justincoslor (justincoslor) wrote,

Book 1 of Possibility Thinking Explorations in Logic and Thought

This is an unfinished work and I disclaim all liability.
Copyright 6/3/2005 Justin Coslor
Patterns In Context and Question Asking Systems for Object-Oriented
The patterns in contexts model of knowledge representation and question
asking systems based on forming networks of questions and networks of patterns
in networks contexts can be used to make a profoundly sophisticated
object-oriented programming system capable of doing analogical reasoning,
deductive reasoning, as well as induction and recursions that are simply not
representable in other systems. In this system there is a constant
acceleration of computational complexity, all of which is progressively
designed to simplify the system while augmenting abilities and understanding.
Copyright 5/30/2005 Justin Coslor
Complexity Progressions
Every state of a complex pattern can be said to be the result of a
progressive augmentation of the previous state or model/version by a new or
repeated pattern, or by multiple patterns. That is, unless data loss has
occurred due to random deletion or a random addition process.
Copyright 5/31/2005 Justin Coslor
Pattern Details & Randomness
Every pattern is the iterative accumulation of modulations and
augmentations of sub-patterns, right down to the atomic repetitions that
are the first forms that are recognizable from randomness.
Atomic repetitions may come in a wide variety of non-interoperable modes
of partitioning, each of which is subject to a unique perception system that
is capable of buffering and filtering its own particular spectrum of atomic
repetitions that are partitioned from patterns and randomness that are
unrecognizable to that mode.
Randomness comes in two main forms: there is randomness that is compatible
with the partition mode of a given perspective system, thus being countable or
measurable via the mathematical comparison of the atomic repetitions of that
mode (because it is just a randomization of those atomic repetitions);
and the other kind of randomness is composed of randomized patterns that are
partitioned in modes other than that which is compatible with the
current perspective system.
It is undecidable whether or not there exists a randomness that cannot be
partitioned by any mode of perspective, i.e. a randomness that is not the
randomization of some set of patterns or atomic repetitions.
Copyright 9/7/2004 Justin Coslor
Metaphoric Operations on Patterns Across Contexts
I want to learn LISP and use it to make an intelligent agent capable
of doing metaphoric operations on patterns across contexts.
2/17/2005 Update by Justin Coslor:
I guess now, most Artificial Intelligence Programming is starting to
be done in Java since it is cross-platform and simple to use.
Copyright 9/8/2004 Justin Coslor
To do this, the sub-agents will need to be able to research raw data
configuration sets to look for algebraic repetition that can be considered to
be patterns in the sea of cached buffered inputed/observed/recognized
In order to recognize something, it will have to have a known set of
basic recursions (repetitions) to begin with. The prime numbers ar a good
source to start out with (since they are the natural balance points in the
Then it will need to try to describe each data configuration set
(data map) whose atomic repetition symmetries can be characterized or
parsed. This description will be known as the pattern's type, and
patterns with similar types will be grouped into classes.
To describe a metaphoric operation will require generalizing the
differences between each type description in a particular class, and
then mapping the observed relations (between each of these types) in the
form of a nodal network. That nodal network will be a metaphoric object
that summarizes the class.
Create metaphoric objects for all of the classes in the context (aka
scope) of your total original cached raw data. Then form relations
between different metaphoric objects, and combine and reconfigure
different metaphoric objects, with the original metaphoric objects being
treated as axioms of that particular context. The metaphoric object
relations can be treated as templates for filtering other raw data
contexts in the search for known patterns which contain their own
distinct uniqueness, that will will warrant the generation of new types
in new classes. Every context has its own types in their own classes.
In other words, every raw data set has its own patterns in their own
contexts. This is how to relate different raw data sets to extract their
relational axioms, and the combination and reconfiguration of different
contexts' axiom sets (metaphoric objects) is what I call metaphoric
Copyright 8/23/2004 by
Justin Coslor.
Information Theory Quotes
""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)."
Copyright 8/26/2004 by Justin Coslor:
"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 (partitions) of data,
where each partition is part of a local or dislocated
repetition (a symmetry, an 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
Here's another quote from my journal Copyright
11/24/2003 by Justin Coslor:
"Information is a symphony of symbolism and symmetry."
Here's another journal entry Copyright 12/23/2003 by Justin
"Information, by it's very nature, is a division. Yet
it strives to become whole again, and at the very
least, to become balanced."
::Metaphoric Operations::
Metaphors are geometrical, in a sense, that is to say they follow mathematical
geometries. That is to say, metaphors can be thought of in terms of
geometrical patterns and systems. This is because metaphors can be diagrammed,
and diagrams have a relative/nodal/graph-theoretic logic about them, and
through the logic of their patterns and systems they can be recognizable as
having a sort of relational geometry (at least in the unseen
Platonic-reality). Patterns have an algebraic repetition at their foundation,
and the most basic repetitions are symmetries. The most basic symmetries can
be perceived through prime numbers, in that they are the fundamental building
blocks of more complex symmetrical and a-symmetrical structures. A-symmetrical
structures are constructed out of symmetrical structures, just as non-prime
numbers (composite numbers) are constructed out of prime numbers and
relations/functions. Metaphoric operations are relational templates that are
axiomatic, adaptable, reconfigurable, and versatile. This is because they are
collections of relations whose options have been generalized to optimize those
qualities for relating similar, and different qualitative domains across
contexts. Each context's qualities' relations are unique to that context's set
of axioms. One might say that domains are qualitative, while the domain's
ranges can be qualitative OR quantitative. Metaphoric operations relate
different consistent, recursively complete, contexts by copying or moving
elements from each context into the separate but more versatile context of the
metaphoric template. Once the elements have leave their original context,
their original context's axiom set(s) may be altered, as well as some of the
context itself (and sub-contexts, if any are relevant). Metaphoric contexts
may only need to copy some of the axioms of their element's original contexts,
because they have axioms of their own that help to allow for the relation of
the axioms that are buffered in from multiple other contexts. The metaphoric
template's original axioms also help to relate the qualitative elements which
are the current primary focuses, that were constructed out of relevant axioms
from the external contexts. New knowledge is created when the qualitative
elements' axioms sets are adapted to form new qualitative elements and
relations out of the augmentation of the metaphoric template's context's axiom
sets, by the elements' external axiom sets. With metaphors, anything that
isn't explicitly cross-domain related is ignored. Qualities are itemized as
they are noticed or as they are deemed relevant. Personally, I feel like the
diagram of metaphoric operations is a lot prettier than the description...
Copyright 12/25/2004 by Justin M. Coslor
Copyright 1/9/2005 Justin Coslor
Visual Dictionaries and Axiomatic Abductive Simulations
Maybe as part of building the logical framework for a systematic visual
dictionary, we could try representing each image both as a set of angular or
situational perspectives; but also I think it's important to try to axiomatize
the image properties into contexts, and by doing so we can do abductive
creative constructions (and abstractions of those to some approximate goals),
such as by perceiving each image as a series of nodes (graph theory vertices)
and connections that are all linked together both contextually in the physical
space, and conceptually in the historical-timeline/platonic interaction space.
By doing this, the heuristic (guess-work) training can be semi-automized
and the intelligence data on the scenario objects can have a far deeper
meaning and farther reaching applications. Deepening the understanding of
content and its abductive recombinations and metaphoric
transcombinations, both increases the potential for creating new applications
and tools, and increases the versatility and effectiveness of existing tools
and applications. Deepening understanding of content creates new contexts and
reconceptualizes stuff by augmenting axiom sets that the contexts are based
Copyright 1/21/2005 Justin Coslor
Axiomatic Visual-Layer Interpretation
Forming stronger linkages between axiom sets deepens the meaning of
content of all structures that are based on those axioms. It can also
complicate things by cluttering the contexts that those structures act
within if the linkages are formed sub-optimally. Such is the case of an
image with ambiguous layering. This has applications to steganography,
computer vision, and virtual-reality educational environments, etc.
Copyright 8/7/2005 Justin Coslor
Patterns In Contexts: 3D Engine
I think Java3D, combined with some inexpensive virtual reality equipment,
will be the ideal environment for exploring Patterns In Contexts theory
visually. Critical to that is a software that is able to parse video data into
2D objects and build 3D geometric reconstructions of those objects along
with the parameters of their observable range of motion, and do heuristic
guessing at the backsides of the objects that are hidden from view or just
make the 2D objects into 3D avatars that always face you regardless of which
side of theme you are on. That way, video data can be geometerized and
represented as Patterns In Contexts, and 3D worlds can much more easily be
created by mixing together objects and behaviors from an enormous archive of
experience (from video sources) that is all parsed and sorted categorically by
a visual dictionary that maps adjectives and nouns and verbs to pattern
properties such as qualitative geometric relations, axiomatically defined
variables and operations, and contextually associated references of objects
and their pattern groupings. Each entry of the visual dictionary will contain
an up-to-date list of all objects in the pattern archive that contain the
geometric or otherwise visual property defined by that visual dictionary
entry. Scale, color, orientation, state, position, and quantitative data in
many cases can be ignored by the visual dictionary, unless the entry is
directly intended to describe one or more of those properties.
Copyright 1/9/2005 Justin Coslor
Graphical Representation and Visual Heuristics
Make a website loaded with graphs, diagrams, flowcharts, and simplified
geometric reconstructions of stuff, events, places, flows, tools, intellectual
understanding, interpretations and translations, programs, systems, etc. Call
it "mapworld" or "graphworld." Make webcrawling intelligent agents that
generate extensive thorough, and systematic visual dictionaries online.
Similarly, there should be a webpage utility where you can enter the
URL (Uniform Resource Locator = website address) to some text or copy/paste
in some text directly and it could try to abstract visual perceptions of the
text content's meaning and represent it in the form of a diagram or graph,
etc. It could also try researching images on the internet that are related to
the text. I realize that the second part might be difficult, since there
aren't very many visual dictionaries in existance yet, and computer vision and
machine learning technologies may not be that advanced yet (but maybe they
are...?). Heuristics (guess-work on visual data and in language processing is
just a matter of logical deduction, manual training of Bayesian statistical
and Connectionist techniques, and
metaphoric/analogical/cross-domain-relational mappings across contexts,
to bridge systems not yet adapted to each other.
Copyright 7/20/2005 Justin Coslor
Creativity & Understanding
Language is permutations of semantics, governed by syntax and context,
with meaningful intention.
What is the language of creativity?
What are its semantics?
What is its syntax?
What is its context?
The language of creativity always contains either:
1. new semantics or new permutations of semantics, and/or
2. new syntax, and/or
3. new context.
*Creativity does not always convey meaningful intention.
The semantics of creativity are new patterns and/or old patterns thought
of in new ways (recontextualized patterns). The syntax of creativity is
either internally defined by the language of the format (if the format is
known), or else (if the format is new) it is externally defined by the
naturally occurring partitions and connections of the organic objects and
systems of developments of the natural universe, or by the connections and
partitions present in the diagonalizations of synthesized patterns juxtaposed
through a relational operator or operation, and/or the diagonalization of the
juxtaposition of synthesized patterns and natural patterns juxtaposed through
a relational operator or operation, and/or the diagonalization of the
juxtaposition of natural patterns juxtaposed through a relational operator or
The context of creativity is always at least partially new. Creative
expressions composed entirely of entirely new patterns (not just modified
ones) in entirely new contexts with external syntax that has never before been
known of and that is unrelatable to known syntax will always appear random and
entirely undecipherable unless the person or interpretation program is capable
of analogical abductive reasoning. However there will be no conclusive proof
that the analogies drawn will be correct. The analogies may be qualitatively
correct in the metaphoric sense, but they will never be proven quantitatively
correct to the knowledge of the analyst. There has to be some decoding method,
key, or common ground known to the analyst in order to decipher such a
creative expression.
Copyright 7/17/2005 Justin Coslor
Layers of states and states of layers (As in "finite element state
machines" and similar systems):
Mathematics -> connections and differences in maps of possibilities
Philosophy -> depth of possibility maps models of truth progressing
Science and Technology -> exploration of possibilities through careful
experimentation and adaptation to discoveries
Can you think of more? It is definitely possible.
Look for stuff like those descriptions. Juxtapose operators and abductively
reason into applications.
Copyright 7/8/2005 Justin Coslor
Measurement Systems
In measurement, two or more quantities or qualities are compared to one
another, such as a unit of measure applied to a starting point and ending
point of another object. When a unit of measure is undefined, you look for the
minimum unit(s) of commonality between the objects and mark the overlap points
and the center-points between the starting and ending points, and the center
points between those points, etc. If any number systems or other patterns are
used as division or counting units (such as prime numbers), as well as
center-point binary tree parsing, we realize that "all measurement is really
comparison by parsing or partitioning". The units of the partitioning or
parsing can be native common denominators of the observer's perception system
and the object.
The intersection of the juxtaposition of multiple objects is another
native unit of parsing, which itself can be parsed into smaller units via a
number system or other pattern. Common ground or compatibility is necessary
for comparison, and since measurement is a form of comparison, measurement is
an act of perception adaptation via parsing or partitioning. It's the act of
trying to perceive of an object via the perception system of something
else, and often times perception systems miss a lot because there are often
lots of valid ways for a particular observer to perceive of things, and it's
an undecidable problem about whether a perception system is not recognizing
other undefined potential aspects of the object, let alone know what it is not
perceiving through its axioms and atomic units of partitioning, and methods of
parsing and grouping, and methods of determining anchor points,
interpretation, starting and ending points, edge detection, pattern layering,
and buffer sizes and contextualization, etc.
Active measuring is when ea system's partitioning structure and
methodology/reasoning system is constantly updated as something is being
measured. An example of active measuring is a system capable of learning, such
as an adaptive or evolutionary perception system, such as an artificially
intelligent reasoning system or human being. A perception system that is
merely adaptive but not evolutionary is autonomous or semi-autonomous, but not
intelligent, since it only knows the context that it currently exists in. By
storing perception systems adapted to multiple contexts, a system can then
often map out the commonalty and differences between each context and form a
general common-sense perception system which can be analyzed inductively,
deductively, and abductively by its reasoning engine.
Analysis via comparison of the domains and ranges of functions that exist
in different contexts is an abductive reasoning process since it is a form of
analogical reasoning. Once again common ground must be mapped between the
functions being compared or else an external perception system will have
to artificially map its units onto both functions so that compatible parsing
and partitioning can proceed in a measurable, if not blind (thus artificially
simulated) representation.
Passive measuring is when the measurement and perception system's
reasoning engine is not updated by internal induction, deduction, or abduction
during measurement, nor after measurement. Passive measurement is merely
mechanical and not adaptive or evolutionary.
Copyright 7/2/2005 Justin Coslor
Re-contextualized Patterns
It's interesting how patterns and their implications change as their raw
data is re-contextualized and/or perceived from different perspective systems
and contexts. The parameters of each context shapes the possibilities of its
patterns' applications, implications, and recognized states of existence.
Often times the possibilities of contexts overlap, and are subjective in
the sense that there may exist several possible ways to perceive of and
interpret a context, where each way may have equal or varying levels of
probable truth in its systems, depending on the perspective system and
intentions/expectations of the observer and/or the controller.
Copyright 6/25/2005 Justin Coslor
Observing patterns and differences
Combining my poem about "Sight" with my poem about "Reasoning Engines",
leaves me thinking about the line "from color comes shape" and the line about
"thinking as storing and grouping knowledge", and how it takes a pattern to
perceive of a pattern, such as one colored shape outlining or juxtaposing
against another colored shape, and how each of these shapes (and color
information) gets stored as a piece of knowledge (a pattern), and how both are
grouped together by their situational context. The differences between them
are patterns not origininally apparent in either piece of knowledge prior to
their comparison, unless those patterns are stored in the perceiver's virtual
knowledge base from prior experience or innate programming.
So you can try grouping every atomic pattern with every other atomic
pattern (time allowing), and as long as you're working with more than a
one-dimensional medium, the differences between each atomic pattern being
compared one-to-one will constitute a unique atomic pattern. This sort of
comparison is one way of coming up with new knowledge in mediums that exist in
two-dimensional (or greater) qualitative and/or quantitative and/or
conditional mediums, and mediums that combine different types of properties.
* Comparing unequivalent objects always creates partitions in either one or
both of the objects. The remainder partitions are sometimes entirely knew but
virtual objects. *
From color comes shape,
and from shape comes size,
we triangulate images
that come into our eyes.
"Reasoning Engines"
1. Knowledge as patterns in contexts.
2. Thinking as storing and grouping knowledge.
* Language contextualizes perceptions. The language used in each perception
identifies and indicates patterns that have been parsed through comparison. *
Copyright 6/24/2005 Justin Coslor
Pattern Matching
Previously I've written about how if you divide a circle into a
bunch of equiangled sectors and if there is a prime number of sectors
then no symmetrical alternating coloring patterns exist, but if there is
a non-prime number of these equiangled sectors, then you can color in
alternating sectors or groups of sectors to form symmetrical patterns
that correspond to each of the composite number pieces.
To apply this to pattern matching, simply cut the circle so that its
sectors lie in a straight line and then look at the coloring patterns to
match pieces of that linear pattern to strings of numbers, where each
color might be a particular number, or just do it in binary. In this
manner you can make numerical landmarks in raw data streams to look for
patterns within potentially random data.
When only a piece of one of these composite number symmetry patterns
shows up in a linear data stream, that may indicate that other layers of
patterns may be overlapping it. The thing that makes these patterns
recognizable from randomness is the juxtaposition of their unique
alternating prime partition patterns. An individual prime partition
pattern piece that has been linearized is indistinguishable from any
other linear prime partition pattern piece unless you know for sure that
you're seeing the whole thing. But when you juxtapose two or more of
these patterns together in the form of a composite symmetry pattern even
a fragment of that pattern can dramatically narrow down the
possibilities of its origin. Copyright 6/20/2005 Justin Coslor
Remote-Controlled Contexts Via Preprocessor Switchboards (See Diagrams)
Instead of having injective, surjective, and bijective, maybe there
could be a preprocessor module that is bijective that goes in front of
all surjective and injective relations. For a surjective relation: P1 =
surjective ARP1 = bijective ARB = surjective = ACP1B For an injective
relation: ARP2 = bijective P2RB = injective ARB = injective = ACP2RB A
and B are domains P1 and P2 are preprocessors R is a relation, C is a
cross-domain relation.
In effect, the preprocessor becomes a duplicate of the domain
element in A, but independent of the context of A. So since the
preprocessing is done outside of A, you can have single-line inputs from
A, and you can take several domain elements out of their contexts and
perform their relations via remote control.
In the second diagram, the cross-domain relation BCP2 is turned off,
so context D doesn't contain its relation (P2RD) unit P2 gets turned
back on. In that diagram, D is a remote-controlled context via the
preprocessor operations switchboard S.
A, B, and C are each in their own contexts and they combine in
context D. The preprocessor modules allow for simple remote control like
an operations switchboard. Copyright 6/12/2005 Justin Coslor Definitions
Defining something by cataloging it's properties and relations is
blind unless you specify the particular context of the thing, and the
sub-contexts of the properties and relations it is composed of. Context
is both an exoskelletal structure as well as an endoskelletal structure.
Context is is defined by both the external limits as well as the
internal limits. Copyright 6/5/2005 Justin Coslor Geometric Abstractions
When doing abstraction on geometries and photos of patterns (symmetry
formations, repetitions of patterns, and that which is recognizable from
randomness), maybe all that is needed is a map of intersection points
for each level of connectivity: i.e. a map of all points where two lines
intersect, a map of all points where three lines intersect, etc. The
union of all of those maps should form a sufficient geometric
abstraction to recreate a recognizable approximation of the original
model of photo patterns. Copyright 6/4/2005 Justin Coslor Index of
Topics *(Remember to finish adding topics to this index, as it is only a
partial list of ePIC-related topics I've written about so far.) choice
creativity patterns contexts variables properties relations:
quantitative, qualitative, cross-domain, analogical abstraction models
simulations axioms: key, branch knowledge: implicit, explicit,
representation intuitions complexity progressions pattern details
randomness analogical recursions question asking systems question
expectation templates object-oriented processing operation spaces: grids
v.s. networks analogy metaphor examples Copyright 6/4/2005 Justin Coslor
Abstract relations are relations described by descriptions that are
the simplified form of lexicons, where the details have been stripped
and only the categorical data remains, along with some quantitative data
(possibly. . .I'm not sure yet....), such as the dimensions and data
types. Relations are fairly easy to abstract because you can just build
an itemized list of the operators and verbs used on or in the general
context of the domains that use them. Copyright 6/3/2005 Justin Coslor
(See example diagrams) If a domain A is cross-domain related to a domain
B analogically, that relation can be injective, or subjective; or if it
is bijective, even if it's bijective to another element in the domain
than the starting point, then we can say that the relation is recursive.
This is an example of analogical recursions, because since all bijective
relations are recursive, and analogical reasoning deals primarily with
cross-domain relations, then all cross-domain relations that are
bijective are analogical recursions. Another form of cross-domain
analogical recursions comes from alternating back and forth through a
set of relations between two or more domains, where the active element
in the active domain is determined by some function on the ordering of
the elements in that domain (a sequence function on the cardinality).
Injective analogical recursions can also exist in a back and forth
system that ultimately loops between the various domains of two or more
contexts. Copyright 5/25/2005 Justin Coslor Implicit V.S. Explicit
In knowledge bases, facts and data are stored in patterns and
contexts explicitly, but that same information may also belong to other
contexts, and can be arranged into different patterns and may have
unidentified relations to patterns in that data set and/or to patterns
not in that data set.
Often times there are multiple hierarchical levels and recursions of
patterns in contexts and sub-contexts in patterns, and bridging across
these levels are more of the same in many cases. Data that is implied
can be treated as though it is hidden, though its role may be very
important in the context of the data that depends on it. In the
perception of questions, lots of implicit patterns and contexts are
necessary to generate and adapt simulated models of the knowledge that
is involved with the possible ways to represent the meaning of the
question, as well as for generating models of the expectation parameters
of the context templates involved with goal search, answer retrieval,
and answer formulation (for discovering or constructing suitable content
of the right level of detail). This is because every question is the
intersection of multiple contexts, or rather every question is an
attempt at adapting multiple contexts into compatibility, and thus
unknowns must be declared. Copyright 5/16/2005 Justin Coslor Analogy,
Metaphor, and Examples Now due to my lack of a dictionary on hand I'll
create some of my own definitions (the names can be changed later). An
analogy is like half of a metaphor. An analogy gives an elaborated
example of a relation, whereas a metaphor gives an example of a relation
across multiple contexts (a cross-domain relation). An example of an
analogy is like saying: An apple is like an onion. Both rot, and are
edible. An example of a metaphor is: Apple is to onion as postman is to
salesman. An analogy is essentially a simile plus a moral or
explanation/elaboration. A metaphor may describe the same relation(s) as
an analogy in that it juxtaposes two or more pieces of information. This
is similar to generating a unique diagonal length from a box generated
by using one sequence or variable quantification as the x axis and
another sequence or variable quantification as the y axis to produce a
unique qualitative variable or sequence... Add more dimensions to the
diagonalization to combine more variables or sequences or functions...
Then just rotate the diagonal axis until it is horizontal. But metaphor
goes a step farther and presents another example of that relation, but
in a different context. *Examples are contextualizations of patterns. A
relation between qualitative variables is thus a diagonalization of
their quantitative mappings. In this way, qualitative mappings can be
represented geometrically. Patterns are composed of variables and
relations between variables. **Variables are usually qualitative
property sets that have been quantitatively mapped into juxtaposition
with their enumerated algebraic repetitions. Juxtaposition via
diagonalization is a form of an operator. ***Operators are forms of
juxtaposition of variables and patterns. Addition sequentially
juxtaposes variables and patterns on a grid. Subtraction is the opposite
of addition, as it removes variables and patterns from a grid.
Multiplication sequentially adds to columns of categories, one category
at a time. Division de-references and parses columns of categorical
values, and is the opposite of multiplication. Addition, subtraction,
multiplication, division, 2D geometry, trigonometry, algebra, calculus,
etc, ... all are operations that can be performed on a grid. Change the
operation space (i.e. change the context), and the axioms that these
operations are based on may no longer apply; but some may, and those are
the axioms we want to collect for a wide range of adaptability, and can
be used in forming general systems theory grids and networks.
As far as I know about operation spaces, there are grids and there
are networks. Each can be within each, they can come in many different
forms, and translations are possible between them, but the translation
between a grid and a network always relies on a core set of axioms that
are in common between the two data structures. Copyright 5/4/2005 Justin
Coslor (Based on a theory I had around the year 2000) Sight --------
From color comes shape, and from shape comes size, we triangulate images
that come into our eyes. --------------------------- Fall 2001 to
4/25/2003 Justin Coslor My fundamental theorem of Computer Vision: I
believe that from color comes shape and from shape comes size;
comparatively/relatively/contexually. I'll have to read about the
cognition of vision to fill in the details and check out software and
plasticware/firmware/hardware models of visual perception. Learn known
mathematical techniques. Copyright 5/6/2005 Justin Coslor Rules Are
Behavioral Expectations Here are some types of rules: Laws, priorities,
environmental limitations (physics), trends, norms, common sense,
personal limitations, societal beliefs, personal beliefs, lazy
tendencies & optimizations, conditions, terms of use or license
agreement, policy, ethics, morals, probability judgments, priority
judgments, game theoretic strategy, preemptive negotiation, real-time
negotiation, post hoc proc negotiation, design considerations,
navigational control, pattern guidelines, pattern maps, mathematical
modeling and calculation, combination possibilities, case-by-case
possibilities; forum dimensionality, axioms, theorems, and restrictions;
units and parsing and sorting methods and requirements; activation,
deactivation, and flow control theory, network access methods, network
exchange methods, network dynamics. Here are some qualifiers for those
kinds of rules: Global, situational, regional, local, continuous,
temporal, static, dynamic, linear, parallel, hierarchical, symmetric,
independent, context specific, general, intentional, unintentional,
conscious/unconscious, automatic, manual, modal, type, categorical. Find
an ontology that lists concepts related to a given concept, in a
hyper-linked format. Similar to encyclopedia references (see
Wikipedia.org) or book topical references in the public library's card
catalog. Copyright 1/7/2005 Justin Coslor Categories: Part 1 Even if
categories get proven to be inaccurate (*Are accuracy proofs based on
any subjective information?), then useful information about the
compatibility of the data elements can be discovered as parameters get
refined. Ultimately, it is the compatibility of the elements, both in
and between data sets, that makes the fundamental definitions of the
categories. 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.
Guessing about Neural Architectures... This is a journal entry,
Copyright 9/12/2004 by Justin Coslor.
I could be totally wrong about this, but it is currently presumed,
by me at least, that neural architectures tune to, receive, translate,
and transmit various wavelengths of patterned energy configurations. The
tuning functions may be in one unit, the receivers/input devices may be
in another unit; the translation/manipulation apparatus may be in
another unit; the translation/manipulation apparatus may operate in a
unit of its own, and the transmission/re- communication apparatus may be
in a unit of its own as well.
There is likely data loss in the imperfections and limitations of
the tuning apparatus, the receiving apparatus, and the re-transmission
apparatus successively; however, the translation/manipulation apparatus
may apply experience-based heuristics to fill in the holes and sharpen
or simplify the distortions and puzzles in the data field. Each cluster
of nodes, as well as the relation nodes themselves sometimes perform
negotiations for syntactic and semantic consistency. Such negotiations
are likely interfaces composed of multi-purpose reconfigurable general
cellular nodes. Meaning might be derived from information streams by
creating translations and equivalence representations in other classes
and other contexts, and by defining and rating utility functions and
organizing them in such a way that their priority can easily be
determined relevant to the general function of the class of relations
they belong to in generalized/easily-specialized contexts. The neat
thing about information, rather than cause and effect, is that it can be
re-conceptualized and re-contextualized and re-framed/re-patterned.
10/22/2004 Justin Coslor (after reading pg. 11 “Modern Algebra” by
Gilbert and Vanstone) Some methods of Proof: - Assumptions (context) -
Examples of problems or experience - Critical questions of interest -
Representative language choice -Translation/Mapping -> same or different
context? - Inventory of context axioms - Define critical question's
search scope - Assume all questions are somewhat answerable - Convert
other knowledge into current representation and abstract relationships
without regard to hierarchical depth - Group compatible relationships -
Mark partial compatibilities as overlapping sub-contexts - Hypothesize
mappings that assume each relationship to be the answer to a series of
questions - Look for hypothesized questions similar to questions of
interest - If found, remap original examples in terms of those similar
mappings of hypothesized questions - Define inconsistencies and address
them - Represent conclusion - Explore relations of conclusion to other
contexts - Blah blah blah, I should study more. 8/12/2004 Justin Coslor
Axiom Notes (Here are some note I took at the public library today.)
Structuring XML Documents / David Megginson CLP MAIN SCI&TECH QA76.76H94
M44 1998 The National Strategy To Secure Cyberspace February 2003
http://www.gpoaccess.gov - Perhaps people and machines should be trying
to prove the limits of proof. - There are many shapes of non-Euclidean
geometric reality. - Perhaps quanta of energy is a form of matter that
exists on non-Euclidean spiral and tubular planes? Maybe quanta breaks
off from matter and electrons that exist on non-Euclidean spherical
planes during orbit changes and altitude changes? I read part of the end
of the book Thinking about [TLC] LOGO: A graphic look at computing with
ideas. pg. 206&207 ISBN 0-03-064116-0 Each set of axioms is based on a
unique working model of the universe. (Regardless of the completeness of
the model.) In many cases, there is some overlap between different sets
of axioms, because many contexts have some properties and/or patterns
that are in common. Metaphoric operations describe the relations between
the properties and/or patterns that are in common between unique
contexts. More than that, each set of axioms attempts to define a
working model of the universe, and that no model of the universe is
complete (hence it is a model) other than the universe itself; and from
within the universe, a model of the universe can only be approximated,
and to a varying degree of accuracy and/or applicability at that.
8/20/2004 Justin Coslor Update: So essentially, a set of axioms is only
as good as the model they attempt to describe. Copyright 6/8/2004 Justin
Coslor Contexts
A context is a relation that defines a group of patterns. A pattern
that is not related to any other patterns is isolated, and can for the
most part be considered "invisible" to other contexts. A context can
also be considered to be a pattern, and can sometimes also be considered
as subject to this "isolation" concept. Patterns that exist within
networks of contexts are the most easily located, since cross-domain
relation-based experimental search and discovery methods need not be
applied to locate or define them, as is necessary in many cases to find
isolated patterns (i.e. island knowledge). Networks can consist of
relations (surjective, injective, and bijective ) and cross-domain
relations (which are potentially multi-node route reverse-surjective
relations). Data turns into knowledge as the patterns and contexts and
networks of contexts are mapped out. Copyright 6/5/2004 Justin Coslor
Every multi-state organization or cognitive organism exists on a
higher plane than it is capable of perceiving, because nothing can
monitor every aspect of itself (unless every cell is symmetrically
identical) since the monitoring devices (sensors, etc), even when
recursive, cannot monitor every aspect of themselves. This is because in
order to perceive of something we must classify it in terms of something
else we have perceived, and since we were born in motion, our
consciousnesses pass forward from state to state, processing information
(perceiving of things in terms of the physical universe) until parts, or
the entirety of our bodies have fully ceased to move (i.e. until the
breakdown of the subparts).
As Godel's theorem implies: "no set can map its powerset". After
some developed mental subparts have broken down, the structures of the
consciousness that they were physically translating may continue to
operate outside of the rest of the brain's physical time-frame. The
latency of the various cognitive architectures in the brain may have a
great deal to do with the relativistic self-observations of
multi-sensory experiences. Since after all, some parts of the mind/body
connection and mind/brain connection operate at near the speed of light
(as electrons flow between the parts of each cell). Copyright 8/10/2005
Justin Coslor Perception -- continued from 6/5/2004.... On 6/5/2004 I
wrote that "The latency of the various cognitive architectures in the
brain may have a great deal to do with the relativistic
self-observations of multi-sensory experiences." In other words, people
think at different rates and depths from time to time, and that can
create recall and encoding obstacles in grouping and interfacing
memories between different cognitive states. However, those kinds of
qualitative and quantitative differences between the contents of
memorized perceptions can create bridges into depthier re-perceptions
for recognition into fine- tuned contexts. 5/17/2003 Justin Coslor A.I.
Notes Today I did a http://Google.com search on OpenCYC
Thought Treasure V.S. OpenCyc came up. I guess both are major
knowledge base ontology management systems, i.e. Reasoning Engines.
Thought Treasure seems to have more stuff for Natural Language
Processing than OpenCyc, but it is only free for noncommercial use. The
Cyc technology though is the world's largest and most complete general
knowledge base and commonsense reasoning engine. The CIA uses it, and
did about 500 man-years worth of data-entry into to. OpenCyc is a much
smaller subset of Cyc, and is open-source.
Cycorp runs opencyc.org, and also makes ResearchCyc for R&D in
academia and industry. Dependencies: none Languages: CycL, SubL, Java
(other API's on the way) Platforms: Linux (Win32 coming soon) Sites:
http://opencyc.org foundry.ai-depot.com/Project/OpenCyc /Amygdala /Fear
/GAUL /Joone /LogicMoo /OpenAI /SigmaPi /Simbrain 10/20/2004 Justin
Coslor Mission Statement
Free open-source software is quite possibly the best hope, in
conjunction with the freely accessible Internet, to give the common
citizens a fighting chance at building foundations for their decendents
in the midst of the mechanized empires of greed that thwart and encroach
on their liberties and livelihoods in their attempts to squeeze and
control the creative potential of supposedly free individuals who might
otherwise be nurtured to blossom as citizens of a humbly selfless and
harmonious planet Earth, that we all know can happen.
This is an unfinished work and I disclaim all liability.
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