Dichotomy

Comes from the Greek dichotomia, from dichotomos, divided, from dich-, in two + temnein, to cut.

My own research (IDM) shows that the process of dichotomous analysis, one of the main tools humans seem to use to make maps, has a set of properties that are often projected onto the object under analysis, leading to the confusion of map and territory. Here is the list of properties, indicating we as a species have a "Sense of Dichotomy":

The Principle of Dichotomy

A fundamental tool used in prediction is the derivation of a classification system. In Western civilization, we can trace this back to the works of Aristotle (1) and the concept of dichotomy. A dictionary describes dichotomy as:

"1. (logic) division into two classes, one positive, the other negative. 2.(botony) a mode of branching by repeated bifurcation"

As will be shown, these are somewhat 'gross' representations.

The concept of dichotomy allows for the enabling of a frame of reference, a universe of discourse, where classes are created such that, for example, an object is symbolized as either being in 'A' (in the class) or in '~A' (outside the class). We can therefore symbolize the universe of discourse by the symbol '1', and thus:

    
                              A U ~A = 1

The symbol 'U', from set theory, represents the concept of Union.

For any class, 'A', that includes less than the whole universe, what remains in 1 is '~A'. This is the aristotlian approach linked with logic in the above definition. From a symmetry focus, the negation aspect covers dichotomies that are anti-symmetric. This is subtly different from the use of XOR in dichotomies where the focus is on clear seperation of element A from element B where B is identifiable as NOT-A but not in its pure negative form.

What is implied here is the 'wholeness' of 1, the universe of discourse within which I make my indications of A/~A. This simple process can then be applied to each element of this dichotomy where the element takes on the mantle of the universe of discourse and I can, for example, form B/~B within the context of ~A. The latter in fact shows the emergence of hierarchic forms based on dichotomous processes and this is the approach linked with botony in the above definition. The latter introduces the concept of indication in that the emphasis is on an aspect of the whole rather than an independent entity.

The use of negation(~), as is found in Aristotle's A/~A, leads us into the two forms of dichotomy, dichotomies of opposition (anti-symmetry) and dichotomies of complementarity - asymmetric - (the latter being an abstraction of the bifurcation concept mentioned in the above definition. Working backwards, the two elements join into one. What also needs to be considered is that dichotomies can be read as either two extremes that have the same absolute values (like the two ends of an axis - the linear point view) or as text and context, where one element forms the context(background) for the emphasized other(forground). This implies that their absolute values are NOT the same, at least qualitatively if not quantitatively - we see here the dichotomies of the 'gaussian' type, where the elements of the dichotomy are symmetric, vs the 'power law' dichotomy where the elements of the dichotomy are asymmetric (bringing out a focus on mediation dynamics that can be short term or eternal) - we can add to this the mix of the two to give us as third - hierarchic form of anti-symmetric. As such we self-reference:

A dichotomy represents sequence. (ordinality bias, hippocampus-related dynamics)
A dichotomy represents magnitudes. (cardinality bias, amygdala-related dynamics)
A dichotomy that mixes these qualities to give us a sense of hierarachy (in turn we can map out forms of hierarchy covering the non-nested to the nested, where the former is rigidly hierarchic, control focused, and so pyramidal in form; there is a focus on issues of difference to sameness management. On the other hand, the latter is less rigid, more open to dependencies across levels and a such leading to a web-like structure and so 'flat' hierachy with an overall sense of working with levels of sameness - refinements of the known etc)

As such we see here the development of symmetric, asymmetric and anti-symmetric perspectives. The methodology of our sensory systems and the neurology indicate that each moment is represented by all three perspectives and so is analysable into all three for the analysis of details.

).

Dichotomies of opposition ('gaussian' dichotomies, symmetry, difference from sameness) are used more in analysis and clear assertion of A from NOT-A, and so this includes where the two elements are often destructive when combined (negations), and clearly differentiated (Exclusive OR). More so the focus is on deriving difference from sameness where the elements of the dichotomy are, generically, the same (as in differentiating/differentiating OR integrating/integrating). When we consider hierarchy, so these sorts of dichotomies apply to elements sharing the same level in the hierarchy. Of special interest is where we try to impose symmetric interpretations of an asymmetric reality.

Dichotomies of complementarity ('power law' dichotomies) are used more in mediation and synthesis, where the two elements are seen as parts of a whole with the whole emerging when the parts join - (Inclusive OR or more so sharing of space as equivalents (EQV)) - with the final whole being the universe of discourse. The dichotomy spans all levels of the hierarchy and as such reflects all levels of that dichotomy. This form of dichotomy is assymetric where we focyus on deriving sameness from difference (i.e. differentiating/integrating) - what is the 'common' ground - this covers acts of mediation. Our brains reflect this form of dichotomy as the foundational (as reflected in the WHAT/WHERE focus of our brains in processing information). Note that 'complementarity' covers the relabelling of the same thing - as such an label of 'equilibrium' and 'far-from-equilibrium' can serve as a complementry dichotomy where the 'far-from-equilibrium'' element is an exaggeration of the 'equilibrium' element - as such there is not 'cut' but more a difference in energy expenditure, a re-configuration of topology to bring out a 'difference'.

We can see anti-symmetric, asymmetric and symmetric dichotomy dynamic in, for example, the dynamics of the asymmetric dichotomy of fermions/bosons (from particle physics) out of which comes the anti-symmetric dichotomy at the fermion end of positron/electron where their CLEAR, exclusive OR, qualities and so A/NOT-A and their negations. If we move to the bosonic side of the dichotomy the positron/electron transform into a pair of bosons as thy come together to share the same space (analogy to a BEC and the symmetric). What this brings out at the level of thought is the ability to describe something by what it is NOT and so the equivalence of A and NOT-A.

All of this said, it needs to be noted that the destruction of the elements in a dichotomy of opposition is in fact more a transformation; for example, matter/anti-matter join into a burst of energy, just as minus and plus join to become zero (neutral). However, there is no hierarchic change of level. As found in dichotomies of complementarity, I can often recover the elements from the whole whereas the union of oppositional elements cannot be reversed from the result.

Closer examination of the dichotomization process also suggests that dichotomy has in fact three types of dichotomous contextual relationships that affect states (four if you consider position as important e.g. many:1 as well as 1:many):

One : One
This is the conventional logical and 'scientific' point of view with a single context, relational analysis bias. e.g. in the dichotomy of Positive/Negative there is a one:one bias in that text and context for both elements are considered equal. This is the common type for dichotomies of apparent opposition, where each element is treated as a whole and context is almost ignored (or else very 'gross'). In dichotomies of complementarity, each element is treated as a part with the context being the whole (aka the next level in the hierarchy). In a mathematical sense, the absolute values of each element are equal.
One : Many
One context to many - hierarchy analysis. This seems to 'map' the current model of the hemisphere functions of the brain and suggests a representation of a 'balanced' state. e.g. in the dichotomy of Individual/Sociological there is a bias in that the context of Individual is singular (one state) whereas the context of Sociological implies many states (hierarchy). In a mathematical sense, the absolute values of each element are never equal. The closest a 1:many dichotomy can get to a 1:1 is at the level of 1:2. This brings out the main attributes of asymmetric dichotomies, as expressed for example in our brains usage of mediating with reality through the what/where dichotomy aka differentiating/integrating. Overall there is an asymmetric, mediating, focus where asymmetric dichotomies are compact representations of TRI-chotomies where subject-mediation-object is the dynamic.
Many : Many
'Un-scientific' point of view due to weakness in prediction - too many variables; a hierarchy to hierarchy. This is usually 'removed' by treating both elements as 'ones' of a higher class - the act itself showing hierarchic thinking - or else using the process of idealization to extract one element from each 'many' and treat them using dichotomous analysis of the one:one type, and then doing the same for other elements. The fuzzyness of the degree predictabilty is manifest in the 'fact' that, mathematically, the comparison of the absolute values of each element could be equal or not - context is a strong influence here.

Summary of the properties of dichotomy

There is a subtle distinction here. Although hierarchy implies relationships, they are fixed. The emphasis on relational and hierarchical emphasises the dynamic and static concepts.

from continuity comes the ability to use wave analogies and the concepts of parts and aspects as harmonics of the whole; the whole treated as if an octave. The continuum also emphasizes the concept of bias rather than absolutes. What should be noted when making a wave-biased analysis is that the use of sine/cosine based functions will always have an aspectual, analog character compared to the tan based functions that are more discrete.

each element of a dichotomy exists within the context of the other and both exist within the context of a whole. In dichotomies of complementarity (mediating) the elements can enfold back into the context; they can occupy the same space. Dichotomies of opposition, although in the same context, cannot occupy the same space, thus suggesting these dichotomies have their elements treated as if wholes (or more so as 'objects')

This has an interesting consequence when considering dimensional maps based on orthoganal relationships. It suggests that the derivation of information using orthoganal relationships, and thus a bias to contextual independence, in fact hides the hierarchic relationships and thus the contextual dependence. The process of orthoganal emphasis is in fact the emphasis on dichotomies of extremes expressed geometrically where attempts are made to avoid hierarchy. For an example, in the MBTI we find that the supposed orthoganal dichotomies hide the underlying context-dependent dichotomies that form the hierarchy. Overall the focus here is on the dynamics of recursion. and from there the emergence of languages as a consequence of mediation. (.pdf file).

Here we find that the states generated within each hierarchic level have specific descriptive characteristics analogous to terms used to describe types of mixing. Although these terms can get more complex the more levels we go through, they are found to be hybrids of four mixing types combined with the characteristics of (5). The four types are Blend, Bond, Bound, and Bind. These characteristics are the root of dichotomous meaning in that objects with dichotomous roots that the individual finds as 'valued' will enable the ellicitation of the same meaning when other objects have the same characteristics (and thus become also 'valued'). This valuation often occurs out of 'real time' context since the only context in the template is mixing. - In other words, the qualities of 'power law' dichotomies are fixed. We simply re-label them to fit a particular context.

For example, astrologically-based descriptions of one's persona, since they are based on the dichotomies of fire/water and air/earth, will ellicit mixing responses that have previously been set off by more dichotomy-based 'common sense' descriptions of persona (e.g. MBTI or tests using the 'BIG-5', or just a degree of self-reflection). This resonance can then favour the individual declaring that there is something of value in astrology, not realizing that it is the dichotomous roots of both systems that is resonating and creating 'meaning'; they treat the metaphor (Astrology) as if 'fact'.

The 'wave' nature previously described introduces probability concepts and the suggestion that the moment we make a dichotomy we inherit one of it's properties - the normal distribution curve. This is the gaussian dichotomy. From a distributions perspective the basic form is binomial - from there comes guassian and poisson distributions.

Using a mediating dichotomy, one can never get a whole picture, only a very refined picture. Thus any model that has dichotomous roots will be found to have a degree of incompleteness. Since most of scientific 'fact' is symbolized mathematically, and since mathematics is founded on dichotomy, all of the models within Science will show a degree of incompleteness; as will any other models developed within any other dichotomously-derived system of analysis.

Godel found this in Mathematics. Heisenberg found this in Physics. Yeats emphasized this, as did Lao Tsu in 450 BC - you cannot 'cut' the whole. On the other hand, this statement is made within the context of dichotomy and so there may be something else that can help resolve the incompleteness 'problem'.

This is all brought out in asymmtric dichotomies and so issues of mediation combined with the emergence of an anti-symmetric dichotomy of rigid, excluded middle, assertions. E.g. the concept of uncertainty from the play of position and momentum where the former is overall a symmetric dichotomy of position ve all others and the latter covers movement and so a mediating emphasis.

As we build our 'whole', so the degree of complexity increases due to the large amount of 'cutting' that occurs. This cutting means we create more borders and it is on borders that complexity/chaos thrives. Thu information can turn apparently entropic (or more so, increase in fragmentation leads to increase in specialisations that in turn create their own languages and so that can appear extreme - too much specialisation elicits 'noise').

However, patterns emerge within this apparent chaos that show a degree of stability and from the complexity can emerge 'new' behaviours. This gets into the relationship of phase transitions and power laws. As we 'cut' so we create borders and so enter the realm of complexity/chaos. However, we also enter the realm of phase transitions and 'far-from-equilibrium' bifurcations.

Thus the use of the sense of dichotomy will lead to the emergence of the above characteristics within the object under consideration not as a result of the intrinsic nature of the object but due to the nature of the sense. Just as the eye does not hears pictures nor the ear see sounds so the abstract sense of dichotomy too has it's forms of representations and it's limits. What is implied by this is that 'meaning' is only valid within the initial context of dichotomy. The proposed template is a template of metaphor-derived meaning based on whole, part, aspect analysis. Thus all dichotomously derived systems of analysis are metaphors for whole/aspect analysis - which is what the basic neurology deals with. Of interest is the observation that (point 13), since mathematics has dichotomous roots, and since chaos and complexity have emergent properties, so these properties should exist within the overall brain system.

14. Differences in logic operator outcomes when applied to different types of dichotomy.

A cognitive analysis of the outcomes of applying logic operators to bit patterns derived to represent 'something' using symmetric, asymmetric, or anti-symmetric dichotomies (as done in IDM using the self-referencing of 0/1) indicates that in symmetric dichotomies the XOR operator gives a result of pure difference between the elements of the dichotomy. On the other hand, if the dichotomy is asymmetric, and so mediating, then the XOR outcome is in the form of an analogy covering part/whole relationships (e.g. entity A is expressed within entity B where the expression is described by analogy to entity C). An anti-symmetric dichotomy covers negation through rotation.

This also holds for the EQV (equivalence) operator and as such it is indicated that these differences hold for all other logic operators when applied to elements of symmetric, anti-symmetric, and asymmetric dichotomies where those elements are represented by bit patterns reflecting layering of dichotomies to assert some meaning.

For example, if we focus on symmetry then 100001 XOR 111111 = 011110. The 011110 pattern will be found to reflect the pure difference between the bit patterns. On the other hand, if the dichotomy is asymmetric and so mediating then the same pattern is now found to be working as an analogy describing the expression of the nature represented in aspect/part represented as 100001 expresses in/through the whole that is 111111. What is indicated here is that a focus on asymmetric dynamics introduces us to a realm covering a "Logic of Relationships".

Dichotomies and complexity/chaos dynamics

Any dichotomies in 'attractor' language map to the IDM perspective, in particular the development of pairs from self-referencing a dichotomy. The dynamic of the pairs emerge once one moves past the formal differentiation of each (point). The moment you have a dichotomy and start self-referencing the pairs reflect extensions from a point perspective to a limit cycle and on to strange where meanings covering the core elements are in the form of trajectories around such - the uniqueness of each expression (and so difference) in relation to the sameness of meaning at each instant. - thus the stability of an archetype, when exposed to local contexts is customised semantically and from that link with finer and finer local distinctions 'fragments' but still retains a core sense of stability 'around' which expressions of meaning move, but never 'touching' the universal meaning and also oscillating across the core 'split' of the meaning into a pair of meanings - where form A can suddenly flip to form B etc.

Dominating dichotomies include positive/negative feedback properties where they reflect isomorphism to properties of differentiate/integrate, difference/sameness etc (and so we move into the characteristics of expression dependent upon the Lyapunov exponents wbere such characteristics map to the generic form of dichotomy of positive/negative, differentiate/integrate etc)

The organic development through self-referencing is an ad-hoc process such that some meanings are well defined, others not. With increase definition comes increase in border creation and so increase in complexity/chaos dynamics.

The 'formal' methods of self-referencing give us 'order' as in:

000, 001, 010, 011 etc etc but these are ideal representations where in reality this is 'messy' (e.g. rate of period doubling being dependent for each dichotomy on influences of context) BUT still behaviourally distinct.

Thus the pair of 000,001 reflects mixing of sameness (00) and difference (01) and I can take the pair and form them into a dichotomy that is then self-referenced to cover the range of dynamics across such a pair. THAT range will also come in pairs due to the root of the process being in self-referencing a dichotomy (and so pair).

Each dichotomy can be interpreted as a unit axis and self-referencing gives us dimensions of unit axis form (XYZ coordinates of Cartesian representations are unit axis forms of 'positive/negative' when we do not extend them with numbers (that reflect multiple sameness)).

If I stick to 'bit' sequences in generating patterns the we move into cellular automata dynamics and with that the chaos game and the Sierpinksi gasket etc (See Wolframs "A New Kind of Science" or sections covering the gasket in such well known texts as 2nd edition of Peitgen, Jurgens, & Saupe "Chaos and Fractals : New frontiers in Science") - and so the same dynamics overall but mapped to bit patterns (sequencing over magnitude).

A 'bit' represents a point in phase space. The stability of such can be interpreted as a universal in that change of context does nothing, the bit remains a constant.

We can extend this into considerations of the formation of a ratio as a trajectory approaches the point; the trajectory can oscillate either side of the 'value' of the point and so reflect negative feedback dynamics as we approach the point. We can also spiral in to a point, but the form of the spiral relates to a negative feedback-derived ratio (recall the precision issues covered in IDM where a circular like spiral reflects roots in the Fibonacci sequence and the more precise we get so the more square becomes the spiral as we approach the binary sequence to elicit more precision, more 'XOR'ness so precise expression of 'the point')

So -- in the context of meaning generation we can, with a universal, approach it directly or oscillate 'around' the meaning or spiral into it.

When we move to periodic attractors (limit cycle) we cover information 'bit' repetition in the form of 0 to 1 and back. The periodicity is mapped and can represent meaning shifts regarding context (e.g. the dynamics of fight/flight in the form of predator/prey presence). In bit formats we can map out the cycle through extending representations to reflect cycle across the attractors of 000/111 through states of:

000,001,010,011,100,101,110,111

The main emphasis here is the stability - in the point it is constant, here it is constant but over time. In weather prediction the 'snow in the sahara' condition reflects an extreme but the system quickly returns to 'normal, cyclic' weather conditions.

Note in the above bit representations the order is rigidly binary and so reflecting the tight link of each bit representation with the next. (if you want to work numerically, read the patterns right to left to give you the decimal equivalents of 0,1,2,3,4,5,6,7)

We can combine limit cycles to give us extended forms of attractor - a torus. In bit representations I can 'wrap' the sequence back to itself to form a toroidal representation.

Ad-hoc distinction making in a 'meaning space' reflects dynamics of exponentiation and that relates to 'period doubling' dynamics. In the ideal form of A/NOT-A the exponent is an integer (2^n). (adding a value thus takes our eight-element cycle to 16 etc)

In the bifurcation dynamics we reflect a negative feedback aspect (focus on approach and use of limits) in the form of a developing constant in the form of the Feigenbaum number all associated with bifurcation periodicity. How does this relate to mind? It’s a bit like the need when thinking gets too complex to 'add a dimension'. The rate of increased complexity relates to the reaching of a bifurcation. (recall that the brain will oscillate across both hemispheres when dealing with the new OR COMPLEX. The oscillation reflects a period dynamic and repeated such reflects self-referencing that 'doubles' the choices possible in deriving a meaning WITHIN the range of possible meanings. - each double is equivalent to adding a dimension but there is also scope for moving from exponential development to hyperbolic, 2^n becomes n^2)

If we add to this 'sensitivity to initial conditions' then we have to add, from a mind perspective, current set of memories that serve as feedback to input regulation. This allows for the smallest of comments to elicit some extreme emotional reaction due to the 'hidden' influence of memories on the moment. What we find in the IDM work with XOR is a state that can neutralise such an expression (it’s a bit like a Nash equilibrium state given some zero-sum game condition)

An issue with ad-hoc development of meaning(education etc) is that meaning 'trajectories' are not necessarily 'in line' with each other, there are sharp differences in understanding even though the understandings are 'next' to each other. This is the difference between a 'well rounded' education vs an overly specialist education or 'ad hoc', context dependent, education.

These issues move us into 'strange attractor' dynamics that allow for 'sudden' jumps in dynamics. The best analogy is to ad hoc education allows for associations 'all over the place', the mixing of metaphors if you like, such that the 'stability' of a rounded, universals-focused, education is surrendered for recognition of stability amongst a lot of instability (one is 'all over the place' and yet there is a 'boundary', a containment present to encapsulate the instability - all meaning trajectories are still within the overall containment area (memory/mind). It is possible to map this to extended exposure to a range of inputs will, over time, cause the smooth link-up of meaning across trajectories; a rich associative memory develops from such a state!

A periodic attractor is akin to a routine in behaviour and so sets down stability over time. A strange attractor will contain periodic forms but overall can 'jump around' and its 'mixing of metaphor' style reflects a symmetric element overall in that any X (metaphor) is interchangeable with any other X - IOW there is a lack of rigid order, a lack of syntax globally - as such a strange attractor is very post-modern!

From a meaning position, a point attractor is a universal, consistent, eternal. A limit attractor adds time and so some 'variations' are possible but the 'preferred' meanings are retained as the foundations. With a strange attractor there is an entanglement at work, somewhere is the 'universal' but metaphors take over (meaning trajectories)such that we move 'around' but also 'jump' around and with that comes an invariance with probabilities distributions(given enough time to map them all out); IOW metaphor X is as useful as, as probable as, metaphor Y - interchangability rules!

There is of course a LOT more coverable BUT the dynamics cover issues of self-referencing of dichotomies (or more so the containment of noise elicits 'order' through self-referencing - aka the Chaos game at work)

Dichotomies and "Cartesian Coordinates"

we will focus on the use of Cartesian coordinates to represent 'data' and the use of mediation to derive categories.

The FORMAL establishment of such a coordinate system is first to set down the X axis. What are the GENERIC properties of such? (a) left/right orientation and (b) negative side/positive side, origin.

In its TRULY generic form we have a dichotomy of positive/negative, no extensions as yet, just potentials.

GIVEN the X coordinate I then assert the Y coordinate 'orthogonal' to the X and sharing the origin with X. This too is a dichotomy of positive/negative and as such, other than the orientation is IDENTICAL in form to X BUT it is also 'moveable' along the X axis if need be.

Of ESSENTIAL notice here is the development of the Y axis WITHIN the assertion of the X. From a logic perspective, if I find a 'Y-axis' then there MUST BE and X-axis present. BUT, if I find an X-axis there is NO NEED for there to be a Y-axis present. From a self-referencing perspective, this relationship of Y to X is akin to that of a second dichotomy 'emerging from' the self-referencing of a dichotomy (where the dichotomies are positive/negative). As such we have:

(T1) X = 0/1
(T2) X = 00/11, Y=01/10

From a logic/set theory perspective, Y <= X

Note carefully there is no extension of this dimensions as yet, they are still 'positive/negative', no numbers yet.

GIVEN X,Y and can add another dimension 'orthogonal' to XY and label it Z. It is a dichotomy of positive/negative and as such what makes it appear 'different' is the orthogonality and the label. BUT, GIVEN the method of derivation we now have Z 'emerging from' XY as Y 'emerged' from X and we have the relationships of Z <= Y <= X

AS such, if I find a 'Z-axis' there MUST BE a Y and given a Y there MUST BE an X. But the converse is NOT true.

Given T1 and T2 so we now have T3:

X = 000/111
Y = 010/101
Z = 110/001 but we also see emerge 011/100

This is interesting in that the 011/100 patterns relate to time issues (sharing of time) as compared to space issues (sharing of space covered in 110/001) ... but we wont touch on this for now, all we are concerned with is the layering of three IDENTICAL dichotomies that we differentiate from each other with X,Y,Z and allow for asymmetric, symmetric, and anti-symmetric representations.

Now comes the fun in that the use of such a coordinate system is the use of a methodology that comes with properties that are invariant regardless of what you let the dichotomies represent, I/E, P/J, difference/sameness, yin/yang, fight/flight etc etc etc

Thus the yin/yang representation of yin-yin-yang and the 0/1 representation of 0-0-1 are, underneath the labels, the same.

Included in all of this 'sameness' is the dichotomy of differentiate/integrate aka what/where. What is special about this is that this dichotomy is associated with brain dynamics and the categories derived from this dichotomy come with feelings sourced in the neurology. If I map out these categories onto our positive/negative form, due to the symmetry in all of these dichotomies the basic set of meaning derived from the neurology will 'shine through' any labels we use in any dichotomy that is self-referenced.

It is this sameness that lets me interchange any dichotomy with the 'template' form 0/1 and, using logic operators, map out 'hidden' relationships across categories. Whatsmore, what is done here manifests what we call 'entanglement' and so how any self-referenced discipline can be 'asked' to describe itself.

NOW start adding numbers to extend the dimensions (which is a form of recursion itself).

To summarise:

Given current understanding of brain dynamics and the development of consciousness, cardinality quantifies sameness and in so doing elicits a difference from such.

This reflects the symmetric nature where any dichotomies reflect Gaussian distributions in that the core elements are same (1/1) but we then focus on the aspects (+/-) and so extract difference from sameness. - IQ testing reflects this sort of focus.

The realm of the asymmetric is more associated with power laws/spectra etc and so the ubiquitous 1/f identification (aka 1/many, aka fundamental/harmonics) - here we map sameness across differences.

Our sensory systems convert difference to sameness through eliciting the universal responder - emotion - where our brains are sensitive to sensory harmonics and the underlying sameness is in the neurology's focus on frequencies/wavelengths/amplitudes - which allows for the interchangability of harmonics and the development of synesthesia where we interchange senses (or more so their meaning content).

The issue of origin and so issues of the 'absolute' is that, from a meaning perspective, the focus is on sameness and 'perfect' sameness means no differentiation and so detection of difference, i.e. self. As such the 'absolute' is unknowable since it is all sameness, no differentiation, but it is considered as a potential ;-)

This is related to the notion of entropy and associated 'heat death' in that there are no highs, no lows, all is 'same' and so no distinctions made nor possible due to the 'waste heat' context.

The IDM material maps the ground of meaning in the form of objects/relationships dynamics ('refined' into such dichotomies as noun/verb, difference/sameness, discrete/continuous etc) and derives a set of categories from that dynamic.

The 'chaos game' covers the property of any containment of noise will elicit spontaneous order through self-referencing. Since pure asymmetric perspectives are 'random' (as in not repeatable, no history) so the translation of asymmetric difference to symmetric allows for the self-referencing to take place (the IMP operator is interpreted as if XOR and the self-referencing is then of XOR/EQV characteristics) but with a loss in precision in that the metaphors are, being metaphors, interchangeable.

Since we can map any metaphor to a dichotomy (due to the self-referencing and symmetric perspective) so the differences in dichotomies are in fact only in the labels, beneath them is sameness.

We can see this with Mathematics and the use of the Cartesian coordinate system (and so how we can get 'meaning space' from that system).

The first axis is the X axis and in its generic form, without numeric extensions, is a dichotomy of negative/positive.

The second axis is the Y axis and its generic form is identical to that of the X, a dichotomy of positive/negative, but its orientiation is 'orthogonal' to X.

The third axis is the Z axis and its generic form is identical to that of the X and Y but its orientation is orthogonal to the XY.

All of this maps to the representation of Z <= Y <= X

From this we can in fact extract the symmetric, asymmetric, and anti-symmetric perspectives used on the creation of, communication of, meaning.

BUT also note the layering of dichotomies of the one kind. The Y is placed WITHIN the scope of the X and if we take the dichotomy and make it self-reference we get this:

(T1) x = 0/1
(T2) x = 00/11, y = 01/10

The Z is placed WITHIN the bounds of XY and so we move into working backwards with reasoning, given Z I can predict the presence of X & Y, given Y I can predict the presence of X but from X there is no guarantee of the presence of Y or Y of Z. This is an asymmetric perspective and covers the IMP operator. Symmetry translates that into the XOR operator (Different but symmetric).

Of further interest here, when we translate Cartesian coordinate dichotomies into the self-referencing of the single positive/negative dichotomy so we have at T3:

X = 000/111, y=010/101, z=001/110 and there is emergent another, 100/011 what is that?!

What is indicated here is that the development of the Z axis as 'pure' 3rd dimension is an illusion and the analysis of categories in self-referencing indicate that the 100/011 properties are in fact those of time.

The logic here is that 2D representations are of a 'slice' of space-time but the moment we go beyond that to what we have called '3D' we in fact add depth (more than a slice) and with that MUST move into issues covering time (and the arrow of).

Given all of this, now note that since each 'dimension' of X, Y, Z, is interchangeable (not the label, the positive/negative dichotomy) so ANY discipline using this form of representation is interchangeable with any other - which covers why Mathematics works in the first place, it being a specialisation and so metaphor.

Of essential note here is that one of the infinite number of dichotomies that can 'fit' here is that of differentiating/integrating aka what/where. This dichotomy, and the oscillation across it and so its self-referencing, is hard coded into our brains. IOW we have identified the 'ground' from which all meaning is developed - different metaphors, different contexts, same meanings - and so psycholinguistics, etc etc are all derived from the one source where the specialisations create labels to replace/represent the 'hard coded' forms.

Also note that a property of self-referencing dichotomies is when we do so and include indeterminism - we get patterns of 'wave interference'. IOW the wave/particle duality perspective comes our of the methodology we use in interpreting reality (and the interchangability of wave/particle emphasises the presence of symmetry and use of metaphor) If that methodology is used in the creation of experiments to investigate particle physics so it will come up with 'wave/particle' duality, but not necessarily as a property of the universe, but definitely a property of our method of thinking (we can in fact see this process going on in learning by experience where the dichotomy of our brain will have seemingly 'unique' experiences that will, in the form of memory, start to link up to give a rich associative memory and so reflecting the property of symmetry - all is connected.


A note on dichotomous contextual development

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