ABSTRACT

Professor Muller, in his review of my commentary titled "A COMMON LANGUAGE", seems to be requesting clarification of some of the points made, in that my inclusion of references to Peircean thought seems to have clouded some of the issues. He emphasises the point that "...I would agree with him that it is necessary to step back from implicit (exclusive) objectivity, but I think the goal of this distancing process has to be a non-ontological view rather than subjective explanations of objective (ontic) processes". He also raised issue with the over-emphasis on the pre-supposition of mathematics.

This point is taken-up in this reply where I will also show the source of mathematical descriptions and so their proximity to 'reality' based purely from 'in here'.

<1>
The brain processes information in the form of wholes and their aspects. When I say 'brain', I do not just mean the human brain, I mean all animal brains, although the initial distinctions were only possible through the extensive work of Roger Sperry et al on human brains in the 1950s and 1960s. These findings have been reinforced over the last forty years with both neurological and psychological research on humans and other life forms, stressing a line of neurological development that culminates in humans in it's most refined form.

<2>
With this point made, let us stick to considering in some detail the methods of information processing possible in a system that only 'sees' wholes and their aspects.

<3>
The first question raised is "what is meant by the term 'aspects'?". This term covers a number of areas that we can divide into three 'basic' categories:

<4>
PARTS - areas of the whole that we find are removable and so seen to be independent of the whole. We can include an abstract list of all of the possible 'parts' that the whole can be cut into (1/2, 1/3, 1/4...[in mathematics this is called the harmonic series]).

<5>
STATIC RELATIONSHIPS - when observing the whole, patterns emerge that reflect relational formats. These patterns can be created either by considering groups of parts or else consideration of a single part in relation to the whole. These patterns help us to refine our description of the whole and so can be used to make whole-to-whole comparisons where it is aspectual differences that enable differentiation rather than an overall difference in form.

<6>
DYNAMIC RELATIONSHIPS - here we observe a whole in relation to other 'wholes' where the source of the relationship seems 'invisible' -- thus the whole seems independent of anything else but at the same time seems to be involved in some sort of 'partnership' e.g. the Earth going around the Sun whilst Earth and all the other planets travel with the Sun, and so as a 'whole', through space.

<7>
One important distinction is the fact that a PART can be treated as a WHOLE in it's own right and so we add another aspect -- context, and so emerges the distinction of text (foreground) from context (background) as well as consideration of multiple contexts and so hierarchy and dependence. Thus text is more 'whole/part' oriented emphasising self-containment and 'single context' (and in an idealised form NO context).

<8>
The final distinction is more one of direction, in that wholes can be perceived to expand and/or contract, as can relationships, and so we have a basic set of elements that we should be able to use to describe ANYTHING:

contractive wholes, parts, static relationships, dynamic relationships.

expansive wholes, parts, static relationships, dynamic relationships.

<9>
We can in fact show a path of derivation of these terms in the form of a binary tree:

(1) WHOLE

(2) WHOLE/PART

(3) WHOLE/STATIC/PARTS/DYNAMIC

<10>
Note that at (2) there is the emphasis on separation but still with a bias to independence and objects; only at (3) does emerge the distinction of objects from relationships where relationships are divided into, using modern-day programming terms, properties (static) and methods (dynamic) (in passing note that methods enable transformations).

<11>
Also note the ORDER at level 3, namely that STATIC relationships emerge in-between wholes/parts since that is where we find them -- they are 'non-removable' patterns of the whole that are at the same time distinguishable from the whole (like an object's colour) or else are made-up of grouping parts of the whole.

<12>
Furthermore note that in our culture's teaching of wholes and their aspects, we START with the whole and then study STATIC relationships and THEN detailed parts and FINALLY dynamic relationships; thus our methods of teaching are shown horizontally but the derivation process is 'vertical'. (in maths we start in pre-school with whole numbers and dont get into complex numbers and the detailed consideration of dynamic relationships until out teens; I think this is the same with any 'language').

<13>
If we take the basic 'template' in <9> and mirror it so we get the EIGHT possible 'basic' elements that are then seen in text/context relationships with each other, but what could be ment by 'contractive' wholes? This can be expressed as negation or opposition or a whole that 'pulls inwards' compared to an expansive whole that 'pushes outwards' or else is expressed as something 'positive'.

<14>
What is striking about this primitive 'template' is that we find that all of our maps of reality -- both 'in here' reality and 'out there' reality (as well as the interactions between 'in here' and 'out there') seem to be based on creating labels for these basic elements or their combinations (see below)

<15>
A simple example of this is in the origins of our number system in that the abstract terms of whole, irrational, rational, and complex seem to be refinements of the basic whole/aspects elements, thus:

Whole numbers (primes + composites) -- wholeness

Rational numbers (1/2,1/4...) -- parts

Irrational numbers (PI, e, sqrt(2)) -- static relationships

Complex numbers (i, a+bi etc) -- dynamic relationships

To this we 'add' contract and expand in the form of negative and positive. (we can count with wholes and parts but NOT with relational symbols e.g. PI, e, i, etc.)

<16>
Without considering anything else, here we have a direct link between whole/aspects descriptions and mathematical descriptions; we can in fact create ANYTHING using mathematical terms since they are directly linked to whole/aspects mappings since that is where they come from. (as stated before, combining the basic elements enable rich, complex expressions in that we can have 'whole numbers' in a complex context -- as we find for example in 'quantum jumps'.)

<17>
The difference between mathematics and all other 'languages' is that mathematics is context-resident in that the formulas and 'laws' serve to guide mathematical expression and so most of it 'lives' in our context; as do syntax and grammar rules, for it is context that guides and controls text. Spoken language is 'text' oriented in that the words serve as symbols for patterns of local 'meaning' and so words are more 'cultural' in that in maths '1' is '1' whereas in spoken language there are many terms for '1'.

<18>
What this implies (obviously) is that the whole/aspects template is also 'in' our context and serves to guide us in our processing of information. This template is what I call 'middleware' in that it sits in-between neurology and psychology as chemistry sits in-between physics and biology; mathematics is 'on the border' between middleware and psychology and so its 'universality'.

<19>
We now come to the interesting part in all of this, and that is the elicitation of 'meaning'. By this I mean that beside the terms used (whole/parts/static/dynamic) so there seems to be a sense of 'feel' that is describable and directly linked to the wholes/aspects template and it is from here that develops our sense of meaning.

<20>
We start by noting the implied presence of dichotomisation in the whole/aspects distinction. This appears in the form of relational emphasis of 1:1, 1:many and many:many types. together with this we note the presence of dichotomy in the expression of emotion -- a la the fight/flight dichotomy (amygdala linked -- there seems to be a range of four base types which through mixing become more complex in descriptions. Galen and Hippocrates developed temperaments in the form of anger+sad neutral+happy. More recent work has demonstrated these 'basic' biases are present across the neocortex with the right hemisphere being negative and the left neutral/positive (e.g. see Gainotti, G., and Caltagirone, C., (eds) (1989) "Emotions and the Dual Brain" Springer-Verlag ). The neutral state seems to be more of a state of emotion cancellation where A/~A emotive expressions cancel each other out and in personas this 'area' is where we find 'rationalists'.)

<21>
A heuristic study, based on reading the descriptions of many dichotomy-based relationships across many different disciplines, leads to the realisation that humans actually seem to describe things by how they MIX the elements of the dichotomies, and that there are four basic ways to mix:

(A) BLEND -- combining two into one such that a 'new' identity is formed.

(WHOLE) For example, in whole number math 1+1 = 2 is a 'blending' and is the emphasis on purity (prime numbers and their composites).

(B) BOND - physically link A to B but allow for A and B to retain some identity (STATIC RELATIONS). For example, in irrational numbers, symbols like PI manifest static part-to-whole relationships and so described as a 'bonding' -- In the unit circle the concepts of diameter and circumference are maintained but a 'bond' is emphasised in that separation is not possible; the two entities are dependent on each other by explicit observable linkage and this is shown by the use of irrational numbers.

(C) BOUND - let A enclose B or visa versa -- the emphasis on distinction but no 'link' (PARTS). Thus in rational numbers we find all of the parts that we can cut the whole in the form of distinctions -- 1/2, 1/3, etc etc.

and

so 'independent' units. Any part can be then analysed as if a 'whole' since the whole/aspects distinction works at all scales.

(D) BIND - A and B are 'independent' except for some 'invisible' relationship observable through time. (DYNAMIC RELATIONS) With complex numbers we express oscillations and transformations where objects are binded together 'invisibly'.

<22>
If we then add the 'contract'/'expand' dichotomy, these above four terms become eight basic elements:

contractive wholes -- expressed emotively as 'contractive blending' or words synonymous with this.

contractive statics - 'contractive bonding' -- A and B together -- a relationship (bonded)

contractive parts - 'contractive bounding' -- a protective boarder between A and B.

contractive dynamics - 'contractive binding' -- A and B 'dance'

<23>
All of the above emphasise a drawing inwards whereas the expanding element emphasises pushing outwards and in the context of left/right brain biases so contractive whole/aspects descriptions are more 'right' and context bias than the more expansive text biases of the left. (note that I stress BIASES).

<24>
Thus the 'simple' distinctions of wholes, parts, statics, dynamics, also encode emotive forms in those of blend, bound, bond, and bind and when we, at the psychology level, describe things we unconsciously use words that link to these basics, or 'primes', and their composites.

<25>
as an example - consider the generic concept of contractive bounding in a context of expansive blending. We can re-write this as in a context of wholeness we have a distinction of parts in the form of 'them' from 'us'. Using a dichotomy-based whole/aspects biased tool like the MBTI to generate social personas for the text and context we find that expansive blending (the context) ties with negotiator types; those who seek a blend (wholeness) by getting agreement -- the success of the process elicits a feeling of 'wholeness' in the negotiator. Contractive bounding (the text) ties with conservationists and protectors -- those who set-up barriers (boundaries) to preserve what is inside. (thus CONTRACTIVE bounding. Expansive bounding is described by Scientists in that they push boundaries outwards by making maps of reality...).

<26>
Since the MBTI does not explicitly go to this level of analysis, the 'mixing' of these two persona types is described in another dichotomy-based system that DOES go to this degree of analysis and that system is the I Ching -- the "Book of Changes" that originates from China. This whole/aspects categorisation system (we ignore it's divining aspects) gives us a symbol, called a 'hexagram', that captures the 'behaviour' described by the generic text/context descriptions given in <25>. This hexagram is called "Waiting/Serving" and the emphasis is that in the process of expanding one's self (expand blending) there are times when we must wait for external forces to 'do their thing'; so do not get involved (the distinction of 'them' from 'us/me') but serve and wait for the 'right' moment. (for details on this hexagram see http://www.ozemail.com.au/~ddiamond/h05.html)

<27>
This generic description of 'waiting' defines a state of being that results from mixing expansive blend and contractive bound and captures the overall meaning of the pattern created by the mixing. Thus to describe the process of being or becoming 'whole' I will use terms that link to a 'feel' expressed by the term 'blending'; there will be MANY possible terms but they will all 'point' to this 'blending' pattern. In the above context, this seeking of wholeness (the driving force if you like) 'meets' an outside force that creates a distinction and this whole scenario is thus describable using the hexagram.

<28>
Note that the generic concept of distinction (bound) in a whole-biased context (blend) is also describable mathematically in the form of rational numbers in a whole number context. This 'scenario' deals with considering potentials (what could be -- harmonics of the whole) rather than 'actuals' (what is) and thus the consideration of potentials can generically imply 'waiting'.

<29>
My point is that this 'middleware' is shared by ALL humans and it is what enables us to get around 'local' expressions and so understand each other; it is thus initially independent of 'out there'. Furthermore it demonstrates that ALL of our maps created at the psychology level are in fact symbols and metaphors for whole/aspects interactions and so need not be taken too literally as many are (e.g. Astrology, Tarot, QM, Mathematics etc etc. etc.). The ease with which we make analogies across these disciplines is because it is the whole/aspects template that enables resonance -- e.g. all 'wholes' have a 'blend' feel and so are 'the same'. Different cultures will create different words that all 'point' to the same feeling of 'wholeness'.

<30>
The presence of a whole/aspects template 'in here' enables the abstract distinction of 'out there' together with developing a 'feel' for these distinctions and so a sense of 'meaning' both at the abstract level and at the 'gut' level. These basic categorisations are fed back into each other to create more complex representations that we then label with words, and so allowing for the distinctions of 'hate' (totalist - whole) from 'dislike' (more aspectual), or 'hope' (future biased reactive state) from 'anticipation' (future biased proactive stae).

<31>
These complex representations have simple roots that 'colour' or 'set the tone' for the overall complex descriptions; the basic elements of the template are like those of chemistry for that is where the template resides -- in-between neurology and psychology like chemistry resides in-between physics and biology.

<32>
The linking of patterns leads to the establishment of 'meaning' in that 'good' patterns are maintained and 'bad' ones thrown away. It should be noted that 'good' patterns are not 'true' patterns -- and so a well-structured illusion can elicit staggering degrees of 'faith' in individuals; to the extant that when demonstrated to be 'illusions' they are hotly defended and it can take a generation or so for these patterns to be removed from the culture (if at all..flat earthers are still around).

<33>
I hope that the readers will be able to see that from very simple whole/aspects distinctions we can create rich maps of 'reality' -- some 'true' and others 'false' -- and that these maps do not need to have ANY validity outside of the culture (or even the individual); they will 'feel' right regardless of 'out there' and only the passage of time (and so feedback) will determine their having any 'universal' worth. (e.g. Newton's specific form of mathematical representations are no longer used but the overall ideas are.)

<34>
In modern times, due to the whole/aspects template and the development of mathematics so a degree of global consensus has arisen about 'out there'; standardisation in teaching methods and content ensure that 'your' wholes/aspects distinctions are similar to 'our' whole/aspects distinctions and so there is no need for believing in 'external' forces to describe the origins of mathematics or of any other system of description -- we all use whole/aspects and that serves as the base for the symbolic and metaphoric diversities we see; the problems arise when we fail to recognise that our symbols and metaphors are just that -- they have a 'hidden', 'literal' layer based on the categorisation of sensory information as wholes/aspects, and lack of awareness of these processes can lead us astray.

For a more 'detailed' study see http://www.ozemail.com.au/~ddiamond

Chris Lofting.

[Analyst-Programmer for Computershare Ltd
e-mail <clo@fmsc.com.au>]