Book 1 of Possibility Thinking Explorations in Logic and Thought 
[Dec. 3rd, 200709:17 am]
justincoslor

This is an unfinished work and I disclaim all liability.  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 crossdomain 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 Objectoriented 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 CrossDomain Relations in Analogical Relations 6/3/2005 Patterns In Context and Question Asking Systems for ObjectOriented 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 Recontextualized Patterns 6/25/2005 Observing patterns and differences 6/24/2005 Patterns Matching 6/20/2005 RemoteControlled Contexts Via PreProcessor 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 crossdomain 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 K13 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, singlerepetition 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 crossdomain 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 firstlevel 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 crossreferences. * 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 selfdefined 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 Ndimensional 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 deallocating 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 pseudosophomore 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 selfupdating 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 writeup 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 (alphanumeric, 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 "comonality." 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 unaffected. (*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) crossrelates the elements of definitions & functions from multiple (or different) contexts. That is why crossdomain 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 nonetheless, 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 crossdomain relations between generalized nouns, adjectives, and systems within a semisubjective context of perspective. The descriptive mappings of metaphors and multilayered 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 reapplication 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 > crossdomain 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 crossdomain 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 lowestterms 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 crossdomain 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 (roundabout scenicroute) 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 chooseyourownadventure story, but more like a chooseyourownperspective 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 bestfit 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 crossdomain relations that operate on analogicallymatched 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. Crossdomain 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 openended; 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, transsubstantiation (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, subcontexts 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 Objectoriented 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 objectoriented 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 subnetworks (& 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 crossdomain 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 crossdomain 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 Ndimensional 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 subpatterns are apparent; also, these smallest parts exist and their repetitions make them algebraicly recognizable due to certain axioms, which act as fundamental truths (selfevident 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 0574219552 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 opensource 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 crossexamination of different contexts, but those "patterns" are elements of a greater scope of context than any of the contexts being crossexamined, that is to say, when those crosscontext 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 crossdomain 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 crossdomain relations (new domain perspectives) for both the operations of potentially all applications of the data set; and sometimes new crossdomain 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 crossdomain relation search for shorter routes to each aspect has been completed, we will have generated the optimal route map to our goal. Crossdomain 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. Crossdomain 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. Crossdomain 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 crossdomain 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 CrossDomain Relations in Analogical Relations A true crossdomain 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.  

