The following covers a method of encoding information using self-referencing of dichotomies where any particular
dichotomy overlays a template that contains within it connectivity mapping all elements to each. This connectivity
is a property of self-referencing (recursion) and so operates in ANY self-referencing context - be it our brains
mapping WHAT/WHERE or our molecular biology encoding RNA/DNA codons from the self-referencing
of the purine/pyrimidine dichotomy - same patterns, different labels, different scales. As such, the ONE set of
categories are repeated in all contexts with the labels differentiating one context from the other. The benefits
of this in setting down databases and in basic information management are 'obvious'.
Notes, identified in the text as numerals within braces [], are at the end of the article.
ABSTRACT
As part of an analysis on the derivation of meaning it has been necessary to focus on self-referencing. In that focus a property of self-referencing has been identified where that property does not appear to be covered in the general literature on self-referencing. Since there is the indication of the human brain utilising self-referencing in meaning derivation, so this property contributes to that derivation and its understanding is essential for getting a good perspective on the derivation and communication of meaning.
George Kelly, the founder of Person Construct Psychology, makes the assertion that:
"Our psychological geometry is a geometry of dichotomies rather than the geometry of areas envisioned by the classical logic of concepts, or the geometry of lines envisioned by classical mathematical geometries. Each of our dichotomies has both a differentiating and an integrating function. That is to say it is the generalized form of the differentiating and integrating act by which man intervenes in his world. By such an act he interposes a difference between incidents -- incidents that would otherwise be imperceptible to him because they are infinitely homogeneous. But also, by such an intervening act, he ascribes integrity to incidents that are otherwise imperceptible because they are infinitesimally fragmented. In this kind of geometrically structured world there are no distances. Each axis of reference represents not a line or continuum, as in analytic geometry, but one, and only one, distinction. However, there are angles. These are represented by contingencies or overlapping frequencies of incidents. Moreover, these angles of relationship between personal constructs change with the context of incidents to which the constructs are applied. Thus our psychological space is a space without distance, and, as in the case of non-Euclidian geometries, the relationships between directions change with the context." (Kelly, 1969)
In his original text, The Psychology of Personal Constructs Vol 1, Kelly spells out the concept of Hierarchical scales (pp 99-100) where he writes:
"Just as it is possible to express an infinite number of gradations of value in terms of binary number systems, so it is possible to express an infinite number of gradations of value in terms of a dichotomous construct system. One may construct such a scale by assuming a hierarchy of construct.
Consider a hierarchy of four constructs in the order of A, B, C, and D, each of which has two possible values, 0 and 1. A hierarchical scale of values may be built up from these four constructs. It will have log2^-1 4 or sixteen steps. The values of the sixteen steps can be represented by the first sixteen numbers of the binary system as follows:
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
Suppose we build a hierarchical scale of integrity vs disintegrity out of four basic constructs of honesty vs dishonesty, candour vs deviousness, courage vs defeatism and objectivity vs subjectivity. Suppose also that these constructs are arranged in that hierarchical order. Let the binary digit 1 represent the first of each pair and the binary digit 0 the second of each pair. A dishonest, devious, defeatist, subjective person would be represented by the scale value 0000 and would be at the disintegral end of the scale. An honest but devious defeatist, subjective person would be represented by the number 1000. Because if the high relevance of honesty to integrity, he rates in the upper half of the scale. A person who was dishonest, devious, defeatist, and objective would be represented by the number 0001 and would still be near the bottom of the scale" pp99-100
Given these two quotes, lets move away from Kelly for a moment and into research on recent brain dynamics in the processing of information. From there we will find we return to issues covered in the above.
In the context of deriving meaning from self-referencing, lets create an abstraction in the form of a dichotomy of 1/0 that we will the self-reference. This self-referencing will after, say, three iterations derive eight representations:
111, 110, 101, 100, 011, 010, 001, 000
Each of these represent a quality, be it a hue from mixing the RGB/YMC of colour or a complex sound, a chord from mixing different auditory waves; OR a generic quality free of association with senses and solely associated with the neurology and its oscillations across the differentiate(1)/integrate(0) dichotomy (out of which come the senses of wholeness, partness, static relatedness, dynamic relatedness, and their composites)
If we interpret these representations as a set of all possible hues mixing RGB or YMC so they form a set of qualities usable to communicate 'something', this is also true for audition as it is for basic neurological dynamics. Thus besides the perception of a colour there is also a possible association with a concept derived from some memory linking the colour or chord with a context. Thus the colour, once just an instance, now as a category, becomes a class that is manifest in some instance where it communicates 'something' besides just being a colour derived from light absorption/reflection.
With music we can make the our representations more complex and in doing so still retain a skill in differentiating each note in the chord - something we find very hard to do if we use the hues of colour. These differences in sense bringing out differences in precision between audition and vision but maintain a retained sameness in that through both forms of representations we can communicate what the neurology categories cover - a sense of wholness, of partness, of static relatedness (sharing space), and of dynamic relatedness (sharing of time).
These basic categories then form composites to allow for more complex representations and we can represent these complex forms by taking our eight representations derived above and applying them to EACH form. This is called hyperbolic development (N^2 rather than exponential form of 2^N) and so we jump from 8 to 64, 64 to 4096, 4096 to 16+million and so on. Initially this application of the set of eight to each element in the set is an application of analogy that is turned into an experience of the literal when the hues/chords formed are experienced in reality. (this also gets into the derivation of the power set of set, each member having meaning)
Thus the chord/hue represented in 000 elicits a set of chords/hues covering representations of:
000-000
000-001
000-010
000-011
000-100
000-101
000-110
000-111
Remove the hyphen to create 000010 etc as complex forms. We can THEN apply the same rule of hyperbolic development to give us 000010000000, 000010000001 etc etc where these bit sequences can represent chords and so summing of sound waves as they can summing of colours, where BOTH summings in fact represent the generic summing of frequencies that elicit the qualitative, emotion-linked, sensation we get from colours or sounds or smells or tastes or touch.
In our neurology these packets of frequencies are responsible for eliciting emotional resonance such that a hue or chord can elicit anger or sexual attraction or fear or grief.
Now lets zoom-in a bit at the level of six bit representations (000000 to 111111).
There are 64 representations we can call symbols where these make-up a sort of lexicon but not of letters forming words, of sensory data forming feelings.
If we focus on music, the bit representations are of waves of different frequencies (notes) that make-up the complex chord. BUT we also have to recognise the influence of context on a chord - where in music the context is set by the key.
Thus our set of 64 representations can vary in expression depending on the context in which they are placed where the dependency elicits a relation of text representation with context representation that requires an 'adjustment' by the text representation to maintain harmony in the fit with the context representation and so present text and context as a harmonised, pleasing 'whole'.
What this means is that a particular aspect of the text representation needs to be expressed in a way such that it appears as if some other representation from the set of all possible representations.
Again a music example, where a chord containing C will need to modify that C to a C# in some contexts. But C# is one of the possible representations and so we have a situation where representation A expressed in a context of representation B will appear to be, is best described as, representation C or more so, representation C serves as analogy in describing the mixing of A as text with a B context.
Now lets zoom-in a bit more. Given a set of all possible representations (here being 64 in number but we can easily increase this to 4096 etc) so each is unique in form and can serve as a representation of text or context but the text will be more 'refined' than the context. By this I mean that bit pattern 101101 as text is more refined than when it serves as context. The bringing something into the foreground does this naturally in that the act of bring is an amplifying act.
With a pattern serving as context so, using the music analogy, a representation can serve like a key and all other representations can operate in that context but only with modification within that key.
What IDM has uncovered in the context of meaning derivation is this:
Given the self-referencing of differentiate/integrate, and the finite set of all possible bit representations at some level, where each representation is of some quality such as that associated with 'beginning' or 'ending' or a sense of 'boundary' etc we can:
(a) represent the quality as a bit pattern.
(b) use XORing to elicit the expression of one bit pattern 'through' or 'in a context of' some other bit pattern by analogy to a third bit pattern.
For example the bit pattern of 100000 can represent 'beginning' and if XORed with, say, the bit pattern of 110101 will give us the expression of 'beginning' when in the context of 110101:
100000 text (sense of 'beginning')
110101 context
------- XOR
010101 expression ('beginning' in the context of pattern 110101 is described by analogy to the generic characteristics of pattern 010101)
Furthermore, given the expression as a bit pattern so the same dynamics are applicable overall. By that I mean that given the above expression representing the 'beginning' pattern of some context, so the 'end' pattern can (a) identify the end of the context ('end' pattern applied to context) as well as (b) identify the end of the beginning of that context, and so on ('end' pattern applied to (XORed with) the above expression pattern (010101)). As such we are dealing with a finite language that allows us to re-use the one set of qualities ad infinitum as long as we keep an ordering of contexts and so a hierarchy of such - but that in itself is represented by a bit pattern! (overall, any self-referencing system can describe itself through using bit representations and XORing)
Due to the self-referencing, this zooming-in on meanings of meanings reflects the infinite regress of self-referencing as manifest when we zoom-in on Mandelbrot's image; but here we are dealing with qualities of meaning and we introduce pragmatics where we stop the zooming as we sense an increasing diminishing of returns. As such, one of the traits of learning is to learn discernment in how far down the rabbit hole we go.
The above dynamic has been identified by IDM to be a property of self-referencing in general and so a property of anything derived from such - in particular the categories and meanings derived in the Chinese "I Ching"
http://members.iimetro.com.au/~lofting/myweb/introXOR.html
as well as the categories of personalities derived in the MBTI.
http://members.iimetro.com.au/~lofting/myweb/type.html
BUT in all cases the emphasis is on the general and so on collectives. This fact comes about when we recognise that the patterns of, for example, beginning and ending are present in each pattern and as such encodes 'purpose' to a pattern and so determinism - as such we are dealing with a genetic perspective. However, we are also aware of the realm of consciousness and its focus on the mediating and the random - as such a source of variation to the determinism of the identified patterns.
The main point here is that ANY self-referencing will elicit these sorts of patterns of meaning etc and so that applies to, for example, the fermion/boson dichotomy of particle physics or the purine/pyramidine dichotomy of molecular biology (and ITS seeding of the RNA/DNA dichotomy) and the overall focus on wholes, parts, statics, and dynamics and the differentiating/integrating dichotomy.
Consider the dichotomy of 0/1. Label this as 'level 1'. In that consideration, apply the dichotomy to itself.
This is symbolised as:
00, 01 / 10, 11
Label this as level 2.
This self-referencing of 0/1, aka the recursion of 0/1, will give, for each level of recursion, categories reflecting
finer distinctions of the original 'space' represented by the original 0/1 dichotomy. This 'space', from Aristotle's
perspective, is the "Universe of Discourse" and as such represents some 'whole' of some kind.
If we apply recursion again we end up with:
000, 001, 010, 011 / 100, 101, 110, 111
Label this as level 3. What is qualitatively noticeable here, but still hidden in the 'bit' [Binary-digIT) form
of expression, is that these representations reflect a movement from the general to the increasingly particular,
not only WITHIN each category left-to-right, but ACROSS the whole set of categories from 000 to 111. This form
of representation takes on the structure of a spectrum from low frequencies (0) to high frequencies (1).
We can in fact consider each position in each category, and each category in the sequence of categories, as a marker
of wave frequency, if it is 'on' or 'off' where each position is double the frequency of the previous. This form
of understanding will be found to be of benefit later.
If we immediately move to six levels of this recursion (practising hyperbolic, N^2, rather than exponential, 2^N,
development) we find that the set of categories in level 3 above are now applied to EACH category of level 3 and
we moved from eight categories to 64. For example, at level 6 we now have extended the level 3 category of 000
into an octet of:
000-000
000-001
000-010
000-011
000-100
000-101
000-110
000-111
Replacing the left side (000) with each of the other categories will give us a list of 64 categories.
Each step in this recursion is taking the "Universe of Discourse" and making finer distinctions, and
so eliciting finer detail, by repeated application of the 0/1 dichotomy. This detail is in fact, for each row,
made-up of PAIRS of categories, each element of the pair representing the qualities associated with each element
in the original 0/1 dichotomy where the qualitative differences in each category express the accumulated qualities
from the previous levels of the recursion.
Thus 000,001 make up a pair derived from the previous level of 00 with the third 'bit' manifesting the application
of 0/1 in the recursion. If we use the wave analogy, the only differences in 000, 001 is in the phase of the highest
frequency.
What is indicated in this process of building category representations is the entanglement of the elements of the
original dichotomy, and so, by association, the "Universe of Discourse" within each category.
Thus each continuation of deriving categories allows for the whole set of categories in one level (and so the "Universe
of Discourse" as a whole) to appear as expressions WITHIN each category at later levels.
This dynamic makes the original 0/1 distinction into a complex pattern of information that is structured 'left-right'
but also entangled in each category 'bottom-top'. [torus dynamic]
What is indicated by this is that the 'simple', linear, representation of '000-011' contains a lot more information
than is displayed by that representation. Is there some way in which we can gain access to that information?
A method of the brain when extracting details from a complex pattern appears to be similar to the use of the
XOR operator of Logic (http://en.wikipedia.org/wiki/Exclusive_or
). We can see this process at work in the dynamics of sensory paradox processing (http://members.iimetro.com.au/~lofting/myweb/paradox.html)
The 'truth table' of XOR is:
X | Y | X XOR Y
0 | 0 | 0
1 | 0 | 1
0 | 1 | 1
0 | 0 | 0
Thus when comparing two sequences of 'bits' if there is a one in a column in either sequence but NOT the other
then a '1' is written down as the result. For all other combinations we write 0. Thus we have:
0010101
0000100
------- XOR
0010001 Result
To implement the XOR operator in the brain requires one neuron to accept input from and then feedback upon another.
Thus differentiation as a whole is a cybernetic activity where the focus on regulation and so control and issues
of precision dominate with their roots in self-referencing.
This process also comes out in acquiring a spectrum of 'something'; the XOR is more like a particular frequency
applied to the 'complex pattern' that brings out all material in some way associated with that frequency - this
is a dynamic of holographic workings.
What is implied here is that the recursive process brings out 'entanglements' or more so the representation of
each entanglement that makes up the whole. Thus each category derived for the set of categories of each row of
recursion, when in 'bit' representation as above, serves as a key to extract descriptions of that category expressed
THROUGH any other. That key is in the form of the application of the category to each of the others using the XOR
operator.
The Universe of Discourse can thus be treated as a complex wave form, a superposition made up of contributing waves
to the expression of that Universe of Discourse. The XOR operator is a method, when using bit (0/1) forms of representation,
to extract information on the contribution of each wave to the whole.
Thus, the category 000-010 is (a) a clear-cut unique category (an 'object' or 'pulse' form) of the whole where
that whole is made up of a set of 64 categories (2^6), and (b) is 'entangled' (and so a 'wave' form) with each
of the other categories and so a part of each category in the set where it contributes, in a distorted way, to
each category's expression and so that category's unique nature.
The extraction of the details of that expression of 000-010 in any other category is derived through XOR-ing the
category with the other to elicit another category as a form of analogy to describe the expression.
For example, given a category 010-110 serving as the category of focus, the 000-010-Ness of that category is derived
using XOR thus:
010-110 (category under analysis)
000-010 ('harmonic', X-ness of the above category)
------- XOR
010-100 The derived category serving as analogy of the "000-010-ness" of 010-110.
Why the analogy? We see here the beginnings of language where a finite set of symbols is supposed to represent
"all there is". Since each row in the recursion has a finite set of categories, the representation of
'anything' by that finite set can only be, in the majority of cases, by analogy or metaphor; but by analogy/metaphor
to what? By analogy to some other category in the set being used to represent 'anything' ('all there is') where
in that "all there is" is the set of categories itself.
Another example: given some context represented by 000-110 we are in fact seeing a distortion of the "Universe
of Discourse" that favours the 000-110 category but in that favouring sorts all of the other possible categories
'behind it' into an ordering from best-fit to worst-fit for the LOCAL context - this sorting being a consequence
of the entanglement of all categories in the one due to the recursion applied in creating the categories. (this
is akin to a topology model where a finite surface is distorted when one point is in some way 'energised' and all
of the other points, being connected, are also involved in the 'whole' expression but to varying degrees of expression)
This best-fit/worst-fit ordering is akin to extracting the 'spectrum' of 000-110 by XOR-ing EACH of the other categories
THROUGH this one, and so generating a list of 64 categories describing the characteristics of this one category.
Thus the 001-010-Ness of 000-110 is described by another category derived from XOR-ing:
000-110
001-010
------- XOR
001-100
What this 'says' is that the qualities of the 000-110 category, when expressed through 001-010 using XOR, become
filtered/distorted to appear LIKE the generic qualities of 001-100. By applying all of the categories, using XOR,
to a particular will give us a sequence of 64 'analogies' describing that category in full.
In the human brain, the extraction of a particular from a complex pattern (a general whole) is more like analogy
where sensory paradox is saying 'this pattern extracted from the complex pattern is 'like' two cubes sharing the
same space' - as in the Necker Cube paradox. (...additional examples given above in the link to the paradox page)
Further consideration of the brain brings up the fact that there is present strong lateralisation, and so asymmetry,
where oscillations across the lateralisation elicit behavioural qualities reflecting characteristics of self-referencing
the WHAT/WHERE[1], aka differentiating/integrating dichotomy[2].
The basic differences between the elements of the dichotomy indicate issues of precision where the differentiating
element (WHAT) allows for identification down to the 'point' or 'dot', when compared to the integrating element
(WHERE) that requires a coordinate system to link (integrate) at least two 'dots' or 'points' to make-up a 'whole'
(more on this below).
Indicated here is that the differentiate/integrate dichotomy is 'embedded' in the brain in the properties and methods
of neurons and manifest at the intellectual level in the asymmetry of the hemispheres of the neocortex. ([1])
Studies of the oscillation indicate that it allows for 'emergence' when operating across hemispheres but not within
hemispheres[3]. The need to oscillate across hemispheres is when complex data is being analysed
and this dynamic is indicative of self-referencing the dichotomy and so allowing for the 'emergence' of more choices
in categorisation of the complex data.
Other sources indicate that once information has been labelled so the brain dynamics create a label, a representation,
that is then used as a universal in identifying other 'like' information. With a label the brain dynamics operate
WITHIN a hemisphere (for labels this is usually the left hemisphere where labels appear to be stored [4]).
As such, combined with the attention system and so an ability to encapsulate, the oscillation will apply that differentiate/integrate
dichotomy to itself; i.e.
No connection of moments gives, for each moment, choices of:
T0 - 0 / 1
T1 - 0 / 1
T2 - 0 / 1
T3 - 0 / 1
Etc
Connection of moments (memory), self-referencing, gives, for each moment, choices of:
T0 - 0 / 1 {0 / 1}
T1 - 0 / 1 {00, 01 / 10, 11}
T2 - 0 / 1 {000, 001, 010, 011 / 100, 101, 110, 111} Etc
Thus a history of some event of interest would be a 'thread' through these possible choices. Furthermore, a particular
thread could be reused where the only difference would be in local context - and so a system would be needed to
identify that difference; and one exists in the form of labelling.
What is implied by this is that the properties and methods described above in the context of the recursion of 0/1
apply to basic information processing of the brain where now '0' represents integrating (relationships) and '1'
represents differentiating (objects). The 'bit' values can then be read in their general-to-particular format as,
for example using 011 "I integrate in general to then differentiating so I can then differentiate in particular".
This behaviour relates to some generic quality associated with the category (e.g. the concepts of 'anticipation'
and 'cultivation' show the generic behavioural dynamics represented by 011).
Of note in the use of the differentiating/integrating, aka WHAT/WHERE dichotomy is the presence of issues with
precision. These issues come from the structure of the dichotomy that is, given the characteristics of the elements
of the dichotomy, asymmetric.
The characteristics are such where differentiating is always down to a point, whereas integration is never down
to less than TWO points. As such there is an issue of resolution power where the differentiating is always of higher
precision than the integrating where that differentiating precision is focused on 'thing-ness', the dot, the point,
rather than 'connected-ness', and so the 'field' (or 'enclosed' as a point - corse resolution as compared to refined)
Thus, with differentiating there is precision but in that precision isolation of what is focused upon - this isolation
manifest in the general characteristics of metaphysics - when compared to the integrating where (!) there is always
present a link to something else and so a more dialectic focus. It this link that reduces precision of 'thingness'
where the focus on an 'object' can exclude consideration of linkage when reality is rich in linkage.
Dichotomies of an asymmetric form, when self-referenced, elicit patterns more associated with spectrums and power-law
dynamics. What is thus indicated here is the differentiating element 'emerging from' the integrating element as
in such notions as 'far-from-equilibrium' (high energy, 111 representation) vs 'equilibrium' (low energy, 000 representation).
If we consider symmetric dichotomies then we are considering those of the form of differentiating/differentiating
or integrating/integrating. This form of dichotomy favours more the detection of difference from sameness and as
such is more associated with the Gaussian, or Normal, Distribution Curve. Here the 111/000 representation is more
of qualitative difference such as +1/-1 where the sameness is in the 1/1 and the difference the +/-.
Thus these issues of precision are issues that would be present in a self-referencing human brain, and for that
matter most other neuron-dependent life forms (to implement XOR in the neurology requires one neuron to feedback
on the other and so self-referencing is required). Together with these precision issues is also the implication
in this assertion of brain function as recursion of the presence of the mentioned dynamics of XOR applied to details
processing.
Given the differentiating/integrating dichotomy, and considering the basic categories we all share as humans,
i.e. a sense of wholeness, partness, static relatedness (Sharing space with another/others) and dynamic relatedness
(sharing time with another/others), we can form a set of categories that are generic enough to apply to 'anything'
and yet have enough 'meat' to be useful:
111 - Sense of Wholeness through differentiation
110 - Sense of Static relatedness through differentiation
101 - Sense of Partness through differentiation
100 - Sense of Dynamic relatedness through differentiation
011 - Sense of Dynamic relatedness through integration
010 - Sense of Partness through integration
001 - Sense of Static relatedness through integration
000 - Sense of Wholeness through integration
If we move to level 6 in the recursion so all of these categories contribute to the description and so expression
of each of them, and we can elicit more 'organic' terms where the focus is on feelings. Thus we have generically:
Sense of wholeness - Blending
Sense of partness - Bounding
Sense of Static relatedness - Bonding
Sense of Dynamic relatedness - Binding
In passing, what is of interest here is the isomorphism of the above feelings with the qualities of the types of
numbers we use in Mathematics:
Blending - Whole numbers
Bounding - Rational numbers (partition, boundary, harmonics)
Bonding - Irrational numbers (sharing of space with another/others)
Binding - Imaginary numbers (Sharing of time, cyclic/morphic change)
At the level of 6 bit representations the bit values can now be represented by such qualitative terms as "000-010
: Bounding (010) in a context of Blending (000)" and so on. What also becomes evident is that we are developing
a template usable in deriving a logic of relationships.
Analysis of the bit template shows us the development of a "logic of relationships". In this logic,
the template form is based on 'opposites'. We can describe this using the 0/1 dichotomy recursed to three levels
to give:
000, 001, 010, 011, 100, 101, 110, 111
The recursion brings out relationships of:
General
000 is to 111 as 000 is to 111
001 is to 110 as 000 is to 111
010 is to 101 as 000 is to 111
011 is to 100 as 000 us to 111
Local
000 is to 001 as 000 is to 111
010 is to 011 as 000 is to 111
100 is to 101 as 000 is to 111
110 is to 111 as 000 is to 111
This form of relationships is derivable for each level of recursion. We can then recurse each category to bring
out derived relationships thus:
Recurse 001 gives:
001, 101, 011, 111, 000, 100, 010, 110
The major, general, relationships are still in the form of opposites (001-110 etc) but now we have local values
as in:
001 is to 101 as 001 is to 110
011 is to 111 as 001 is to 110
000 is to 100 as 001 is to 110
010 is to 110 as 001 is to 110
Etc
If we extend this to level 6, we have a mapping of the logic of relationships for each possible pair in the 64
where representation of this logic is derived from self-referencing of all categories. Furthermore, we can refine
this information by repeated self-referencing.
The above material has been derived from consideration of general principles and as such is 'vague' and highly
abstract.
Are there any examples of this working at the level of semantics/semiotics, based on the 'ad hoc' development of
categories and on into the formation of ideas? Are there any categorisation systems in our cultures that show this
form of modelling at work? Yes there are.
There are not many categorisation systems formally derived to 64, 4096, or 16+million categories; most work
to levels of 8, 16 or 32 (e.g. personality typologies or the formal categorisations of human emotions etc) but
there is one that goes as deep as 4096 although it is usually used at the level of 64 categories. This system is
the I Ching or "Book of Changes" - originally a divination system but later developed into a source of
information on the dynamics of the self-referencing of yin/yang and contributing to Chinese Philosophy[5].
This I Ching text has developed over millennia through the 'simple' recognition of the self-referencing of yin/yang
- qualities generalised to those of integrating/differentiating. In this self-referencing, categories have been
formed representing the dynamics of integrating/differentiating and these categories where originally used in divination
processes (with accompanying esoteric prose etc).
When applying self-referencing to yin/yang, and replacing the terms of the dichotomy with 0 (yin) and 1 (yang)
so the identified qualities of self-referencing discussed above apply to the I Ching and that should include the
XOR material and this is in fact found to be the case. Furthermore, an analysis of the creation of the Myers-Briggs
Type Indicator, a very popular test for identifying generic personality traits, find the same properties present
where for each category a spectrum can be acquired covering the contribution of all of the categories to the expression
of each.
I will give two examples from each of these specialist typologies.
In the I Ching, when we recurse yin/yang to six levels, and so derive 64 categories, there is as category labelled
as 27 that represents a new infrastructure into which we are about to put all of the 'furnishings' - and this includes
mind and our 'feeding' it with ideas etc. With this representation comes a warning about the need to use quality
control regarding what we put into our 'mouths'.
This category 27 is represented using 0/1 notion as "100001". As a category it is a 'stand alone' identity,
unique in expression but as a consequence of recursing 0/1 it is also 'entangled' with all of the other categories.
This entanglement is in the form of contributing to the expression of EACH of the other categories where that contribution
is identifiable by XOR-ing 27 with each of the other categories. What this does is generate a representation of
the expression of the characteristics of 27 THROUGH each category in the form of another category serving as a
source of analogy/metaphor to be use in that description.
For example, if we XOR 27 ("100001") with the category labelled 01 ("111111") we derive "011110",
which is labelled as category 28.
100001 (27)
111111 (01)
------ XOR
011110 (28)
When we look-up the general description of category 01 it is described as "singlemindedness, persevering,
pure 'yang'".
When we look-up the general description of category 28 it is described as "Excess, too full, going beyond
the limits"
The XOR process gives us 28 as an analogy in describing the '27-ness' of 01 where that state of pure yang is described
in its 'generic' or 'skeletal form' as "Excess, too much yang". In reverse, so the 27-ness of 28 is given
as described by analogy to category 01.
Let us now consider category 48 (011010) and its expression through category 57 (011011) - we find that, using
XOR, the 48-ness of 57 is described by analogy to 23 (000001):
011010 (48)
011011 (57)
------ XOR
000001 (23)
Category 57 is about cultivation, becoming influential etc and so a focus on anticipation. This focus gets its
nourishment (represented by the qualities of 48, "The Well"), what keeps it 'going', from qualities represented
in 23 - a focus on a sense of pruning, of housekeeping. I think you can see how this focus on pruning/housekeeping
sets the foundations for the development of full blown 57 with its focus on cultivation/anticipation.
(An internet page covering 48-ness)
On the other hand, the 27-ness of 57, describing 57's skeletal form prior to adding the 'furniture' etc (the notion
represented in 27), is described by analogy to:
100001 (27)
011011 (57)
------ XOR
111010 (05)
Hexagram 05 represents waiting for the 'right' moment to come along and to then take the opportunity. Thus the
27-ness of 57 is described by analogy where the basic sense of cultivation/anticipation is in waiting for the 'right'
moment. That is the skeletal form that develops into full blown 57.
(An internet page covering 27-ness )
I think the above examples demonstrate the entanglements of categories derived from self-referencing and so how
it is possible, for each category, to derive a category's "spectrum" by using bit representations and
the XOR operator; thus the 0/1 template can be overlayed with any dichotomy to bring out the relationships within
and between the categories derived from the self-referencing of that dichotomy.
The second example of this is through consideration of the Myers-Briggs Type Indicator. Again we are not focused
on the 'truth' of the system but on the relationships formed due to the methodology involved in creating the categories[6].
The issue with the MBTI is where to start? The original material comes from the work of Carl Jung and his development
of Analytical Psychology where he developed a typology of personality based on three dichotomies:
Introversion/Extraversion [I/E]
Thinking/Feeling [T/F]
Sensing/Intuiting [S/N]
To these were added, by Myers and Briggs, the dichotomy of Judging/Perceiving. [J/P]
Since the general categories derived from self-referencing focus on STRUCTURES, the functional dichotomy of introversion/extraversion
is the last to be delt with, leaving us three dichotomies to form categories.
A cognitive analysis of the various prose covering these categories indicates self-referencing at
work eliciting the following 'order' of levels:
NF / SP ( 0 / 1)
NF, SJ / NT, SP (00, 01 / 10, 11)
NFP, NFJ, SFJ, STJ / NTP, NTJ, SFP, STP (000 ... 111)
An alternative category system, tightly bound with MBTI categories, is the Kersey Temperament Checker and it allows
us to give more meaningful labels:
Identity Seekers:
000 - NFP - Advocates (disciples) (Seekers, Journalists)
001 - NFJ - Mentors (Authors, Pedagogues)
Security Seekers:
010 - SFJ - Conservators (preservers, providers)
011 - STJ - Monitors (inspectors, administrators)
Solution Seekers (problem solvers):
100 - NTP - Engineers (architects, inventors)
101 - NTJ - Organisers (mappers, strategists)
Sensation Seekers:
110 - SFP - Players (composers, performers)
111 - STP - Operators (artisans, troubleshooters)
What is often confusing with these typologies is that they come out of the statistical realm and so the realm of
the particular/general rather than the singular. The confusion is where a conscious individual, and so a SINGULAR,
considers the PARTICULAR as if SINGULAR and so he/she "IS" of the given type when they take these tests.
This is not usually the case. For example, to get categorised as an INTP means one shares identity with about 3
million others in the USA population (given the distribution of INTPs to being 1% of that population - this can/will
vary in different countries etc) Thus the results are obviously reflecting a GROUP nature, a PARTICULAR group amongst
all groups making-up the MBTI GENERAL.
Local CONTEXT can then 'push buttons' to elicit answers to questions that give us a persona for that moment. Regular
testing may bring up consistent choices in answers and so show a general bias to a 'temperament' mixing nature/nurture
but the WHOLE set of possible types is present in all of us as the "Structure Of Personality" and context
can elicit 'best fit' personalities where we can be 'child-like' in expression due to never having experienced
that context before and so lacking skills in that personality (and often would try to express our 'preferred' form
even if it did not 'fit' properly)
The differences between Analytical Psychology and the MBTI is that the former aims for the individual, in the form
of the SINGULAR, to experience all forms of expression, whereas the MBTI aims for the individual, in the form of
the PARTICULAR, to stick to one preferred (or even genetically favoured) form of expression (the tool being used
for team creation etc and so a need for the individual to NOT change, not explore, else that upsets the structure
of the team).
What is of interest here is where does the XOR material come up? Where can we get a 'spectrum' of a persona and
so more details on that 'general' expression?
Since the MBTI does not formally go beyond 8/16 categories, and the XOR material is too 'vague' at the level of
8 categories, can we extend the categories? The answer is yes due to the involvement of self-referencing.
If we move back to the 0/1 representations of self-referencing we found it is easy to 'jump' from eight to 64 categories
through formats of:
000-000
000-001
Etc etc
Analysis of the 'blending, bonding, bounding, binding' categories fit the MBTI forms derived above e.g. blending
applies to the NFP (wholeness by drawing something 'in' - as do disciples/advocates in their support/promotion
of someone/something) and to the STP (wholeness by pushing outwards - as do trouble-shooters, artisans etc where
they 'get off' on the mediation dynamics interacting with 'out there' etc)
Thus it is possible to extend the eight MBTI categories given above (where we exclude the I/E function dichotomy)
by doubling-up the categories and so their representations. Thus the category of NTP (100) is refined into the
level 6 representation of 100-100 where this new category extends the MBTI into 64 categories rather than eight.
The qualities of an NTP are here associated with the representation of 100-100 that is itself associated with the
I Ching category of 'Thunder' and the particular, level 6 category 51.
The 27-ness of 51 is:
100001 (27)
100100 (51)
------ XOR
000101 (35)
The generic characteristics of category 51 in the I Ching is of the 'new' the 'sudden', the 'surprising', the 'enlightening'.
The generic characteristics of category 35, the category describing by analogy/metaphor, the 'skeletal' form of
51, covers the 'bringing of <something> into the light'.
The 48-ness of 51, where 51 gets its nourishment, what keeps it sustained, is:
011010 (48)
100100 (51)
------ XOR
111110 (43)
Category 43 covers the notions of 'spreading the word', of 'seeding' ideas in others. In other words the source
of nourishment of 51 reflects the 'bringing <something, a fact/truth etc> into the light' as an instinct.
All of these properties derived from the I Ching XOR process reflect general characteristics of the XNTP type ("Engineers")
of the MBTI (http://www.typelogic.com/intp.html & http://www.typelogic.com/entp.html
), showing both the I Ching and the MBTI as different forms of representations, of expressions, of core qualities
of meaning derived from self-referencing.
This relationship allows for the derivation of a spectrum for each MBTI category, as well as the extension of the
MBTI categories to 64 or even 4096 in number - each with their own spectrums and so increased details on properties
and methods of these types. This extension is possible through the use of I Ching categories as sources of analogy/metaphor
in fleshing out some other specialisation that uses the same method in deriving categories - self-referencing of
a dichotomy.
Of essential emphasis is the properties of the XOR operator that indicate that ANY form of categorisation, be it
micro or macro, utilising self-referencing, will include in it a rich level of information encoding extractable
using the XOR operator and a 'bit' form of representation.
Thus another example of self-referencing and so the implicit presence of XOR material is in the derivation of DNA/RNA
nucleotides and their codons from the recursion of the purine/pyrimidine dichotomy. Indicated here is the brain
dynamic of information encoding/decoding at the cortex level represents a fractal dynamic sourced in the molecular
biology level that in turn shows a source in characteristics of categories in particle physics, in particular those
categories derived from self-referencing of the fermion/boson dichotomy. (all of these reflecting the differentiating/integrating
dynamic overall).
The overall dynamics in self-referencing show a focus on increased regulation/control through making of finer distinctions.
For a focus on the emergence of reason from emotion, emotion from cognition etc, see reason.html
For a focus on the derivation of human emotions from the self-referencing of the fight/flight dichotomy see http://members.iimetro.com.au/~lofting/myweb/emote.html
for a linking of the categories of emotion with the categories of the I Ching see http://members.iimetro.com.au/~lofting/myweb/EmotionalIC.html
For a linking of the MBTI categories with those of the I Ching see http://members.iimetro.com.au/~lofting/myweb/type.html
For a model of generic meaning derivation using self-referencing, see my IDM (Integration, Differentiation, &
Meaning) project - http://members.iimetro.com.au/~lofting/myweb/idm001.html
Given the findings covered in part 1, so we move onto implications of that material in the context of prediction
of singular/particular/general
dynamics:
Teleology is focused on the presence of purpose, of there being an 'end' to things/being etc and is mostly linked
to the 'guiding hand' of some 'god'.
In the studies on various life forms to date the only 'guide' has been in the form of genetics where they develop
phenotype and that's it - the rest is up to chance and/or cultural guidance.
However, with the discovery of the entanglement of categories derived from recursion of differentiate/integrate,
the dichotomy 'embedded' in the brains of neuron-dependent life forms, comes the realisation that included in those
categories are states marking the 'beginning' and the 'end' and as such the presence of categories basic to 'purpose'.
The difference of course is that this 'purpose' is derived from the methodology of self-referencing and self-referencing
is derived from the containment of 'noise' by sensory systems that can include the brain as a sensory system of
information.
Any sensory 'noise' entering a container, when mapped, as it 'bounces around' in that container, leads to the map
taking on the generic 'form' of the Sierpinski gasket and so showing the favouring/encoding of self-referencing
dynamics; from the random comes order (and that appears to include 'purpose').
As covered in the post on "some properties of recursion of a dichotomy", using 'bit' representations
and the XOR operator we can identify the categories derived from self-referencing and then identify the 'spectrum'
of each category in the form of their unique expression of all of the other categories THROUGH them. Included in
this are categories covering 'beginning' and 'ending'.
These categories, being general, are not focused on the singular, conscious, individual, but on the particular
that is a local expression of the general, the species. As such the 'beginning/ending' elements are elements with
a statistical foundation where *ideally* any instance of the category will 'complete' itself by achieving the ending
but the environment can act to distract or destroy that instance.
Thus any 'ending' is an ending for a GROUP made-up of instances of the one category where all it takes is one to
reach the 'end' for the 'end' to be achieved - as we find in the flood of sperm aimed at fertilising an egg where
the multitude of sperm completes the task when one reaches the egg (and so the 'purpose' of sperm is to fertilise.
Its 'end' is either in success and so transformation (fertilised egg develops) or failure followed by 'death')
When we move to the position of Psychology and a focus on determining temperaments we find that the most successful
of these determinations are based on deriving categories from self-referencing - of particular commercial success
has been the Myers-Briggs Type Indicator (MBTI).
Since this typology system works off self-referencing so the categories derived are isomorphic to those derived
from differentiating/integrating in that it is the differentiating/integrating of the brain in general that forms
the infrastructure of the typology in particular.
Our unique consciousness can introduce 'novelty' in layouts, labels, etc for the typology and often work in a seemingly
'ad hoc' manner, but the truth is that consciousness is more so 'filling in the dots' of the template that emerges
from self-referencing of dichotomies.
As shown in the previous post on recursion properties, the categories of the MBTI DO 'fit' categories derived from
differentiating/integrating and in that fitting comes the inclusion of the XOR dynamics and so of each 'type'
of the MBTI coming with a spectrum covering both properties and methods of that type and that includes idealised
'purpose'.
Previously I have emphasised the distinctions of singular, particular, general where the particular/general focuses
on our genetic natures, as in being a member of the species, and so a particular of the general, as compared to
our singular nature that is representative of the developed sense of 'self' that comes in early infancy.
It is this singular that works like a 'random variable' in that its nature allows it to be 'unpredictable' and
capable of seeding behaviours of both particular and general that can go against the group 'purpose'.
When we consider the dynamics of singular/particular, where they share the one 'space' in the form of the individual,
so the particular, the genetically-determined individual, comes with 'purpose' but at the group or statistical
level.
Under these conditions, one's individuality is of no concern to the GROUP dynamic on pushing to reach its 'end',
its 'purpose'. Thus, if a particular falls by the wayside there is no recognition of that, it is 'meaningless'
in the eyes of the group focus; casualties abound, keep moving.
It is the presence of the singular that can act in re-defining the 'purpose', by exploiting it for local gain but
in doing so elicit 'conflict'
where singular goals clash with particular ends.
Thus the singular can fight against the particular due to its focus, its 'end', of self-autonomy, on total freedom
and so escape from external regulation and that includes the re-configuration of the genetic element responsible
for the goals, the ends, of the particular/general.
The other side of the coin is the cooperative side of singular working to aid in the achieving of the goal of the
particular and so of the general, in other words a focus on social development rather than personal development.
The testing set-up for the MBTI is designed to map out four dichotomies over more than a hundred questions and
so hide the nature of the dichotomies - and so bring out unconscious aspects of one's nature and so a more particular
focus rather than singular.
The other side of the coin is to bring out the nature of the singular by asking only four questions based on the
dichotomies where the interpretation is not of a 'hard coded' nature but of one's current, immediate, nature that
can change depending on context and that includes one's 'mood'. This 'works'
since being singular does not in some way magically 'remove' the properties of self-referencing.
In other words the categories of self-referencing are still present in the singular but now open to interpretations
based on immediate, local, dynamics that elicit shifting goals, ends, and so cooperating or competing with the
influences on the particular individual (especially if the singular is not aware of the explicit goals/ends of
the particular and is functioning off
'whim'.)
Since both singular and particular are self-referencing and so using the same set of categories, complex forms
of categories can be created reflecting the interaction of the two sets - where the nature of the particular sets
down a basic, genetically-determined, 'type' as context and within that operates the full spectrum of possible
categories representative of the singular.
With this singular/particular configuration local context works as stimulus to 'push' for a response from the singular
but at times also from the particular where the latter can overwhelm the former (well recognised in the influence
of basic emotions overpowering derived emotions and/or reason etc as such the singular can be floundering, wondering
what is going on as elements of the particular 'take over' or else work 'independently' and so seemingly outside
of the singular's control)
What is noticeable here is the hierarchy of categories:
Particular/general
Singular/particular
Where the particular is differentiating when compared with general but integrating when compared with the singular.
This dynamic appears to be a fundamental when building hierarchies around the differentiate/integrate dichotomy.
Given the presence of a seemingly 'teleological' element in our species as well as in our unique identities, there
is the suggestion for a need to re-evaluate exactly what are our 'natures' are, both as species-members and unique
individuals, and so consider refining our development given an understanding of our 'ends'.
Chris.
--------------------------------
Notes/References
[1] The WHAT/WHERE dichotomy applied to the brain is well recognised and documented to such a degree
it is an axiom contained in introductory texts on neurosciences. E.g.
"Two pathways from the striate cortex to extrastriate regions convey prominent streams of information. One
pathway flows for V1 [main area of visual input processing] to the temporal lobe (ventral pathway or "what"
pathway) and conveys analysis of stimulus features and their conjunctions, and ultimately the information is used
to carry out form discrimination and object identification. The other pathway projects from V1 to the parietal
lobe (dorsal or "where" pathway) and carries information about a stimulus motion and localisation within
visual space" p51-52 Gazzaniga, M.S., et al (1998) "Cognitive Neuroscience : The Biology of the Mind"
Norton
The 'WHAT/WHERE' reflects properties of the general dichotomy of differentiating/integrating (see [2] below)
Also see the diagram
http://members.iimetro.com.au/~lofting/myweb/neuron2.gif
The left/right hemisphere relationship reflects the same sort of pattern as does work focused on surface/core analysis
of the brain - thus there is a dimension derived from self-referencing of differentiate/integrate that is ubiquitous
in the brain and we can trace that down to the axon/dendrite, FM/AM dynamic of the single neuron. See diagram
http://members.iimetro.com.au/~lofting/myweb/Neuron.jpg
[2] Definitions of differentiate/integrate:
"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
[3]
To cover issues of brain function showing parallel dynamics, neural hierarchy, and 'emergence' (with additional
comments in ()):
"We have garnered evidence for the emergence of properties of inter-hemispheric communication by demonstrating
that the nature of processing when both hemispheres are involved cannot be predicted by the processing performed
for each hemisphere individually. We obtained such evidence in a paradigm that compared processing when information
is directed unilaterally to single hemisphere against that which occurs when both hemispheres receive the same
information. In our studies two words were either presented only in one visual field (RVF, LVF) or one word was
presented in each visual field (bilateral visual field - BLF). The critical finding was that a manipulation of
the font and case of the words did not affect performance across conditions for LVF or RVF trials. Nonetheless,
this same manipulation did influence the pattern of performance across conditions on BVF trials (Banich & Karol
1992).
If the whole is simply the sum of the parts, such a pattern of results should never have been observed. If communication
between the hemispheres was completely constrained by processing within each hemisphere, then the lack of effect
of the font/case manipulation on unilateral trials would have predicted no effect of the font/case manipulation
on the BVF trials. These results make clear that processing of the hemispheres in relative isolation cannot be
used to predict the effects of communication between the two hemispheres. Rather, interaction between the hemispheres
can have effects on processing that are emergent, above and beyond those brought about by a single hemisphere."
Banich, M.T., "Hemispheric Interaction" IN p 270 Hugdahl,K., & Davidson, R.,(eds)(2004)"The
Asymmetrical Brain" MITP
"If interactions between the hemispheres can have emergent properties then how might these properties influence
information processing? Our research ha indicated that interaction between the hemispheres is particularly useful
when tasks are attentionally and/or computationally demanding" ibid
"When tasks are computationally simple, it is advantageous to have information processed by a single hemisphere.
In this case, the processing of resources of one hemisphere are ample for the task and interaction between the
hemispheres imposes a communication overhead.
The net result is an advantage for within-hemisphere processing. However, when task complexity increases to the
point that the resources of a single hemisphere are overly taxed, another process comes into play. Under such conditions,
it becomes advantageous to divide processing across the hemispheres so that more computational power can be brought
to bear. Because both hemispheres can process almost all tasks to some degree (although in different manners) a
division process is possible. Because the hemispheres are somewhat autonomous processors (e.g. Friedman & Polson
1981), an interhemispheric division of processing provides extra computational power." P 271 ibid
(This is equivalent to resolution power in telescopes etc. and so the general focus on increasing bandwidth to
process something 'now'.)
"These studies provide strong evidence that the hemispheres dynamically couple and decouple their processing
as a function of task complexity. When task demands are relatively simple, the hemispheres decouple their processing
and work independently; when task demands are more complex, the hemispheres unite by invoking across-hemisphere
processing." p 284 ibid
(Other work shows that the experience of the new/undifferentiated/unknown elicits a dynamic that is right to left,
general to particular, unknown to labelled and so known. Any following exposure to what is now labelled is immediate
left response (where labels are 'stored' in the left as universals) and so a 'within' focus as compared to 'across'
when we have to deal with the unknown. Thus once something is named the tasking is easier.)
Cref from the article:
Banich,M., & Karol (1992) "The sum of the parts does not equal the whole: Evidence from bihemispheric
processing" Journal of Experimental Psychology :Human Perception and Performance 18, 763-784
Friedman,A & Polson,M.,(1981)"The hemispheres as independent resource systems: limited capacity processing
and cerebral specialisation" Journal of Experimental Psychology : Human Perception and Performance 7, 1031-1058
(More recent work brings out the differentiating/integrating dynamic within and across the hemispheres as well
as front/back dynamics.
The major points are on independent functioning of 'modules' together with their 'entanglement' or 'recruitment'
for complex processing AND a consequence of EMERGENCE in this dynamic)
[4] see, for example:
Goldberg, E.(2001)"The Executive Brain : Frontal Lobes and the Civilised Mind" OUP
[5] We are not interested at this point on the 'truth' or 'falsity' of the I Ching, we are focused
on the manner in which it has been derived and the relationships between categories that are artefacts of that
methodology - self-referencing - for an IC page covering this material see http://members.iimetro.com.au/~lofting/IChingPlus
and associated essay page http://members.iimetro.com.au/~lofting/myweb/newindex2.html
[6] For a page mapping the self-referencing in deriving MBTI categories see http://members.ozemail.com.au/~ddiamond/mbti.html
