Abstract
Through an analysis of a property of recursion we can derive nuances in expressions for a general 'pure' expression given a particular context. This process is here demonstrated using the Myers-Briggs Type Indicator® as the source of expressions. The prime focus is on deriving a source of meaning for AI systems but we can also see how our own brain seems to derive meaning through this use of recursion of dichotomies.
Keywords: AI, meaning, recursion, brain, dichotomies, MBTI, emotions, typology, neuroscience, cognitive science
Of interest in the development of AI systems, be they for games or general computer-human interface, is the ability to encode and reflect meaning in a context-sensative manner and so be able to take a universal persona temperament or type and give it nuances in behaviour depending on context.
In the process of identifying sources of meaning in humans I have been able to identify a method of generating behavioural nuances through a property of the method of deriving a universal set of meanings through recursion.
What is recursed is any dichotomy that reflects the general extremes in meanings. For this example I will use a dichotomy associated with the popular persona categorisation system called the Myers-Briggs Type Indicator, the MBTI® and its offshoots. (e.g. see http://www.braintypes.com/16_types.htm)
In the MBTI we can identify the 'root' dichotomy of this recursively developed typology as made up of an element we can call "Identity Seeking", the general NF temperament, and an element we can call "Sensation Seeking", the general SP temperament. The fundamental differences here are in the integrating, context sensitive bias of the Identity seeker vs the differentiating, context insensitive (or more so context universal) bias of the Sensation seeker; as such, focus for the sensation seeker is on the 'point' irrespective of context, whereas focus for the identity seeker is all that surrounds and is behind the 'point'.
These extremes are so sharp as to be able to be symbolised in a rigid A/NOT-A format, reducable to the bits, BInary digiTS, of 1 (for A) and 0 (for NOT-A). Since '0' is more often associated with 'off' so we associate it with the NF state, the identity seeker, and thus '1' is associated with the SP state, the sensation seeker.
The process of recursion applied to a dichotomy acts to 'stretch' the possible qualities expressed in the range across the dichotomy. Thus a first level recursion of 0/1, where we apply the dichotomisation to each element in the dichotomy, we end-up with FOUR 'types':
00, 01, 10, 11
The middle two types, 01 and 10, have emerged from the 'middle' of the dichotomy in that they represent less extreme states of 0 and 1, we are starting to focus on nuances. If we apply recursion again we get EIGHT 'types':
000, 001, 010, 011, 100, 101, 110, 111
The 000 and 111 symbols represent the 'pure' NF and SP types we used in the original dichotomy but these are more refined here with a further six types being derived to 'flesh out' the possible qualitative differences identifiable through recursion. What is of note is the ordering of the bits in that the order represents text-context relationships, such that 01 means a quality made-up of a CONTEXT identified as '0' and a TEXT, identified as '1', operating in that context. These relationships are then expressed as the whole form of '01'. As we add bits so the new bits operate within the context set by the sum of all others - we see here develop a hierarchic format represented here as a sequence of 1s and 0s.
If we go back to the FOUR types, we can identify four general categorisations derived from the MBTI and associated typologies:
00 - identity seeking (NF)
01 - security seeking(SJ)
10 - solution seeking (problem solving)(NT)
11 - sensation seeking(SP)
Thus the 'security seeking' persona has emerged from the general 'identity seeking' persona ('0') serving as context within which is introduced the sensation seeking persona as text ('1'). As a whole this persona type works from behind a barrier of some sort with a bias to identifying things from a moral standpoint ('right' or 'wrong', 'them' and 'us') etc. There is a suggestion that this security seeking type reflects an identity seeking type that has experienced fear but there is also the possibility of the type being born due to genetic diversity such that they can go through life with a base sense of fear that in fact has no foundations in reality. (the energy distributions across these types as they establish/express identity form a Power Law, spectrum, distribution from energy conserving (NF) to energy expending (SP) - the more energy involved the more we are operating out of a mediation position):
The 'solution seeking' persona has emerged from the general 'sensation seeking' persona ('1') serving as context within which is introduced the identity seeking persona as text ('0'). As a whole this persona type works from behind a barrier of some sort with a bias to identifying things from a rational standpoint ('fact' or 'fiction', 'true' or 'false') etc. There is the suggestion that this solution seeking type reflects a sensation seeker that has experienced fear and deals with it through the creation of maps, ontologies, etc. There is also the possibility of the type being born due to genetic diversity and as such go through life forever solving problems out of a fear that has no foundations.
Continuing recursion, the eight categories derived at the next level seem to form a fundamental set of qualities usable to categorise personas in general, with the recursion of one more level, taking us to sixteen qualities, reflecting all of the types of the MBTI in particular.
These levels of qualities are, due to the method of recursion, sorted in order from one 'pole' to the other 'pole', and as such each level forms a continuum of qualities with repeated acts of recursion introducing finer degrees of granularity in precision, we move from coarse grain to fine grain.
In general recursion, where we move from general to particular, regardless of what is being recursed, the qualities in each level are representative of UNIVERSAL qualities, they reflect 'ideal' expressions and as such are only expressions of magnitudes, of cardinality, and are thus SCALARS in form. There is a weak form of ordinality in that the qualities are ordered by the method into a scale but this scale lacks formal elements of a temporal format in that the scale is reversible at any point - like a thermostat control etc.
The work on analysis of the source of meaning has led to the identification of a pattern in recursion I call "Variations on a Theme". Simply put, the differences between the first N/2 qualities in a sequence and the last N/2 qualities in a sequence is only in the first bit; all other bits in each quality are the same as their counterpart in the other N/2 set of qualities. Thus, using the above list of eight qualities we have:
000, 001, 010, 011, 100, 101, 110, 111
And when paired into first N/2 and last N/2 we have:
000, 001, 010, 011
100, 101, 110, 111
where the top and bottom qualities of the columns reflect the variations in the form of their difference only being the first bit.
If we do a cognitive analysis of, say, 000 and 100, (the MBTI categories of XNFP and XNTP) we find strong similarities in behaviours other than the 000 is more integrating and focused on people, the 100 more differentiating, but still integrating, but focuses on things (ideas etc). The common theme in both personas is they achieve 'internal harmony' THROUGH 'something/one' (e.g. as devoted parents through the success of their children or devoted thinker through the success of their idea(s)). As such, these categories are still 'scalars' and the focus is on BETWEEN the different qualities. We must, to achieve our goal of identifying behaviour nuances for a universal type, focus on WITHIN a quality.
As luck would have it, using bits to represent the qualities allows us to derive a sequence of qualities from WITHIN a single quality by applying recursion. This process is easy when we recognise that we can generate the sequence we need by simply 'bit flipping' the bits used to identify a particular quality. We are thus doing to a three bit pattern what we did to the original 1 bit pattern reflected in the original dichotomy of 1/0.
Thus the eight qualities we have used so far lead to the following eight sequences (which here form a matrix), each focusing on qualitative differences WITHIN a general quality (the general quality being represented by the first symbol in the sequence). Thus the first element reflects the 'raw' form of a quality and all others reflect degrees of that quality from 'highly represented' to 'minimal/no representation. For example, the quality represented by 000 is found to be a dominating influence WITHIN the quality represented by 100 and be totally lacking in the quality represented by 111, thus these sequences identify the degrees of expression of a quality from 'most dominating' to 'least dominating' :
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
Through a cognitive analysis of these sequences something of interest 'pops' out and relates to the "variations on a theme" concept in that for each sequence, forming a complementary sequence out of SWAPPING the order of the first N/2 with the last N/2 (and so lining up the variations on a theme patterns) leads to the derivation of a sequence that identifies all of the POSSIBLE expressions of a SPECIFIC quality (the root quality in each of the above sequences) given a context.
From the above we can identify a method to derive the expression of one 'archetypal' quality being expressed THROUGH a context described by another quality. See the patterns described in the I Ching metaphor page on line positions meanings. (this is NOT the same as an archetype operating WITHIN a context of another) - as shown in the associations of I Ching and MBTI.)
So, to summarise the steps so far:
We take a dichotomy and apply recursion. At the level of the 3rd recursion we have a set of qualities that are scalars in form, mapping magnitudes in expressions but in a general format and containing 'lumps' due to the method of derivation - the sequence we 'see' is not made-up of single values but of PAIRS. Thus is a consequence of the methodology, the recursion.
To focus on the expression of a specific quality across the whole spectrum we apply recursion to that quality deriving a sequence representing the degree of influence of a specific quality in all of the others.
Due to the properties of the methodology, we can take this last sequence, swap N/2 elements (first with last) and derive a sequence that identifies the expression of the quality given a context.
In GENERAL, the ordering of the qualities in the "variations on a theme" sequence reflect the possible expressions, the variations, of the quality given a context where the order in the sequence reflects development from a 'raw' state to a 'refined' state.
Linking this set of possibles with a context will elicit a set of probables and this act reflects the concept of the state vector and the use of the wave equation in quantum mechanics and at the more wetware level reflects the human brain's use of probabilities thinking as it zooms-in for very high-precision details on something/someone.
As such, the application of recursion to a scalar elicits a higher degree of expression where we move into the realm associated with vectors and tensors and as such 'full spectrum' mapping of an entity such that we can predict its dynamics in any context identifiable by the finite set of qualities we currently use to derive meaning.
Recursion allows us to extend these scalars to any degree of resolution or until our sensory systems fail to resolve difference. As such, a 4K set of qualities elicits a 4K set of possible expressions of a single quality given a context, and so on.
Limiting our selves to the above eight qualities, the NF type (quality 000) comes with the following list of qualities ordered from 'raw' to 'refined' where the 'everyday' nature (000) is always at the fifth position and the values 'beyond' the everyday position seem to reflect the quality in a DYNAMIC form as compared to the first five positions that reflect development in STATIC form:
General format: 000
Derived: 001, 101, 011, 111, 000, 100, 010, 110
What this order seems to 'say' is that the quality '000' in its 'rawest' format is describable by analogy to an under-exaggerated expression of the quality 001. As we move from left to right so we pass through increasingly 'refined' descriptions by analogy until position 5 where the quality is at its 'purest' as a static form. When we move into positions 6, 7, & 8, these describe by analogy the 'least' and 'best' it can do dynamically. Here for example, the quality 000, at its best level of expression, in a dynamic 'peak experience', will express itself in a manner described by analogy to an exaggerated form of quality 110. (In MBTI terms, an XNFP persona [000], operating in 'peak' performance mode, can come across as a well developed, an overexaggerated, form of XSFP[110]. In its rawest form, the XNFP comes across as an underexaggerated XNFJ [001])
The relationships identified are relationships created by the method of derivation of qualities, through the application of recursion to a root dichotomy who's elements represent the 'extremes' in the range of qualities considered usable in describing 'reality'.
The above example has been limited to three levels of recursion and so eight types. There are in fact no bounds other than those of our senses or, more usually, those of our pragmatism.