The focus on general-to-particular development is a focus on an in-built hypothesis system, namely the instincts of the species. At the level of collectives and of the individual we rely more on the development of habits in real-time, within the lifetime of the individual/collective, and as such move from particular-to-general. We can identify three methodologies that cover these processes, Induction, Abduction, & Deduction.
Induction reflects the basic process of generalisations in the form of identifying local events that seem to share something in common and from that awareness we derive a hypothesis which we can then validate through deduction. There is a 'leap of faith' element in induction that is reflected in genetics where adaptations to a context are in the form of a gene developing and being 'thrust' into a context and if it survives - great. As such there is no assumption of an existing hypothesis, an existing filter, through which we can relate to the context and so adapt quickly.
There is a form of induction called Mathematical Induction that is a dominating feature of Mathematics and deals simply with defining a value N and inferring from there N + 1. The point to note with induction is its natural sense of the linear, of a sequence of events that go to assert 'something'. This is also a property of spoken language where we choose particular words and then link the words elicit a meaning and as such this sequencing is a property of particular-to-general development.
Abduction has its roots in the work of the American philosopher Charles Peirce . Abduction comes in two fundamental forms, reactive abduction and proactive abduction.
Reactive abduction is where we recognise a particular pattern as the manifestation of characteristics of a general pattern/law/principle/hypothesis. For example, seeing something fall to the ground can elicit the conscious recognition of the principles of gravity at work; we know what is behind the observed process.
Proactive abduction is where we notice what appears to be a particular (local) pattern and try to place that pattern in the 'correct' context, we seek a general pattern that incorporates the particular where initially nothing comes to mind other than the assumption that there may be meaning here.
In proactive abduction we actively place the particular in various existing or imagined contexts to try and get a 'match', to establish clear explicit meaning to the local pattern that has elicited in us an implicit sense of there being meaning in the pattern; we assume there is something behind the pattern. As such, proactive abduction emerges strongly in intellectually well developed cultures where we are encouraged to 'not rewrite the bible' - see if there are any existing hypotheses covering the particular pattern before you create a new one.
Deduction comes in two forms - instinctive and derived. Instinctive deduction is where we are driven by our habits, thus there is present a species-level hypothesis about reality in the form of 'rules' hard-coded in the species over millions of years. Derived deduction is where we create habits, be they minor, as in how one hold's a cup, or major, in the form of onotologies about the Universe, ontologies we use as filters to interpret the Universe ,and deduce from these filters.
What is noteworthy about abduction and deduction is that they BOTH ASSUME MEANING. For deduction we move from a given general, in the form of a hypothesis/principle/law etc, to a particular and this process adds to, or reduces, value in the general.
For abduction we move from a particular to a general and in doing so also validate the general (in the case of proactive abduction we can validate an illusion over a long period of time where, once the illusion has been asserted as 'meaningful' so it becomes part of the deduction/reactive abduction pool of contexts).
The fundamental difference between abduction/deduction and induction is that induction does not assume meaning to exist, there is no initial distinction until the inductive process moves from the particular to the general where the general is the formation of an hypothesis/law/principle. There is an subtle 'error' here in that there IS meaning, in the form of our species-level hypothesis/model/theory of reality that we call 'instincts'. But since this is hidden in our unconscious so it is often ignored as being an example of a 'hard coded' theory system.
Peirce tries to explain the processes of induction/abduction/deduction in his group of signs all placed within a firstness context - Qualisign, SinSign, LegiSign - where firstness is the state of initial focus of attention on a quality. Thus a Qualisign is a pure quality as a potential, a SinSign is an indicator, and a LegiSign is a symbol of a law. We can see these expressed in such trichotomies as Aesthetics (beautiful/ugly), Ethics (right/wrong), Logic (true/false) noting that this trichotomy is in fact applied at the indicative position (called secondness) where we 'colour' the quality of firstness with meaning.
|
Charles Saunders Peirce's Matrix of Basic Signs |
|||
|
Firstness as Text |
Secondness as Text |
Thirdness as Text |
|
|
Firstness as Context : |
QUALISIGN |
SINSIGN |
LEGISIGN |
|
Secondness as Context : |
ICON |
INDICES |
SYMBOL |
|
Thirdness as Context : |
RHEME |
DICENT |
ARGUMENT |
Induction thus reflects the (a) pure experience of a local followed by (b) description of one local using another
as analogy and (c) the realisation of a general principle/laws behind all of these locals e.g. the experience and
analysis of red, blue, green etc leads to the development of an hypothesis about principles/laws of colour. This
hypothesis then becomes the context for validation; we no longer see colour 'as is' but falling within a context
that sets meaning.
In the move to secondness, where a 'meaningful' context is assumed to implicitly or explicitly exist, so the unilateral movement (particular to general) found in firstness becomes bilateral (abduction - particular to general, deduction - general to particular), this process emphasises the use of dichotomisations in analysis. The group of signs Peirce related to a context of secondness is Icon, Indices, Symbol. There is a development path here in that an icon, a sign that reflects what it represents, e.g. a picture of the queen of England on a stamp, can be transformed over time to being a symbol - e.g. as the queen ages so the representation on the stamp no longer reflects the queen 'as is'. Refurbishment can restore the iconic emphasis - we make a 'new' picture that reflects the aged queen 'as is'.
In the context of primary and secondary thinking processes (discussed elsewhere on this website), the abduction/deduction loop is an example of secondary processing where relational considerations takeover from the initial identification process (that has succeeded in reactive abduction and initially failed in proactive abduction other than the primary identification of the pattern); abduction/deduction either explicitly or implicitly assume a general context within which local distinctions are made and as such are resistant to random processes where there is nothing 'behind' an observed pattern (see article on markov chains).
Classical Science was more firstness oriented where observation was paramount and we did not move past the identification process. Modern Science, with its emphasis on refutability (in principle) and so a recognition of negation combined with an attraction to discover what is BEHIND what has been identified, favours secondness/thirdness as fundamental to establishing 'meaning'; firstness, at the base level, takes an experience 'as is' and does not initially make any assumptions re meaning etc. This does not allow for refutability, something that can only happen when you have moved into secondness/thirdness processing.
We can see the recognition of this in Karl Popper's approach to Science where refutability is paramount in 'doing' Science.
Abduction can be seen as reflecting inductive processes but within a context, either existing or ASSUMED TO EXIST. We can identify creativity processes at work here in that as we attempt to link a local pattern to a general (and so include negation in our analysis) so the placing of that pattern in real or imagined contexts can lead to 'innovations' in that an unexpected link is made.
Adaptive creativity is where, given a context, we vary the local pattern and so allow for variations on a theme. In this sense we hold the context as invariant and vary the text (local pattern) as compared to the innovative creative process of making the text (local pattern) invariant and vary the context.
What is noteworthy from the IDM perspective is that the levels of development, the working from no filter to developing a hypothesis reflects the recursion process where the initial particular, the conscious awareness of 'something' reflects the 'whole' which we then 'cut' through identifying differentiation/integration biases that, if unsuccessful in identification we apply recursively to derive additional qualities we can use in the identification process. Abduction ASSUMES someone has already done this and so we scan existing sets of qualities to fid a 'fit'.
IDM is itself a hypothesis and so a filter which we use to DEDUCE 'facts' about reality. Peirce's concepts of firstness, secondness, thirdness reflect the F(A,B) = C equation thus:
A = firstness (stimulus)
B = secondness (response)
F() = thirdness as mediation
C = thirdness as representation (formation of a symbol and a habit)
Abduction/Deduction emerge from B post mediation processes which include recognition of the historic development of the collective, an intellectual context. The Mediation function this has two perspectives - (1) the analysis of a NEW stimulus and so derivation of a customised response and symbolisation (2) the RE-analyse of the existing symbolism and habits and their refinement or bifurcation to allow for a variation on the original theme.
In IDM we have the following mappings:
A = BLEND (IS as a potential - stimulus)
B = BOUND (IS/IS-NOT assertions - response)
F() = BIND (linking A and B into a formal way if B does not 'fit' A or there is no formal response to A)
C = BOND (representations and as such share the same space as the original but are not the original)
The process of recursion applied from general to particular, when performed on the D/I dichotomy, leads to a set of qualities being defined for each level of recursion. After three recursions we have eight qualities, as previously presented.
These qualities are SCALARS in that these qualities are measurements of magnitude, as you would measure temperature or temperament. As such the qualities derived form a scalar FIELD in that each quality fills a position within the whole set and as such occupies a POINT and all points sum to be the scalar field.
The process of recursion from general to particular reflects the process of differentiation, where we zoom-in on the points in a field, but each SET of points, and so a field, still reflects the original context of the general and as such the expressions of the qualities are general. Note that the variations in expressions of each scalar reflect differences in point-to-point relationships and as such a scalar field.
To zoom-in further, to identify the core elements of a particular quality require us to apply differentiation to each of these general qualities, the derived scalar values. This process, of differentiating a scalar, leads to the emergence of a vector.
A vector describes not only the magnitude of a quality but also a direction (all in the universe is dynamic, even if appearing 'still'). By deriving a vector for each of the scalars we introduce the concept of a vector field which describes such concepts as electric fields where, when measured, each point in that field, will show expression as a strength (magnitude) as well as a direction; as such a vector reflects a SEQUENCING, an ordering, of values and so reflects a linking process and as such integration within differentiation.
Thus, unlike a scalar that just expresses a particular quality amongst a set of general qualities, a vector can represent the development processes WITHIN the particular quality. The subtle difference here is that the set of scalar values can be used to represent temperatures and as such can be formed into a thermometer and as such a form of 'vector'. But this formation allows for reversibility in that I can go from 1 to 2 to 1.5 to 0.9 etc etc A vector starts to gets us into the irreversible but allows for the repeatable and as such the identification of cyclic patterns as well as morphic patterns; transitions, transformations, transcendences (although phase transitions reflect more the elements of the reversible, e.g. ice-water-steam-water-ice-water)
In most areas of Science you can work with scalars and vectors but in this development of a basic model of categorisations we have to include the concept of tensors where the collecting of vectors (all one dimensional in form but can contain n-dimensions as components), leads to the emergence of a tensor where we deal with the transformation of vectors.
We have in fact been describing tensors all along, in that a tensor is something that has degrees of expression and we have just covered two of them in that a tensor of degree 0 is another way of saying a scalar; a tensor of degree 1 is another way of saying a vector. To get a 'real' tensor we move beyond vectors to tensors of degree n where n is greater than, or equal to, 2.
A tensor applies, like the scalars and vectors, to a point and a tensor field is a field of points ( a continuum of points) all with their own corresponding tensors. A tensor field will reflect, for example, stress on a point/points in the field and there are such concepts as the strain tensor, the inertia tensor, the conductivity tensor etc. (as such a tensor FIELD represents more a tensor with functions as values).
These tensors are all 'hyperdimenstional' objects but note that a tensor is an expression of QUALITATIVE DIFFERENCES in the expression of a point GIVEN A CONTEXT, in other words we are dealing with responses to stimuli; more so the response/sequence-of-responses comes with a string of POSSIBLE values (properties) intrinsic to the point. For example, a 'pure' point, surrounded by other points, and so a context, will express itself in different ways (be 'deformed') due to the influences of the context. As such, tensors being 'hyperdimensional' objects can be, to a degree, FELT rather than SEEN. Since the focus is more on qualitative expression, there is an element of differentiation within integration. Thus we have:
General-to-particular -> scalars (differentiate) -> vectors (integrate) -> tensors (differentiate)->new configuration (integrate). The FIELD perspectives reflect integrations across these singular concepts.
The tensor concept does not just reflect physical processes, e.g. a force applied to a car at a specific point changing the response of the car (as such context pushing the car) The concept applies at the mental level where a 'force', be it a command or a request can cause a change in the response of an individual/collective/species.
All scalars, vectors, and tensors are representable in the form of Matrices (order 2 tensors are referred-to as matrices, 2 dimensions) where a scalar is a single value, a vector is in the form of a matrix column or row (single dimension), and a 3 dimensional tensor has nine vector columns (3 x 3 ,matrix - 3 dimensions for rotation concepts) and so on. There are different forms of representations (indices format etc) and they are of no concern here, what is of concern is the understanding of the concepts of scalars, vectors, and tensors.
The recursive application of the D/I dichotomy comes with some properties we need to identify prior to continuing fleshing-out the categories themselves.
In the development of the set of qualities used to categorise, a subtle difference emerges when we consider the original context within which we categorise. Differentiation, by its nature, focuses on the one whereas integration, by its nature, focuses on at least two (or a ratio of some sort other than 1:1). Thus in the path from integration to differentiation we are in fact moving from the general to the particular. As covered in the previous section, when we apply recursion to a general-to-particular development, the qualities derived are all SCALARS - they are expressions of magnitudes where the intense focus on the particular gives us nothing but 'pure' expression.
On the other hand, when the development is from particulars-to-general, from differentiation to integration, the act of linkage that is a property of the method introduces qualities that reflect VECTORS - magnitudes + direction; there is an emphasis on SEQUENCING and as such a focus more on Ordinality as compared to the focus more on Cardinality that comes with the initial scalar perspectives.
An analysis of the manner in which our species seems to derive meaning indicates
that we move initially from general to particular, especially when exposed to something new in that we seem to
identify that something through analysis of that something with its immediate context, we recruit the local context
to aid in identification, and so we move from an approximation to clearly identifying that something.
The IDM reflects this movement from general to particular where the particular is the final categorisation of,
for example, DDI. The use of dichotomies to derive meaning reflects the use of layering dichotomies, as we layer
dimensions in geometry in the form of X, Y, and Z axis where the elements of the dichotomy are 'either side' of
the divider, the '/', and as such a dichotomy is representing a number line of -1/+1 and as such reflects the use
of X, Y, and Z axis but limited in 'lengths' to 1 either side of the origin (this gets into analysis of the interval
of [0,1] in Mathematics which is shown to be 'infinite' - and it is in that recursive dichotomisations of this
interval will lead to the emergence of a continuum)
In Science we use the concept of 'orthogonality' in our layering of dichotomies such that the Y axis is orthogonal
to (at right-angles to) the X axis and both are orthogonal to the Z axis and so on. In other words we attempt to
maximise the distance, and so maximise the semantic distance, between the dimensions. WITHIN each dimension the
orthogonality is in the form of the elements of the dichotomy being EITHER positive OR negative and the choice
of an element is EITHER A OR NOT-A (aka B etc).
In geometry this orthogonality allows us to move from a number line (X dimension) to a number plane (adding the
Y dimension perpendicular to the X) and onto a number cube/sphere (the Z axis that comes 'out' of the paper, perpendicular
to the origin of the Y/X.)
Reducing our representations to dichotomies, we realise that the BINARY nature of the dichotomy, the A OR NOT-A,
reflects orthogonality expressed qualitatively. As such, we can encode dimensions in the form of dichotomies into
BInary digTS, bits, where the value of a digit is either 1 or 0.
The layering of dichotomies initially develops out of identifying a qualitative ordering where the initial dichotomy
represents the concept of the X axis, the number line as such, and where, due to the dichotomisation and our use
of 1/0 rather than +1/-1, will be either a value of 0 or 1.
If the initial bit reflects the X axis, then the next bit reflects the Y axis and we move from TWO possible values
to FOUR:
00, 01, 10, 11
If we now add a third axis, the Z axis, we now move from four two-bit representations to eight three-bit representations:
000, 001, 010, 011, 100, 101, 110, 111
If we lay these dimensions out together in the order of derivation we get the following pattern:
1st 0/1 dimension : 0 / 1
2nd dimension: 00, 01 / 10, 11
3rd dimension: 000, 001, 010, 011 / 100, 101, 110, 111
This is a binary tree
and as such reflects our movement from the general, the EITHER/OR of the 1st dimension, to the particular where
at 3 dimensions we have eight possible expressions of 'something', eight QUALITIES we can use to describe 'something'.
As actuals, we will follow a thread through this set of potentials to one of the qualities expressed at the 3rd
dimension.
We see here a relationship of RECURSION to processing of dimensions as well as the notion of emergence in that, at level 3, a
FOURTH dichotomy emerges from the recursion process. The recursion is where the original dichotomy of 0/1 is applied
to itself - this is called self-referencing. In the above we are applying recursion to a dichotomy and as such
each level of recursion reflects the development of exponentiation of powers of 2n, where n = number of levels of recursion from 0 upwards.
The 'orthogonality' in all of this is in the form of the ORDER of the dichotomies where the initial bit represents
the X axis, the second bit the Y axis, the third bit the Z axis and so on. What is demonstrated here is the emergence
of values from the ordering of dichotomies BUT the order is based on qualitative distinctions where the initial
'bit' sets-out a context within which we place the second bit (the Y axis) and this PAIR in turn serve as the context
within which we place the third bit (Z axis) and so on. Since the relationships WITHIN each dimension are orthogonal
(1 OR 0, A OR NOT-A) so are the relationships BETWEEN dimensions such that at the 3rd dimension we have the SUM
of the previous two (XY as 00, 01, 10, or 11) IN RELATION to the third - this reflects the TEXT-CONTEXT, FOREGROUND-BACKGROUND,
concepts applicable to this relationship.
Thus as we develop along the binary tree, each level reflects a set of qualities, a set of ordered qualities, that
can be used to describe 'something' and as such act as a symbol of meaning.
In the IDM we use three dichotomies such that we work in three dimensions, represented in bit form as:
1) 0/1
2) 00, 01 / 10, 11
3) 000, 001, 010, 011 / 100, 101, 110, 111
This first level, or first degree, of recursion means that the symbols represent GENERAL qualities, what we call
scalars, in that all that we have are magnitudes where we have taken the general, opposing qualities of 0/1 and
drawn out of the middle a set of more 'refined' distinctions.
If we convert the bit patterns to their decimal representations then we get a list of numbers for 0 to 7 at level
3, 0 to 3 at level 2, 0 to 1 at level 1.
We can use the set of scalars both to identify unique expressions but also to represent simple, reversible, measurements
of something, for example a temperature gauge from 'low' to 'high', or , as we do with the IDM, a sequence of qualities
we associate with expressions of generic categories applicable, for example, to a context of creating typologies
- categorising individuals, their 'personas'.
These personas are here very general, very universal, in form in that repeated recursion can refine the distinctions
but we are still dealing with scalars - archetypal forms where we have not identified the nuances in expressions
that can occur when a specific 'type' is placed in a novel context and so out will pop a difference in expression
where the context can act to PUSH us. That said, the more charismatic personas will attempt to assert their own
context to replace the novel one and so a rich dynamic emerges in text-to-context interactions and their identifications.
BUT, how do we identify these 'nuances', these differences in qualitative expression sourced WITHIN a particular
archetypal expression?
A typology such as the Myers-Briggs Type Indicator, the MBTI®, and all other dichotomy-derived disciplines,
is a parts-list, an ontology, that we use to interpret reality but specifically the reality of psychological and
social interactions. Being an ontology, it serves as THE source of meaning, of IS-ness, and as such ALL MEANING
is sourced WITHIN the scope of the discipline. In other words the MBTI describes 'all there is' such that all nuances
in descriptions must be made using the set of qualities of the MBTI.
Thus, to describe nuances in expression of a particular type I must do so by using analogies to qualities expressed
by the other types. How do we do this?
It so happens that the use of recursion to derive categories comes with some interesting properties, one of which
is that, due to the nature of the process, the WHOLE is encoded in ALL PARTS (and as such we could re-construct
the whole from a part - this process reflects the concept of a hologram where the whole is encoded in all parts))
To 'flesh out' the whole encoded in each part we have to use - recursion.
It is here that our use of bits to represent qualities becomes useful in that I can apply recursion to a bit pattern
by simply moving through the pattern 'flipping' the bits (0 becomes 1, 1 becomes 0) in an order reflecting counting
in binary. (and so I flip the bits of the quality in question, e.g. 000, in an order of 1st bit (giving 100), second
bit (giving 010), 1st+2nd bit (giving 110), 3rd bit (giving 001), 3rd + 1st (101), 3rd + 2nd (011) 3rd + 2nd +
1st (111))
To retain some degree of ease in expression I will focus on the EIGHT qualities we have at level 3 above, namely:
000, 001, 010, 011 / 100, 101, 110, 111
If I apply 'bit flipping' to each of these qualities I will derive the following sequences (which here form into
a matrix):
000, 100, 010, 110, 001, 101, 011, 111
001, 101, 011, 111, 000, 100, 010, 110
010, 110, 000, 100, 011, 111, 001, 101
011, 111, 001, 101, 010, 110, 000, 100
100, 000, 110, 010, 101, 001, 111, 011
101, 001, 111, 011, 100, 000, 110, 010
110, 010, 100, 000, 111, 011, 101, 001
111, 011, 101, 001, 110, 010, 100, 000
The interesting thing about these patterns is that they reflect a concept identified by the ancient Chinese (yin
into yang), ancient Greeks (enantiodromia) and Hegel (dialectical logic and the change of A into NOT-A). The emphasis
is on these being SEQUENCES, you MUST go through the given steps to get from, say, 000 to 111. We also note that
an oscillation is present in the first bit in each sequence showing a tighter degree of integration of 1/0 in the
first bit (in the original, first degree recursion the change was 'wide', first four had bit 1 as 0 and then the
second four had bit 1 as 1 - we have in fact taken the original sequence and
rotated it, turned it 'on its head' - this reflects process moving from
particular to general rather than general to particular).
This bit flipping process as such reflects the process of change, the steps of change for each quality in the form
of identifying the change process through analogy to the other qualities available for use at this level of analysis.
Thus the first step in the change of a quality into its opposite, such as 000 into 111, is described by analogy
to another quality in the set of those possible, here in the form of 100. This in turn changes to 010 that in turn
changes to 110 and so on until we get to 111.
The method of recursion used so far derives a sequence of qualities in an order reflecting oppositions, in that
if I fold one half of the sequence onto the other their bit patterns reflect oppositions of 1s and 0s, 000 'maps'
to 111 as 001 maps to 110 and so on.
Examination of the products of recursion show us another property of the method, what we can call "Variations
on a Theme". This property stems from the fact that 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:
000, 001, 010, 011, 100, 101, 110, 111
if we move the left four 'under' the right four we get:
100, 101, 110, 111
000, 001, 010, 011
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:
000, 001, 010, 011, 100, 101, 110, 111
becoming
100, 101, 110, 111, 000, 001, 010, 011
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 000 and 100 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 000, derived from the first degree recursion to level
3. When we apply second degree recursion we get the sequence of:
000, 100, 010, 110, 001, 101, 011, 111 which we associated with change. BUT if we now focus on variations on a
theme we take this change sequence and derive:
001, 101, 011, 111, 000, 100, 010, 110
this is the 'variations on a theme' sequence but focused on WITHIN the quality of 000. What this sequence shows
is the QUALITATIVE changes of 000 from its 'rawest' form, derived by analogy to an under-exaggerated 001, to its
most refined form 'free' of context, where the analogy is to itself, 000 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 100) to the 'best it can do' (analogy to an over-exaggerated
110).
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.
With the above derivations of additional patterns of meaning using recursion, we are in a position to dramatically extend the eight basic categories defined earlier in this work. This extention starts-off through the use of hyperbolic development where we recruit the eight basic categories and use the set as a source of analogy for describing nuances in expression of each quality (this has been demonstrated above in "Hyperbolic Development - Extending the Categories")
We will here list all of the possible expressions derived from the recruitment process where the 64 expressions are interpreted as SCALARS - expressions of magnitude. I have added the I/D categories where the interpretation is the second operating in the context of the first and that composite format elicits a quality usable to describe something. The focus is in 'refinement' such that "III-III" reflects III expressed in a very refined form:
000000 : III-III
000001 : III-IID
000010 : III-IDI
000011 : III-IDD
000100 : III-DII
000101 : III-DID
000110 : III-DDI
000111 : III-DDD
001000 : IID-III
001001 : IID-IID
001010 : IID-IDI
001100 : IID-DII
001101 : IID-DID
001110 : IID-DDI
001111 : IID-DDD
010000 : IDI-III
010001 : IDI-IID
010010 : IDI-IDI
010011 : IDI-IDD
010100 : IDI-DII
010101 : IDI-DID
010110 : IDI-DDI
010111 : IDI-DDD
011000 : IDD-III
011001 : IDD-IID
011010 : IDD-IDI
011011 : IDD-IDD
011100 : IDD-DII
011101 : IDD-DID
011110 : IDD-DDI
011111 : IDD-DDD
100000 : DII-III
100001 : DII-IID
100010 : DII-IDI
100011 : DII-IDD
100100 : DII-DII
100101 : DII-DID
100110 : DII-DDI
100111 : DII-DDD
101000 : DID-III
101001 : DID-IID
101010 : DID-IDI
101011 : DID-IDD
101100 : DID-DII
101101 : DID-DID
101110 : DID-DDI
101111 : DID-DDD
110000 : DDI-III
110001 : DDI-IID
110010 : DDI-IDI
110011 : DDI-IDD
110100 : DDI-DII
110101 : DDI-DID
110110 : DDI-DDI
110111 : DDI-DDD
111000 : DDD-III
111001 : DDD-IID
111010 : DDD-IDI
111011 : DDD-IDD
111100 : DDD-DII
111101 : DDD-DID
111110 : DDD-DDI
111111 : DDD-DDD
When we choose to extend these categories we move into a realm of 12-digit representations that can be unweildy as in 000000-000000. We can resolve this issue through a little 'trick' in that we can retain the 6-digit representations by extending the possible choices of expression for each of the 6 positions in the representation. Thus the static '1 or 0' becomes dynamic (as in 'more choices') in the form of '1' or '0' or '2' (also interpretable as '1 changing into 0') or '3' (also interpretable as '0 changing into 1'). This process allows us to represent the 12-digit representations as 6-digit representations combined with increased choices of each position. Thus 000000 = 000000-000000 and 000003 = 000000-000001. There are thus 64 possible expressions of '000000' - made-up of cycling through the use of '3' as well as '0'. This allows us to encode 4096 (642) possible representations in 64 just as the same process can allow us to map 64 (82) representations in 8.
We now move on from the scalars to the derivation of vectors in that we take one of the 64 scalar categories and apply recursion WITHIN it. This will give us a list of 64 possible analogies describing the qualitative differences in possible expression from 'beginning' to 'end' for each quality (If we add-in the range from 0-3 so we encode 40962 possible categories).
The 64 symbols derived from the recursion applied to a single category reflect the re-ordering of the scalar sequence to reflect qualitative change and so a sense of the irreversible but also the repeatable; once you are 'in' the sequence there is no going back other than to the beginning to start again. As such each step is a 'transcendence' of the previous and as such reflects a qualitative change that cannot be reversed since the change replaces the previous quality. This is the focus of 'pathwork' or the loss of innocense we all experience in that moving along the path will change you. (Scalars allow for representation of phase transitions that DO allow for immediate reversal - as water changes into steam and back to water. Thus within the quantitative of 98, 99, 100, 101 so there is a qualitative change at the 100 point. A scalar perspective does not recognise this qualitative change since the focus is on expressions of energy THROUGH the concept of 'temperature', not changes in form)
Applying these processes of deriving generic meaning patterns to which we associate specific contexts allows us to uncover patterns in different specific contexts that are reflected across all of the contexts, different labels, same meaning. As an example, lets consider the mapping of the generic elements of IDM onto the specific elements of the Myers-Briggs Type Indicator as well as the specific elements of the Chinese I Ching (Book of Changes).
The properties and methods of any specialisation will be such that it will 'attract'
the likeminded in that we can identify different persona types that 'fit' with different disciplines in that these
types 'resonate' with the properties and methods of the discipline. There are, therefore 'natural' MBTI types, 'natural' Mathematics types and
so on. The 'natural' processes of recruitment and abstraction we find at the neurocognitive levels also apply at
the individual/collectives level and so allow for perspectives to be 'highjacked', usually by charismatics of some
sort.
Within each specialisation is the full spectrum of our species BUT with skewed elements and as such charismatics
can 'take over' a discipline, especially if their 'type' resonates well with the discipline; they work 'smoothly'
within the discipline and that is obvious to those who struggle a bit.
The charismatics perspective is high energy focus and so zooms-in on 'is-ness' as a source of transcendence. From
the neurocognitive levels we can identify two prime functions associated with context:
(a) Transformation function - the learning of 'good' habits and the use of those habits and the instincts of the
species to integrate with a context. This allows for 'shape-shifting' where core sense of 'self' is retained but
quick adaptations to context changes allow for a 'smooth life' in that context by protection of the species.
(b) Transcendence function - under extreme conditions it becomes a 'need' to escape a context and so break a habit/instinct.
The 'drive' is therefore to escape a context - to replace the existing with something 'better'. This can be as
(a) replacing the existing context with one's own (assertion of self) or (b) the escape from this context to another,
'safer' or 'better' (as in exploitable) context.
Function (b) seems to be the source of such notions as 'transcendence', of 'alchemy', etc etc. and so of exaggerations
in general. At the neuron level we find a focus on synchronisations (and so recruitment of others) to aid in 'transcending'
a sensation etc. where these processes allow for the 'breaking' of a habit, causing an 'interruption' that can
lead to an error occurring or, hopefully (that 'leap of faith' again) a 'new' experience that allows for the replacement
of the context.
It is from the transcendence function processes that the focus on hierarchy develops in that the synchronisations
function across neural networks and 'up' to left/right brain hemisphere oscillations that affect expression of
mental states (e.g. see Pettigrew's
work on bipolar disorders )
The development of a 'high energy' specialisation forces the development of thinking that is (a) hierarchic and
(b) replacement oriented (and so journeys through 'levels'). This takes us into the realm of control - as demonstrated
in the analysis of social collectives by Bradley and Pribram - see their derivation of the control/flux dichotomy
to categorise different collectives:
Bradley, R.T. (1987) "Charisma and Social Structure : A Study of Love and Power, Wholeness and Transformation"
New York : Paragon House
Bradley, R.T., & Pribram, K.(1998) "Communication and Stability in Social Collectives" IN Journal
of Social and Evolutionary Systems 21(1):29-81
Of note in IDM is that the properties and methods of the control/flux dichotomy are those of the IDM-identified
basic dichotomy template of differentiations(control)/integrations(flux). As such, the IDM perspective is that
all 'meaningful' dichotomies fall into the same general pattern that is linked to the species' set of basic qualities
used for deriving meaning - In other words the words are 'meaningless', it is their resonance with differentiation/integration
that elicits a sense of meaning. A such, I can make anything 'meaningful' as long as the properties and methods
conform to the basic template of 'objects and relationships' (and so fiction can be made into fact).
The hierarchy allows for the re-labeling of brain level sensations such that 'new' languages develop for 'new'
disciplines that develop to a degree where their metaphoric nature - their words being metaphors for 'objects&relationships'
meanings - are taken literally. Thus the 'mind' emerges from the 'brain' (see examples of this re-labeling in the
page on our adaptation to light)
and with that comes over-reduction of the 'everyday' and so experiences of 'paradox' that in fact reflect 'out
of context' thinking -- and we get into the loop of 'perpetual transcendences' - we get off on the 'buzz' of the
'new' and so lose sight of our species nature.
In persona mappings, as made in such specialist disciplines as the MBTI, there is a fundamental distinction between charismatic personas and non-charismatics, Bradley & Pribram's dichotomy of control(charismatics)/flux(non-charismatics). The role of charismatics in social interactions has been an area of study for some time in Sociology.
I here try to flesh-out the categorisation of charismatics across the Structure
of Personality with reference to the IDM material and in particular the interactions possible between the MBTI
and the I Ching. This also leads us into the area of charismatic collectives as well as charismatic individuals.
In the process of recursion, the process seemingly used by the brain to categorise, each derived row is made-up
of PAIRS, reflecting the root characteristics of the elements of the originating dichotomy. In the MBTI this root
dichotomy reflects that of the qualities of differentiating vs integrating such that we can overlay categories
of the MBTI onto those derived by IDM's recursion of differentiation/integration where the qualities of each position
are shared between the MBTI and IDM:
IDM Recursion process using 1 = differentiate, 0 = integrate:
level 0 - 0 (integrated whole)
level 1 - 1 : 0 (we differentiate from the integrated)
level 2 - 11, 10 : 01, 00
level 3 - 111, 110, 101, 100 : 011, 010, 001, 000
(the pairing at level 3 is [111, 110] - [101, 100] - [011, 010] - [001, 000] )
Corresponding MBTI-associated qualities symbolised as:
level 0 - NF (focus on integration)
level 1 - SP : NF (we differentiate from the integrated)
level 2 - SP, NT : SJ, NF
level 3 - XSTP, XSFP, XNTJ, XNTP : XSTJ, XSFJ, XNFJ, XNFP
The focus is not on these formal symbolisations but on the qualities expressed in MBTI texts describing these categories.
You will not find in any MBTI text (a) the above chart and (b) the assertion of 'NF' as fundamental. the chart
has been derived from analysis of the qualities expressed in each category and their correlation with the IDM qualities
rooted in the brain's use of the WHAT/WHERE dichotomy to derive meaning (aka differentiate/integrate, objects/relationships).
The 'logic' of the MBTI is rooted in its use of four dichotomies to derive meaning and that is its focus, highly
specialised. BUT the IDM work shows that the use of dichotomies is done in a manner that is influenced by unconscious
processes that orders things in a manner reflecting recursion as the source of the ordering. This ordering is 'fixed'
where the same qualities are used but re-labelled for different disciplines such that these specialisations all
seem 'different' - IDM shows that at the generic level they are not, they are all metaphors for what the brain
deals with - objects and relationships, differentiations and integrations.
The realm of 'charisma' is that of differentiation and so the realm of 'charismatics' is that of those personas
focused upon differentiating more than integrating, a focus on high energy expenditure, on 'sticking out', on asserting
'their' context over the existing, rather than a focus on integrating and so focusing more on energy conservation.
As such the above level 3 sequence of the MBTI categories reflects charismatics more to the left, non-charismatics
to the right. BUT the PAIRING process of the recursion ensures that within the given generic categories are both
differentiating and integrating. Thus the XNFJ, part of the integrating side of level 3, is more differentiating
in manner than the more integrating XNFP.
This pairing is a property of recursion and pops up in all of our specialisations.
When we keep applying recursion (and so go beyond the usual 8 to 16 types of the MBTI) so each category of level
3 'contains' expressions described by analogy with each of the level 3 categories - we move from 8 generics to
64 increasingly specifics (8 x 8).
If, for example, we zoom-in to the XNFP category, synonymous with the IDM category of 000 ('pure' integration)
we can map-out all of the different expressions possible given the categories we have to use where we represent
these categories as a category as text (top expression) operating within a category as context (bottom expression):
XNFP XNFJ XSFJ XSTJ XNTP XNTJ XSFP XSTP
XNFP XNFP XNFP XNFP XNFP XNFP XNFP XNFP
This process is called hyperbolic development and seems to be a property of our brain's categorisation toolkit.
Since the I Ching is also a reflection of IDM so we can directly map these MBTI categories to those derived in
the I Ching by listing all of the hexagrams with Earth as base (pure integration, 000 for IDM, XNFP for the MBTI).
I here list these I Ching categories by their traditional numbers as well as their binary representations, bottomline-to-topline
(0 = yin, 1 = yang):
02, 23, 08, 20, 16, 35, 45, 12
000000, 000001, 000010, 000011, 000100, 000101, 000110, 000111
Linking MBTI with I Ching and IDM we have:
The XNFP/XNFP persona reflects the generic qualities of hexagram 000000 (02)
The XNFP/XNFJ persona reflects the generic qualities of hexagram 000001 (23)
XNFP/XSFJ reflects the generic qualities of 000010 (08)
XNFP/XSTJ reflects the generic qualities of 000011 (20)
XNFP/XNTP reflects the generic qualities of 000100 (16)
XNFP/XNTJ reflects the generic qualities of 000101 (35)
XNFP/XSFP reflects the generic qualities of 000110 (45)
XNFP/XSTP reflects the generic qualities of 000111 (12)
From the analysis of IDM/IChing etc we can identify the pairings of differentiation/integration from the top line
of the hexagrams - yin = an integrating bias, yang = a differentiating bias. For example,
hexagram 02 is associated with being a disciple, a follower, a total truster in another/others - a high degree
of devotion that focuses upon integrating self with other.
hexagram 23, the 'twin' of 02, is associated with pruning and weeding, with removing all of the chaff from the
wheat, of stripping the bed (iow the beliefs one rests upon) to their basics, their 'true' expressions. This is
an act of devotion as reflected in hex 02 BUT it is also an act of differentiation rather than integration; we
seek the 'true faith' to stick out from all of the 'crap', from all of the 'exaggerations' that develop with any
faith over time.
Note that the recursion process has led 02 (000000) and 23 (000001) to emerge from the same 'space', that of five
lines of 'yin' (00000) where we find the root focus on devotion. When we move to the six lines so the generic quality
of 00000 will bifurcate, will branch, to reflect (a) differentation operating in a context of generic devotion
(example is hex 23) and the other quality will reflect the integrating focus of devotion (example is hex 02).
Furthermore, hexagram 23 reflects a more charismatic persona type than hexagram 02, operating WITHIN the general
non-charismatic theme of integrating, of blending-in (as determined by reference to the base line, the first line,
of the I Ching hexagrams)
From the MBTI perspective, a persona of type XNFP/XNFJ would thus show a bias to 'pruning' and 'weeding' in general
behaviour when compared to the overly devoted, but less differentiating, persona of the XNFP/XNFP.
In an exaggerated form the XNFP/XNFJ type reflects the 'high priest' protecting the 'true faith', continuously
'housekeeping' to maintain that faith. The requirement to do this is best served by a more charismatic persona
than by an 'everyday' disciple. (using the Keirsey Temperament Checker labels so XNFP/XNFJ reflects a MENTOR operating
in a context of a DISCIPLE/ADVOCATE. The mentor is here the GUIDE, or more so the TEACHER that ensures the faith
is always 'right')
If we step back up to the eight generic MBTI categories of XNFP etc (level 3) so the set of eight variations possible
for each category when we move to 64 categories become potentials for that generic persona type - CONTEXT acts
to determine which of the eight 'best fits' the context. Too much focus on 'parts' means that we can create contexts
that DEMAND one variation such that over time no other choices in expression become possible - one becomes 'fixed'
in one's persona - too specialised.
To aid in mapping charismatic categories of the I Ching, IDM, and MBTI, here is a list of I Ching hexagrams sorted
into a matrix of 8 x 8 where the first four rows reflect the range of charismatic types across the set of possible
categories, most strongly expressed to least expressed (but still charismatic) - and the second four rows reflect
the more 'non-charismatic' types, from least (43 - more charismatic than not but overly integrating in form) to
most non (02). It is easy to map the hexagrams to MBTI complex personas as used in MBTIPlus (use the diagram above
or for 64 hexagram representations see the larger diagram
of recursion)
01 14 09 26 10 38 61 41
13 30 37 22 25 21 42 27
44 50 57 18 06 64 59 04
33 56 53 52 12 35 20 23
43 34 05 11 58 54 60 19
49 55 63 36 17 51 03 24
28 32 48 46 47 40 29 07
31 62 39 15 45 16 08 02
Overall, the top 32 focus on differentiations to varying degrees, the bottom 32 focus upon integration to varying
degrees -
The first 16 hexagrams in the above 64 differentiate within a differentiating context, the second 16 differentiate
within an integrating context. The third sixteen integrate within a differentiating context. The fourth sixteen
integrate within an integrating context.
Thus hexagram 43, that is all yang bar the top line, is integrating overall in that its focus is on seeding, on
spreading the word and as such integrating WITHIN a context of differentiating (the base line is yang - in other
words THE word over all others that is to be 'robustly' spread). The MBTI persona type is XSTP/XSFP, the Keirsey
category would be PLAYERS in a context of OPERATORS.
I hope the above has in some way aided in understanding the relationship of the MBTI to IDM and, through IDM, to
the I Ching.
