is but an approximation of the possible combinatorial

translations.

11/20/2004 Epistemology thoughts on Metaphor Abduction

Metaphors hide cross-domain relations between generalized nouns,

adjectives, and systems within a semi-subjective context of perspective.

The descriptive mappings of metaphors and multi-layered metaphoric operations

are generallymore foundational than their analogical counterparts, as the

metaphoric objects and relational context is generalized (from set, type, and

categorical specifics), which simplifies the computational complexity of the

models' qualitative factors, and provides new bases for consideration and

re-application of data, relations, and knowledge. Metaphor generation provides

the architectural basis and objective of considering newe relations and data

experimentatiopn for deriving and arriving at new models of understanding.

data --> context unknown

patterns --> hypothetical contexts

relations --> categorical context parsing

metaphoric relations --> cross-domain functions across contexts

specific knowledge --> contextual scope focusing/narrowing

analogies --> applies metaphoric relations to different examples of specific

knowledge for partial transitivity

new knowledge --> modifies existing contexts to incorporate new axioms.

4/6/2005 Prioritization and choice in decision systems

(Part of a reasoning engine.)

----------------------

New action (such as prioritization or actual action)

^---^

Evaluaction ->criteria

^---^

outcome

^---^

choice

^---^

initiative factor(s)

^---^

prioritization

^---^

evaluation-->criteria

^---^

possibilities

----------------

4/24/2005

Inventing industries with patterns in contexts

What the world needs more of in order to support the ever rising

population levels, is more industries. An entire industry can be created

simply by developing a new kind of alagorithm, or an algorithm that creates a

niche for people to fill with services or products.

**********************

An algorithm can be developed by applying an axiom to a new context.

**********************

This may require forming or describing a new context or kind of context, with

intentions and expectations and attributes or properties in mind, as axoms are

chosen and adapted to make that possible. Theorems can then be derived from

those axioms, that are specific to that context, and when possible, they can

be metaphorically related to theorems in other contexts. This is the basis for

the patterns in contexts model for creating new information. It relates

directly to abductive reasoning, analogical reasoning, and cross-domain

relations.

Axioms depend on which dimensions they can exist in and apply to.

For they are the links that connect different dimensions, parts of dimensions,

and sets of dimensions, with the goal of unique lowest-terms representation.

Usually they incorporate at least some implicit knowledge or material

structure in their model.

Copyright 5/1/2005 Justin Coslor

Property grouping axioms in cross-domain relations.

(See diagram.)

1. All variables have properties.

2. All properties are independent of their variable's context(s).

3. All properties have some combination of qualitative relations, quantitative

relations, existential locations, and existential conditions.

4. Every variable exists within a context and can vary from context to

context.

5. Contexts are composed of networks of patterns, patterns are composed of

networks of variables, and variables are composed of networks of properties.

6. Information can be represented as patterns in contexts, and in that way it

can be represented metaphoricly through analogical reasoning and abductive

reasoning. Relations of various kinds, location(s), and condition(s) (apon and

of) exist at all of the various levels, and those are the data access points.

As writer and owner of this piece of intellectual property I hereby declare it

universally free for use and modification, except I don't condone it's use in

weapon systems or for deception of any kind. This legal agreement cannot be

modified ever, and all modifications of this logic and/or data are bound by

this same agreement. You may sell applications and/or services that use this

logic (or its modifications) but you may not sell the logic itself and you may

not try to prevent others from understanding or using the logic in any way

except if they try to use it for deception or military weapon applications.

Sincerely, Justin Coslor. May 1st, 2005.

Copyright 8/5/2005 Justin Coslor

Augmenting Ideas: Generating New Perspectives on Information

Today in the 61C Cafe I was talking to my friend Jason Bacasa telling him

about how I come up with ideas. Besides keeping an ever growing network of

questions in the back of my mind, I take a topic or generate a topic by

combining keywords, and then think about how that topic is typically

represented, then I try to epistemologically dissect that representation and

then rebuild the content using different, if not more foundational

contextualization of those concepts. Then I go off on a tangent exploring the

most interesting parts by associating other concepts, patterns, contexts,

and operations to the new representation of the concepts in the original

topic.

It is often very valuable to have alternative representations of ideas

and concepts and topics because each representation can yield a useful

perception. If there is any word sense ambiguity, or use of metaphor,

then each alternative representation can yield many perceptions, each of

which could uncover previously unseen or unconsidered aspects of the topics,

ideas, and concepts. So in the end, exploring and mapping out alternative

representations of concepts, ideas, and topics is a way to augment their

knowledge base, by generating new perspectives on the information, which

can generate entirely new contexts, which can generate entirely new

knowledge bases, by treating all information metaphorically. People are

currently very good at metaphoric interpretation and analogical reasoning.

Computer programs currently are not. It's the next step towards

computational methods of abductive (round-about scenic-route) reasoning.

Anyway, Jason said I should make a program that does what I do, i.e.:

a program that recontextualizes information from different perspectives

of association, sort of like a choose-your-own-adventure story, but more like

a choose-your-own-perspective program. Like a computer program that generates

alternative representations of ideas, topics, and concepts. Or even more

generally, a computer program that generates alternative representations of

patterns (thoughtforms) in a variety of contexts (settings).

Copyright 8/6/2005 Justin Coslor

Epistemology Systems

Categories, and complete dictionaries as foundations. Quantified objects

(and systems) can be juxtaposed into relations that balance alternative

representations of objects and systems via a structural or syntactic

methodology that acts as a transformation into some of the possible

alternative representations of the quantified objects and systems.

Algebras as alternative representations of information. Algebras can

rename, or point to representations of information, as well as interconnect

and dissect informational objects and systems. All objects and systems

are named.

Simulations, recontextualizations, and "polymachines" as alternative

models of systems.

Proof is contextual, in other words: proof is dependent on perspective and

representation. In much larger contexts than the original context in which

something was proven, most "proof" becomes incomplete or uncompatible, and

sometimes even false if more foundational epistemological structures are

found to have been overlooked. Proof is complete, logically consistent

introspection of perceptions of concepts.

Any given proof is only applicable to specific axiom sets. I.E. a proof

based on one axiom set may be incomplete or uncompatible or even false in a

context composed of a different set of axioms. Therefore concepts must be

analogically translated into other contexts and their translations must be

formed concurrently with their proof validity in their new context, as a

best-fit categorical search procedure. The proof is a complete, concise

system, so the proof in it's new context can be considered to be a

polymachine, since it is an alternative representation of that system. A

polymachine is a set of cross-domain relations that operate on

analogically-matched patterns from an original context to a new context, and

represents an alternative form of a system in a different context.

Polymachines are created by inductive, deductive, or (in the case of

analogically translated proofs) abductive reasoning. Cross-domain relations

are relations that analogically match the domain of a relation in one context

to the domain of a relation in another context whose range approximates the

same infrastructure and quantitative parameters while leaving the qualitative

parameters categorically open-ended; they are a form of analogical reasoning.

Input Devices->Internal model buffer->Association and repetition

filter->Analysis/comparison engine->Perceptions on experience->Algebraic

Conceptualization->Character sets and dictionaries, or number systems and

axiom sets -> statements, arguments, inquiries, propositions, implications,

operations, filtrations, combinations, exegesis, dissertation, assignments,

contextualizations, templates, associations, compositions, dissections,

introspections, modifications, adaptations, introductions, translations,

transformations, distortion, refinement, recontextualization, proof,

mapping, search, buffering, sorting, indexing, encoding, decoding,

regulation, pattern formulation, trans-substantiation (joke), frollick.

Copyright 5/23/2005 Justin Coslor

Some definitions for patterns in contexts theory

Metaphoric objects are informational objects defined by their

relational properties. In relational contexts, sub-contexts of each

property are independent of the application context. Qualitative factors

are computed by mapping and defining a lexicon of their properties.

Qualitative factors are reflective and algebraic usually. Quantitative factors

are computed by counting and performing materialistic operations on them,

and mapping them in that way. Quantitative factors are materialistic and

geometric usually.

Copyright 8/2/2005 to 8/3/2005 Justin Coslor

Cliff Partitions

Cliff partitions are perceptual references that distinguish deeply layered

patterns from surface patterns, much like a cliff wall bordering the ocean.

In the ocean, every couple of feet down an ocean wall is a new layer, much

like how layers of pixel groups can be laid out on a visual canvas, with some

stacked up several layers high on an edge.

Cliff partitions are essential markers of where a topology has a steep

slope that may or may not be an overhanging awning above a hidden hollow or

cave. In topology, cliff partitions are useful for analyzing the depth

perception of a view.

In linguistics, cliff partitions may indicate a sentence that is placed in

the wrong order, or it may indicate a sudden change of topic, or a jump from

one perspective of a context to a deeper or more superficial depth of

perspective of that same context. Cliff partitions in linguistics may also

indicate the boundaries of a given context, where one context ends and another

begins. Cliff partitions are only conceptual perceptual references in

linguistic domains, as writers and speakers linearly paint a nonlinear

picture with their words.

Copyright 5/23/2005 Justin Coslor

Object-oriented processing

Grids (a.k.a. manifolds), networks, and gridded networks all can house

patterns in contexts of information data sectors as the representation of

knowledge (knowledge is information that contains meaning). Grids, networks,

and gridded networks are materialistic operation spaces for knowledge

representation, whereas the notion of "patterns in contexts" are the Platonic

operation spaces that form the meaning behind the scenes on the materialistic

operation spaces. Identifying the representation of knowledge in an operation

space as "patterns in contexts" and specifying the details allows us to work

with the information in an object-oriented manner.

Copyright 5/27/2005 Justin Coslor

Simulated Models and Utility Axioms

If a network or grid is composed of N elements, then it is capable of

simulating every possible permutation of those elements by forming internal

networks and sub-networks (& grids). Grid networks allow for an infinite

number of combinations to be simulated though, but only some simulations are

of any use. Maybe there are utility axioms that can be defined to tell us what

classes of models contain useful representations. It seems like some factors

that might determine whether or not a model is useful would be:

1. Compatibility with existing useful models.

2. Novel representation or novel perspective.

3. Incorporation of new information.

4. Novel capability.

5. Ability to link two or more other models together.

6. Ability to prune other models.

There may be many more factors directly related to evaluating the worthiness

of a model. Simulation allows for recontextualization of models and problems

and systems.

Copyright 5/22/2005 Justin Coslor

Operation Spaces continued - Tomographic Data Structures

In the gridded network system, as described previously, a multidimensional

array is built between selection of nodes in a network, where elements of this

array can be used to build internal networks between the primary node anchors

of the array, or between other nodes in other networks --as in cross-domain

relations. This process can repeat to an infinite depth, in the order of

network node to array anchor to array node to tomographic network to

cross-domain relation network to array grid, cyclically. This is a way of

creating tomographic data structures of an infinite depth and of infinite

permutations, due to the potential for infinite depth, all without adding any

extra primary nodes. Every array element and every node represents a relation

to or between their anchors or parent nodes.

Copyright 5/21/2005 Justin Coslor

Operation Spaces: Grids V.S. Networks

Rows and columns and layers are dimensions of a grid, but dimensions can

also be parts of an N-dimensional array. Each of the dimensional intersections

form a unique partition that relates or is categorized by it's parent sets'

position along their own sequences. So in this way, elemenets on a grid

(i.e. in an array) come from multiple parents, wheras elemenets in a network

can often come from only one parent (an injective branch). However, in some

networks, such as where a planar geometry can exist by the interconnection of

more than two nodes, multiple parents can be a grid of subspaces between the

nodes on the plane that they make, and in those subspaces multivariable

position and quantized quality relations can be said to exist, that are

anchored to multiple origin points (each vertex be treated as an origin,

and angles between them only serve to define the partitioning of the planar

grid). I'll call this kind of transformation of a network "a subspace grid

of vertices". Maybe this combination of a grid network can enhance the

operation space by making any nodes on a network able to be related to

eachother, in grid format, between particular data sections on the subspace

grid as well as between other primary nodes.

The other kind of operation space is the Swiss cheese like structure that

surrounds a subspace geometrized grid transformed network. The inner edge of

that space is where one context ends and other contexts may begin to exist.

Copyright 5/14/2005 Justin Coslor

Key axioms and branch axioms in pattern collections.

Patterns are composed of smaller parts, with the smallest parts being

repetitions of unique elements in which no sub-patterns are apparent; also,

these smallest parts exist and their repetitions make them algebraicly

recognizable due to certain axioms, which act as fundamental truths

(self-evident assumptions) for which no proof is said to be needed.

This being said, we can say that all patterns that are unique in some

manner must contain at least some unique axioms, and if we look at a

collection of basic patterns and determine what is unique about each one

and what is in common between them, and then figure out how those

similarities and differences ar ordered on an axiomatic level, we may discover

key axioms and branch axioms which can be represented in a nodal network

graph.

The value of this is that we can then understand, at the most basic level,

what makes a pattern exist, what makes a pattern recognizable and similar to

other patterns, and what makes a pattern unique.

We can use that understanding to select axioms suitable to generate a set

of patterns with a measurable degree of flexibility/adaptability, to use

in constructing a system of perception, similar to a painter mixing paints on

an artists pallete, while he mixes concepts in his mind's eye.

Copyright 11/7/2004 Justin Coslor

Hypothetical Relation Highlighting in Undefined Data Sets:

If categorical names have been assigned to finite elements in a domain,

the rest of the data in the set can be hypothetically considered to be

relations or parts of relations (on those elements and elements not in that

buffered data set). Or they may be elements of categories you don't yet

recognize or know of yet.

9/23/2004 Justin Coslor

Am I reinventing the wheel?

Today while studying a diagrammatic map on "Can Computers Think?" that

Seth Casana gave me I learned of work that has already been done in Artificial

Intelligence that is very similar to some of the concepts that I came up with

on my own.

For instance, there has been work done in the area of making computer

software that can understand "analogies". That is very similar to my concept

of "metaphoric operations". Also, in 1989 in seems, Keith Holyoak and

Paul Thagard created ACME, which is a connectionist network that discovers

"cross domain analogical mappings." That soundsd just like my concept of

"cross domain relations for alternative route mathematics", that I have

written about prior to reading anything about it, and I came up with it all on

my own earlier this year. Here are some Analogy Systems:

Copycat - Douglas Hofstadter and Melanie Mitchell 1995.

SME - Brian Falkenhaimer, K. Forbus, and D. Gentner, 1990.

ACME - Keith Holyoak and Paul Thagard, 1989.

8/20/2004 Justin Coslor

Programming

In the preface to the introductory computer programming book

"The Little Lisper" second edition ISBN 0-574-21955-2 it says: (that in LISP)

"the primary programming activity is the creation of (potentially) recursive

definitions." Now to me, that sounds like the main task (and goal) is to map

out and/or define patterns that are either finite or infinite and to put them

into a relational context that is capable of transforming incoming data

patterns by relating them to stored data patterns, so that the output can be

1. represented, 2. stored, and 3. used/manipulated. I believe this because

nothing is more recursive than a pattern (nothing is less recursive than a

pattern as well, except that which is totally random). Patterns always exist

within a context or contexts, otherwise they are not recognizable and look

like random garbage (see Godel's Theorems). On page vii it also says that

"LISP is the medium of choice for people who enjoy free style and flexibility.

LISP was initially conceived as a theoretical vehicle for recursion theory and

for symbolic algebra." (and likely Lambda Calculus & the EMACS environment for

Artificial Intelligence)... LISP syntax looks very similar to my old nonlinear

style of thought notation, with its parenthesis within parenthesis (which was

good for scaling depth on tangents and concept descriptions).

Copyright 8/4/2005 Justin Coslor

Programming Languages

"Programming languages are formal languages that have been designed

to express computations." - How to Think Like a Computer Scientist -

Java Edition

In other words, programming languages are mappings of balanced processes.

The flow of any kind of process can be mapped, if not only approximated by a

systematic contextualization of patterns and relations involved in the

process. Every system is like a state machine in motion, where the elements

and operators are encapsulated by their interconnectivity via

contextualization, which is a form of perspective of finite scope.

Formal languages have fully defined axioms, and are consistent and

complete in the mechanics of their methodology. But what is the methodology of

mappings of balanced processes in general? The universality concept applies to

them: they are consistent and complete because they are balanced about a tight

contextualization, where the interconnectivity of the process's elements acts

like a fulcrum (when thought of quantitatively), with no element left

unconnected. That's why patterns in any context can be transformed through

operations into different patterns, so long as there is a method of

representing both sets of patterns. The balance comes from having multiple

methods of representing each state of the elements in the process. The mapping

comes from being able to contextualize the processes, which is only possible

if the processes have finite scope, and are completely defined (thus

interconnected), and must be systematic (thus logically consistent) in

order to be precisely mappable with regularity throughout their states of

operation.

Copyright 9/22/2004 Justin Coslor

Patterns In Context Cognition Kernel

[Database]-> [Metabase]-> [Context Rotator]-> [Experiment Application Field]

-----------------------

The following are *a. Subjectively and *b. Objectively

1. Expandable,

2. Adaptable,

3. Translatable, &

4. Summarizable:

------------------------

Metaphoric Linkers

------------------------

Pattern Toolkit

------------------------

Augmentation Socket Parameters

------------------------

*Considerations:

-----------------

I. Analysis

II. Scope Dimensionality (of input/internal perspective "eyes")

III. Geometry & Quantitative & Qualitative properties of simultaneous

interrupts and their instantaneous functional interrelations and interactions

across multivariate sequence states (such as time & symmetry equivalences).

**Every set state is but an approximation of the possible combinatorial

translations.

Copyright 6/13/2004 Justin Coslor

Complexity

Commercial or proprietary software is surjective or injective, but free

open-source software is bijective.

Part of the FRDCSA Tutorial (Free Research Database Cluster Study and

Apply) on frdcsa.org says a blurb from an ACM paper about measuring the power

of a set of axioms in order to measure the information contained within the

set of theorems that can be deduced from those axioms. It says that one can

only get out of a axiom sets what one puts in. The paper says something like:

"If a set of theorems constitutes t bits of unique information, and the set of

axioms that the theorems are based on contains less than t bits of unique

information, then it is impossible to deduce those theorems from that set of

axioms."

My friend Andrew J. Dougherty of FRDCSA says that to understand the

general necessity of having more software, simply replace "theorems" with

"problems", and "axioms" with "programs", and "deduce" with "solve" in the

previous statement. Doing that we get: "If a set of problems constitutes t

bits of unique information, and a set of programs contains less than t bits of

unique information, then it is impossible to solve these problems using just

that set of programs. By "problems", I think he means "explicitly defined

problems", because an explicitly defined problem is a program that has yet to

be executed. Abduction may be necessary to define all of the elements and

operators of a problem in the process of turning a problem into a program.

I say, replace "theorems" with "context", and "axioms" with "patterns",

and "solve" with "create". This yields: "If a set of contexts constitutes t

bits of unique information, and the set of patterns that the contexts are

based on contains less than t bits of unique information, then it is

impossible to create those contexts from that set of patterns."

Copyright ?/5/2004 Justin Coslor

This is part of my method of knowledge representation for my

epistemological representation of artificial intelligence through Patterns in

Contexts. Contexts come from patterns that are combined. There can be patterns

noticed in the cross-examination of different contexts, but those "patterns"

are elements of a greater scope of context than any of the contexts being

cross-examined, that is to say, when those cross-context patterns are not

noticable when only examining any one of those contexts in relation to itself.

This method of knowledge representation may hopefully prove to be useful in

the abductive search for new axioms within and across representable contexts.

A context is represented by its systems of patterns (a.k.a. it's system of

axioms).

Copyright 6/5/2004 Justin Coslor

New patterns can be discovered by experimenting with data sets: analyzing

them in relation to metaphoric operations on other data sets. Metaphoric

operations are operations that translate, juggle, predict/locate, and/or

transform specified elements across specified contexts.

Copyright 6/7/2004 Justin Coslor

New metaphors can be discovered by combining axioms that come from

multiple number sets, orderings, and/or algebras. Metaphors are esoteric

relations. The application of a metaphoric operation on a data set sometimes

results in the discovery of new axioms through the new perspective's set of

relations brought about by the application of esoteric relations.

Metaphoric perception is all about cross-domain relations. This is because

the application of metaphors brings about both:

1. relations between the range of the metaphor and the range of all applicable

operations (operations of applications) of the data set, and

2. new cross-domain relations (new domain perspectives) for both the

operations of potentially all applications of the data set; and sometimes new

cross-domain relations and new ranges for the system and set of relations

that algebraically defines the metaphor (when applying the unmatched relations

that are not bijective of the operations of applications of the data set)

metaphorically (i.e. algebraicly to the metaphor).

Copyright 6/5/2004 Justin Coslor

Linker patterns

Linker patterns require both an observation buffer (that is at least of

equal size to the sum of the contexts to be linked), and linker patterns

require an operation buffer that is at least as big as the observation buffer

(though far larger is necessary for some observations, even though the amount

of data that ends up in the operation buffer may be far less, in some

instances, than the amount of data filtered out of the sum of the contexts

into the observation buffer).

Data gets filtered out of every applicable context by the linker

pattern's "filter specifications", right into the linker pattern's

observation buffer. Then the linker pattern's set of metaphoric patterns

operates on the observation buffer one at a time or in parallel, but inside

the operation buffer.

The linker pattern contains a set of metaphoric patterns whose elements

are referenced algebraically to the applicable data elements present in the

observation buffer for every possible metaphoric pattern combination present

in the linker pattern innately.

Metaphors which are algebraically a complete set of elements to

applicable/valid data elements are used in the observation buffer, then inside

the operation buffer they perform their calculation (translating, juggling,

and/or transforming of the data section by the metaphor) and the linker

pattern then places the output in an organized form (so it can be referenced

later), and those outputs are placed into a buffer called "the unified

context" of the original contexts. This "unified context" includes the linker

pattern's filter specifications and metaphor set that was used (i.e. the set

that was computable).

Linker patterns can duplicate themselves to divide up the work of

applying their metaphoric pattern sets to the observation buffers' data (and

they update each other with each successful operation).

Each linker pattern is like a mobile set of operators that copies select

groups of contexts and gives birth to unified contexts (which are new

contexts). It is each linker pattern's unique set of filter specifications

that differentiates one linker pattern from another.

New axioms and theorems that are found elsewhere and within each operation

are found and get added to the metaphor set after the valid discovered

patterns are provably generalized. They are placed in all of the linker

patterns.

Linker patterns can also update each other's set of metaphoric patterns by

sharing ones the other doesn't have, and copying new ones from the other.

The observation buffer performs general quantifier type matching.

Copyright 5/31/2004 Justin Coslor

Patterns In Context Cognition

A context is any specified number set, ordering, or system of numbers that

is representative of something (symbolic).

Take the desired outcome (the goal) and break it down into unique aspects.

Treat each aspect as an element of a context that contains it, or as an

element of several contexts that contain it. each element/aspect may have its

own unique context at first. We will be striving to find the pattern or

patterns that link all aspects of the goal into one context.

A "linker pattern" can be a linker of the contexts that each of the

elements of our goal exist within. Such a pattern links contexts together by

assigning a system of translating, juggling, predicting/locating, and/or

transforming the specified elements across their specified contexts.

This "linker pattern" is metaphoric, and can act as the "unified context" in

which we will search for the aspects of our goal, as well as search for

alternate routes to each of these aspects (for optimization).

After this experimental search has completed and an optimal cross-domain

relation search for shorter routes to each aspect has been completed, we will

have generated the optimal route map to our goal.

Cross-domain relations can also be thought of as possible associations, or

simply as patterns. They can very explicitly depict ambiguous relationships,

such as when they are used with graph theory. Cross-domain relations are

a little bit like surjective and bijective networks in logic but where two

domains lead to the same range in a number set, even when the domains come

from different contexts. They can also be thought of as alternative routes.

Cross-domain relations can be searched for that relate aspects of our goal

that are also aspects of goals that have different unified contexts than our

goal. It's important to mark the optimal routes out of the cross-domain

relations, but keep the other relations (possible routes) for use in future

goal structures. By linking multiple goals in this manner, we expand our

network of understanding.

Copyright 9/7/2000 Justin Coslor

Knowledge Mining

Maybe amassing huge intelligent databases that can draw conclusions and

make abstractions and predictions towards goals that can recognize & ask for

specific data it needs to output one or more units of truth, which could help

demystify fields of study and help major breakthroughs occur, if not by simply

abstracting and relating so much specific data and general patterns in so many

areas; to help bring everything to one's fingertips. A massively parallel

search and correlation engine:

The computer has to be able to understand a goal enough to figure out how

to better understand that goal, so that it can design it's own searches

(determine its own search criteria), and know what a conclusion would look

like and would require to be complete enough to make an abstraction.

What is the criteria of a conclusion? Is a conclusion just one particular

perspective in every situation? How can the perspective be intelligently

shifted and rotated in a search to generate and array of complimentary

conclusions? At what point does the difference in goals generate opposing

conclusions? (i.e. when do conclusions become apparently contradicting when

using the same set of data...) Taking this into account, what difference

in goals produces contradictory conclusions (perceptions) when searching

(parsing) intersecting sets of data?

Input something like a handbook of chemistry and physics, with a goal of

making valid correlations that are not a listed part of that original data

set. Start out with general patterns like input types, leading to language

semantic patterns, leading to patterns of contextual settings, leading to

metaphoric patterns between contexts, *leading to applications of the

generalized raw data to the metaphoric patterns, leading to generalized

predictions of the outcome of the previous step*, parsing the conclusions

listed in the raw data and matching it to the metaphoric mold (the pattern and

logic) that led the contained data elements (or equivalents) to that listed

conclusion. . .in short: enable the software to understand how the data

elements were led to the conclusion listed in the raw data, so that those

patterns (metaphoric molds or logic operations) can be understood enough to be

applied to the raw data in different permutations (ways) to uncover

conclusions of previously unconsidered possibilities. Those patterns and

derivation/discovery methods could also be used as a guide for designing

new patterns built from recombining the old patterns with unique data.

And since unique data almost always is unique due to its being composed of

at least some unique patterns; parsing the old (known) patterns from new

(unknown) patterns might make it easier to clarify what exactly the new

pattern is or at least how it operates (or at the very least, its function).

This is knowledge mining. . .One form of artificial intelligence.

Circular Reasoning:

I aught to look up the dictionary definition of a bunch of the key words

in this.. Hey, why not all of the words? A number could correspond to the

number of words the dictionary definition of each word had to reference

(on every level of the tree of lookup words, each branch pausing when it ends

up at it's own word (a loop)) until the parts of the world applicable to the

context of the base word have been described (mapped)), until an upper limit

has been reached on each word. The highest number out of all of the words will

be the number of words in the applicable dictionary to the context of that

paragraph (no repeats). It will be a complete system of circular reasoning.

A complete system of circular reasoning is where every word in a

dictionary is mapped to at least one other word in that dictionary. Some may

be mapped to every word in that dictionary. A complete system of circular

reasoning is one unit. It is aversion/perspective model of a truth. And

different ones can be combined to build complex systems of truth. Like

mitochondria building cells building structures.

Copyright 7/13/2005 Justin Coslor

Pattern Occurrences

Some patterns are designed or brought about intentionally, and other

patterns are brought about naturally, and others are brought about as an

unintentional consequence of bringing about intentional patterns, such

as in unintentional contexts that are created as a result of layering

patterns, and grouping patterns, and modifying patterns.

Some patterns occur naturally according to certain variable probabilities

specific to their contexts, while others are subject to haphazard creation,

randomness, and free will.

Copyright 7/14/2005 Justin Coslor

Since all patterns are composed of repetitions, and since the repetitions

are what makes the parts recognizable, and since anything that is recognizable

can be considered a pattern, the reference pieces for the parts of each

pattern can be local, as part of the pattern's context, or the reference

pieces can be remote, as part of other contexts that are accessible to the

perception system. The reference pieces are instances of the repetitions that

make the parts recognizable, and are usually cataloged by order of exposure to

them, as well as by associations.

When new patterns are encountered they are either recognized (thus

categorizable), or they are unrecognizable (thus not categorizable) because

their parts and properties are unknown, or they are partially recognized (thus

potentially categorizable and partly referencable). If the pattern is

new and it is recognized, then its parts are already known but are arranged in

a new configuration and with potentially new properties due to the novel

association of its parts.

So basically, once the perception system is exposed to contexts, the

pattern matching/classification system begins its task of dissecting new

patterns into reference pieces, and classifying recognizable patterns into

association contexts and utility contexts, and assigning priority ratings to

everything so that the perception system can decide what to pay attention to.

Priority ratings get constantly updated, and depend on how much bandwidth and

processing power the perception system and reasoning engine have available.

The reasoning engine does all of the heavy calculations, task and priority

assignments, memory management, simulation modeling, and most of the decision

making.

Copyright 7/5/2005 Justin Coslor

ePIC Goal Representation

(ePIC = electronic Patterns In Contexts)

A goal is an abstract construct, and the attainment of a goal is to fill

in all of the details of the goal either:

1. in Platonic Reality (information space), or

2. in physical reality (matter configuration space).

If the details have been filled in in Platonic Reality, then the result is a

simulation. If the details have been filled in in physical reality, then the

result is a working model. A prototype can be a preliminary model or

preliminary simulation.

The abstract construct of a goal is the starting point for changing your

reality in some way. One need only be able to partially perceive of the

abstraction to initiate the existence of the goal, but to fully specify it, a

viable plan needs to be formulated. Usually there are unknown variables in

every abstract goal, and specifying each variable becomes an iterative

process. Often the abstract goal can be stated in the form of a question, and

is the result of the questions that arose from some problem. Often times

further questioning of the problem impetus is necessary to specify the goal

and in doing so, the problem gets solved as the unknowns become decided or

calculated.

Many goals are qualitative/categorical subjective/objective priority

system calculations, that rely on preference, perspective, universal truths,

contextual restrictions, and contextual properties. However, all problems,

goals, and solutions can be represented as patterns in contexts, such as

undecided patterns in partially determined contexts, that evolve through

storing and grouping of categorical, qualitative, and quantitative patterns

across different contexts into an experimental buffer/model space towards the

sufficiently representative construct or construction of networks of

systems of patterns, that satisfy the objectives of the problem and goal,

in the context of the final form of the problem and goal.

The Patterns In Contexts concept is an epistemological language,

which I strongly believe can be used to represent anything, any concept,

and any information of any kind, including first person, second person,

third person information in past present or future tense,

and it adapts well into any other language.

Copyright 6/3/2005 Justin Coslor

Cross-Domain Relations in Analogical Relations

A true cross-domain relation would have two domains that each lead to the

same range. Analogical relations do something very similar to this, however

not quite. In an analogical relation, the relation between the domain and

range of one context is mimicked across a somewhat similar domain and range in

a different context (only some properties need to be similar for the analogy

to be formed, since a barely recognizable similarity needs to exist).

The result is like having generalized an abstraction of the two

domains and the relation, and using that abstraction to perform the

abstracted relation on the second domain in the other context.

--------------------------------\

This is an unfinished work and I disclaim all liability.

--------------------------------

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