Copyright © 2009 C. J. Lofting
1 distinguish, discriminate, contradistinguish, separate, contrast, oppose, set off or apart, tell apart: They must learn how to differentiate one species from another.
2 modify, specialize, change, alter, transform, transmute, convert, adapt, adjust: All organisms possess the power to differentiate special organs to meet special needs.
integrate v. combine, unite, blend, bring or put
together, assemble, merge, amalgamate, join, knit, mesh, consolidate, coalesce,
fuse; US desegregate: We must integrate all the parts into a coherent whole.
Several cultures have been well integrated into our community."
Through an analysis of the manner in which the brain appears to deriving categories of meaning, an upper ontology is established by creation of an abstract domain model usable to translate meanings across specialist domain models, where such models are derived from recursion, and in so doing highlighting the core methodology used in the brain for meaning derivation, real or imagined. The focus of the work is on (a) identifying the general methodology for meaning processing by humans and (b) introducing a basic ground for meaning derivation/communication by AI systems. In the process of identifying the general methodology in meaning derivation we identify a core property of recursion that allows for the emergence of language and consciousness.
In accord with the perspective of a common ground for all meaning, George Spencer-Brown wrote:
“It becomes apparent that if certain facts about our common experience of perception, or what we might call the inside world, can be revealed by an extended study of what we call, in contrast, the outside world, then an equally extended study of this inside world will reveal, in turn, the facts first met with in the world outside: for what we approach, in either case, from one side or the other, is the common boundary between them” p xxv Spencer-Brown. G., (1972) “Laws of Form” EP Dutton
The IDM (Integration, Differentiation, and Meaning) template, defined in the following, represents an abstract domain model derived from considerations on what the brain appears to do in the derivation of meaning. The general focus is in the context of an upper ontology:
"In information science, an upper ontology (top-level ontology, or foundation ontology) is an attempt to create an ontology which describes very general concepts that are the same across all domains " from a detailed text at Wikipedia
The IEEE group focused on such (http://suo.ieee.org/) covers:
“Ontology : An ontology is similar to a dictionary or glossary, but with greater detail and structure that enables computers to process its content. An ontology consists of a set of concepts, axioms, and relationships that describe a domain of interest.
Upper Ontology : An upper ontology is limited to concepts that are meta, generic, abstract and philosophical, and therefore are general enough to address (at a high level) a broad range of domain areas. Concepts specific to given domains will not be included; however, this standard will provide a structure and a set of general concepts upon which domain ontologies (e.g. medical, financial, engineering, etc.) could be constructed.”
The IDM work derives a set of categories stemming from recursing the differentiate/integrate dichotomy, simplified into the WHAT(who,which)/WHERE(when,how) dichotomy used in neuroscience texts, as used in our brains. Given the recursion of that dichotomy, the IDM work takes specialist domains derived from recursion of dichotomies and shows how they can be mapped semantically through the IDM template and as such show those specialist domains as products of brain oscillations as the brain derives categories usable for meaning derivation in general where particular forms are expressed in specialist labels of specific domain models.
From studies on the neurology we map out a base level set of categories of ‘meaning’ pre any act of symbolism/metaphorcation. We demonstrate this base level as the seed for all symbolisms/metaphorcations and bring out the use of recursion to move perspectives from a mechanistic, literal, descriptive dynamic to an organic, figurative, normative, and so teleological, dynamic.
This base level reflects properties associated by Jung with the notion of the Collective Unconscious:
“…it must be pointed out that just as the human body shows a common anatomy over and above all racial differences, so, too, the human psyche possesses a common substratum transcending all differences in culture and consciousness. I have called thus substratum the collective unconscious. This unconscious psyche, common to all mankind, does not consist merely of contents capable of becoming conscious, but of latent predispositions towards identical reactions. The collective unconscious is simply the psychic expression of the identity of brain structure irrespective of all racial differences. This explains the analogy, sometimes even identity, between the various myth motifs and symbols, and the possibility of human communication in general. The various lines of psychic development start from one common stock whose roots reach back into the most distant past.” From “Commentary on ‘Secret of the Golden Flower’” CW 13 par. 11
Jung then went on to write:
"The collective unconscious - so far as we can say anything about it at all - appears to consist of mythological motifs or primordial images, for which reason the myths of all nations are its real exponents. In fact, the whole of mythology could be taken as a sort of projection of the collective unconscious" from the "Structure of the Psyche"
As such we see above the isomorphism of the AI concept of an “Upper Ontology” and Jung’s concept of the “Collective Unconscious” where both cover the sense of a core template for all meaning.
In the following, three specific domains are modeled - those of primary emotions and the categories derived from recursion of the fight/flight dichotomy, that of the I Ching and the categories derived from recursion of the yang/yin dichotomy and that of the classes of numbers used in mathematics.
Initially, each of the specialist models takes an applicable dichotomy and recurse it to the level of forming eight categories. There is a mechanistic, descriptive base at work here. These are then extended hyperbolically (N2 as compared to exponentiation's 2N) to give us 64 categories that reflect a previously un-identified property of self-referencing, the organic, the normative, the teleological. (the set of categories serves as a source of analogy in identifying finer details of each category. We see here emerge the core properties of language and that includes ability of a language to describe itself).
In the context of dichotomy usage, George Kelly, the founder of Personal Construct Psychology, wrote:
"Our psychological geometry is a geometry of dichotomies rather than the geometry of areas envisioned by the classical logic of concepts, or the geometry of lines envisioned by classical mathematical geometries. Each of our dichotomies has both a differentiating and an integrating function. That is to say it is the generalized form of the differentiating and integrating act by which man intervenes in his world. By such an act he interposes a difference between incidents -- incidents that would otherwise be imperceptible to him because they are infinitely homogeneous. But also, by such an intervening act, he ascribes integrity to incidents that are otherwise imperceptible because they are infinitesimally fragmented. In this kind of geometrically structured world there are no distances. Each axis of reference represents not a line or continuum, as in analytic geometry, but one, and only one, distinction. However, there are angles. These are represented by contingencies or overlapping frequencies of incidents. Moreover, these angles of relationship between personal constructs change with the context of incidents to which the constructs are applied. Thus our psychological space is a space without distance, and, as in the case of non-Euclidian geometries, the relationships between directions change with the context." (Kelly, 1969)
Kelly brings out the recursive hierarchy in defining categories where, in his original text, The Psychology of Personal Constructs Vol 1, he spells out the concept of Hierarchical scales (pp 99-100) where he writes:
"Just as it is possible to express an infinite number of gradations of value in terms of binary number systems, so it is possible to express an infinite number of gradations of value in terms of a dichotomous construct system. One may construct such a scale by assuming a hierarchy of construct.
Consider a hierarchy of four constructs in the order of A, B, C, and D, each of which has two possible values, 0 and 1. A hierarchical scale of values may be built up from these four constructs. It will have log2^-1 4 or sixteen steps. The values of the sixteen steps can be represented by the first sixteen numbers of the binary system as follows:
Suppose we build a hierarchical scale of integrity vs disintegrity out of four basic constructs of honesty vs dishonesty, candour vs deviousness, courage vs defeatism and objectivity vs subjectivity. Suppose also that these constructs are arranged in that hierarchical order. Let the binary digit 1 represent the first of each pair and the binary digit 0 the second of each pair. A dishonest, devious, defeatist, subjective person would be represented by the scale value 0000 and would be at the disintegral end of the scale. An honest but devious defeatist, subjective person would be represented by the number 1000. Because if the high relevance of honesty to integrity, he rates in the upper half of the scale. A person who was dishonest, devious, defeatist, and objective would be represented by the number 0001 and would still be near the bottom of the scale" pp99-100
Recursion, extending into the concept of self-referencing, utilises (a) a generic dichotomy, (b) our attention system, and (c) the passage of time, to generate the set of basic, universal, categories mentioned previously. The attention system focuses and so encapsulates 'something'. The generic dichotomy is any specialist form that is synonymous with the WHAT(who,which)/WHERE(when,how), also known as the differentiating/integrating, dichotomy. This dichotomy is fundamental in that it reflects the information processing dynamic of our brains and is a dichotomy of mediation - a property of all asymmetric dichotomies (these are in fact compressed forms of TRIchotomies).
At the level of the ‘collective unconscious’ or our abstract domain model of our upper ontology, (layer “0” in the below diagram) we are dealing with meaning in a SINGLE context, a base level of the neurology. As such there is isomorphism between Jung’s concept of a Collective Unconscious and the AI concept of an upper ontology and what IDM claims is in identifying this base level structure of meaning.
Thus ANY concept will relate to this base level and so understanding the properties and methods of this level presents us with the set of POSSIBLE meanings ecapsulated in any concept/symbol developed in levels “1” and “2”. The APPLICATION of a meaning is then validated heuristically and so brings out the influences of context on ‘skewing’ perceptions/cognitions.
Included in this set of concepts and associated meaning is the concept of “consciousness” and so the ability to lay out all classes of consciousness where uniqueness is in an instance of a class where local context contributes with specialist associations etc.
All of the DIFFERENCES we see in attempts to define, for example, consciousness reflect specialist domains and so attempts to define a set of labels and all highly subjective since each is proposed by a unique being.
Consideration of the dynamics of the neurology, we notice its hierarchy and so maintenance of ‘old’ structures rather than eradication of those structures. The brain has developed from mindless evolution and so dialectical negation (keep the ‘good’ bits) dominates over analytical negation (being ‘born again’ – wipe the slate clean) – most of the theorists seem to be idealist and analytical in thought but nature appears to be more materialist and dialectical in behaviour.
Thus the level of LABEL creation is a giant leap in mulitiple context/sub-context management but is still resting on the older levels that are single context in focus.
Given this, so we can create sets of labels, zoom down to the ‘same context’ level where meaning as patterns/feelings flow (the ‘collective unconscious’ realm etc) and map those labels across to the same patterns associated with another set of labels.
Thus the CORE set of POSSIBLE categories of “consciousness” are manifest in the ‘collective unconscious’ level or ‘upper ontology’ level (as an abstract domain model) and IDM maps out the properties and methods of such categories to give us all that is communicatably possible (anything outside of that set will be interpreted from WITHIN that set and so present as if paradox).
What is implicit here is consciousness as an agent of mediation and so an agent grounded in symbol manipulations, both verbally and non-verbally. As such the hierarchy present suggests what is BELOW the level of label production is BRAIN and what is at and above that level is MIND. MIND is not ‘free’ of BRAIN but reflects an emergent property of such hierarchies grounded in neural mass and connectivity.
The MORE we develop ‘mind’ so the MORE we develop language and our mediation focus and so the MORE we develop consciousness.
MIND is dependent upon BRAIN, can never be free of such, IS SUCH, for meaning derivation and that includes the use of analogy/metaphor where such covers the emergence from LITERAL, same context, experiences to communicating many contexts through use of the FIGURATIVE in the form of label creation/usage.
Overall this dynamic covers the translation of differences and the asymmetric to sameness and the symmetric, where it is the realm of the symmetric that allows us to communicate through consensus (‘sameness’). This realm of the symmetric is also the realm of instincts/habits and so generals that act to filter experiences. Thus the use of instincts/habits act to generalise an experience but in doing so can lose precision in that experience. (This can have an affect on the development of logic in the species - see such works as Matte-Blanco's "The Unconscious as Infinite Sets":
Ignacio Matte Blanco, The Unconscious as Infinite Sets, Karnac Books, 1998 (originally published 1975)
A cognitive analysis of specialist perspectives bring out the grounding of such perspectives in the single context identified in the above diagram, where all difference in the form of labels is removed to give us the basic qualities of differentiating/integrating. An example of some of these specialist perspectives, in the form of specialist dichotomies, covers the context of information processing where it does not matter what is going on physiologically, the overall focus is on dealing with patterns derived from recursion of the differentiate/integrate dichotomy (reflected in brain oscillations and lateralisation) where such is specialised into such forms as:
discrimination / registration
difference / sameness
XOR (exclusive OR) / EQV (equivalence) (mediation across this dichotomy covers asymmetry and the IMPlies operator of logic)
object (thingness) / relationships (implicit object through linking relationships)
concentrated (point) / diffuse (point as if field; covers lack of resolution power)
metonymy (part as if whole) / metaphor (whole through analogy/metaphor use - and so all metaphors are interchangeable where this brings out a focus on equivalence where such is a property of symmetric perspectives and covers the post-modernist view of 'any metaphor will do' in describing/representing reality. Issues then emerge when the metaphor is taken literally.)
We can turn these into TRIchotomies with the act of mediating across the dichotomy and so making the dichotomy asymmetric (IOW an asymmetric dichotomy is a compressed form of trichotomy. When mediation stops so we fall back onto the stimulus/response nature of the dichotomy. More formally:
Representation = mediation(stimulus, response) first time through (where mediation is a function and stimulus and response are parameters) and then:
Representation = mediation(representation) ad infinitum (more so the recursion involved will elicit language).
Representation is in the form of a symbol for the original stimulus (and so a generalisation/simplification where we extract 'essentials') and a habit for the original response.
The nature of mediation covers positive feedback dynamics where we discretise and amplify something - and so tie to object formation. Thus we can add to our list:
positive-feedback (discretisation and amplification) / negative-feedback (error correcting, 'getting closer to' perfection)
far-from-equilibrium / equilibrium
single, local, context, "NOW" / multiple contexts (as memories, possibilities) "past/future"
FM-quality / AM-quality
holographic-like reference beam (the single context) / wave-interference patterns (hologram-like)
what was/is/will-be / what could-have-been/is-not/could-be
Of note is that the brain asymmetry (where we juxtapose anti-symmetry(part) with symmetry (whole) in the form of brain hemisphere differences etc) reflects the LEFT element of each of the above dichotomies as a 'part of' or 'emergent from' the right element.
At the same time the overall energy dynamics and interactions with local context bring out the left as more open-system, local context, enabling of transcendence, and the right as more closed-system, non-local context, enabling of transformation.
The path to transcendence is where we can transcend a part-as-whole paradox condition to 'give birth' to a new 'whole' (or perception of) in that a part can break free of the symmetry that is was bound to. This gets us into the dynamics of symmetry breaking and symmetry making.
Brains reflect attempts to manage all of these patterns and cover the development of that management in an ad-hoc form, reflecting the dynamics of networks where the determined, all is connected, properties of a regular network (genotype) are exposed to random network (environment) to elicit development of a small world network (phenotype). The ad-hoc nature of these developments brings out the dynamics of mindless evolution and so no knowledge of what is going on. With the development of consciousness we are getting to a point of now knowing what the brain is trying to do and so we can use consciousness to refine such activities.
Given our curent understanding of the neurology we can flesh-out the properties of the regular network and so identify the set of all POSSIBLE meanings. This is done through the simple recursion of the differentiate/integrate dichotomy as covered in the next section.
The methodology of recursion is where, once I make the distinctions of A and NOT-A, something as compared to all else, any attempt to go further in the analysis reflects taking the original distinctions of A/NOT-A and applying the A/NOT-A dichotomy to each element within the dichotomy, thus I zoom-in on the A and try to identify purer aspects of A as well as those aspects that are more NOT-A. This process means I am trying to differentiate all of the parts of what is under analysis, where the differentiation can be at the local level of what is WITHIN something, or at the more general level of relationships BETWEEN somethings, the latter being that I need to differentiate the nodes, the objects, between which there are relationships.
In general, for all
members of the species, the WHAT(who,which)/WHERE(when,how) dichotomy of our
brain focuses on (a) differentiation of some 'thing', and so focus on
discreteness, on an 'object', and (b) integration of many 'things' (at least
two) and so a focus on continuum, on relationships within and between 'things'.
From this cognitive level we can move into category/concept formation by
deriving basic categories abstracted from differentiating/integrating. These
A sense of wholeness.
A sense of partness.
A sense of static
relatedness (sharing space with another/others).
A sense of dynamic relatedness (sharing time with another/others).
We can extend these categories through use of a qualifier derived from the differentiating/integrating dichotomy to give us:
Wholeness through differentiation.
Wholeness through integration.
Partness through differentiation.
Partness through integration.
Static relatedness through differentiation.
Static relatedness through integration.
Dynamic relatedness through differentiation.
Dynamic relatedness through integration.
We can 'ground' these categories in the form of feelings that bring out the qualities:
Wholeness - sense of BLENDING
Partness - sense of BOUNDING
Static relatedness - sense of BONDING
Dynamic relatedness - sense of BINDING
Compound forms of these basic categories are derived where we focus on text/context relationships, thus we can have the category of "differentiated wholeness in a context of integrated dynamics" - or relabelled to use the contract/expand dichotomy and the qualities as expansive blending in a context of contractive binding.
The methodology used in deriving these categories is in the form of recursing the WHAT(who,which)/WHERE(when,how) (also known as Differentiating/Integrating, WHOLE-as-differentiation/WHOLE-as-integration) dichotomy to give us, after three loops, the above set of categories in the order of:
A cognitive analysis of the properties of differentiating as compared to integrating shows that there are issues of precision with the differentiating nature being more precise, more 'point' oriented, when compared to the integrating nature that is more 'field' oriented in that integration requires AT LEAST two points to be 'integrating'. Thus the precision of integrating covers the two points as compared to differentiating that can focus on one point. What this difference demonstrates is that the WHAT(who,which)/WHERE(when,how), or Differentiating/Integrating, dichotomy is ASYMMETRIC and as such, when made to self-reference, will elicit patterns associated with spectrum formation and so power laws.
A Symmetric dichotomy is where the elements of the dichotomy are structurally the same; it is their intrinsic values that differ. These sorts of dichotomies, when made to self-reference, elicit patterns associated with the Normal Distribution Curve (NDC - also known as a Gaussian Distribution). Symmetric perspectives lack the precision of the asymmetric but conserve energy through that focus on approximations. Thus it is LOCAL context that elicits high energy expenditure and so the non-local reflects a focus on conservation and maintaining equilibrium over the long term.
Of note here is the association of these dynamics with the Chaos Game - The containment of noise leading to the elicitation of spontaneous order by self-referencing. See such as covered in many websites on the 'net or in such texts as chapter 6 ("The Chaos Game: How Randomness Creates Deterministic Shapes") of:
Peitgen, Jurgens, & Saupe (2004)"Chaos and Fractals : New Frontiers of Science(2nd Edition)" Springer
The categories derived above apply to a SINGLE context and reflect a ‘brain’ level of meaning processing where there are no labels to differentiate DIFFERENT contexts. As such these categories present us with an “Abstract Domain Model” we can use, through labelling to represent and communicate ‘all there is’.
The following tables cover the generic form identified by IDM in the derivation of classifiers (categories as equivalence classes) for labelling to communicate meaning.
The Fundamental Object/Relationship Template Bottom-Up
The Parts(Object as relationship)
The Whole (Object)
When we include the expansion/contraction dichotomy, we get the full template serving as an abstract domain model:
The extended object/relationship template bottom-up
Contractive Static Aspects
Contractive Dynamic Aspects
Expansive Dynamic Aspects
Expansive Static Aspects
The Whole (Object)
We can covert the above to a "Feeling" format where we derive the four Bs of blending, bonding, bounding, and binding:
The mixing template bottom-up
The Whole (Object) - Blending
In principle this template is extendable through further self-referencing and forming composite classifications. Once we have set out this template we find that we can populate it with the fundamental characteristics of various dichotomy-derived disciplines and as such their domain models.
A major point to cover here is that the development of categories of meaning from recursion is initially mechanistic and descriptive. Reflections of such indicate it will disappear into the realm of the infinite regress and no more.
However, through analysis of meaning derivation we find that given depth in the recursion we hit a point where there is a ‘sudden’ change in that the categories derived become usable as expressing the literal and the figurative and there is a shift from the mechanical to the organic, the descriptive to the normative and so an emphasis on issues of logic, of ethics, of aesthetics.
When analysed from the BIT domain (described in the next section) we find that this sudden change stems from the application of recursion to what has already been recursed. There is a tie here to issues of symmetry and rotation in that rotation elicits a ‘parts list’ of a whole and reflects the use of anti-symmetry.
Spencer-Brown’s “Laws of Form” he writes:
“The theme of this book is that a universe comes into being when a space is severed or taken apart. The skin of a living organism cuts off an outside from an inside. So does the circumference of a circle in a plane. By tracing the way we represent such a severance, we can begin to reconstruct, with an accuracy and coverage that appear almost uncanny, the basic forms underlying linguistic, mathematical, physical, and biological science, and can begin to see how the familiar laws of our own experience follow inexorably from the original act of severance.
…Although all forms, and thus all universes, are possible, and any particular form is mutable, it becomes evident that the laws relating such forms are the same in any universe” p xxix G. Spencer-Brown “Laws of Form” EP Dutton (1972,1979)
"Anything that can be represented can be represented (in principle) as a string of binary digits via an isomorphic mapping, ... The process is similar to producing a string that is rather like the record of an extended game of twenty questions, with 1s conventionally representing affirmation and 0s representing negation. A successful series of guesses produces a truth table row that represents the original thing." (http://www.kli.ac.at/theorylab/jdc/information/information.html) In IDM we identify core qualities represented as 'bit' patterns (orderings of 1/0) serving as sources of meaning across the species, in GENERAL where the set of meanings are derived from mediation dynamics.
If we take the 1/0 dichotomy and recurse it we establish the BIT domain up to three levels of recursion with each BIT pattern read left-to-right, general-to-particular:
The BIT domain bottom-up
We note here the emergence of languages from each level of recursion. Thus:
The first level of the domain presents us with an alphabet of [0,1] symbols. The second level gives us an alphabet of [00, 01, 10, 11] and so on. As such each level gives us an alphabet of 2n symbols where n is the level number starting with n = 1.
Sentences are strings of symbols such that 100100 is interpretable as:
A string of 1s and 0s (level 1 alphabet)
A string of three pairs, 10, 01, 00 (level 2 alphabet)
A string of two triplets, 100, 100 (level 3 alphabet)
An incomplete string of level 4 and level 5 alphabets
A string of one hexagram 100100 (level 6 alphabet)
A language is a set of sentences.
A grammar is a finite list of rules that determine the expression of the language.
In the context of recursion, each level generates an alphabet derived from more generic symbols of the previous level’s alphabet and as such inherits generic meanings from those previous alphabets as well as enable the emergence of finer distinctions and so meanings.
Thus the first level alphabet of [0,1] is still interpretable at the second level but we also now have more complex terms in the form of pairs that cover the alphabet of [00, 01, 10, 11]. These paired symbols reflect an emerging hierarchy of meanings where the second ‘bit’ is interpreted WITHIN the context set by the first ‘bit’. This the level two alphabet is also interpretable from a first level point of view – the pairs are not seen as pairs but as sequences of 1s and 0s. As such we have TWO forms of interpretation available.
When we move to level 3 we have THREE forms of interpretation available with the three-bit patterns being the most complex of expressions, they show a qualitative improvement in expression due to there being eight possible meanings covered whereas the level 2 perspective is limited to pairs and the level 1 to singletons.
The jump from level 3 to level 6 covers a jump from incomplete alphabet interpretations (levels 4 and 5) to the next complete level given 6 bits of data. Here we have:
(a) level 1 interpretations
(b) level 2 interpretations
(c) level 3 interpretations
(d) level 6 interpretations
An essential feature of what makes a language a language is its ability to decribe itself and in the BIT domain we find this is possible using the logic operators. Of particular interest is the use of the XOR operator where, when applied to a dichotomy class focused on part/whole relationships, allows us to extract a parts list of any bit pattern interpreted as representating a whole. This A XOR B presents B as the whole and A as a part and the result is C that is an analogy covering the expression of A through B. See the Domain Translations section for more on this feature.
We will show this BIT domain as being essential in interpretations/translations of other domains through the use of logic operators, in particular the Exclusive OR (XOR), Equivalence (EQV) and Implication (IMP) operators. We will also show differing forms of interpretation of dichotomies as:
The anti-symmetric/symmetric categories cover fundamental aspects/whole dynamics and a focus on stimulus/response. The asymmetric covers mediation dynamics where an original stimulus/response in some way 'fails' and mediation is required. Given the above abstract domain model, we now move into specialist domain models grounded in recursion.
To continue the theme on structure, so the categories derived from recursion of 0/1 form a sequence of bits we can call the 'natural binary sequence' - where the term 'natural' reflects the fact that the sequence is derived from simple recursion of the 0/1 dichotomy - no more. What we find in this process is a primitive 'logic of relationships' where, given the core focus on 0/1 as 'opposites' so the relationship of 0 to1 is reflected in all PAIRS of structures derived. For example, if we recurse to the level of three-bit sequences, we have:
000, 001, 010, 011, 100, 101, 110, 111
The relationship of 000 to 111 is of 'opposites'. This relationship is repeated in the other sequences as:
001 to 110 (read as "001 is to 110 as 000 is to 111")
010 to 101
011 to 100
BUT, due to recursion so it is also reflected in such pairings as:
000, 001 (read as "000 is to 001 as 000 is to 111")
010, 011 (read as "010 is to 011 as 000 is to 111")
This 'little' pattern is in fact extendable to cover ALL relationships where, for example we can map out the general relationship of 010 to 101 to particular bit sequences, but how?
Given the method of deriving the above sequence of three-bit patterns from 'natural' recursion, we find that if we rotate that particular sequence it gives us a sequence that reflects changing values 'up' a bit-sequence - in particular the two sequences of 000 and 111. This rotation in fact reflects applying recursion to a three-bit sequence. Given this fact, if we (a) apply recursion to 010 we will get the 'changing line' sequence 'up' that bit-sequence and related to the opposite of 010, 101.
(b) ROTATING the sequence derived in (a) will give us the same pattern of a 'logic of relationships' as we have in the 000-111 pairing described previously. The particular patterns we get for 010-101 are:
(1) 010, 110, 000, 100, 011, 111, 001, 101 - rotate to give:
(2) 010, 011, 000, 001, 110, 111, 100, 101
This now reads as:
010 is to 011 as 010 is to 101
000 is to 001 as 010 is to 101
110 is to 111 as 010 is to 101
100 is to 101 as 010 is to 101
This method applies to all of the three-bit sequences and onwards. Thus if we insert some pair of specific categories in the 0/1 position of the template, recursion takes us to rich six-bit levels and recursion through those bit patterns give us a logic of relationships of the qualities of the initial two categories expressed through all other pairs of categories derived from the recursion.
A practical example of such is presented in the section in the Emotional I Ching material.
Given the derivation of a row of categories as a closed system, so the recursion acts to encode the whole in all parts through the emergence of the ability to use all categories defined in the row as sources of analogy in describing the detailed content of any particular category. This methodology has been identified where taking a dichotomy as an asymmetric form (e.g. part/whole, anti-symmetric/symmetric) presents us with bit sequences representing the spectrum of the whole. As such each category is interpretable as a whole but also as a part and use of the Exclusive-OR operator (XOR) allows us to derive detailed descriptions of a category through analogy to all of the other categories. See the "Domain Translations" section below for an example of this.
We note that the ability to do this emerges only from a level of six steps in recursion or more, any less than that lacks resolution power in the meanings. What is indicated here from a neurological position is that language emerges from rich distinction making, where such is dependent upon recursion, any less of a focus just gives us categories not differentiable to be taken literally or figuratively. Close examination of the BIT domain reflects we are dealing at level 6 with the recursion of the already recursed. With depth this ability emerges and with it the development of language, if but initially 'vague'.
To flesh this out a bit more, consider the following:
"Boltzmann-Maxwell Statistical Mechanics informs us that entropy is a combinatorial property determined by the number of possible distinct microstates which a system may exhibit. We assume that all of these states are equally likely to manifest so that the probability of any particular one appearing is the inverse of the total number of states. Taking the logarithm of this probability (and multiplying by an appropriate constant) returns a quality of the same absolute value as the system entropy but the reverse sign. What does this mean? Entropy represents the capacity of a system to manifest a certain number of those particular states. The more physical states the system can manifest, the greater the entropy. Information is the distinguishing of one of those particular states. It is the selection of one unique member from the total set. In essence, entropy is the count of unresolved physical possibilities of a particular system, whole information is the resolution of this system to a particular state; it is the collapse of potentiality to actual selection.
... Memory is also central to the concept of distinguishability of consecutive temporal states of a system." p54-55 Muller, S.J., (2007) "Asymmetry : The Foundation of Information" Springer
Given a finite set of possible bit patterns to represent some state, the range of such over, say, six steps is 64 possible categories and the chance of one potential being actualised is 1/64.
If the local context is dynamic and random then the chances of all 64 categories being expressed will vary according to the context demands where a random bit may not be actualised due to context influences. Furthermore, the chance element alone will not guarantee that all 64 possible states will occur. Thus we see that local context conditions can 'sort' the set of categories into a order of 'best-fit/worst-fit' and so bias the probabilities of patterns being actualised in that particular context.
In using bit patterns to represent 'all there is' so the patterns must include ability to describe themselves through analogy to all of the other patterns in the finite set of such. In our brains we can identify a core dichotomy that is recursed to give us classes of meanings covering patterns of differentiating/integrating (the IDM template). The BIT domain allows for representation of such and in doing so brings out a focus on a specialist dichotomy of difference/sameness. In other words a set of finite bit patterns needs to be able to describe itself through analogy to patterns of difference/sameness and this is possible through use of the XOR and EQV operators of logic.
Furthermore, the BIT domain covers the brain's focus on anti-symmetric (aspects), symmetric (wholes) and asymmetric (aspects/wholes) classes of dichotomies. The application of operators to these classes enables finer extraction of information covering the three classes of dichotomy and their recursions.
The recursion of asymmetric dichotomies give us a dimension in the form of a spectrum/power-law and presents us with a methodology of extracting the full spectrum of some whole (represented in a particular bit pattern) in the form of analogies to other bit patterns in the set of bit patterns where these are interpretable as parts. The extraction process is through partials analysis but we can also identify an ordered string of parts in the form of a ‘spectrum’ – this derived by applying recursion to those symbols already derived.
Symmetric interpretations cover:
Difference: A XOR B = C where C serves an analogy in describing A/B differences. The relationship is symmetric. (Normal distribution curve patterns)
Sameness A EQV B = C where C serves as an analogy in describing A/B sameness. The relationship is symmetric and covers EQV as NOT XOR. (Even distribution curve patterns)
Asymmetric interpretation covers:
Part/Whole, DIFFERENCE/SAMENESS A XOR B = C where C serves as an analogy of the EXPRESSION of the characteristics of A THROUGH the 'whole' of B. (spectrum/power-law patterns).
An example of asymmetric usage is given in the I Ching domain model below where we bring out the I Ching as a language. What is noticeable here is the transformation of a mechanistic dynamic to an organic dynamic, a descriptive focus to a normative focus and so teleological dynamic in that with the self-referencing discussed the emergence of an autological element brings out the encoding of PURPOSE at the class level of being. As such we see the realms of physics and chemistry and their mechanical natures lead into the realm of biology and its organic nature. This ability brings out the emergence of the normative sciences through filtering/application of logic, ethics, and aesthetics.
This encoding is simply derived from the mindless mechanism of recursion in that, since all categories end-up in some way being encoded in each of them, so each category comes with a 'begin' and 'end' property and so what can be interpretable as 'purpose' - if but at the level of a collective rather than individual. (see the section at the beginning of this book concerning the genotype/phenotype representations. Implicit here is that our thinking is tied to our chemistry and as such reflects RNA/DNA dynamics in the processing of information)
In the context of the bit sequences, each bit of a six-bit sequence is interpretable as representing a particular frequency and allows for a representation of parallel experience as well as of serial experience.
011110 represents sine
0 2cps (low sample rate)
1 16 cps
1 32 cps
0 64 cps (high sample rate)
This ordering gives a movement from the general (2cps) to the particular (64cps) and covers levels of precision. (note that 1 cps covers the ground, the background hum of meaning – the original distinction thus shifts us up to 2cps) Thus this can cover a hierarchy with each level semi-autonomous in function in dealing with reality but the sum of all levels elicits meaning.
Thus the summing of these give us a unique wave pattern derived from the constructive/destructive interference of the different sine waves (or their square wave forms as bit representations of 0 XOR 1) and so that wave pattern gives us an immediate, parallel, experience that is also expressed in bit format as a delayed, serial, experience.
There is NO GENERAL DIFFERENCE in meanings if we use this wave method or the 0/1 bit ordering methods. What is of interest is that we can map out the individual waveforms and their meanings from consideration of these six forms:
(a) 100000 ( see the section where the specialist domain model is the I Ching and this pattern covers a vague sense of the new/re-new)
(f) 000001 (covers a vague sense of quality control, pruning)
Thus we have 100001 = the summing of (a) and (f) etc thus the new/renew of (a) in which is operating a sense of quality control (f). In the I Ching domain model, the hexagram 100001 covers quality control of infrastructure (the new) and so a warning about what you put into the skeletal form, the quality of the muscle/skin etc (and this so covers the metaphor of filling in infrastructure)
What we see here is the conversion of bit patterns to waveforms through constructive/destructive interferences – and so the conversion of abstract bit patterns to the language of the neuron – frequencies, wavelengths, amplitudes. All of this comes out of self-referencing and so "wave/particle", or more so wave/pulse, nature is part of our being, our methodology in interpreting reality.
We have covered the dynamics of mediation through oscillations in our brains. This realm of mediation is a source of categories of meaning and so of interpretations and, if we go deep enough, the development of language through the use of pattern matching, also known as analogy making.
One interesting property of this oscillation is when we introduce indeterminacy – the consequence of which is presented in the following where the mediation act elicits the perspective of ‘wave/particle’ duality
Given the recursion of ANY dichotomy to 26 - 64 states - and combine that with indeterminacy as to LOCAL distributions, a probabilities mapping will emerge that is 'wave-like' in expression. (if we use LESS than 26 the pattern is not strong, if we use MORE the pattern does not change, it just gets bolder).
Note that the Schrödinger wave equation is a mathematical construct that is a dimension of probabilities of particle X being in state/position Y out of the range of POSSIBLE states - the probabilities mapping reflects the dimension elicited out of recursion of the probabilities - either as 0/1 or as -1/+1. This set of UNIVERSALS is then sorted into 'best-fit/worst-fit' ordering and measurement then indicates ONE of these out of the full SET as being 'best fit', but the others are also possible and in being so contribute to the 'whole' measurement.
If you map out the 64 possible states from recursing a dichotomy to 26, and then fold-in indeterminacy in distributions we get a pattern of 27 peaks/troughs. 19 of which are 'superposition' states, 8 are invariant over the transformation (since the recursion is open-ended, IOW we can run the experiments 'forever' so the patterns that are generated just get bolder).
If you review carefully the POSSIBLE events for EACH trial in a double-slit experiment we have:
(t1) L XOR R
(t2) L XOR R
(t3) L XOR R
If at each moment a particle goes through EITHER slit A XOR slit B. We can represent these as Yin or Yang to show the patterns of development of hexagrams etc.
If you then add some memory source then the set of POSSIBLE events becomes dependent on previous such that we get:
L XOR R = L / R
L XOR R = LL, LR / RL, RR
L XOR R = LLL, LLR, LRL, LRR / RLL, RLR, RRL, RRR
Etc etc etc
When we add indeterminacy we skew perceptions by trying to stay at one level. We can see this come out with the MINIMUM configuration possible with indeterminacy - a PAIR - we cannot reduce past that – as such we are adding-in a perception of EQUIVALENCE (EQV).
The moment we move to a PAIR we move from a differentiating position to an integrating position if we insist on keeping the notion of a 'pair' rather than accept that we have lost resolution power such that the 'pair' does not exist.
Lets review the pairs :
If you read the literature on Quantum Mechanics, the LL and RR position are replaced by L and R with no consideration of ORDER of the elements in the pair. BUT, order becomes an issue with LR vs RL. What the literature indicates is that these orderings are ignored (since they cannot be determined due to the lose in resolution -- this is like doing the marble exercise but only focus on pairs of marbles to ensure 'indeterminacy')
The moment you ignore LR/RL and clump them into a category X, so we have moved resolution from fours into threes. BUT the L and R mappings are considered as 'definite' since mathematics allows for two of the same to be folded into one of the same. SO we have definite L, definite R, INDEFINITE X. (in other words we are confusing SAMENESS with DIFFERENCE - we reduce LL and RR to representations of sameness, but try to do the same for LR and RL when they are in fact eternally DIFFERENT - we just cannot detect it. This distortion means we are operating within the realm of BETWEEN-ness, between FOUR or TWO categories that are 'whole' just different in resolution - as such we are focusing on the space 'in between' 1 and 2 AS IF that space is 'whole' when in fact it spans 'in between'.)
This dynamic guarantees 'interference' patterns. To demonstrate, let’s first map out the POSSIBLE states: first column is the set of POSSIBLE 64 patterns of LR dynamics. The second column is the 'compression' of that pattern into patterns of three symbols, each representing a PAIR in the original, where LL = L, RR = R and RL + LR = X (this being a source of distortion):
(01)LLLLLL - LLL
(02)LLLLLR - LLX
(03)LLLLRL - LLX
(04)LLLLRR - LLR
(05)LLLRLL - LXL
(06)LLLRLR - LXX
(07)LLLRRL - LXX
(08)LLLRRR - LXR
(09)LLRLLL - LXL
(10)LLRLLR - LXX
(11)LLRLRL - LXX
(12)LLRLRR - LXR
(13)LLRRLL - LRL
(14)LLRRLR - LRX
(15)LLRRRL - LRX
(16)LLRRRR - LRR
(17)LRLLLL - XLL
(18)LRLLLR - XLX
(19)LRLLRL - XLX
(20)LRLLRR - XLR
(21)LRLRLL - XXL
(22)LRLRLR - XXX
(23)LRLRRL - XXX
(24)LRLRRR - XXR
(25)LRRLLL - XXL
(26)LRRLLR - XXX
(27)LRRLRL - XXX
(28)LRRLRR - XXR
(29)LRRRLL - XRL
(30)LRRRLR - XRX
(31)LRRRRL - XRX
(32)LRRRRR - XRR
(33)RLLLLL - XLL
(34)RLLLLR - XLX
(35)RLLLRL - XLX
(36)RLLLRR - XLR
(37)RLLRLL - XXL
(38)RLLRLR - XXX
(39)RLLRRL - XXX
(40)RLLRRR - XXR
(41)RLRLLL - XXL
(42)RLRLLR - XXX
(43)RLRLRL - XXX
(44)RLRLRR - XXR
(45)RLRRLL - XRL
(46)RLRRLR - XRX
(47)RLRRRL - XRX
(48)RLRRRR - XRR
(49)RRLLLL - RLL
(50)RRLLLR - RLX
(51)RRLLRL - RLX
(52)RRLLRR - RLR
(53)RRLRLL - RXL
(54)RRLRLR - RXX
(55)RRLRRL - RXX
(56)RRLRRR - RXR
(57)RRRLLL - RXL
(58)RRRLLR - RXX
(59)RRRLRL - RXX
(60)RRRLRR - RXR
(61)RRRRLL - RRL
(62)RRRRLR - RRX
(63)RRRRRL - RRX
(64)RRRRRR - RRR
Reviewing the RIGHT column we find we have lost resolution power such that there are many duplicates. When we move along this column, grouping the duplicates in the area of their duplication we get 27 groups - 8 of which have one member each, reflecting a 'perfect translation', 19 are what can be called 'superpositions', different forms now sharing the space due to the loss in resolution. Graph all of this and we get:
THAT is a wave interference pattern (more so a double slit diffraction) in the SAME form as we get in QM etc etc (we can use double slits, down converters, polarisers etc etc - same method overall in eliciting POSSIBLE distributions). Of note here is that in the above we have compressed bit patterns or more so only focused on 11, 10, 00 where the order of 10/01 has been replaced by X – in other words we ignore the order (unique identity of sequence) ; 11 reduces to 1, 00 reduces to 0, 10 and 01 reduce to X. This is akin to using two coins and only recognising three states – HH, HT, and TT, and compressing them with H, X, T
In quantum mechanics the statistics used in mapping bosons is called Bose-Einstein statistics where the focus on HH,HT,TT formats where we find such naturally eliciting wave forms (and so mapping to light waves etc and so a tie to the concept of a superposition).
On the other hand, in QM, the fermions-related form of statistics is called Fermi-Dirac statistics and it comes with a rule forbidding two or more entities (particles) sharing the same space – thus the compression is not permissible and we have a more XOR focus (there are no equivalents). If we set up an experiment without indeterminacy we get a normal distribution curve so the above pattern reflects the distortion of such a curve.
Thus in ‘double slit’ experiments, putting detectors flush to the slits brings out the Fermi-Dirac perspective, move away from such and focus on some recording medium and you bring out the Bose-Einstein perspective.
If we take into consideration the XOR/EQV dynamics of our brains in paradox processing, so the LEFT column in the above orderings reflects XOR (fermionic) and the right column reflects EQV (bosonic). In such paradox as the Necker cube, the right column is the 'complex line drawing' and the left column the two cubes we detect trying to share the same space. This dynamic is not just limited to vision, it is also present in audition etc. and as such appears to reflect a fundamental nature of our brains - XOR/EQV dynamics. THAT nature then gets into our experiment designs without awareness of what we are doing, and we end up with 'paradox' where there is none.
ANY experiment set up in this fashion, with a method of storing the results will give us a 'wave interference' pattern in the EQV position DERIVED from the XOR dynamics in the left column.
The point being that as the left column is XOR to the right column's EQV, so each entry in the left column is an EQV in its own right, reflecting the expression of ALL of the other entries in that column.
What this shows us is the implicit wave-ness still present in the seemingly discrete elements in the left column. (the left column can be used to represent the left hemisphere as the right column can be used to represent the right hemisphere - this left/right dichotomy of course applies all the way down the scale of the neurology, form temporal/parietal dynamics in each hemisphere to axon/dendrite dynamics across the whole neurology etc)
Now move to the level of how we CATEGORISE and the XOR/EQV dynamic continues - be it in the MBTI or in human emotions or in the I Ching or in types of numbers in Mathematics. (And so the IDM model of how we derive meaning IN GENERAL)
No matter what level of recursion you are at, the set of elements recursed contribute to the expression of EACH category, and that contribution is extractable using XOR/EQV dynamics - IOW there is a LOT more to categories then just a sequence of 'types' that we then flesh-out ad-hoc, we do in fact have access to a spectrum of qualities for each!
From the abstract level of the L/R dichotomy applied recursively, I can extract the '53-ness' of EACH category in the above list using XOR/EQV processing. By this I mean that due to the entanglement of all qualities so each will reflect all others in some way or another. Thus pattern 53 contributes to the expression of each of the other patterns and we can detect this - the WHOLE that is the XOR column is in fact COMPRESSED into the WHOLE that is the EQV column. Our CONSCIOUSNESS is more associated with XOR dynamics and as such is one step removed from the EQV column that is representative of our integrated species-nature.
The two columns show us the PRECISION issues we experience, where our left-column consciousness is more precise than our right-column speciesness but in that precision thinks it is reality "AS IS" when in fact it is reality "AS INTERPRETED". This bias feeds into our thinking in general about reality and so we can create paradox where there is none. (as such "AS IS" reality is reflected in the photographic plate)
The categorisation of the main classes of numbers used in Mathematics can be mapped in the same format as the IDM model:
The mathematics template bottom-up
Negative Whole Numbers
Positive Whole Numbers
We can identify isomorphism thus where we have:
Blending - focus on whole numbers (where this category still reflects differentiate/integrate in the form of prime vs composite numbers)
Bounding - focus on rational numbers (harmonics)
Bonding - focus on irrational numbers (sharing of space with another/others, invariance)
Binding - focus on imaginary numbers (sharing of time with another/others - morphic/cyclic change)
Real numbers are made up of wholes, rationals, and irrationals. Complex numbers are made up of Reals and Imaginary.
The development of cardinality reflects grounding in the symmetric and with that grounding comes symmetric 'laws' (associative, commutative, distributative). With the development of ordinality (AFTER cardinality and in tune with the development of hippocampus activities focused upon sequencing) comes a focus on vectors - we add to scalars a sense of 'direction'.
Thus the development of finer and finer levels of precision shift a focus from the symmetric to the anti-symmetric and on into the asymmetric. We see this in the classification of numbers from real into complex, complex into quarternions, quarternions into octonions.
The conjugate requirement of complex numbers mean they reduce to sets of real 'pairs' thus:
Real - (a,1)
Complex - (a,b)
Quaternion - ((a,b),(a,b))
Octonion - (((a,b),(a,b)),((a,b),(a,b)))
The core focus here, from a meaning context, is the isomorphism of generic categories of IDM with those cover classes of numbers in Mathematics. To summarise:
In IDM mathematics is shown to be a language and grounded in the IDM template categories and they stem from the mediation dynamics of the neurology - in particular the oscillations that come with processing data.
The oscillations occurring WITHIN the bounds of our attention reflect the recursion of the differentiate/integrate dichotomy (equates with "what/where" as it does left/right, front/back dimensions in the neocortex and on down to the FM/AM of the humble neuron) and from that comes the categories. Memory can conserve energy here where we can recall previous levels of category derivations and so don't need to 'rewrite the bible' each time. It is this recall that allows us to form analogies of new experiences with general categories of previous experiences in totally different contexts etc.
The adaptation of the neuron to environment indicates an abstraction process where essentials are extracted to form the basic IDM categories of wholeness, partness, static relatedness (sharing of space), and dynamic relatedness (sharing of time) and their composites.
Thus a focus on the classes of numbers give us:
wholeness - whole numbers (IDMs blending)
partness - rational numbers (harmonic series) (IDMs bounding)
static relatedness (sharing of space) - irrational numbers (IDMs bonding)
dynamic relatedness (sharing of time) - imaginary numbers (covers cyclic/morphic change) (IDMs binding)
whole + part + static = real numbers.
real numbers + dynamic = complex numbers.
The recursion brings out more complexity in the form of pairings:
pair of real = complex
pair of complex = quaternions
pair of quaternions = octonions
These are all called
'division algebras' and they lose their universality/symmetry at the level of
octonions. The development of these classes also bring out the development from
scalars (magnitudes) to vectors (magnitudes + sequences) and reflect
development differences in, for example, amygdala (magnitudes (emotional
intensities)) and hippocampus (sequencing). Thus the emergence of a sense of
whole/part comes out of the symmetric realm through objectification of
relational space (and so fragmentation of the 'all is connected', the vague,
topological, whole of
of the incompleteness of Mathematics was more so a discovery of a property of
ALL languages - they are grounded in mediation and so uncertainty and any
The derivation of Mathematics as a language and so analogy/metaphor dynamics allows for the interchange of mathematical perspectives of some context with other perspectives - e.g. Physics and Mathematics. The common ground is in the IDM patterns in that ALL languages will have these patterns due to their development from mediations (and so brain oscillations). The "difference that makes a difference" is in the forms of representation that come out of these specialist perspectives. Mathematics as such comes in two flavours, its pure form and its applied form, the latter is where it serves as analogy/metaphor for representing other perspectives. The former covers mathematics turning in on itself and so able to represent states not apparently possible in a thermodynamic reality 'as is' (e.g. flatland etc).
Living in a thermodynamic universe suggests that the best format for living is through energy conservation and that introduces us to symmetry as a natural response to thermodynamic contexts. As a species we are determined by our genes and as such have our 'being' grounded in symmetry and so the dynamics of instincts/habits. These dynamics cover interactions with differences to elicit aggregation of 'essentials' to form habits (samenesses) usable in response to contexts; as such context pushes our species-nature.
As conscious beings, and so singular beings, our sense of uniqueness emerges as a sense of self over the first two years or so of life. This uniqueness is ASYMMETRIC and introduces us to the emergence of consciousness and language as agents of mediation. Since mediation is grounded in uncertainty so any reflections on the output of mediations will elicit perspectives not necessarily 'true' of reality 'as is' but more so of reality 'as interpreted'.
of the incompleteness of Mathematics (or Heisenberg's of the uncertainty of
Quantum Mechanics etc etc) was more so a discovery of a property of ALL
languages - they are grounded in mediation and so uncertainty and any
Certainty for us as a SPECIES is in the unconscious, symmetric realm in the form of instincts/habits/memories and these are customised, generalised, forms and so miss a lot of details, lack resolution power, of each moment for the sake of energy conservation and pattern aggregation to deal with future events.
The derivation of Mathematics as a language, and so representative of an analogy/metaphor dynamic, allows for the interchange of mathematical perspectives of some context with other perspectives - e.g. Physics and Mathematics. The common ground in this sharing of space is in the IDM patterns in that ALL languages will have these patterns due to their development from mediations (and so derived from brain oscillations as we focus attention and zoom-in for details).
The "difference that makes a difference" for specialist perspectives is in the forms of representation that come out of these specialist perspectives. Mathematics as such comes in two flavours, its pure form and its applied form, the latter is where it serves as analogy/metaphor for representing other perspectives. The former covers mathematics turning in on itself and so able to represent states not apparently possible in a thermodynamic reality 'as is' (e.g. flatland etc). The notion of number, the emergence of classes of such from basic brain dynamics, introduces us to a very refined form of representation.
The recognition of incompleteness in mathematics comes from the methodology of mediation where any mediation is grounded in uncertainty - thats WHY one needs mediation in the first place, to resolve some uncertainty. Move to a meta-level analysis (and so the mathematics of mathematics aka the language of language) and out will pop this uncertainty/incompleteness sense - but it is not a ground of the universe, it is the ground of mediation.
The dynamics of mediation cover language and consciousness development such that the richer the language skills the better consciousness can describe itself. This covers the IDM-identified property of recursion of meanings - at a particular level in the recursion the categories formed can be taken literally but also figuratively and so we move into analogy/metaphor usage.
In this focus on consciousness and language development we note that infants and primitive languages tie strongly to context whereas demands for finer and finer distinction-making makes the individual more context-insensitive and so able to 'fit in' to any context upon demand (or create their own language to do so). The higher the number of distinctions made, the higher the precision in communicating any context, however there are accuracy issues present.
The accuracy issue comes with the realisation of uncertainty where such reflects mediation issues in that mediation never gets to the 'point', there is always 'more' and so pragmatism comes in as 'close enough for jazz' etc.
Social dynamics is governed by symmetric interactions and so a loss of precision in that precision comes out of the asymmetric but the asymmetric is the realm of mediations and so considerations of that realm will hit the ground of that realm - uncertainty. Thus in the realm of the symmetric we practice 'rounding-down/rounding-up' to 'complete' the precision.
From the species perspective, certainty is in the form of instincts/habits and covers issues of energy-conservation as context pushes us. Accuracy issues abound in that the realm of determinism covers GENERAL responses to stimuli - all determinism is grounded in symmetry dynamics and so a degree of approximation when compared to what is possible in the anti-symmetry/asymmetry dynamics of high precision analysis.
The precision focus of the brain is to make finer and finer differentiations and so move to the precision of the point. When we extract a detail from a whole we encapsulate it and so discretise and amplify it - this dynamic reflects positive feedback at work. But WITHIN what has been discretised is still negative feedback holding things together.
Keep zooming-in, keep discretising, and one gets to the point - and THAT position is a position where the distinction of negative feedback has disappeared - the reduction process has exhausted any possibility of negative feedback and so the integrating, dimensional, realm - this dynamic covers pure algebra etc where it is non-dimensional with its focus on a point.
This disappearing of negative feedback within the confines of the positive feedback discretisation and amplification, so necessary for precision, moves us into precision being manifest in infinite sets where such are the natural product of the loss of negative feedback and so the loss of the sense of 'begin/end' and so of symmetric forms. (All that is discretised and amplified by reductionism is through use of positive feedback to give us the high precision of a point)
The accuracy issues of mediation, the uncertainty present, disappear when we focus on infinite sets since accuracy is represented as a continuum when we take tight relational concepts (e.g. PI in the context of unit circle relationships that define the form 'perfectly') and convert them to high precision sequences of points (the infinity of PI's mantissa).
Implicit in this is that 'certainty' is not a measurable form from a point perspective since high precision has no 'ending'. Pragmatics (use of probabilities etc) then determines an 'ending', e.g. '22/7' etc to 3 decimal places is 'good enough' - and in mindless stimulus/response dynamics the responses cover general properties to apply to some stimulus to 'as limited a precision as possible' since we cannot expend too much energy in encoding the precision that is potentially 'infinite'!
What is indicated here is that high level mediations take us into uncertainty OR certainty in the form of infinite sets! - which is, for us, 'not certain' since where we stop is up to us (and so the increasingly subjective if allowed)!
This brings out the roots of meaning in symmetry and the emergence of the asymmetric as the agency of mediation (and so our languages and unique consciousness). We can see here the sense of consciousness tied to experiencing the 'infinite' in that precision demands there be no ending! - this covers the dynamics of abstractions.
If we review the definitions of logic etc with regard to 'truth' we find association of this truth with symmetry (the sense of complete, of 'one') not asymmetry/anti-symmetry. As such truth is 'whole', undifferentiable, the 'one'. Any act of trying to quantify this 'oneness' (and so use of unit forms - a2 + b2 = c2 where a=1, b=1)) will introduce us to infinite sets since any act of quantification will be an act of 'rounding' and so be not 'exact', not 'perfect'.
A simple example is of a circle - the PI contribution is to the perfection of the unit circle - you cannot measure it quantitatively in that to do so would demand rounding but in such an act we surrender the perfect precision. The presence of the square root of two covers the same 'perfection' manifest in the unit right angle triangle.
The aesthetic element of irrational numbers is well covered in literature (mathematics, art etc) and brings out the 'perfection' in dimensional forms reduced to non-dimensional forms as 'infinite sets' where the ultimate in precision is this form of set! This then moves us into considering irrational numbers and their association with 'perfect forms' and so symmetries and dimensionalities. (the 'perfection' of the circle or right-angled triangle is manifest in the presence of irrational numbers as representations of these 'perfect' forms, these 'ultimate' precisions that cannot be 'rounded off').
Implicit in all of this is that within symmetry there is no 'infinity' as an actuality, as a real concept, since a symmetric form is a closed system. The development of high precision converts the geometric forms of symmetry to algebraic forms and in doing so reduces all to the dimensionless. In doing that all we have for precision are infinite sets - and hierarchies of them all due to the hierarchic syntax bias of our differentiating parts of our brains.
In IDM we note the tight relationship of BONDING (sharing of space) with BLENDING (wholeness), of irrational numbers with whole numbers; a bond is a relational focus, a summing of elements from the harmonic series into a 'guiding' form the precision of which is extreme to the point (!) of being manifest as 'infinite'. Thus 'perfection' expressed in sequencing is in the form of infinities since that is the only form that covers the highest levels of precision - any attempt to 'round off' the result is a movement to an approximation and so 'not perfect'.
The roots of emotional meaning are in the hard-coding of the fight/flight dichotomy across the amygdala of the brain. There are also ties to the striatum and hippocampal activities. This domain is grounded in aspects/whole distinctions and covers the association of emotional 'colourings' to experiences through the neurology processing of sensory secondary harmonics (colours, chords etc) and eliciting an emotional response to such.
Table 1 - Generic Concepts Derived from Recursion of 'Whole'
At the bottom row we have
a very generic set of eight qualities usable to describe 'something'. We can go
further or stop and use what we have. Memory allows us to 'save' the categories
and continue later if need be. These generic qualities are derived from the
perspective of the species and as such are unconscious at the level of
the everyday expressions of individual/collectives where we use highly specific
Thus the process of differentiation allows for identification of 'something' from all else, as does the process of integration where the identification is more implicit, resulting from the integration of 'things' into a pattern that identifies (or re-identifies) 'something'. The recursion allows for finer distinctions that can also serve as unique perspectives allowing for, by example, a perspective that derives meaning from the analysis of parts as compared to an alternative perspective that derives meaning from the analysis of dynamic relationships etc. The generic distinctions of 'wholes' and 'parts' etc can be converted to synonymous terms reflecting more of a very generic sense of feeling:
Table 2 - Qualities Synonymous with the Concepts of Table 1
These generic terms, blend, bond, bound, bind, will again be fully defined later in this section but in general the above qualities are unconscious and serve as the set of universals we share as a species with which to derive general meaning that is localised through linking the general qualities with a local context out of which we can develop a lexicon used to communicate. The added benefit is the ability to exaggerate communications, to modulate, and so derive what we call emotions. It is these generic feelings that enable us to make analogies so easily across seemingly very different disciplines etc. and so allow us to communicate even when we do not understand each other's spoken/written word.
In the research into
emotions and their categorisation, Robert Plutchik (Plutchik, R., (1994)) has
identified four dichotomies reflecting primary emotions (as compared to
secondary emotions that stem from a developed sense of SELF (Kircher &
Here we trace these dichotomies back to their derivation from fight/flight (also known as the biases of: push forward/pull back, expand/contract, positive/negative, differentiate/integrate etc) and further to a generic condition covering the communication of intent in dealing with context, either to replace it or coexist with it. The dichotomies of primary emotions are given by Plutchik as:
Using Plutchik's dichotomies, the root dichotomy that maps directly to the nature of the species is anger/fear, fight/flight.
The process of recursion
to the level of identifying eight 'types' of emotions expressed in the form of
opposites made-up of four dichotomies is reflected in the use of the previously
identified set of binary digits, and their recursion to 3 levels, to identify
all possible forms. Thus we have:
level 1 : 1 (fight) / 0 (flight)
level 2 : 11, 10 / 01, 00
level 3 : 111, 110, 101, 100 / 011, 010, 001, 000
At level 2 we have four qualities, two of which are 'pure' in form and two of which are 'derived' through the entanglement of the elements of the root dichotomy used at level 1.
Thus 00 = 'pure' flight (we cannot differentiate text from context), 11 = 'pure' fight. 01 = a CONTEXT of flight within which we add a TEXT of fight. 10 = a CONTEXT of fight within which we add a TEXT of flight. This focus on context reflects the brain's emphasis on (a) setting a context and (b) identifying all else within that context. This reflects the 'first impressions' nature in our behaviour where once made, the first impression is very hard to change and as such lasts 'forever' and at best is 'neutralised' but seemingly not forgotten, just 'repressed'.
A cognitive analysis of Plutchik's dichotomies, based on the patterns of meaning derivation identified in IDM, indicates that the 'best fit' for the level 2 categories of 01 and 10 are the concepts of disgust (reject) and acceptance. These are GENERAL terms and as such reflect the distinctions made in IDM of these two categories reflecting combinations of the level 1 elements to a degree where there is a border which is put-up such that 01 pushes things AWAY with the focus on maintaining what is inside the boundary, whereas 10 pushes outwards to PULL IN, to encapsulate, ingest, 'something' to the benefit of development.
As such, disgust reflects the walling-up to protect 'in here', whereas acceptance extends the boundary to include something; the wall is dynamic as such and so pushes outwards.
Thus we have:
level 1: anger / fear
level 2: anger, acceptance / disgust (reject), fear
Here disgust reflects
the composite of fear with an element of anger whereas acceptance is anger with
an element of fear. (The terms 'fight/flight' and 'anger/fear' are terms that
do not do justice to the underlying elements of differentiation/integration.
For example, fear can be based on an instinct (gene driven) or on a past
experience (habit formed) where the focus is on what could happen if I dont
withdraw etc - Disgust as such means I express my 'fear' but hold my ground.
However I will retain these terms since they are well used in the literature so
the reader needs to just treat them warily when I use them at these general
levels of application - they come into their own at more refined levels. As
such, these basics of what Plutchick labels as fear, disgust [rejection],
acceptance [ingestion], anger, are identifiable in the very early behaviours of
infants, possibly even with a degree of decision-making aspects within the
amygdala - see such papers as Kahn et al (2002).
The intense focus in the category of 'anger' reflects the single context perspective and the influence of what IDM identifies as the transcendence function whereby there is an issue regarding replacement of an existing situation with something considered 'better', as compared to the association of fear with more the preservation of an existing situation [associates with IDM transformation function], be it your own life or the life of your clan/species etc. Thus transcendence deals with replacement of context, transformation with the retaining-of, further integration with, the present context.
In the context of the development of the emotions, so the root fight/flight is reflected in reptiles where we include the lack of distinction of 'family' etc. (if you stay around you may be eaten!) Thus, for example, what we have identified as 'acceptance' is a term more applicable at later levels where here, at level 2, the concept is more on 'ingestion'. The abstraction of that process, in level 3, allows for 'ingestion' to be refined into acceptance of 'others' etc. in a mammal perspective, the movement along the dimension from fear to anger reflects the movement from a position in a hierarchy of being 'rejected', the 'runt' of the litter, to being approved of (as in alpha male/female dominated collectives etc).
Given our level 2 mapping of generic emotions we need to identify the 'slots' into which we can place Plutchik's remaining dichotomies of:
The IDM mappings indicate the following generic expressions for level 3:
anger, anger+accept, acceptence, accept+anger / disgust+fear, disgust, fear+disgust, fear
(the above order differences reflect differences in context+text relationships).
Behaviourally, we can
identify a negative/positive thread here in that 'anger' and 'acceptance' have
an aire of being 'positive' in one's perspective as compared to a more negative
property of fear/disgust. This being the case, the concept represented by
Plutchik as 'joy' belongs to the anger/accept side of things but in expression,
as in energy used, belongs more to the anger+accept 'end' of things and when
associated with this generic category reflects the close relationship of
aggression and pleasure (sex) [reptilian sex can be extremely aggressive, as
can some mammal forms of sex. All of these seem to indicate the shared space of
'anger' and 'joy' rather than they being fundamentally 'poles apart']
This association of joy with anger means, due to the polar relationships of the dichotomies, that the concept represented by Plutchik as 'sadness' belongs to the category derived from fear; here we see a tie of sexual love and grief where they are the sides of the coin labelled ‘passion’. Thus our initial level 3 format is:
anger, joy, acceptance, X, X, disgust, sadness, fear
surprise/anticipation dichotomy slots into the positions labelled above as X,
but which is which? The overall distinction in the levels is that of fear/anger
synonymous with contract/expand, integrate/differentiate but also recall the
aire of 'what could be' associated with fear, there is a sense of being
motivated by an aire of awareness of consequences more so than we find with
anger, UNLESS there is no escape where we SUDDENLY turn and fight.
Thus our level 3 set of emotions is formed into:
anger, joy, acceptance, surprise, anticipation, disgust, sadness, fear
This derivation process in tabular form is:
Table 3 - Mapping of Fight/Flight Dichotomy Over the Concepts and Qualities of Tables 1 & 2
Thus sadness stems from
fear as anticipation stems from disgust. Surprise stems from acceptance as joy stems
from anger. These are all general terms tied to emotions but IDM uses even more
generic terms sourced in generic neurocognitive processes that are more
reflective of the generic nature of expressions in that the emotions we
identify today have been DERIVED from 'baser' forms. Thus the universal
response system of emotions is also tied to a more encompassing set of
categories that reflect general perspectives used to be proactive as well as
reactive and these perspectives, declared in Table 2, are here defined as:
contractive blending - includes Plutchik's fear (it is like escape through curling up into a ball, or 'disappearing' by playing dead or freezing, in the latter where natural colourings etc can allow one to 'blend in' with the local context and so not be seen - the overall focus is on total integration and the use of context to aid by determining expression. In IDM the link is to the concept of Transformation reflected in such concepts as 'shape shifting' as a defence mechanism. At the level of collectives etc this 'contractive blending' gets us into the concept of security in numbers, drawing someone/something 'in' through which one asserts one's identity. The main focus is the recruitment of the context to 'hide' as well as assert identity through someoneelse/somethingelse - thus concepts such as 'devotion to someone/something' and so 'trust in OTHERS' can be derived from the basic emotion of fear)
contractive bonding - includes Plutchik's sadness (For Plutchik this gets into issues of death, of grief, of qualitative distinctions. In IDM, for the more generic term of 'contractive bonding' there is a focus on sharing space with someone/something but maintaining one's sense of identity. There is a relationship to the representation of fear but not fear itself. Bonding as a whole reflects SYMBOLISM - e.g. a marriage certificate reflects the 'blending' of male/female but is not that blend, it is a representation of that blend. A 'de facto' relationship is more 'bond' than 'blend' in that both parties retain their own sense of identity and as such are not 'one'. Sadness is also a representation in the form of being sad about something compared to being fearful of something. Both blend and bond deal with sharing of space but bond not as 'intense', not as total, as blend – we can add here the sense of passion associated with the grief for a lost or impossible love as we can the sense of discernment learnt from trust in others))
contractive bounding - includes Plutchik's disgust (the boundary focus to protect 'inside', rejection of others. Basic rejection at the level of the individual can lead to the collective/species level where values are protected and others rejected. From this realm and the next emerges such concepts as morality/ethics where 'good/bad' determinations are made from within the boundary, keeping the bad 'outside' . There is an overall sense of 'security seeking’ as there is a loss of trust in others/another, a sense of betrayal leads to putting up walls to protect')
contractive binding - includes Plutchik's anticipation (relationships over time, management, umpires, auditors etc thus an intial experience of disgust and so rejection leads to the development of a sense of anticipation of rejection and so a sense of 'monitoring' as well as a need for cultivation develops in that through anticipation of 'troubles' one can nip them in the bud but at the same time this 'negative' perspective can be used to cultivate)
expansive binding - includes Plutchik's surprise (relationships with time, 'new' paradigms, enlightening experiences, sudden assertions of 'something'. This whole area of 'expansive' concepts comes with an aire of 'transcendence', reflected in the totalist attributes of expansive blending, see below)
expansive bounding - includes Plutchik's acceptance (formation of ideologies, sense of direction, of belonging, ingest. The boundary here reflects more a Science perspective in that the focus is on organising, mapping, planning such that the maps contain what is 'true' vs 'false' and this and the previous category [expansive binding] focus more on 'true' or 'false' rather than 'good' or 'bad' - they seem to form the roots of rationality and problem solving)
expansive bonding - includes Plutchik's joy (self-reflection, reflection of others who see themselves in 'you', performer-audience, reproduction, passion. The link of aggression and reproduction is well demonstrated in society but assumed to be 'opposites'. IDM identifies their common root. The repeated recursion we use to analyse anything will allow for us to interpret love/hate, joy/anger as opposites and so flesh-out elements within the pairing but the ROOT of love/hate, joy/anger is more in the very generic notion of 'singlemindedness' that comes with expansive blending and its 'pairing' derivative (the integration bias) in expansive blending). With sexual love comes a focus on context replacement by through copies of oneself rather than the more eradicating, competitive nature of the next category) – More recent work covers neurons eliciting a flood of hormones to elicit ‘bonding’ states – in particular that of trust. Of interest is the involvement of the dendrites of the neurons in this release that allows for integration (bonding bias) where in IDM we identify the dendrite areas as biased to issues of integrating and the formation of instincts/habits. (Rosoni et al., 2008) – Further work in this area is covered in texts/websites on ‘boids’ and what is called ‘flocking behaviour’ – as is reference to Hans Jenny’s “Cymatics” (Jenny, 1974) – republished recently – this material also applies to contractive bonding covering loss that is turned into quality control and trust in others..
expansive blending - includes Plutchik's anger (total faith in oneself, singlemindedness, intense, destroying/creating focus - total differentiation in the form of replacing the existing context with one's own - something seemingly 'better') For IDM the brain is not aware of 'joy' or 'anger' etc in that the basic brain is driven by, developed upon, mindless stimulus/response such that 'joy' and 'anger' etc are terms created at the level of mind (conscious brain, brain function at the level of awareness) that represent the 'mindless' patterns that the brain deals with at the basic level across all brain-dominated species. What can stem from this 'passive' recursion is the set of qualities given in the table at the beginning of this section.
"...The hypothesis, which we shall call the "2^6 rule", is, then, that irrespective of race, culture, or evolutionary level, culturally institutionalized folk taxonomies will not contain more than 2^6 entities and consequently will not require more than six orthogonally related binary dimensions for the definitions of all of the terms. ...In the area of cultural semantics, we are suggesting that a somewhat similar principle applies...the evolution of cultural complexity is limited, in so far as folk taxonomies are concerned, by the two-to-the-sixth-power rule. ...What is limited is the complexity of the taxonomies which are components of the various cultural sub-systems" (Wallace 1961)
Wallace,A.F.C.,(1961) "On Being Just Complicated Enough" Proc. of N.A.S. 47 (1961): 458-464
The I Ching covers a methodology of interpreting something as yang/yin - the symbolism of lines allows for the layering of such to form trigrams and hexagrams.
Thus a trigram (three-line symbol) in an upper position of a hexagram has a slightly different interpretation than when in a bottom position. This stems from using the refinement bias in the I Ching (we move up from a gross state to a refined state):
Traditional Bottom Top
The Receptive Devotion Trust (double-minded)
Keeping Still Self-restraint Discernment
The Abysmal Containment Control
The Gentle Cultivate Influence(become influential)
The Arousing Enlightenment Awareness
The Clinging Guidance Direction
The Joyous Self-Reflection Intensity
The Creative Perseverance Confidence (single-minded)
A full derivation of the I Ching domain model is covered in the book "The Emotional I Ching : A Language of the Vague"
The next map is based on Western Astrology:
|Aquarius| Gemini | Leo |Sagittar| Pisces |Scorpio | Virgo | Taurus |T3
| Air (Libra) | Fire (Aries) | Water (Cancer) |Earth (Capricorn)|T2
| Air | Earth |T1
| (The Whole) |T0
The generation of Astrological symbols.
The sign associations stem from the fact that each element has a 'cardinal' sign which is the more 'stable'. The other signs are called 'fixed' and 'mutable'. Using this method of classification we find strong correlations with the other maps as well as the template. What is implied in this is that the signs at T2 are more 'global' than the refined ones at T3. All of the signs at T2 are considered the 'leading' signs in their specific sign group. There is some question, however, to the positions of the cardinal/fixed signs. Since we move from the 'whole' and a state of equilibrium (T0) to increasing levels of complexity and change the more 'unchanging' signs should be at level T2 rather than the 'leading' sign. For fire signs this is the Leo/Aries dichotomy.
Comparing with the other maps, Aries (T2), for example, with the trigrams of The Arousing and The Clinging in the I Ching and overall with the concept of bounding and binding. At T3, the more 'refined' levels link Leo with The Clinging (I Ching), and Bounding (group, boundary). In maths this links with rational numbers (parts). Sagittarius, on the other hand is more binding oriented (The Arousing). BOTH have traits of Aries, the 'root' of the fire symbols.
We can start with Roger Sperry's work in the 1960s covering dealing with epilepsy through the cutting of the connections between the left and right hemispheres of the brain. What this did was bring out the differences between the hemispheres of the brain where one side (the left in most) was biased to differentiating and 'parts' (anti-symmetry) whereas the other side (the right in most) was biased to integrating and 'wholes' (symmetry).
As more and more research went on it became evident that oscillations across the hemispheres of the brain contribute to the derivation of meaning or more so categories and so classes of meaning where a local instance of a class gets a special label to represent that link. E.g.:
The specialist terms for hemisphere differences are simplified to the “what/where” dichotomy where the dichotomy applied to the brain is well recognised and documented to such a degree it is an axiom contained in introductory texts on neurosciences. E.g.
"Two pathways from the striate cortex to extra striate regions convey prominent streams of information. One pathway flows for V1 [main area of visual input processing] to the temporal lobe (ventral pathway or "what" pathway) and conveys analysis of stimulus features and their conjunctions, and ultimately the information is used to carry out form discrimination and object identification. The other pathway projects from V1 to the parietal lobe (dorsal or "where" pathway) and carries information about a stimulus motion and localisation within visual space" p51-52 Gazzaniga, M.S., et al (1998) "Cognitive Neuroscience : The Biology of the Mind" Norton
The 'WHAT(who,which)/WHERE(when,how)' dichotomy reflects properties of the general dichotomy of differentiating/integrating and that dichotomy maps to the brain from the neuron to left/right, front/back, surface/core etc of the neo-cortex and out into our collectives through the socialisation of individuals. From a symmetry perspective, WHAT associates with anti-symmetry dynamics and a parts bias (differences emphasis) and WHERE with symmetric dynamics and a wholes bias (sameness emphasis). Join these terms into a dichotomy and the differences in oscillations across this ASYMMETRIC dichotomy are covered in such work as:
Banich, M.T., "Hemispheric Interaction" IN p 270 Hugdahl,K., & Davidson, R.,(eds)(2004)"The Asymmetrical Brain" MITP
Banich,M., & Karol (1992) "The sum of the parts does not equal the whole: Evidence from bihemispheric processing" Journal of Experimental Psychology :Human Perception and Performance 18, 763-784
Friedman,A & Polson,M.,(1981)"The hemispheres as independent resource systems: limited capacity processing and cerebral specialisation" Journal of Experimental Psychology : Human Perception and Performance 7, 1031-1058
Passarotti, A.M., Banich, M.T., Sood, R. K. & Wang, J. M. (2002) “A generalized role of interhemispheric interaction under attentionally demanding conditions: evidence from the auditory and tactile modality” Neuropsychologia 40 (2002) 1082–1096
Lomber, S.G., & Malhotra, S., (2008)”Double dissociation of 'what' and 'where' processing in auditory cortex” Nature Neuroscience 11, 609 - 616 (2008)
Monaghan, P., & Pollmann, S., (2003) “Division of Labor Between the Hemispheres for Complex but Not Simple Tasks: An Implemented Connectionist Model” Journal of Experimental Psychology: 2003, Vol. 132, No. 3, 379–399
What is brought out by the above is that oscillations across both hemispheres is more common when dealing with the new/complex, whereas dealing with the known/simple elicits more so intra-hemisphere dynamics. We can extend this to cover behavioural differences stemming from oscillation anomolies where, for example, too much oscillation time spent over one side of the brain will cause the characteristics of that side to emerge and seed general thought:
Pettigrew JD and Miller SM 1998 Proc. Roy. Soc. B 265: 2141-2148
PETTIGREW, J., & MILLER, S.M., (1998 ) “A "sticky" interhemispheric switch in bipolar disorder?”
Further research showed that this oscillation was not just left/right but also front/back (associated with circadian rhythms) and also across lobes within either side (e.g. temporal/parietal) and within a lobe (front/back temporal) and on down to the humble neuron. (e.g. Buzsaki 2006)
The TIMING of oscillations brought out the price of mis-timing, of timing 'anomolies' where accumulated time 'over' one side led to the characteristics of that side influencing thinking in general (e.g. Pettigrew 2002 ) and so bringing out mania/depression dynamics.
Other work covering frontal lobes and left/right oscillations brought out the SHARP distinctions in most of a dichotomy of differentiating/integrating 'spanning' our brain and the dynamics of manic vs depressive behaviours associated with damages to different sides.
We then find that in the process of encountering new or complex information, oscillations span across both hemispheres as compared to when we deal with the known/simple where these dynamics are limited WITHIN hemispheres (Banich, M.T., "Hemispheric Interaction" IN p 270 Hugdahl,K., & Davidson, R.,(2004))
This moves us into hierarchy and top-down/bottom-up dynamics that allow for properties of one level not being manifest in lower levels and so bringing out issues of contextual robustness needed to enable more complex developments.
We also find a focus on differences to sameness where the known is processed differently from the unknown as is the known derived from the unknown through a 'journey' across hemispheres from right to left (in most, see Golberg, 2001) and so reflecting a shift from relational to object formation (negative feedback to positive feedback, 'getting closer to' to 'amplification' and discretisation to give us the assertion of 'thingness')
When we add the use of attention to this collective of research material (e.g. see Posner (2004)) we include the amplification and encapsulation of 'noise'. A natural property of the containment of noise is the generation of order through self-referencing (Google "the chaos game") and as such self-referencing covers the oscillations across the elements of a dichotomy where in our brains that top level dichotomy is that of differentiating(aka WHAT/object/noun)/integrating(aka WHERE/relationship/verb).
What is noteworthy here is that the dichotomy of differentiate/integrate is ASYMMETRIC within which is the SYMMETRIC. If we let differentiating take on the value of 1 and integrating the value of 0 then self-referencing the dichotomy will give us dimension of values where each iteration (Tn) moves us from the general to the particular and so brings out a hierarchic emphasis:
T1 - 0 / 1
T2 - 00, 01 / 10, 11
T3 - 000, 001, 010, 011 / 100, 101, 110, 111
T4 - 0000, 0001, 0010, 0011 .....
As such we derive representations of differentiating/integrating in a hierarchic scale left-to-right but also top-down (and so maintaining the general-to-particular bias).
Careful consideration of the properties of differentiating/integrating bring out a core set of categories and so classes of meaning covering:
Since our brains use the same oscillation dynamics across the hemispheres regardless of general context, so the oscillations generate a set of constants that can be relabelled to represent some unique context. As such the elements of the differentiate/integrate dichotomy take on different forms and so bring out the metaphoric nature derived from recursing the dichotomy - thus dichotomies such as difference/sameness or asymmetric/symmetric or fight/flight share the same GENERIC form and so elicit properties that are isomorphic and so reflective of the properties of Jung’s “Collective Unconscous”.
Given the general understanding of the brain dynamics we can make some conclusions based on more precise research. Here we find that:
(1) The hemispheres of the neocortex function as high and low band information filters.
The left hemisphere (in most, there is a BIAS here as well as genetic diversity that allows for differences in the sameness) amplifies and process high frequency data. The right hemisphere processes low frequency data.
These processing biases are in spatial (visual) processing as well as auditory processing. Since these are the dominant ways in which we process information they are strongly emphasised.
(A good reference is: Ivry, R.B., & Robertson, L.C.,(1998) "The Two Sides of Perception" MITP It is mostly vision data with particular research by the authors as well as extensive reviews of other research in this area.Audition is limited to two chapters).
Further data covering the whole visual system is in: Hoffman, D.D., (1998) "Visual Intelligence: How we create what we see" Norton
For additional refs to cover the audition bias see: In general: McAdams, S., and Bigand, E., (Eds) (1993) "Thinking in Sound" OUP, and In particular: Levarie, S., (1980) "Music as a Structural Model" p236-239 IN Journal of Social Biol. Structure. 3)
The High/Low frequency processing has some interesting consequences namely:
(1.a) High frequency means 'wide' bandwidth (intensity) means clarity and so precision.
(1.b) High frequency means short range and so an emphasis on the local, the particular, and so a SINGLE context.
(1.c) Low frequency means narrow bandwidth means blurring and so approximations.
(1.d) Low frequency means long range and so an emphasis on the non-local, the general.
1.a + 1.b analogous to narrow spotlight, high beam. Intensity. Manic.
1.c + 1.d analogous to wide spotlight, 'diffuse' beam. Ambiant. Phobic.
(1.e) The right's bias to low frequencies means that detected general patterns will contain a larger range of frequencies and so a link to multi-contexts whereas a particular frequency manifests a single context (see 1.b above). This favours the left being 'tonic' or 'key' oriented and the right being more into harmonics and 'linkage' (harmonicA+harmonicB+harmonicC etc).
(1.f) Although for any data the fundamental harmonic is processable by BOTH hemispheres, it is STRONGLY identified in the left hemisphere. In the right hemisphere it is barely differentiated from the other harmonics; it is 'diffuse' due to the low-frequence emphasis of the right.
(1.g) The left/right distinctions are repeated at lower scales, for example at the lobe level the same relationship of particular-to-general is present in the relationship of temporal lobe to parietal lobe in BOTH hemispheres. (The boundary is flexible, there is more of continuum from parietal to temporal and so no strong EITHER/OR line in determining particular-general but the biases becomes 'obvious' reasonably quickly).
(1.h)The left/right distinctions are also at the neural columns levels within a lobe. E.g. (A) the differentiation of left/right visual FIELDS in the occipital lobes is split into the interdigitations of left-eye data/right-eye data.
(B) the frontal lobes, in those areas linked to planning and pre-expression formatting, manifest the same pattern of interdigitations but at an abstract level with the interdigitation links being left hemisphere/right hemisphere. (see P. Goldman-Rakic's work in these areas. The original paper being:
Goldman-Rakic, P.S., (1984) "Modular organization of the prefrontal cortex" IN Trends in Neurosciences Nove 1984 pp 419-424
(C) The primary auditory cortex reflects interdigitations to process audition-sourced wavelength/frequency data.
When you apply various dyes across the brain you see a pattern emerge that is like a fingerprint or the patterns you see in nature on zebras etc etc What seems to be happening is that nature 'completes' the general individual (bias to SAMENESS) and nurture (especially in infancy) act to particularise and so create the particular individual (DIFFERENCE).
What is noteworthy is that the dye process brings out a hierarchic developing of the neocortex where scrapping away the surface of the neocortex shows a diffusion of the dye, unless you change scale. (see for example:
Grinvald, A., et al (1991)"Optical Imaging of Architecture and Function in the Living Brain" IN Squire, L.R., et al (Eds)(1991)"Memory :Organisation and Locus of Change" OUP.)
What this hierarchic format suggests is that the left-high/right-low distinctions are possibly applicable not only at the 'top'/'bottom' of the neocortex but also along the posterior-to-anterior of the whole brain, i.e. from the 'reptilian' brain upwards.
This arguement is reinforced by the tie of the basal ganglia to a sensitivity to CONTEXT, feedback processing and so LOW frequency, harmonics, data. The basal ganglia is just 'underneath' the six layers of the neocortex. These distinctions gives us at least a 3D format. (note that across the neocortex there are two 'paths', dorasal via the occipatal-through-pariatal lobes, and ventral via the occipital-through-temporal lobes. The dorsal is more sensitive to 'WHERE', the ventral to 'WHAT'.)
A good analogy for these left-high/right-low distinctions is the consideration of a gene encoded in DNA vs the same gene encoded in mRNA. DNA coding manifests 'right hemisphere' processing where the gene is 'diffuse' in that it is spread-out through the DNA strand(s). The process leading to expression involves the cut'n'paste of different elements of the gene (i.e. summing of harmonics) into a single thread expressed in the form of a mRNA strand prior to ribosome processing.
Thus the DNA format manifests approximations and the mRNA format manifests precision. The benefit of this, storing the information in a split-up form, is that it allows for an ease in 'playing' with harmonics; e.g. viruses etc were we see sections of strand that are thousands of years old and others that change 'hourly'. (I recall that Bacterial DNA contains genes in a contiguous space which is too rigid, too all-or-nothing. Our format is more flexible.)
The above comments re RNA-DNA are I think 'interesting' in that later I get into a development path that is tracable back to the 'big bang' and with it the suggestion that, from the principles of evolution alone, it would be 'crazy' to suddenly change a system that works to another one. What I mean here is that we 'see' in the neocortex the same 'extraction' processes as we see at the microlevel of mRNA-DNA processes. This said, the METHOD of analysis can create this impression! This is discussed later.
With the above 'simple' left/right distinctions we then consider the next set of information:
(2) The sensory systems, although having unique areas for processing 'primary' data in the neocortex, SHARE neural networks both BEFORE birth and in association areas in developing into adulthood.
This sharing implies the presence of hybridisation in expressions, by this the frequency data from DIFFERENT senses can be combined to give an abstract ('virtual') waveform which captures the 'essence' of both senses and so a sense of 'meaning' that is 'outside' of either sense.
The differentiation at the PRIMARY level is strong such that the degrees of synesthesia we find in infants soon dissapears. How about secondary/tertiary areas? see below re emotions.
(Good ref: Stein, B.E., and Meredith, M.A., (1993) "The Merging of the Senses" MITP. There are a number of popular texts as well on synesthesia etc)
What is implied by the sharing is the use of complex, sensory-based dichotomisations in the form of vision-data/audition-data that are processed (a) in opposition (what I see is not what I hear) as well as (b) cooperation (what I see validates what I hear - congruency). I will 'refine' the dichotomisation concepts further on.
(3) The process of habituation at the sensory (and associations) level suggests a system that has evolved to sense DIFFERENCE and that once the difference has been categorised and experienced further to the degree of being 'common' it enters the realm of SAMENESS and is then ignored; we do not have to keep identifying the 'old', just the 'new' or variations on the 'old'.
(I recall this is covered to some degree in: Posner,M.I., Raichle, M.E., (1994) "Images of Mind" Scientific American Library )
This emphasis on DIFFERENCE suggests the presence of genetically-determined 'seeds' in the form of fundamental distinctions to 'something'. (1) above suggests SAMENESS in the form of an archetypal fundamental together with a set of archetypal harmonics.
Samness links to the concept of a local, a particular. The work discussed in (1) shows that locals do not explicitly influence/interfere with a non-local, generals, but non-locals can influence/interfere with locals. What this suggests is that a sameness can be 'modified' by a difference. What is of interest here is that at the implicit level, local distinctions can create general patterns but there is no 'intent'. E.g. the flocking of birds, neural network synchronisations etc; interactions of 'SAMES' lead to an expression, a DIFFERENCE that is not sourcable to any particular; the flock behavour continues even if a few of the flock wander off.(This data comes from complexity/chaos research and in particular simulators used in Artifical Life programs).
(4) The hemispheres of the neocortex manifest a fundamental dichotomy in the form of a 1:many distinction.
There is a
The 1:many format ties to the processing (extraction/fitting) of TEXT from/into CONTEXT. This has been demonstrated in rCBF studies on negation. In particular, the making of a request, where one wishes to satisfy a context (as in asking a parent/spouse etc "can I go to X's place for dinner") puts the individual in a 'single context' frame of mind. Approval of the request just satisfies the context and so a 'thank you' or 'great' and end of story. But a refusal actually elicits a change in 'dominance' where there is a switch from 'left' to 'right'. What is going on?
The original studies just noted an emotional bias to positive/neutral thinking to the left and negative and so critical thinking to the right.
(See Gainotti, G., and Caltagirone, C., (eds) (1989) "Emotions and the Dual Brain" Springer-Verlag for papers on processing negation etc)
However I find this general interpretation 'weak'. I would suggest that the switch more manifests the use of abductive processes where in one form of abduction the individual switches to trying to find a context that can be introduced to change the refusal to an approval (e.g. "But last time it was OK" or the initial "But why not?") IOW you go through harmonics to find one that can be accentuated to get what you want.
This methodology, abduction, is common in us as a species where we hold a LOCAL text constant (the 1) and scan through different contexts (the many) to get a match. (the difference of abduction from induction is that abduction has, or assumes there is, a context that 'fits' the text. Induction starts local with no initial assumptions of there being a contextual, general, link. For example, mathematical induction stays 'local' by simply emphasising 'if N is the case, consider N + 1.." This emphasises a more 'within' perspective, there is no need to step outside of the local box other than perhaps 'a little'.)
(5) Emotion is the general response system to all sensory inputs, internally derived or externally derived.
As (4) has shown there seems to be an emotional 'tie' to left and right hemispheres. This has been supported over more recent times through the work of such people as A. Demasio and J. Ledoux. In (4) there is also some work by Doty, R.W., (1989) "Some anatomical substrates of emotion, and their bihemispheric coordination" IN "Emotions and the Dual Brain" p57-82
This work links to the limbic system etc and leads to the realisation that it is sensory harmonics, colour from vision and multi-frequencies (chords) from music that elicit 'refined' emotions and these harmonics are of course in the form of frequencies. These 'refined' emotions, being 'many' linked tie to right hemisphere processing biases and there is ample evidence to show that musical chords, colours etc, being SECONDARY+ and not fundamentals (black/white) elicit a more right hemisphere response.
It is only with musical training do you get a more 'left' oriented response to music, especially when reading since the 'dots' are very 'fundamental' in interpretations!; the dots are like words.
Combined with the information from (1) and (4) we can see how the left side is more often linked to 'single context' expressions of emotion whereas the right is more 'multi-context'; there seems to be a degree of 'finess' linked to the right since the expressions of emotions other than as pure forms (all hate, all love, single colour (?), single note etc) require multi-frequency data; the entanglement of harmonics to give more subtle expressions and this is low, multi-frequency data, something the right does 'better' with than the left.(Perhaps we need to make the distinctions of emotions (raw) from feelings (refined) but then this 'containment' of expression is not 'precise', it needs decoding, interpretation. M. Gazzaniga links interpretation (extracting the one from the many) to the left.).
There has been strong links in various texts to the right being 'better' at processing emotions/feelings and the data from the other references above suggest that, other than extreme expressions of emotions, there is more of a bias to emotions being 'in the background' to a communications and so more 'low' in format and so more favouring of the right hemisphere. As we saw from (4) this includes the concept of negation where negation is 'NOT' left, it is considered a harmonic in that to express negation you need a fundamental first.
(See the reviews on hemispheres and emotion in such texts as: Springer, S.P., & Deutsch, G., (1998) "Left Brain, Right Brain : Perspectives from Cognitive Neuroscience (5th Edition)" Freeman, or the ref in (4) above, or any of Ledoux or Demasio books).
To summarise things so far I think we can say that:
The analysis and synthesis of information is done through a set of filters that act to distinguish 'precise' data from 'approximations'; to make 'clear' identifications as well as allow for RE-identification.
This analysis/synthesis process lead to the use of set of fundamental filters expressed in the form of 1:many dichotomies:
SAMENESS : DIFFERENCE
PARTICULAR, LOCAL : GENERAL, NON-LOCAL
TEXT : CONTEXT
PRECISE : APPROXIMATE
POSITIVE/NEUTRAL : NEGATIVE-CRITICAL (dichotomies of emotion. These distinctions are already one level passed the base dichotomy of positive/negative emotion. I will cover this later.)
I suggest that these are 'collapsable' into the dichotomy of
OBJECT : RELATIONSHIPS
and the locational dichotomy of
WITHIN/BEHIND : BETWEEN
Other sources (not needed but useful) verify the general form of these dichotomies with the neurology showing a general bias to the WHAT/WHERE dichotomy, with the WHAT having within it the WHO and the WHICH
(categorical) and the WHERE having within it the HOW and the WHEN (coordinal).
At first you may think that these dichotomisations seem intuitively 'weak', too 'EITHER/OR', mechanistic, however earlier sections cover the emergence of the organic from the mechanistic and in the next part I will show you the results of applying dichotomies recursively such that the A/~A becomes a continuum and that becomes the basis for determining meaning to a degree where all disciplines seem to serve as metaphors for the particular describing of object/relationships data in a particular context. Those metaphors that are close to the 'real' have a more associative emphasis (1:1) but are in fact metaphors in that the lexicons involved contain words that link to the summing of sensory data and as such, these words 'transfer' or 'carry' the meanings.
This focus on dichotomisations brings out an emphasis on encapsulation of data and foreground/background processing where in this process of moving from a whole to its parts, a process of zooming-in for details, so we move from a general to the increasingly particular as we extract features from the 'background' into the 'foreground' (see refs on figures from ground processing in the brain)
As we flesh-out particulars so we gain a better understanding of the whole through the feedback, where the extraction and clear identification (labels etc) of a particular allows us to put that particular back into the whole but now clearly, crisply, identified and so no longer 'vague'. That clarity can then contribute to identifying associated particulars in immediate proximity to the one analysed.
From the level of the neurology, ANY movement from general to particular is a movement from low frequency processing (more so Amplitude Modulation (AM) in input areas (dendrites) to high frequency processing (more so Frequency Modulation (FM) in output areas (axon)), where it is the requirement of high frequency that allows for fine differentiation, finer resolution power, of parts/aspects. (this allows for a more LOCAL but very CLEAR (FM quality), single context (XOR) perspective associated more with left hemisphere or general differentiating areas of the brain as compared to the more general, vague (AM quality), multiple context perspectives (EQV – interchangable and so genrically ‘equivalent’ perspectives) associated with the right hemisphere or general integrating areas of the brain.
In the material previously referenced, we find the single context serves as a base frequency from which to interpret information - this reflects a 'holographic' nature (as it does a ‘key’ or ‘genotype’ nature) where we need the encoding frequency or lower to recall information and this is generalised into the notions of 'state-specific' memories. Under extremely high energy-utilising events, and so very high frequencies, we have 'flash-bulb' memories where these memories are more 'universal' and so context-free for recall (e.g. "where were you on Sept 11th, 2001?" )
The left/right asymmetry shows the 'base' frequency present in the left hemisphere as also being present in the right hemisphere but with no exaggeration - in other words the right shows more a pool of POTENTIALS, all frequencies of 'equal' nature, and the left shows an ACTUALISATION of one of those, an exaggeration, to serve as the 'ground' for interpretation.
That said, the left/right distinctions reflect the asymmetric dynamic at the level of the cortex but this is 'fractal-like' in that as we zoom-in for details so we find the same distinctions WITHIN each hemisphere etc etc (e.g. relationship of left temporal lobe to left parietal lobe, zoom-in again and the relationship is front left temporal to back etc etc) As well as across each hemisphere from back (more general) to front (more differentiating, with integrating more 'sequence' oriented).
We could overlay each of these general-to-particular patterns with an abstraction of the neuron - the core fractal 'shape' at work.
We can represent this movement from general to particular, and so the increase in precision in identification, by representing each level of 'meaning' in the form of a particular frequency - and we can use the recursion of a dichotomy to show this process where each level of recursion is represented by increasing the frequency by a power of 2.
Note that to implement XOR in the brain requires two neurons, one feeding-back on the other, and so a form of self-referencing. The natural oscillations in the brain span specialist areas of differentiating/integrating such that, given the attention system and its ability to focus, allows for 'passive' recursion in a bounded space of the XOR/EQV dynamic. The set of POSSIBLE combinations of XOR/EQV derived from the recursion can be used as a toolkit of 'meanings’.
Given six 'loops' of recursion of a dichotomy, we move from a position of identifying each element of the dichotomy as a wave cycle to give us a base waveform with a frequency of two cycles per second. The "WHOLE" as such is a waveform of one cycle per second and the dichotomy reflects the first level of differentiating, and so a whole is 'cut' into two, vague, but distinct, parts such as 'positive' / 'negative' or 'on' / 'off' etc.
Thus, using the differentiating/left vs the integrating/right, out of the right, the side associated by neuroscientist M. Gazzaniga with "AS IS", comes our zooming-in for details analysis and so the particular that gives us "AS INTERPRETED" - it is this position more associated with mediation dynamics and the nature of consciousness as compared to instincts/habits that are properties of our as-is nature as species-members)
As we recurse the dichotomy so we create finer distinctions made-up of summing the different frequencies of each level of recursion. Thus, for example, at the sixth level we have 26 = 64 representations of 'parts' of the whole, or more so exaggerations of aspects of the whole where the whole is of all aspects encoded as POTENTIALS and LOCAL CONTEXT will then favour the eliciting of one aspect in response to that context over all of the others. (see below comments on emotions on the surface of the face)
We can represent these aspects using the discrete terms of bit values, 0/1, as long as we recognise that each bit in a representation made-up of a string of bits is associated with a particular frequency based on the position of the bit as a power of 2. Thus in the representation in a bit sequence form of 110111, the first bit represents a frequency of 2 cycles per second (cps), the second of 4cps, the third of 8cps (but here it is 'off' or 'negative' and so there is no activity or a cancelling activity), the fourth of 16cps, the fifth of 32cps, and the sixth of 64cps. The SUM of these frequencies (and so reflecting a superposition) will give a unique pattern, a wave form, representing a particular quality - '110111'. (Note if we use the binary representation of a wave, then we are dealing with summing 'square' waves - the analogue version being the 'normal' sine wave)
Since increase in frequency is associated with increase in differentiation and so in precision of expression, so the representation of 000000 is a representation of a POTENTIAL, or vague, and the representation of 111111 is a representation of full, total, ACTUALISATION, or crisp.
At the sixth level of recursion we have 64 '6-bit' forms, representations. Since the neurology appears to work in a more binary format (0s/1s plus modulation/mediation) so these bit representations (and those derived from further recursion where we add no more other than making finer distinctions) can represent DIFFERENCES in expression of neurological states that in turn reflect DIFFERENCES in expression of general physiological states of any neuron-dependent life forms - and as such are representations of states derived from interaction of life form with local context.
The bit representations reflect the ever-improving differentiation of particulars from the general that is represented in the first bit. As we add bits so we create new 'generals', new 'contexts' within which the next set of bits function. For example, in the representation of 1111, this sets a context, a general, for the next PAIR of representations of 11111 and 11110, and so text, particulars that in turn each become context for further development.
What the discrete nature of bit representations 'hide' is the fact that these representations are all WITHIN the whole and as such are expressions of the whole as POTENTIALS - context can push the whole's "buttons" to elicit a particular expression, the 'bestfit', out of the set of possible expressions, but those expressions not explicitly expressed form into a sequence of expressions sorted from 'bestfit-1' to 'worstfit'; in other words they contribute to the expression.
The above dynamic reflects a topological perspective where a bounded surface is pulled this way and that and in that pulling so one area influences, or draws into its expression, all of the other areas (note how this allows for TWO forms of identification - the explicit and the implicit - the latter where analysis of behaviour of other areas can lead to implying a particular area's behaviour.
This 'rubber sheet, geometric' perspective being the case, why use 'bit' representations where they can 'distort' one's perspective of this perspective? Surely the fact is that rather than dealing with discrete units we are more so dealing with a sea upon which are expressed local conditions in the form of wave dynamics etc.?
The benefits of bit representations is this: since each representation is the expression of an ASPECT of the WHOLE so in that expression will be ALL of the WHOLE and so all of the other aspects will contribute in defining the expressed aspect.
In other words, each "ASPECT" is a presentation of the whole in some form of locally-determined expression; the analogy is to facial expressions where the whole is the face and each complement of muscles etc, when acted-upon, bring out a particular expression. We see this expressed on the face in the form of emotional expressions (with the set of POSSIBLE expressions derived from recursing the fight/flight dichotomy at the core brain areas (amygdala) and on into a general cortex dynamics of emotion) and so see a template for communications (the face playing a major part in non-verbal communications and so allowing for the generalisation of facial expressions into general expressions. We can generalise this to cover the sensory cortex of the brain as the bounded surface and dynamics across that surface elicit local expressions etc - same principles, different scales. This allows for such events as synesthesia where specialist senses data is 'confused'. All of this moves us into the realm of "regular" vs "small world" networks where LOCAL context, and that includes sensory biases, can 'customise' the set of POSSIBLE, universal, expressions (regular network) into a set of refined LOCAL expressions (a small world network where these local expressions in turn can be considered as 'universals' from that local level))
How can we extract from each particular expression the contributions of all of the others towards that particular expression? The use of bits reflects the use of high energy analysis, of differentiating, of high frequency processing. Neurologically this is the realm of XOR, the EXCLUSIVE OR, where this realm allows for high precision differentiation of parts from a whole (and that includes attempts to extract what appear to be parts but are not - as we find in sensory paradox processing )
In the analysis of the brain overall, so we keep coming across the XOR/EQV dynamic where the EQV manages all that is 'linked together' and so a relational bias, and the XOR manages discrete units and so an objects bias (But WITHIN each object we find integration, EQV-ness, in the form of hierarchy etc).
As mentioned before, we can in fact trace this XOR-EQV dynamic down to the level of the neuron (below figure), where the EQV nature is represented in the dendrite regions (AM bias, wave) and the XOR nature in the axon regions (FM bias, pulse) - with the basic dynamic that of a analogue-to-digital converter as we extract details from a whole (and feedback allows for refinement of that whole such that we can extract particulars, refine them, and re-insert them into the 'whole' to give a more refined response to some stimulus; we can refine instincts/habits and/or create new ones that allow us as species-members to interact organically, immediately, holistically, with the context).
The XOR/EQV dichotomy reflects the characteristics of an asymmetric dichotomy where the discrete, the XOR, results from the zooming-in, the exaggeration, of a particular in the realm of EQV. This form of dichotomy, when recursed, will give us a spectrum, showing its association with power laws etc. In this spectrum, using analogy to light, so the high energy 'end' is associated with bit representations of 111111 (blue/ultra-violet) as is the low energy 'end' associated with bit representations of 000000 (red/infra-red). In other words the EQV end is an end of POTENTIALS or 'vague' relationships when compared to the XOR end is an end of ACTUALS (and so of crisp "thing-ness" etc - note that the recursion will in fact create a dimension made-up of PAIRS of object/relationship categories getting increasingly more 'discrete' in categorisation as we move towards the high energy end of the dimension)
When working in the realm of XOR and EQV we are working in the realm of 'logic operators'. In this realm we find that to extract the descriptions of the contributions of all possible expressions to any particular expression we XOR all of the other expressions in their bit forms with the bit form of the particular expression. What we are doing is what the brain appears to do in extracting details from a complex system, it applies XOR to the EQV realm (and this can cause paradox at times where we try to reduce the irreducible).
How does this work? Each bit in the bit-representations represents a particular frequency that is contributing to an expression. By turning OFF all other frequencies BAR the particular frequency or frequencies we wish to analyse we set-up a 'bit mask' that, when XOR-ed with any particular expression will bring out that bit-mask's expression THROUGH the particular expression. For example, if we have a bit pattern of 100001, then XOR-ing that pattern with, for example, 101110 will give us:
001111 (The XOR 'rules' are, given a column of two bits, the result is 1 if the bits in the column are ordered 01 or 10, any other ordering (00 or 11) gives a result of 0)
This derived pattern is an analogy in that it describes by analogy the expression of 100001 THROUGH 101110. This dynamic is a property of the recursion and it allows us to deriving meaning of some particular through reference to all of the other particulars contributing to the whole.
What we are dealing with here is the basic dynamics of a finite language where that language is here in the form of 'qualities' expressed as summing frequencies. Since each level of recursion will create a FINITE set of qualities, so their use in representing and so communicating 'all there is', is through ANALOGY/METAPHOR in that we cannot have a 1:1 mapping of our finite qualities to 'all there is' at the level of particulars, but we can have it at the level of analogies/generals. (in formal language we move into the realm of the noun/verb dichotomy that when recursed gives us the full set of noun/verb forms that we then localise through labels that tie the universals to a local context)
Thus, our expression of the '100001-ness' of 101110 can only be achieved through reference to some other bit-representation in the set of possible bit-representations - and here it is 001111. In other words the "100001-ness of 101110 is LIKE the (under-played) characteristics represented by 001111" (this is clearly demonstrated in analysis of the generation of some of our basic, specialist, typologies, as discussed elsewhere)
The question now is "What are these mentioned 'characteristics'"? We have as yet not touched on the details of what these bit values represent OTHER than "frequencies" - but we have made mention of recursion of the dichotomy of fight/flight, where that recursion gives us the spectrum of basic emotions. That recursion can be REPRESENTED using the bit patterns such that (a) ANY dichotomy can be recursed and represented using the described bit patterns, and (b) EACH quality derived can be described through reference to all of the other qualities derived using the described XOR dynamic. What we are dealing with here is isomorphism - same qualities, different labels (see, for example, the translation page )
This is all possible since what we are describing is the root of meaning and its expression. That root is in the dynamics of the neurology where that dynamic elicits patterns of meaning from 'mindless' acts of differentiating/integrating data – this is the realm of ‘sameness’ associated with Jung’s “Collective Unconsciou”. The recursion of the differentiate/integrate dichotomy (something guaranteed by the brain's natural oscillation across brain areas focused on differentiating or integrating) will elicit patterns representable using bit patterns and they apply to ANY synonym of the differentiate/integrate dichotomy - the most common in the neurology being the dichotomy of the GENERAL qualities of WHAT/WHERE (particularised into the sets of (what, who, which) and (when, where, how))
Closer examination shows us that we are in fact dealing with TWO forms
of dichotomy, one symmetric and more LOCAL, one asymmetric and more GLOBAL. The
symmetric dichotomy associates with data reflected in Gaussian, or
As demonstrated elsewhere (see the earlier covering of wave interpretations for a particular mapping of waves to meaning in a specialist context; also see wave structure showing isomorphism across specialist interpretations) , we can, given just six levels of recursion, generate a set of qualities that become universals in their use to communicating meaning. LOCAL context allows for the linking of these universals with that context through derivation of labels, such that that relationship can elicit a specialist language that aims to hide the sameness of the universals across different contexts by the use of labels to emphasise difference. In this hiding, so the local customisation can skew the interpretations of the universals, and even limit their full expression, and so create a 'small world' network out of the set of universals working as a 'regular' or 'context-free' network.
Each 'small world' is a specialisation that from WITHIN can appear to be the world 'as is' rather than 'as interpreted'. Thus we can take the 'figure' for the 'ground' where there is an increase in hierarchic perspectives the details we go for - we move from a semantics perspective to an ever increasing syntax perspective where all that matters is one's 'correct' position in the hierarchy.
In the context of temporal lobe dynamics, consider:
(1) our neocortex etc reflects well-developed neural dynamics for VISION processing.
(2) considerations of the temporal lobe dynamics cover an 'object' emphasis apparently surrounded by 'aspect-sensitive' elements.
Now consider this section from a recent Scientific American article - covering development of colour vision in primates:
(Scientific American Magazine - March 16, 2009
Color Vision: How Our Eyes Reflect Primate Evolution
Analyses of primate visual pigments show that our color vision evolved in an unusual way and that the brain is more adaptable than generally thought
By Gerald H. Jacobs and Jeremy Nathans):
"To explain how randomness helps to produce trichromacy, we must first review how cone cells transmit information about color to the brain. It turns out that having three pigment types, while necessary for trichromatic vision, is just an initial condition. Neural processing of the signals generated by the various photoreceptors is the next step. This step is critical because individual cone cells cannot convey specific information about wavelength. Excitation of each photoreceptor can be triggered by a range of different wavelengths, but the cone cannot signal what particular wavelengths within that band it has absorbed. For example, it could produce the same size signal whether it is hit by 100 photons of a wavelength it absorbs well or by 1,000 photons of a wavelength it absorbs poorly. To distinguish among colors, the visual system must compare the responses of neighboring cones having different pigment types.
For such comparisons to work optimally, each cone cell must contain just one type of pigment, and cones making different pigments must lie close to one another in a kind of mosaic. In fact, in the primate retina each cone cell does contain only a single type of visual pigment, and different cone types are arranged in the requisite mosaic. Yet every cone cell in a trichromat harbors genes for all three pigments. Exactly how a cone cell "decides" to express just one pigment gene is not entirely clear."
and then this basic page on mosaics -
There is an immplication here of temporal lobe dynamics reflecting the abstraction/generalisation of the cone type arrangements to neuron arrangements for general information processing. As such the patterns detected in the original temporal lobe study were in fact manifestation of the mosiac-like dynamics we see in vision.
just to extend things a little - the dichotomy of the eye is that of fovea/para-fovea. The para-fovea reflects 'right brain' tendencies in form detection, pattern matching but 'vague' when compared to fovea that is high details, colour mappings etc, The emphasis on precision, details, brings out a focus to a 'left brain' tendency of local context, rich vision but lacking peripheral vision capabilities (THAT covered by the parafovea).
The fovea develops out of, in the middle of, the parafovea and this emergence is reflected in general hemisphere development of skills as the left 'emerges' from the right and as such the differentiating from the integrating, the particular from the general, the anti-symmetric from the symmetric.
Since the neurology reflects a property of general nature - utilise working systems beyond their original contexts, so the mosaic dynamics re details processing of the eye would be abstracted if successful to general information processing, here in 'object' space as compared to the parietal cortex of relational space.
As such a generalisation is to suggest differentiations being mosaic in form but the neural hierarchy introduces customisations of general to particular mappings and so the asymmetry we observe across apparent part/whole distinctions. In other words the 'small pieces' of the mosaic are of different sizes as we move through the neural hierarchy and so shift resolution powers from low to high and so from 'full vision' to 'fragments'(and so the tie to fractals) - akin to blowing-up a picture to a level of seeing the granules that make-up the image - and so bringing out the anti-symmetry/asymmetry nature overall.
A fundamental tool used in prediction is the derivation of a classification system. In Western civilization, we can trace this back to the works of Aristotle (1) and the concept of dichotomy. A dictionary describes dichotomy as:
"1. (logic) division into two classes, one positive, the other negative. 2.(botony) a mode of branching by repeated bifurcation" As will be shown, these are somewhat 'gross' representations.
The concept of dichotomy allows for the enabling of a frame of reference, a universe of discourse, where classes are created such that, for example, an object is symbolized as either being in 'A' (in the class) or in '~A' (outside the class). We can therefore symbolize the universe of discourse by the symbol '1', and thus:
A U ~A = 1
The symbol 'U', from set theory, represents the concept of
For any class, 'A', that includes less than the whole universe, what remains in 1 is '~A'. This is the aristotlian approach linked with logic in the above definition. What is implied here is the 'wholeness' of 1, the universe of discourse within which I make my indications of A/~A.
This simple process can then be applied to each element of this dichotomy where the element takes on the mantle of the universe of discourse and I can, for example, form B/~B within the context of ~A. The latter in fact shows the emergence of hierarchic forms based on dichotomous processes and this is the approach linked with botony in the above definition. The latter introduces the concept of indication in that the emphasis is on an aspect of the whole rather than an independent entity.
The use of negation(~), as is found in Aristotle's A/~A, leads us into the two forms of dichotomy, dichotomies of opposition and dichotomies of complementarity (the latter being an abstraction of the bifurcation concept mentioned in the above definition. Working backwards, the two elements join into one. What also needs to be considered is that dichotomies can be read as either two extremes that have the same absolute values (like the two ends of an axis – the linear point view) or as text and context, where one element forms the context(background) for the emphasized other(foreground). This implies that their absolute values are NOT the same, at least qualitatively if not quantitatively - we see here the dichotomies of the 'Gaussian' type, where the elements of the dichotomy are symmetric, vs the 'power law' dichotomy where the elements of the dichotomy are asymmetric (bringing out a focus on mediation dynamics that can be short term or eternal) - we can add to this the mix of the two to give us as third - hierarchic form. As such we self-reference:
A dichotomy represents sequence. (ordinality bias, hippocampus-related dynamics)
A dichotomy represents magnitudes. (cardinality bias, amygdala-related dynamics)
A dichotomy that mixes these qualities to give us a sense of hierarchy (in turn we can map out forms of hierarchy covering the non-nested to the nested, where the former is rigidly hierarchic, control focused, and so pyramidal in form; there is a focus on issues of difference to sameness management. On the other hand, the latter is less rigid, more open to dependencies across levels and a such leading to a web-like structure and so 'flat' hierarchy with an overall sense of working with levels of sameness - refinements of the known etc)
As such we see here the development of symmetric, asymmetric and anti-symmetric perspectives. The methodology of our sensory systems and the neurology indicate that each moment is represented by all three perspectives and so is analysable into all three for the analysis of details.
Dichotomies of opposition ('Gaussian' dichotomies, LOCAL symmetry, difference from sameness and so in general anti-symmetric) are used more in analysis and clear assertion of A from NOT-A, and so where the two elements are often destructive when combined. (Exclusive OR). More so the focus is on deriving difference from sameness where the elements of the dichotomy are, generically, the same (as in differentiating/differentiating OR integrating/integrating).
When we consider hierarchy, so these sorts of dichotomies apply to elements sharing the same level in the hierarchy. Of special interest is where we try to impose symmetric interpretations of an asymmetric reality.
Dichotomies of Equivalence (these are like those of opposition in that they present as guassian distributions if selfreferenced, BUT the logic operator is EQV, equivalence, and it covers what Bohm labelled as “differerences that DON’T make a difference” – this reflects the interchangability of the elements of the dichotomy, and so reflecting
symmetry. The elements will be WHOLES in the form of metaphors – e.g. Science/Religion.
Dichotomies of complementarity ('power law' dichotomies) are used more in mediation and synthesis, where the two elements are seen as parts of a whole with the whole emerging when the parts join - (Inclusive OR or more so sharing of space as equivalents (EQV)) - with the final whole being the universe of discourse. The dichotomy spans all levels of the hierarchy and as such reflects all levels of that dichotomy. This form of dichotomy is assymetric where we focyus on deriving sameness from difference (i.e. differentiating/integrating) - what is the 'common' ground - this covers acts of mediation. Our brains reflect this form of dichotomy as the foundational (as reflected in the WHAT/WHERE focus of our brains in processing information). Note that 'complementarity' covers the relabelling of the same thing - as such an label of 'equilibrium' and 'far-from-equilibrium' can serve as a complementary dichotomy where the 'far-fromequilibrium'' element is an exaggeration of the 'equilibrium' element - as such there is not 'cut' but more a difference in energy expenditure, a re-configuration of topology to bring out a 'difference'.
We can see an asymmetric and symmetric dichotomy dynamic in, for example, the dynamics of the asymmetric dichotomy of fermions/bosons (from particle physics) out of which comes the anti-symmetric dichotomy at the fermion end of positron/electron where their CLEAR, exclusive OR, qualities and so A/NOT-A. If we move to the bosonic side of the dichotomy the positron/electron transform into a pair of bosons as thy come together to share the same space. What this brings out at the level of thought is the ability to describe something by what it is NOT and so the equivalence of A and NOT-A.
All of this said, it needs to be noted that the destruction of the elements in a dichotomy of opposition is in fact more a transformation; for example, matter/anti-matter join into a burst of energy, just as minus and plus join to become zero (neutral). However, there is no hierarchic change of level. As found in dichotomies of complementarity, I can often recover the elements from the whole whereas the union of oppositional elements cannot be reversed from the result.
Closer examination of the dichotomization process also suggests that dichotomy has in fact three types of dichotomous contextual relationships that affect states (four if you consider position as important e.g. many:1 as well as 1:many):
One : One
This is the conventional logical and 'scientific' point of view with a single context, relational analysis bias. e.g. in the dichotomy of Positive/Negative there is a one:one bias in that text and context for both elements are considered equal. This is the common type for dichotomies of apparent opposition, where each element is treated as a whole and context is almost ignored (or else very 'gross'). In dichotomies of complementarity, each element is treated as a part with the context being the whole (aka the next level in the hierarchy). In a mathematical sense, the absolute values of each element are equal.
One : Many
One context to many - hierarchy analysis. This seems to 'map' the current model of the hemisphere functions of the brain and suggests a representation of a 'balanced' state. e.g. in the dichotomy of Individual/Sociological there is a bias in that the context of Individual is singular (one state) whereas the context of Sociological implies many states (hierarchy). In a mathematical sense, the absolute values of each element are never equal. The closest a 1:many dichotomy can get to a 1:1 is at the level of 1:2. This brings out the main attributes of asymmetric dichotomies, as expressed for example in our brains usage of mediating with reality through the what/where dichotomy aka differentiating/integrating.
Many : Many
'Un-scientific' point of view due to weakness in prediction - too many variables; a hierarchy to hierarchy. This is usually 'removed' by treating both elements as 'ones' of a higher class - the act itself showing hierarchic thinking - or else using the process of idealization to extract one element from each 'many' and treat them using dichotomous analysis of the one:one type, and then doing the same for other elements. The fuzzyness of the degree predictabilty is manifest in the 'fact' that, mathematically, the comparison of the absolute values of each element could be equal or not - context is a strong influence here.
1. objects of dichotomization - wholes and their aspects
2. dichotomous forms - opposition (clear expression), complementarity (mediating), hierarchic
3. dichotomous relationships - 1:1, 1:many, many:1, many:many
4. dichotomous transformation - induction, abduction, deduction, nominalization
5. dichotomous structure - expansive and contractive
6. dichotomous traits - relational and hierarchical
There is a subtle distinction here. Although hierarchy implies relationships, they are fixed. The emphasis on relational
and hierarchical emphasises the dynamic and static concepts.
7. dichotomous representations - discreteness and continuity (continuum)
from continuity comes the ability to use wave analogies and the concepts of parts and aspects as harmonics of the whole; the whole treated as if an octave. The continuum also emphasizes the concept of bias rather than absolutes. What should be noted when making a wave-biased analysis is that the use of sine/cosine based functions will always have an aspectual, analog character compared to the tan based functions that are more discrete.
8. dichotomous context - each element of a dichotomy exists within the context of the other and both exist within the context of a whole. In dichotomies of complementarity (mediating) the elements can enfold back into the context; they can occupy the same space. Dichotomies of opposition, although in the same context, cannot occupy the same space, thus suggesting these dichotomies have their elements treated as if wholes.
9. repeated dichotomization through time leads to emergent hierarchies.
This has an interesting consequence when considering dimensional maps based on orthoganal relationships. It suggests that the derivation of information using orthoganal relationships, and thus a bias to contextual independence, in fact hides the hierarchic relationships and thus the contextual dependence. The process of orthoganal emphasis is in fact the emphasis on dichotomies of extremes expressed geometrically where attempts are made to avoid hierarchy. For an example, in the MBTI® we find that the supposed orthoganal dichotomies hide the underlying context-dependent dichotomies that form the hierarchy. Overall the focus here is on the dynamics of recursion. and from there the emergence of languages as a consequence of mediation.
10. From 9, specific 'states' emerge from developed hierarchy.
Here we find that the states generated within each hierarchic level have specific descriptive characteristics analogous to terms used to describe types of mixing. Although these terms can get more complex the more levels we go through, they are found to be hybrids of four mixing types combined with the characteristics of (5). The four types are Blend, Bond, Bound, and Bind. These characteristics are the root of dichotomous meaning in that objects with dichotomous roots that the individual finds as 'valued' will enable the ellicitation of the same meaning when other objects have the same characteristics (and thus become also 'valued'). This valuation often occurs out of 'real time' context since the only context in the template is mixing. - In other words, the qualities of 'power law' dichotomies are fixed. We simply relabel them to fit a particular context. For example, astrologically-based descriptions of one's persona, since they are based on the dichotomies of fire/water and air/earth, will ellicit mixing responses that have previously been set off by more dichotomy-based 'common sense' descriptions of persona (e.g. MBTI or tests using the 'BIG-5', or just a degree of self-reflection). This resonance can then favour the individual declaring that there is something of value in astrology, not realizing that it is the dichotomous roots of both systems that is resonating and creating 'meaning'; they treat the metaphor (Astrology) as if 'fact'.
11. Dichotomy analysis includes the normal distribution curve and the power law pattern.
The 'wave' nature previously described introduces probability concepts and the suggestion that the moment we make a dichotomy we inherit one of it's properties - the normal distribution curve. This is the gaussian dichotomy. From a distributions perspective the basic form is binomial - from there comes guassian and poisson distributions.
12. Dichotomous analysis is always incomplete.
Using dichotomy, one can never get a whole picture, only a very refined picture. Thus any model that has dichotomous roots will be found to have a degree of incompleteness. Since most of scientific 'fact' is symbolized mathematically, and since mathematics is founded on dichotomy, all of the models within Science will show a degree of incompleteness; as will any other models developed within any other dichotomously-derived system of analysis. Godel found this in Mathematics. Heisenberg found this in Physics. Yeats emphasized this, as did Lao Tsu in 450 BC -
you cannot 'cut' the whole. On the other hand, this statement is made within the context of dichotomy and so there may be something else that can help resolve the incompleteness 'problem'. This is all brought out in asymmtric dichotomies and so issues of mediation combined with the emergence of a symmetric dichotomy of rigid, excluded middle, assertions. E.g. the concept of uncertainty from the play of position
and momentum where the former is overall a symmetric dichotomy of position ve all others and the latter covers movement and so a mediating emphasis.
13. Continuous use of recursing dichotomy leads to complexity/chaos and the transition from the mechanistic to the organic.
As we build our 'whole', so the degree of complexity increases due to the large amount of 'cutting' that occurs. This cutting means we create more borders and it is on borders that complexity/chaos thrives. Thu information can turn apparently entropic (or more so, increase in fragmentation leads to increase in specialisations that in turn create their own languages and so that can appear extreme - too much specialisation elicits 'noise'). However, patterns emerge within this apparent chaos that show a degree of stability and from the complexity can emerge 'new' behaviours. This gets into the relationship of phase transitions and power laws. As we 'cut' so we create
borders and so enter the realm of complexity/chaos. However, we also enter the realm of phase transitions and 'far-from-equilibrium' bifurcations that also allow for literal categories derived from the recursion to take on the capability of being taken figuratively and so as sources of analogy/metaphor.
Thus the use of the sense of dichotomy will lead to the emergence of the above characteristics within the object under consideration not as a result of the intrinsic nature of the object but due to the nature of the sense. Just as the eye does not hears pictures nor the ear see sounds so the abstract sense of dichotomy too has it's forms of representations and it's limits. What is implied by this is that 'meaning' is only valid within the initial context of dichotomy. The proposed template is a template of metaphor-derived meaning based on whole, part, aspect analysis. Thus all dichotomously derived systems of analysis are metaphors for whole/aspect analysis - which is what the basic neurology deals with. Of interest is the observation that (point 13), since mathematics has dichotomous roots, and since chaos and complexity have emergent properties, so these properties should exist within the overall brain system.
Any dichotomies in 'attractor' language map to the IDM perspective, in particular the development of pairs from recursing a dichotomy. The dynamic of the pairs emerge once one moves past the formal differentiation of each (point). The moment you have a dichotomy and start recursing the pairs reflect extensions from a point perspective to a limit cycle and on to strange where meanings covering the core elements are in the form of trajectories around such - the uniqueness of each expression (and so difference) in relation to the sameness of meaning at each instant. - thus the stability of an archetype, when exposed to local contexts is customised semantically and from that link with finer and finer local distinctions 'fragments' but still retains a core sense of stability 'around' which expressions of meaning move, but never 'touching' the universal meaning and also oscillating across the core 'split' of the meaning into a pair of meanings - where form A can suddenly flip to form B etc.
Dominating dichotomies include positive/negative feedback properties where they reflect isomorphism to properties of differentiate/integrate, difference/sameness etc (and so we move into the characteristics of expression dependent upon the Lyapunov exponents where such characteristics map to the generic form of dichotomy of positive/negative, differentiate/integrate etc)
The organic development through self-referencing is an ad-hoc process such that some meanings are well defined, others not. With increase definition comes increase in border creation and so increase in complexity/chaos dynamics.
The 'formal' methods of recursion give us 'order' as in: 000, 001, 010, 011 etc etc but these are ideal representations where in reality this is 'messy' (e.g. rate of period doubling being dependent for each dichotomy on influences of context) BUT still behaviourally distinct. Thus the pair of 000,001 reflects mixing of sameness (00) and difference (01) and I can take the pair and form them into a dichotomy that is then self-referenced to cover the range of dynamics across such a pair. THAT range will also come in pairs due to the root of the process being in self-referencing a dichotomy (and so pair).
Each dichotomy can be interpreted as a unit axis and self-referencing gives us dimensions of unit axis form (XYZ coordinates of Cartesian representations are unit axis forms of 'positive/negative' when we do not extend them with numbers (that reflect multiple sameness)).
If I stick to 'bit' sequences in generating patterns the we move into cellular automata dynamics and with that the chaos game and the Sierpinksi gasket etc (See Wolframs "A New Kind of Science" or sections covering the gasket in such well known texts as 2nd edition of Peitgen, Jurgens, & Saupe "Chaos and Fractals : New frontiers in Science") - and so the same dynamics overall but mapped to bit patterns (sequencing over magnitude).
A 'bit' represents a point in phase space. The stability of such can be interpreted as a universal in that change of context does nothing, the bit remains a constant.
We can extend this into considerations of the formation of a ratio as a trajectory approaches the point; the trajectory can oscillate either side of the 'value' of the point and so reflect negative feedback dynamics as we approach the point. We can also spiral in to a point, but the form of the spiral relates to a negative feedback-derived ratio (recall the precision issues covered in IDM where a circular like spiral reflects roots in the Fibonacci sequence and the more precise we get so the more square becomes the spiral as we approach the binary sequence to elicit more precision, more 'XOR'ness so precise expression of 'the point') Thus -- in the context of meaning generation we can, with a universal, approach it directly or oscillate 'around' the meaning or spiral into it.
When we move to periodic attractors (limit cycle) we cover information 'bit' repetition in the form of 0 to 1 and back. The periodicity is mapped and can represent meaning shifts regarding context (e.g. the dynamics of fight/flight in the form of predator/prey presence). In bit formats we can map out the cycle through extending representations to reflect cycle across the attractors of 000/111 through states of:
The main emphasis here is the stability - in the point it is constant, here it is constant but over time. In weather prediction the 'snow in the sahara' condition reflects an extreme but the system quickly returns to 'normal, cyclic' weather conditions.
Note in the above bit representations the order is rigidly binary and so reflecting the tight link of each bit representation with the next. (if you want to work numerically, read the patterns right to left to give you the decimal equivalents of 0,1,2,3,4,5,6,7) We can combine limit cycles to give us extended forms of attractor - a torus. In bit representations I can 'wrap' the sequence back to itself to form a toroidal representation.
Ad-hoc distinction making in a 'meaning space' reflects dynamics of exponentiation and that relates to 'period doubling' dynamics. In the ideal form of A/NOT-A the exponent is an integer (2n). (adding a value thus takes our eight-element cycle to 16 etc) In the bifurcation dynamics we reflect a negative feedback aspect (focus on approach and use of limits) in the form of a developing constant in the form of the Feigenbaum number all associated with bifurcation periodicity. How does this relate to mind? It’s a bit like the need when thinking gets too complex to 'add a dimension'. The rate of increased complexity relates to the reaching of a bifurcation. (recall that the brain will oscillate across both hemispheres when dealing with the new OR COMPLEX. The oscillation reflects a period dynamic and repeated such reflects selfreferencing that 'doubles' the choices possible in deriving a meaning WITHIN the range of possible meanings. – each double is equivalent to adding a dimension but there is also scope for moving from exponential development to hyperbolic, 2n becomes n2). If we add to this 'sensitivity to initial conditions' then we have to add, from a mind perspective, current set of memories that serve as feedback to input regulation. This allows for the smallest of comments to elicit some extreme emotional
reaction due to the 'hidden' influence of memories on the moment. What we find in the IDM work with XOR is a state that can neutralise such an expression (it’s a bit like a Nash equilibrium state given some zero-sum game condition)
An issue with ad-hoc development of meaning(education etc) is that meaning 'trajectories' are not necessarily 'in line' with each other, there are sharp differences in understanding even though the understandings are 'next' to each other. This is the difference between a 'well rounded' education vs an overly specialist education or 'ad hoc', context dependent, education.
These issues move us into 'strange attractor' dynamics that allow for 'sudden' jumps in dynamics. The best analogy is to ad hoc education allows for associations 'all over the place', the mixing of metaphors if you like, such that the 'stability' of a rounded, universals-focused, education is surrendered for recognition of stability amongst a lot of instability (one is 'all over the place' and yet there is a 'boundary', a containment present to encapsulate the instability - all meaning trajectories are still within the overall containment area (memory/mind). It is possible to map this to extended exposure to a range of inputs will, over time, cause the smooth link-up of meaning across trajectories; a rich associative memory develops from such a state!
A periodic attractor is akin to a routine in behaviour and so sets down stability over time. A strange attractor will contain periodic forms but overall can 'jump around' and its 'mixing of metaphor' style reflects a symmetric element overall in that any X (metaphor) is interchangeable with any other X - IOW there is a lack of rigid order, a lack of syntax globally - as such a strange attractor is very post-modern!
From a meaning position, a point attractor is a universal, consistent, eternal. A limit attractor adds time and so some 'variations' are possible but the 'preferred' meanings are retained as the foundations. With a strange attractor there is an entanglement at work, somewhere is the 'universal' but metaphors take over (meaning trajectories)such that we move 'around' but also 'jump' around and with that comes an invariance with probabilities distributions(given enough time to map them all out); IOW metaphor X is as useful as, as probable as, metaphor Y - interchangability rules!
Given our discussion so far, it becomes obvious that we need to address the issues of ‘universals’. The dynamics of the nominalist perspective dominates metaphysics and so the realm of ontology where such is grounded in issues of a more anti-symmetric perspective, as is covered in our brains.
If we focus on what neuroscience is telling us, and combine that with what astro physics is telling us in the context of dark energy and dark matter, the implication is that what is missing from our perceptions of our universe is the asymmetric – all we CAN sense is order out of noise and so the symmetry that comes out of historical development – be it in genetics or socialisation or in the ongoing development of the universe. Thus there is nothing ‘missing’ in our universe, what we cannot sense, other than knowing something is ‘missing’ is more that something is uncontained and so has not yet developed order and so symmetry where we need such to derive meaning past ‘the moment’. The universe we ‘see’ as such is one where only the symmetric elements have develop naturally given any chance of aggregation of elements. The adaptation of the brain to this is covered in the anti-symmetric/symmetric nature of our information processing through the asymmetric and its establishment of languages (and so the path to transcendence is through language); the natural dynamics of the brain bring out the grounding in instincts and so determinism and so the symmetric – our basic hypothesis at birth is in the form of an aggregation of instincts and so grounding in symmetry. Without that determinism there is no ‘us’, there is no ground from which consciousness as an agent of mediation can emerge.
When we utilise our brains in observing reality all that is observed and held meaningful must be associated with symmetry since aggregation covers SAMENESS. Thus the sense of universals is a natural sense given a symmetry ground from which we perceive reality – the symmetry present in the form of our neurology and so setting down epistemological foundations for our assertions of ‘is-ness’. LOCAL dynamics are covered through development of high level processing of DIFFERENCE out of which we extract essentials to build-up sameness and so ease adaptation requirements.
Since the development of symmetry DEMANDS differences to then instigate the emergence of sameness so we are customised in development as determined beings (genetics, social history etc) and in that customisation favour detection of sameness through exposure to difference. This is a beneficial act as far as survival is concerned but it has issues in that we get attracted to symmetry and so presuppose symmetry where there is none (yet).
The IDM focus covers the recursion/self-referencing of dichotomies to elicit unique parts of a whole that are then exposed to properties of symmetry – rotations, reflections, repetitions – to give us the sameness of symmetry. The more we focus on this difference-to-sameness dynamic so the more we create symmetry but in doing so we assume ‘out there’ is symmetric when it isn’t - PARTS may be to a degree where we interpret them as ‘wholes’ but that due to our detection of patterns – a detection that comes out of self-referencing. Thus all that we SEE is grounded in development, in ‘clumping together’ of elements that go on to form molecules etc and on into determinism and so symmetric dynamics; the ‘rest’ is meaningless since it lacks symmetry and the ability to be symmetrised; the nature of randomness is its momentary nature, its uniqueness, its unrepeatability. The more we go past the moment we move into some degree of sustainability and so some history and so on into development of symmetric properties and so ‘order’ and ‘meaning’.
Since our models of the universe are seeded by what is POSSIBLE given our neurology so they become increasingly symmetric if left to naturally ‘evolve’ as we map out ‘laws’ etc. But these laws etc are based on what is observable and that demands a symmetric ground – and so all we see are products of symmetry and so cover but a part of ‘all there is’ as far as the universe is concerned. That said, the development of asymmetry allows for the development of consciousness and so the unique. With that ongoing development comes languages used to try and describe ‘all there is’ but this dynamic, being transcending, is perpetual and so never complete – and so all languages, natural or formal, are incomplete due to the nature of asymmetry dynamics that works to manage the anti-symmetric/symmetric relationships
Thus the notion of ‘universals’ comes out of our symmetric ground and covers all symmetric forms such that we can describe universals through the use of universals (e.g. mathematics grounded in classes of meanings derived from recursion of the neurology and expressed formally in “Set Theory”) and so we see the autological nature of self-referencing, we can get such systems to describe themselves. Thus ‘universals’ exist as a product of symmetry, but if symmetry is limited in the universe since symmetry requires development through order, so ‘universals’ are limited to symmetry! As such, universals exist but within the bounds of symmetry and so are useful but not necessarily ‘Universal’.
The next section covers particular examples of XORing at work when applied to an asymmetric dichotomy and so the ability to extract a ‘parts list’ for analysis of finer details.
Cognitive analysis of these specialist domains has brought out their isomorphism with the categories derived in the IDM domain model such that is it possible to take an emotional assessment of some situation and translate that into a representation of the I Ching domain. The demonstration of such is presented in the main text of the Emotional I Ching.
An added feature of the IDM model is the finding that, given depth in the recursion, the classes formed at six levels of recursion or more, form into a language and as such can describe itself by reference to itself - we label this feature as the autological property of recursion where in language it covers the sense of 'self-referencing' – with that identification comes the sense of the organic, the teleological, the normative sciences.
We find that this autological feature is best-brought out using the BIT domain where it represents any of the other domains and allows us to use logic operators. When we interpret the dichotomy as asymmetric, and so 'part/whole', we find that, when using the XOR operator, we can extract 'part' information through use of analogy. What is meant here is (a) the set of 64 categories formed after 6 levels of recursion serve as classes of meanings, (b) cognitive analysis indicates that forming part/whole dichotomies introduces is to all of the categories available becoming usable as sources of analogy, and so a foundation in pattern matching, where each category interpreted as a WHOLE can present us with fine details by XORing that category with all of the others to give us a description of the category's spectrum or parts list in the form of analogy to other categories.
The XOR operator works where, given x and y we create a third representation based on rules derived from this 'truth' table:
X XOR Y
In a cognitive analysis of the general meanings of the I Ching hexagrams (NOT the trigrams) I discovered the 'coincidence' that hexagram 27, in the form of 100001, represented in general the basic infrastructure of some 'new' event or structure. It was associated with the sense of being wary about what one takes 'in' to this structure. In other words it came with a warning about the quality of what we furnish the 'skeletal' form, the 'infrastructure' prior to continued development.
This basic quality was apparently the same as that discovered in all of the other hexagrams in flipping the top and bottom lines. Now look again at the bit representation of hexagram 27 - 100001. The only yang lines are 1 and 6. If we take this hexagram and XOR it with all of the others we get the 'raw' or 'skeletal' form of each hexagram by deriving a hexagram that serves as a source of analogy in describing that 'raw' form; IOW we have possibly identified the source of the 'casual observation'.
Thus, XOR-ing hexagram 27 with hexagram 01 gives us hexagram 28:
27 XOR 01 = Result - Hexagram 28
(line 6) 1
(line 5) 0
(line 4) 0
(line 3) 0
(line 2) 0
(line 1) 1
Put ANY hexagram in the first column and the XOR process will describe, by reference to some other hexagram, the expression of that first hexagram 'through' the middle hexagram - and so an expression of a part. - and so the 27-ness of 01 is described by analogy to the generic qualities of hexagram 28
We can thus get the I Ching to describe itself through using the BIT representations extended to six bits and the I Ching trigrams extended to hexagrams. Each hexagram will display the qualities of all of the other hexagrams when XORed with each to derive an analogy in the form of some other hexagram as shown above where the 'mud' or infrastructure or skeletal form of hexagram 01 (the qualities represented in hexagram 27) are expressed through hexagram 01 in a format analogous to the general qualities of hexagram 28 - excess, too much yang.
Given the properties of XORing we move into consideration of forecasting. There seems to be some 'value' emerging regarding Karl Marx's perspective on history and social development where his perspective focuses on the inevitability of social dynamics regardless of chance events, accidents, and local contingencies.
Karl Popper's focus on Historical Materialism, as covered in the text “The Poverty of Historicism” but also in his "The Open Society and its Enemies - Vol. 2: Hegel and Marx" RKP focused on such elements as that of chance in that chance would neutralise any such predictable developments. However, in the recent work on social networks (Watts 2003; Barabasi, A-L (2002); Strogatz, S., (2003)), based on creating models and letting them 'run' on computer systems, and then comparing the results with reality, two distinct categories of social networks have emerged together with a distinct dynamic that shows one developing and then transforming into the other REGARDLESS of chance/accidents/local contingencies; this dynamic has ancient roots where in ancient Greece it was called enantiodromia - where this concept is identified as a 'fact' of nature and as such reflects the benefit of considering dialectical logic as well as analytical logic in mapping reality - rather than the analytical that favours the competitive (and so denigrates the dialectical) the long term focus is on cooperation and so Logic (capital L) is made-up of analytical&dialectical.
The dynamics of the brain is focused on information processing. That dynamic reflects a fundamental property of that processing, namely the reciprocal relationship of Bandwidth and Time - reflected in the physiology where an increase in energy, and so a need to increase bandwidth, means a distortion of subjective time experience as we focus attention on something to identify it NOW rather than reduce the bandwidth and soak the information in over time.
Why do this? – consider the term "Methodological Individualism":
"[methodological individualism] comes with its complement to form the dichotomy: methodological individualism / methodological collectivism
They are in fact abstract labels for methods in information processing – and map to differentiating (MI) /integrating (MC). The focus is thus on the 'simple' issues of bandwidth vs time where differentiating demands high bandwidth and so exaggerations in energy that distort time experience – we move from 'past-present-future', the arrow of time, the thermodynamic bias, to 'now', or as close to 'now' as we can get. We can still learn an experience with lesser bandwidth but over more time – in other words there is a more integrating focus long term.
Jon Elster writes (in the context of MI):
"...the doctrine that all social phenomena - their structure and change - are in principle explicable in ways that only involve individuals – their properties, their goals, their beliefs, and their actions.
Methodological individualism thus conceived is a form of reductionism. To go from social institutions and aggregate patterns of behaviour to individuals is the same kind of operation as going from cells to molecules.
The rationale for reductionism can briefly be stated as follows. If the goal of science is to *explain by means of laws*, there is a need to reduce the time-span between the explanans and the explanandum - between cause and effect – as much as possible, in order to avoid spurious explanations. The latter arise in two main ways: by the confusion of explanation and correlation and by confusion of explanation and necessitation. The first occurs when there is a third variable that generates both the apparent cause and its apparent effect, the second when the effect is brought about by some other cause that preempts the operation of the cause cited in the law. Both of these risks are reduced when we approach the ideal of a continuous chain of cause and effect, that is when we have reduce the time-lag between explanans and explanandum."
Given the above, we focus here on forecasting:
“Almost all managerial decisions are based on forecasts. Every decision becomes operational at some point in the future, so it should be based on forecasts of future conditions” Time-Critical Decision Making for Business Administration - Professor Hossein Arsham (internet publication)
This section introduces us to the ability to forecast events due to what we can call resonance; where the structure of ‘in here’, in general, is identical to ‘out there’ such that it is possible to ‘sense’ a situation. Given that sensing, and covering the XOR material, it becomes possible to predict the development of a situation and so forecast an outcome.
The forecasting of future conditions covers the need to understand the full set of POSSIBLE conditions and from there to identify the steps that take one from a current condition to some other condition and so be able to forecast such.
Given the analysis so far on mediation methods by the human brain it follows that the ability to describe some condition requires a template of conditions otherwise we are left with the indescribable.
Given the methodology used by our brain in its focus on self-referencing so this action is the creator of POSSIBLE conditions and so categories describing such.
Thus we can map out the generic properties and methods of all conditions by creating a set of analogies (patterns) from self-referencing the brain dynamics of mapping part/whole interactions applied to themselves (self-referencing).
In more generic terms, we cover the anti-symmetric/symmetric dichotomy manifest in the structure of our brains through self-referencing that dichotomy. Since the dichotomy is ASYMMETRIC so we derive a set of categories usable to describe conditions utilising those means and if extended we will find that out pops the ability to create analogies and so a language.
“Forecasting activity is an iterative process. It starts with effective and efficient planning” Arsham
If we equate the elements of the dichotomy of anti-symmetric/symmetric with the dichotomy of 1/0 we can selfreference such and get a sequence of bits that represents some pattern representative of a condition derived from the dynamics of the original, self-referenced, dichotomy.
“Forecasts input come from the decision maker's environment. Uncontrollable inputs must be forecasted or predicted” Arsham
Since the brain takes sensory information and converts it to the language of the neuron – frequencies, wavelengths, and amplitudes – so the patterns in the neurology reflect the decision-maker’s environment.
“Decisions inputs are the known collection of all possible courses of action you might take” Arsham
The set of POSSIBLES are determined by self-referencing the method used to derive meaning – oscillations across the anti-symmetric/symmetric dichotomy where such oscillations reflect mediation at work, spanning an asymmetric relationship in the form of the dichotomy.
There is also hierarchy here where we span the operational, the tactical, and the strategic.
“Interactions among the above decision components are the logical, mathematical functions representing the cause-and-effect relationships among inputs, resources, forecasts, and the outcome” Arsham
As we shall see, any mathematical elements are exploitations of differences through association with samenesses – namely the properties of symmetry as in repetitions, rotations, and reflections. As we will also see, the core meaning derivations come from association of universal categories with a logic operator that brings out the relationships of object and context.
“Interactions are the most important type of relationship involved in the decision-making process. When the outcome of a decision depends on the course of action, we change one or more aspects of the problematic situation with the intention of bringing about a desirable change in some other aspect of it. We succeed if we have knowledge about the interaction among the components of the problem” Arsham
“Decision-making involves the selection of a course of action (means) in pursue of the decision maker's objective (ends). The way that our course of action affects the outcome of a decision depends on how the forecasts and other inputs are interrelated and how they relate to the outcome. “ Arsham
“Forecasting is a prediction of what will occur in the future, and it is an uncertain process. Because of the uncertainty, the accuracy of a forecast is as important as the outcome predicted by the forecast” Arsham
“A Model is an external and explicit representation of a part of reality, as it is seen by individuals who wish to use this model to understand, change, manage and control that part of reality” Arsham
“The purpose of models is to aid in designing solutions. They are to assist understanding the problem and to aid deliberation and choice by allowing us to evaluate the consequence of our action before implementing them.” Arsham
“Cognitive science provides us with the insight that a cognitive system, in general, is an association of a physical working device that is environment sensitive through perception and action, with a mind generating mental activities designed as operations, representations, categorizations and/or programs leading to efficient problem-solving strategies.
Mental activities act on the environment, which itself acts again on the system by way of perceptions produced by representations” Arsham
“Forecasting is a necessary input to planning, whether in business, or government. Often, forecasts are generated subjectively and at great cost by group discussion, even when relatively simple quantitative methods can perform just as well or, at very least; provide an informed input to such discussions” Arsham
E.g. the use of recursing the yin/yang dichotomy reflects a ‘cheap and nasty’ form of predicting events but at a generic level that allows for a useful perception of a situation in general and so scope for ‘zooming in’ to map out details using more precise tools.
“There are two main approaches to forecasting. Either the estimate of future value is based on an analysis of factors which are believed to influence future values, i.e., the explanatory method, or else the prediction is based on an inferred study of past general data behaviour over time, i.e., the extrapolation method” Arsham
Given what we have covered in the XOR material, it now becomes possible to extract data relevant to a situation that has gone ignored before, we can get a situation’s spectrum and so map out finer details both in properties and in methods IN GENERAL. This is flesh this out in finer detail in the main Emtional I Ching work.
The coverage so far on language development from recursion brings us to the usage of serial processes to develop parallel processes in the form of the immediacy of intuition. This dynamic is brought out in the IDM focus on recursing/self-referencing dichotomies and in particular the usage of the 0/1 dichotomy (the BIT domain) as representative of the general process of dichotomisation and self-referencing - this possible due to the isomorphism of dichotomisation - thus 'rote' learning through dichotomisations can elicit, over time, internal connectivity that develops intuition and rich associative memory links.
To cover the possible interpretation differences, given the qualities associated with the representation of 000 and 111 (we can label these as 'pure yin' and 'pure yang') logic operators act to 'customise' the meanings such that we can have:
000 vs 111 as NEGATION (opposites, difference, A/NOT-A, particulars)
000 vs 111 as EQUIVALENCE (sameness, both are examples of 'purity', A=NOT/A, generals)
There is also the focus on expression, "EITHER 000 OR 111" but not both at the same time, in the same space. This covers the exclusive OR.
Analysis of the brain dynamics brings out the core dichotomy of differentiate/integrate expressed as antisymmetric/ symmetric. Oscillations across the neural expression of the dichotomy (e.g. LH/RH or front/back etc etc) combined with the encapsulation skills of the attention system, will apply the anti-symmetric/symmetric dichotomy to itself and so work asymmetrically to give us categories that are usable to communicate.
We can still use the 0/1 representations but the asymmetry allows us to interpret part/whole relationships using the exclusive OR - this dynamic brings out the development of the parallel abilities from the serial. E.g. using the yin/yang examples in the practice document in the 64 hexagram level of the I Ching, hexagram 100001 traditionally covers the generic qualities of the 'new' and issues of quality control. This symbol has been built up one level at a time from line to digram to trigram and on to hexagram (and further if need be to a level of dodecagram (4096 possible forms)).
The build has been from the simple task of assessing a context regarding it being 'yin or yang' and re-assessing the result using the same perspective. As such we move from general to particular. This process reflects the actions of self-referencing and building meaning where we end up with a general, vague, quality usable to represent reality - such as hexagram 100001 that is considered to represent issues around infrastructure and so what to do with the skeletal form,
and as such it represents the mud out of which we build meaning by filling in details. The traditional I Ching focus is on the quality control needed in that filling-in.
What we find with the result of 100001 is that we can XOR it with any other hexagram where the INTERPRETATION is of an asymmetric relationship of PART/WHOLE and this is brought out using the Exclusive OR operator (XOR)
where we have:
A(as part) XOR B(as whole) = C (as analogy describing the expression of A-ness in/through B)
We find that we need to make six+ distinctions to get this to work well, less than that it is all too vague and so lacks depth in differentiation.
In the I Ching the hexagram 111111 represents pure yangness. If we XOR 100001 with 111111 we get an analogy describing the nature of the infrastructure or 'mud' out of which 111111 has developed. This is a PARALLEL operation.
This we have (a) the SERIAL development of hexagrams (1 to 111111 or 1 to 100001 etc) and then the PARALLEL
application using the logic operators, for example the XOR operator:
100001 (hex A, representing a PART)
111111 (hex B, representing a WHOLE)
------ XOR operation applied to give us
011110 (hex C)
Thus we have developed the hexagrams left to right and then apply the logic operator orthogonal to the direction of serial development and so bring out the parallel dynamics.
In the above example, hex C is here serving as a vague analogy of the A-ness of B. In this particular context the infrastructure (represented by A, 100001) of B (all yang, 111111) is described by the generic qualities of hex 011110 where such traditionally represents 'excess', 'too much yang' (as it does the extreme of such where we go the extra distance, do the extra work etc to 'transcend' a situation)
Thus from SERIAL development using self-referencing, where such allows for fine details in the form of unique representations, comes the use of the representations in a PARALLEL method to give even finer details using the existing set of meanings as analogies. Thus the serial learning experience builds up meaning to a level where it is 'set off' by context to elicit an intuition about the context without having to work serially any more (UNLESS refinement is needed to the intuition - Libet's work shows this operation where consciousness aids in refining instincts/habits)
LACK of experience can mean not enough depth to be able to use this Part/Whole dynamic (either totally or partially where one may have had rich experience with some elements but none with the others) but such developed tools as the I Ching etc allow one to understand what to expect and so appreciate the full spectrum of what is possible and so seek out to actualise the possibles through particular experiences.
Work on such categories as emotions or five-phase theory etc etc brings out the SAME results from the methodology and so map out the building of intuition from serial processes and the dynamics of self-referencing where such includes a natural 'break' to any infinite regress issues.
Added to this nurture context is the possible development of individuals with genetic 'biases', the nature context, such that they are born with some areas well differentiated without the experiences, just in need of conversion from rough diamonds to refined diamonds.
The link of the emotions dichotomy of fight/flight and that of yang/yin is covered in the practice file of the categories - there we develop the Emotional I Ching where we use emotions to assess a context and from that derive a hexagram representation.
In other words we demonstrate the emergence of vague languages (emotions, yin/yang etc) from mechanistic recursion turning into organic self-referencing of asymmetric dichotomies where some depth is required before these vague languages can richly describe themselves - this is autology where a system can describe itself.
Refinement is where we surrender the emotional/visual symbolisms for letters that directly relate to sounds where sound is more precise in expression as we build meanings serially to carry emotion and from there develop more precise intuitions.
The IDM model suggests refinements in basic emotions is done through
the recruitment of the whole set to bring-out finer distinctions in EACH
distinction in that these basic emotions are all GENERAL in form. Thus for the
concept represented as 'fear' we can refine the concept into a further eight
categories reflecting the expressions of mixing - this reflects the notion of
hyperbolic development rather than exponential development:
Context = FEAR, 000
Fear+fear = 000000
fear+sadness = 000001
fear+disgust = 000010
fear+anticipation = 000011
fear+surprise = 000100
fear+acceptance = 000101
fear+joy = 000110
fear+anger = 000111
and so on (we move from 8 to 64 using this method. Repeat it to go from 64 to 4096 etc etc reflecting hyperbolic development where N qualities become N2; as compared to exponential growth that is 2N. The order of the bits is from context to text, general to particular).
This recruitment process reflects the 'staying in the box' perspective where rather than recruit qualities from outside, from other disciplines, we recruit what we have initially as sources of analogies to flesh-out the general categories into more refined forms. Once these analogies have been created they can in fact be turned into 'autonomous' qualities within the set of qualities we are using. Thus eight analogies describing aspects of expression of, say, fear, (as above), become stand-alone qualities and so we develop hyperbolically oscillating between literal interpretations and figurative interpretations.
Of note here is that the fear-anger dimension has been on a negative/positive format and as such reflects the archetypal expressions of darkness/light, flight/fight.
In categorisation systems we can in fact recognise TWO degrees of categorisation, the archetypal and the typal. The archetypal focuses on the apparent oppositions of dark/light whereas the typal reflects on the COOPERATION of the dark/light which is reflected in the more typal processes rooted in the conversion of the symbolisms of dark/light into the symbolisms of female/male. As such the refined typal emerges from the archetypal that is an exaggeration of the raw typal in that the raw typal reflects the stimulus/response of the everyday out of which has come the emphasis, the exaggeration, of FLIGHT/FIGHT as a necessary dichotomy of adaptation to the environment. The refinement of that flight/flight dichotomy has allowed for the development of the archetypal out of which emerges a 'refined' form of typal, that of our species nature and as such reflective of our species-reality that we create as we develop.
In the context of archetypal-to-typal development, fear gives way to devotion, to total trust in others in that the fear is reduced through following-of/devotion-to another/others, [security in numbers] just as anger gives way to devotion BUT to self, there is total trust in oneself (and so a sense of 'leadership' develops, the 'anger' can be focused, even turned into a game). Thus the above identified dimension of basic emotions is transformed into a dimension of complex relational processes both between individuals as well as within individuals.
The use of recursion to derive qualities means that all derived qualities are encoded in EACH quality in that they serve as sources of analogy in describing the unique expressions of a general quality given a context. ANY description of 'something' utilising recursion will reflect the SAME general set of qualities we use as a species and as identified in general form in IDM. Thus in emotions, the identification of a general category, e.g. anger, is refined into a set of categories derived from taking the existing general set of categories and making compounds WITHIN a particular category.
What recursion also seems to do is allow for the derivation of a vector within an emotion, identifying the path of 'oscillation' from an emotion's given state into its opposite. This vector can be derived through applying recursion to any of the bit-patterns derived in the previous section. To reduce text, lets just focus on the original eight categories in Table 3, assigning them the bit patterns from 111 (anger) to 000 (fear), covering the range of values derived using recursion.
The process of recursion is reflected in these bit patterns through stepping-through each pattern and flipping the bits in the order of a binary numbering. Thus the initial set of qualities, scalars, expressed in the sequence of:
111, 110, 101, 100, 011, 010, 001, 000
can be fleshed-out into sequences reflecting changes of emotion WITHIN each of the above. This gives us eight sequences:
111, 011, 101, 001, 110, 010, 100, 000 [pure anger to anger-as-fear]
110, 010, 100, 000, 111, 011, 101, 001 [pure joy to joy-as-sadness]
101, 001, 111, 011, 100, 000, 110, 010 [pure acceptance to acceptance-as-rejection (disgust)]
100, 000, 110, 010, 101, 001, 111, 011 [pure surprise to surprise-as-anticipation]
011, 111, 001, 101, 010, 110, 000, 100 [pure anticipation to anticipation-as-surprise]
010, 110, 000, 100, 011, 111, 001, 101 [pure rejection (disgust) to rejection-as-acceptance]
001, 101, 011, 111, 000, 100, 010, 110 [pure sadness to sadness-as-joy]
000, 100, 010, 110, 001, 101, 011, 111 [pure fear to fear-as-anger]
Notice here that the general 1/0 categorisation of the original sequence, reflected in the first bit for the first four being 1 and the second four being 0, has now become particular, very 'tight', also expressed in the first bit of each category where 1/0 now oscillates. What has happened is that the original sequence, derived from what we can call 'first level recursion' is a sequence of scalar values that, when rotated become a vector and focused WITHIN a quality, using the other qualities as sources of analogy in describing change where CONTEXT can act to bring-out particular aspects of a general quality. Thus in these sequences the initial three-bit pattern reflects the 'pure' emotion and the order of the others elements in the sequence reflect exaggerations, extremes in energy, such that the state of basic fear can be exaggerated to the extreme in the form of fear-as-anger.
These vectors are of 'interest' but have properties that at first may seem 'counter-intuitive' until we do one more process. This process is where we derive what is called the 'variations on a theme'.
This property stems from the fact that in recursion of a dichotomy the initial bit, the root distinction, acts to separate the two sides of the dichotomy but as the recursion progresses so the patterns in the derived sequences of qualities are identical on both sides when read left-to-right (or right-to-left) OTHER THAN the first bit. We are no longer dealing with opposition here (aka reflection) but more so with repetition. For example, in the basic sequence of:
111, 110, 101, 100, 011, 010, 001, 000
if we move the left four 'under' the right four we get:
111, 110, 101, 100
011, 010, 001, 000
The only difference in the two qualities in each column is the first bit. The indication is that these pairs of qualities may show common themes only differentiated by the nature of the first bit. As we shall see this is indeed the case such that their approximations in quality allow for their use in referencing each other. By this I mean that swapping the first four in a sequence with the last four, as in:
111, 110, 101, 100, 011, 010, 001, 000
011, 010, 001, 000, 111, 110, 101, 100
allows for the qualities in the last sequence to serve as a source of analogy in describing the GENERAL characteristics of the corresponding qualities in the first sequence. The possibility of this is due to the first bit determining the CONTEXT in which all other bits operate and as such 111 and 011 will have more sameness than difference once the initial difference, as manifest in the first bit, has been identified.
This 'variations on a theme' is possible in any of the sequences, be they the results of first or second degree recursions but the use in the second degree recursions introduces some astonishing relationships beyond a one-to-one comparison we can make using first degree recursion.
These relationships stem from the fact that the sequence generated in a second degree recursion is a sequence applicable to ONE quality, a sequence that identifies all of the differences in expression WITHIN a general expression. Thus, as an example, we have been using the quality represented as 111, derived from the first degree recursion to level 3. When we apply second degree recursion we get the sequence of:
111, 011, 101, 001, 110, 010, 100, 000 which we associated with change. BUT if we now focus on variations on a theme we take this change sequence and derive:
110, 010, 100, 000, 111, 011, 101, 001
This is the 'variations on a theme' sequence but focused on WITHIN
the quality of 111. What this sequence shows is the QUALITATIVE changes of 111
from its 'rawest' form, derived by analogy to an under-exaggerated 110, to its
most refined form 'free' of context, where the analogy is to itself, 111 in the
5th position. When we go 'beyond' this 5th position we link the static with the
dynamic, with 'out there', and as such identify the expressions of the quality
from the 'least it can do' (analogy to 011) to the 'best it can do' (analogy to
an over-exaggerated 001).
W can summarise here by stating that for any 3-bit code there is an 8-step vector. For a 6-bit code there is a 64-step vector, each bit code has a vector with 2number-of-bits steps. This increment reflects resolution of the path. The tensor perspective applies to the 'variations on a theme' perspective identified above and is in the qualitative expressions of each bit/group-of-bits within the basic quality.
To flesh this out further, to develop the awareness that we are not playing with bits but dealing with the fundamental development of emotions through recursion, we need to map-out these "variations on a theme" sequences. I have done that below using combinations of the blend, bond, bound, bind concepts with Plutchik’s terms:
Anger : 110, 010, 100, 000, 111, 011, 101, 001
What the sequence identifies is the qualitative development of the notion of 'anger', from its rawest state to its most refined state where we transcend the normal perspective on 'anger' and move into the dynamics of anger, ending with an analogy to an over exaggerated form of 'sadness' that is more an over-exaggerated form of 'contractive bonding' - reflecting a perspective that covers dealing with the blocking of things but also the development of discernment of things; a developing sense of quality and so of qualitative differentiations. Thus 'anger', single-mindedness, is best when used to be discerning in a qualitative way. (Generically there is also a link to the concept of death that is strong in the category associated with 'sadness'.) In these sequences the fifth position reflects the emotion in its purest form, the only analogy is to itself. The sixth position reflects the first degree of transcendence, of going 'beyond' itself. Thus in the above sequence the initial 'transcendence' of anger is identified using 011 as analogy and so reflecting developing anticipation (of wrong doing).
From this very basic identification of the development of anger we move to the other sequences:
Joy : 111, 011, 101, 001, 110, 010, 100, 000
This sequence identifies the qualitative development of 'joy', or more the generic concept of 'expanding bonding', from its rawest state reflected in the single-mindedness, the intensity of 'anger' through to the dual mindedness, the devotional properties we find in 'fear'. The main point here is to identify 'fear' as falling into the same category as a devotion, and seeking to 'blend in' with the context or to draw-in the thoughts of someone else through which to establish identity. The overall emphasis in fear etc is the recruitment of context, either to 'hide', to disappear in ('fear', 'flight'), or more so to integrate with. Thus 'joy' in its best expression is in the context of integrating with another/others.
Acceptance : 100, 000, 110, 010, 101, 001, 111, 011
This sequence identifies the qualitative development of 'acceptance' from its rawest state reflected in analogy to the generic notion of 'surprise', an initial phase of dealing with the 'new', leading to its acceptance. Acceptance in its 'best' suit is in the form of an exaggeration of anticipation extendable into the concept of cultivation (011).
Surprise : 101, 001, 111, 011, 100, 000, 110, 010
This sequence identifies the qualitative development of 'surprise', or the more generic concept of 'expansive binding'. The rawest state is described by analogy to acceptance or more so an initial sense of a boundary that is crossed. Surprise in its most optimum expression is described by analogy to an over exaggerated state of rejection that includes a sense of security, an initial sense of keeping something 'out'. This dynamic is reflected in the concept of enlightenment where the intense energy to keep something at bay, or an intense struggle to identify 'something' can lead to a 'sudden' revelation that we then need to contain/control.
Anticipation : 010, 110, 000, 100, 011, 111, 001, 101
This sequence identifies the qualitative development of 'anticipation' where the rawest analogy is to a form of disgust/rejection, behaviourally expressed as the rejection of something prior to ingestion rather than immediately following from ingestion. The positive focus here is also that of cultivation and so becoming influential and so, ultimately, accepting (101).
Disgust(Reject) : 011, 111, 001, 101, 010, 110, 000, 100
This sequence identifies the qualitative development of 'rejection' (aka disgust) , or the more generic concept of 'contractive bounding'. The major focus is on a barrier or boundary that differentiates 'outside' from 'inside', 'acceptable' from 'unacceptable'. As such the main focus is on keeping something in or more so protecting something inside from outside. In the sequence the initial analogy is to anticipation of 'something' that can develop, ultimately, to dealing with the experience of something 'new' or 'surprising' (100).
Sadness : 000, 100, 010, 110, 001, 101, 011, 111
This sequence identifies the qualitative development of 'sadness', or the more generic concept of 'contractive bonding'. The major focus is on processing of a blockage of some sort and later the development of a sense of quality, of qualitative distinctions and of self-restraint. The initial analogy is to the category of 'contractive blending' that includes the concept of total fear, total darkness, but also the notions of devotion and trust/faith in another/others. As we pass through the description of sadness itself (001) we move into the 'transcendental' areas reflecting development in acceptance, cultivation, and anger (Plutchik's 'anger' maps to the generic concept of expansive blending - the focus being on single-mindedness and becoming 'one', being positive, and so a focus upon transcendence and so replacement.)
Fear : 001, 101, 011, 111, 000, 100, 010, 110
This sequence identifies the qualitative development of 'fear', or more so the generic concept of 'contractive blending'. The overall focus here is on using context to aid in asserting identity even if that means 'disappearing'. e.g. 'freezing', so that you blend-in with the context. There is a derived behaviour here in a strongly identity-asserting context of asserting identity through others/another/something, where fear leads to the development of collectives, security in numbers etc. and a such one's identity is reflected through the group identity and so a sense of 'dual mindedness'. Note that the 'raw' analogy of fear is to it being like 'sadness' (001) that develops through the formal description of fear itself and on into the 'transcending' forms as in surprise, containment, and joy (!) (Plutchik's 'joy' maps to the generic categorisation of expansive bonding - the focus of which is on REFLECTION, a property of which is to let others see themselves in you and so leave you alone. This is emphasised in disguise, in blending-in with the local context)
These sequences are very generic in form (and though hyperbolic development can become lengthy!) but reflect the rich set of qualities derived from the 'simple' process of recursion of a dichotomy, in particular that of differentiate/integrate that can lead to the derivation of feelings we can use to communicate. As covered in previous sections, self-referencing allows us to form categories and from them, through depth in development, analogies – here we have touched on the categories formable from fight/flight and so the ability to use emotions as analogies and so develop language without the high precision of the serial spoken/written words but with the parallel processing of emotions that allow, for example, transmission of complex emotions through vision or audition or any other sense..
The only issue we have is that the lack in precision of emotional meaning brings out the grounding of emotion in symmetry and so communication is through emotional resonance, through shared ‘sameness’ . SOCIALLY this is useful but there are issues with precision that force emotions to be seconded to consciousness in the realm of communications.