IDM : Abstract Domain Model

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 tbe general methodology in meaning derivation we identify a core property of recursion that allows for the emergence of language and consciousness.

Introduction

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

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

Initially, each of the specialist models take an applicable dichotomy and recurse it to the level of forming eight categories. These are then extended hyperbolically (N^2 as compared to exponentiation's 2^N) to give us 64 categories that reflect a previously un-identified property of self-referencing, the autological (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 - the original definition of "autological" being a word that describes itself - e.g. "English").

Self-referencing, also known as recursion, 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 differentiating/integrating. 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.

In the above figure the “0” level covers basic neurology and emergence of general classes of meaning applicable to the immediate context – what we can SENSE. These classes cover sensations of ‘wholeness’, ‘partness’, ‘static relatedness, sharing of space’, and ‘dynamic relatedness, sharing of time’. Composites then add complexities. But there are no labels as such. These classes serve to set down the foundations for all later-derived symbols/words to communicate meaning outside of the immediate context – we can transcend level “0” gestures of pointing and vague expression of ‘this’ and ‘that’.

Level 1 covers the transcending of the context limitiation of level “0” through symbol usage, be it in the form of primary emotions communications or development of primitive visual/verbal skills. The first set of labels formed in IDM is the set covering the primary emotions and so the first ‘language’. This realm is richly metaphoric and so covers symbols tied to sensory experiences (images etc). As we move into level 2 so we move into the increasingly asymmetric focus of consciousness and the use of, creation of, precise languages that have to be learnt, they lack direct experiencing.

This level 1 realm covers the creation of formal languages first as pictograms, images and so association with the immediate experience of vision, and later development of symbols representing sounds and so the delayed experience, the serial experience, of audition as words. These formal languages can first develop in and ad-hoc manner in level 2 dynamics.

Level 2 covers the development of an increasingly subjective perspective, a well diferentiated consciousness able to SET a context of one’s own (including its own language) ‘over’ the existing context. Symbolic systems represent the creation of labels ad-hoc and their aggregation into a formal system of interpreting reality, the formal set is passed down to level 1 as a social system besides being a personal system; as such a lanaguage can be developed that is then formalised and used in level 1 dynamics – the system becomes the context and as such is ‘layed over’ any other context; it becomes a filtering system.

Given the above, we can take the context of such as yang/yin and the context of such as fight/flight and combine them in a way where patterns from fight/flight are of the same form (isomorphic) to patterns from yang/yin; thus a set of emotional assessments of a situation can elicit an I Ching assessment of that same situation in the form of a hexagram (a six-line symbol); this all done by making a symbolic assessment of a situation (social (level 1) or personal (level 2)) and then journeying ‘down’ into the realm of context sameness (‘collective unconscious’, level 0) and then back up into the realm of context difference on a path leading into a different set of symbols.

At the neurological level the derivation of categories of meaning is by recursion where such elicits a spectrum of classes of meanings (differences) BUT there is no distinction of contexts; the level is all one context and the classes apply to that level; meaning as such is literal or more so lacks the differentiation of literal/figurative; we can point to what we mean, we tie meaning to immediate context.

Only when we introduce symbols and local context customisations of meanings does the ability to make the categories of meaning be taken figuratively do we move into a more higher precision focus that is communicatable; the price for the precision being in an increase in subjectivity. Consensus then keeps some level of agreement on symbols but we can also move into unique symbolisms, only meaningful to the originator of the symbol.

Included in this set of concepts derived at the symbolic level 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 erradication 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 (aka 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 aka 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 outide 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 communciating 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. 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 styles of thought and 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)

IDM and the Recursion of Differentiating/Integrating

"differentiate v.
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." Oxford Dictionary.

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 are:

Objects:

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:
Wholness 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:

Contractive Blending
Contractive Bonding
Contractive Bounding
Contractive Binding
Expansive Binding
Expansive Bounding
Expansive Bonding
Expansive Blending

A cognitive analysis of the properties of differentiating as compared to integrating (or their relabelling into expansive/contractive) 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/WHERE, aka Differentiating/Integratring 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 IDM Template

The following tables cover the generic form identified by IDM in the derivation of classifiers (categories as equivalence classes) for labelling to communicate meaning.

When we include the expansion/contraction dichotomy, we get the full template serving as an abstract domain model:

We can covert the above to a "Feeling" format where we derive the four Bs of blending, bonding, bounding, and binding:

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.

**The Fundamental Object/Relationship Template Bottom-Up**
The Whole	Static Aspects	Parts	Dynamic Aspects
The Whole	The Parts(Object as relationship)
The Whole (Object)

The extended object/relationship template bottom-up
Contractive Whole	Contractive Static Aspects	Contractive Parts	Contractive Dynamic Aspects	Expansive Dynamic Aspects	Expansive Parts	Expansive Static Aspects	Expansive Whole
Contractive Whole	Contractive Parts	Expansive Parts	Expansive Whole
The Whole (Object)

The mixing template bottom-up
Contractive Blending	Contractive Bonding	Contractive Bounding	Contractive Binding	Expansive Binding	Expansive Bounding	Expansive Bonding	Expansive Blending
Contractive Blending	Contractive Bounding	Expansive Bounding	Expansive Blending
The Whole (Object) - Blending

The BIT Domain

In George 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
111	110	101	100	011	010	001	000
11		10		01		00
1/0

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 2^n symbols where n is the level number starting with n = 1.

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 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:

We will show this domain as a being essential in interpretations/translations of other domains through the use of logic operators, in particular the Exclusive OR (XOR), Equivalence (EQV) and Implicaton (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 medition is required. Given the above abstract domain model, we now move into specialist domain models grounded in recursion.

Finer Details - The BIT domain and a Logic of Relationships

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:

The relationship of 000 to 111 is of 'opposites'. This relationship is repeated in the other sequences as:

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:

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.

Finer Details - The BIT Domain and Spectrum Aquisitions.

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) 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, any less of a focus just gives us categories not differentiable to be taken literally or figuratively. With depth this ability emerges and with it the development of language, if but initially 'vague'.

"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.

Futhermore, 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.

Difference: A XOR B = C where C serves an an analogy in describing A/B differences. The relationship is symmetic. (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)

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)

Fine Details - From BITS to Waveforms

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.

For example:
011110 represents sine waves of:
0 2cps (low sample rate)
1 4cps
1 8cps
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)
(b)           010000
(c)           001000
(d)           000100
(e)           000010
(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.

Brain oscillations, indeterminacy, and emergence of the ‘particle/wave’ duality

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).

BTW 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 'bestfit/worstfit' 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:

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.

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. (iow 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, lets first map out the POSSIBLE states: first column is the set of POSSIBLE 64 patterns of LR dynamics. 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 fermion-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)

Mathematics Domain

The categorisation of the main classes of numbers used in Mathematics can be mapped in the same format as the IDM model:

Blending - focus on whole numbers (where this category still reflects differentiate/integrate in the form of prime vs composite numbers)

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 are made up of Reals and Imaginary.

The development of cardinality reflects a 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:

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 occuring 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.

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)

The mathematics template bottom-up
Whole Numbers	Irrational Numbers	Rational Numbers	Imaginary Numbers	Imaginary Numbers	Rational Numbers	Irrational Numbers	Whole numbers
Negative Whole Numbers	Rational Numbers	Rational Numbers	Positive Whole Numbers
The Whole

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
symmetry)

Gödel's discovery 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 META level analysis of a language will bring this fact out. If one is not aware of the neurology dynamics then one can easily consider the uncertainty as a property of the universe rather than a property of mediation. 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 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 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).

Also see my comments on the Cartesian coordinate system in the section in the dichotomy page - covering the marginalisation of dynamics/temporality for the sake of static idealism (or more so, simple ignorance of how we work 'in here' through recursion and are bounded by the qualitative)

Uncertainty/incompleteness in Mathematics

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'.

Gödel's discovery 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 META level analysis of a language will bring this fact out. If one is not aware of the neurology dynamics then one can easily consider the uncertainty as a property of the universe rather than a property of mediation.

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 - a^2 + b^2 = c^2 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'.

Emotions Domain

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.

WHOLE
WHOLE differentiated				WHOLE integrated
WHOLE (dif)		PART (dif)		PART (int)		WHOLE (int)
whole	static relationship	part	dynamic relationship	dynamic relationship	part	static relationship	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 words.
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:

BLEND
BLEND differentiated				BLEND integrated
BLEND		BOUND		BOUND		BLEND
blend	bond	bound	bind	bind	bound	bond	blend

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 & David 2004))

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:

anger/fear
joy/sadness
surprise/anticipation
acceptance/disgust (rejection)

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:

joy/sadness
surprise/anticipation

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

The 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

Table 3 - Mapping of Fight/Flight Dichotomy Over the Concepts and Qualities of Tables 1 & 2

WHOLE integrated
FIGHT ANGER (diff., expand, push out, advance, appear)				FLIGHT FEAR (int., contract, pull in, withdraw, disappear)
ANGER		ACCEPTANCE		DISGUST		FEAR
anger	joy	acceptance	surprise	anticipation	disgust	sadness	fear

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.

I Ching Domain

"...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 interpretating something as yang/yin - the symbolism of lines allows for the layering of such to form trigrams and hexagrams:

Trigams (level T3):
I divide the influences into top/bottom. Thus a trigram (three-line symbol) in an upper position of a hexagram (a hexagram is a six line symbol and would emerge at level T6) has a slightly different bias then 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):

The Myers-Briggs Type Indicator® Domain

The MBTI is a 'typology' originating with the swiss therapist Carl Jung and 'formalized' into it's current form in the 1950's by Katherine Briggs and her daughter, Isabel Briggs Myers.

Studying the categorisations within the MBTI®, I have developed a cognitive-based map of the MBTI on the IDM template. This map (fig 1) emerged from a comparative analysis of the contextual terms found in three structurally similar maps (binary trees) after three levels of dichotomous development. The other maps were of the set of number types used within the context of mathematics, the set of symbols derived within the context of the I Ching, and the set of symbols derived within Western Astrology. 'Behind' these mataphors are the whole/aspects categories of the template.

The MBTI on the template bottom-up to four levels
I	E	I	E	I	E	I	E	I	E	I	E	I	E	I	E	T4
NFP	NFJ	SFJ	STJ	NTP	NTJ	SFP	STP	T3
NF (identity seekers)	SJ (security seekers)	NT (solution seekers)	SP (sensation seekers)	T2
social (NF bias - contractive)	pragmatic (SP bias - expansive)	T1
The "Whole"	T0

It is possible to go beyond four levels, and many users do, but the MBTI favours the above sixteen classifications.

Using this methodology on the MBTI map, it suggests that the root 'types' of personality are identity seekers (NF bias) and sensation seekers (SP bias), and introduces 'hidden' dichotomies that replace those originally defined. For example, the combined SP categorisations and the combined NF categorisations at level T1 function as symbols for the dichotomy of fact-bias(SP)/ values-bias(NF). These symbols are carried forward into level T2, to which are added the time-based dichotomy of What_is/What_could_be. However, to avoid introducing 'new' symbols, we stick to the original MBTI symbols, thus allowing us to show the link to the template based on the overall 'meanings' given to the well-documented MBTI types.

The Astrology Domain

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. Any ideas?

Comparing with the other maps, Aries (T2), for example, links with the NT types in the MBTI (Engineers, inventors, designers etc) and 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), Organizers (MBTI), 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.

Domain Translations

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 Emotional I Ching. - with the derivation of the EIC covered in the text "Categories of Mediation", Theory and Practice (fight/flight and yang/yin dichotomies)

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'.

We find that this autological feature is best-broughtout 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.

An I Ching example

The XOR operator works where, given x and y we create a third representation based on rules derived from this 'truth' table:

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.

Extending Emotions

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
Expanded into:

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 N^2; as compared to exponential growth that is 2^N. 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 inital set of qualities, scalars, expressed in the sequence of:

can be fleshed-out into sequences reflecting changes of emotion WITHIN each of the above. This gives us eight sequences:

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]

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:

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:

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:

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-exaggerted 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 Plutchiks terms:

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', singlemindedness, 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.

From this very basic identification of the development of anger we move to the other sequences:

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 someonelse through which to establish identity. The overall emphasis in fear etc is the recruitment of context, either to 'hide', to dissapear in ('fear', 'flight'), or more so to integrate with. Thus 'joy' in its best expression is in the context of integrating with another/others.

This sequence identifies the qualitative development of 'acceptance' from its rawest state reflected in analogy to the generic notion of 'surprise', an initital 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).

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.

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).

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).

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 decription 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 singlemindedness and becoming 'one', being positive, and so a focus upon transcendence and so replacement.)

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 'dualmindedness'. 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 as we shall see, there are issues with precision that force emotions to be seconded to consciousness in the realm of communications.

Hexagram 27	Hexagram 01	27 XOR 01 = Result - Hexagram 28
(line 6) 1	1	0
(line 5) 0	1	1
(line 4) 0	1	1
(line 3) 0	1	1
(line 2) 0	1	1
(line 1) 1	1	0

X	Y	X XOR Y
0	0	0
0	1	1
1	0	1
1	1	0

IDM as an abstract domain model

Abstract