Alan,
My slowness in responding to this is a measure of not being able to comprehend or relate to it in a way that means I can respond, easily and quickly.
I don't use 'contiguity' in my daily conversation, or writing, so as yet I don't know what it means. I see how you have defined it, as 'infomational connectedness'. When I use 'continuity', which I do use in my daily conversation, I am meaning 'connectedness in time'. So when I see you using it differently I wonder about how others might use 'contiguity'.
Then, for me to understand what you mean by 'gives rise to a new 'transfigural mathematics' in which the intrinsic discontinuity of both classical and modern mathematics, embedded in discrete numbers and 3-dimensional geometry is solved', you will have to take me beyond my present mathematical understanding and show me how it helps me comprehend and work with my world, or at least with my world view, in a way that is at least as powerful as my present understanding of the power of mathematics in my comprehending. For me it needs to be more than a stringing together of new words ('transfigural matehmatics') if I am to follow you there (ie able to test and validate or otherwise deal with the claim that something or other is 'solved').
I am happy to concede that discrete numbers suggest intrinsic discontinuity (in space or time). Classical mathematics has introduced fractions to 'fill the space', and even 'irrational numbers' (though by this stage I may have moved from 'classical mathematics' to somewhere else, I do not know the world of mathematical symbolism all that well).
I am happy to concede that three-dimensional representation of space tends to capture our capacity to conceptualise. I have wondered if that 'threesome' tends to limit our world to groups of 'three' in models conceptualising processes, eg Habermas's 'technical', 'practical', and 'emancipatory' as scoped in Carr&Kemmis. (And I am reminded at this point of George Kelly's suggestion of three-seven being the limits of easy remembrance.)
I do know that I comprehend space in the three dimensional, but not the space-time complex with time the fourth dimension.
I do know I can work with Rubrics cube, but only by pattern and routine, not because I am understanding the relationships of the permutations and combinations.
I have been interested to find, over the past decade, that I have inklings that the matrix is a powerful tool in helping manage complexity and interacting factors, but confess that I am limited, and by the emphasis on the two dimensional page where I do so much of my thinking work, which I can then describe and communicate to another, to a two-by-two matrix, as for instance now conveyed in Kemmis & McTaggart's extension of their conceptualising found in Denzin and Lincoln.
I am instructed that in aesthetic judgement a range of factors is involved in testing a composition: rhythm, balance, tone, contrast, dominance, harmony, ...; but if I do know what I like, I cannot put into words why I like it, and what judgements I am making in executing changes to finish off my sculpture, or to compose my photographic selection.
...
Maybe, as you suggest, I can just be ... my complex self ... but at that point I find I would expect to be even more isolated than what I experience in my struggle to communicate with others. But perhaps that is only wishful thinking ... words on a page look like I am communicating. Perhaps I am not. In which case, it would be wise to withdraw from this enterprise and go and enjoy myself more with my camera and sanding bench and pieces of softwood.
Dianne
Carr, W., & Kemmis, S. (1986). Becoming Critical: Education, Knowledge and Action Research ( rev ed ed.). (Melb.): Deakin Univ Pr.
Kemmis, S., & McTaggart, R. (2000). Participatory Action Research. In N. K. Denzin & Y. Lincoln (Eds.), The Handbook of Qualitative Research (pp. 567-605). Thousand Oaks, Calif.: Sage.
----- Original Message -----
From: Alan Rayner (BU)
To: [log in to unmask]
Sent: Monday, October 08, 2007 6:03 PM
Subject: Innate and conditioned reflex(ivity)
Dear Jack and all,
Some interesting themes might be arising here, which relate to the distinction between innate and conditioned reflex, as well as to the distinction between 'informational connectedness' ('contiguity') and 'spatial communion' ('continuity'), which I think takes us on from Dewey's predominantly transactional thinking into the local-non-local awareness of the inclusional 'complex self as neighbourhood'. I have pasted in two pieces of writing below that relate to these distinctions, one from the 'Research Streams' on our new website, the other from the introduction to a book currently being prepared.
To illustrate these distinctions, I often use the metaphor of a river, whose branching pattern simultaneously conditions and is conditioned by the qualities of its catchment, mediated co-creatively through its banks and valley sides (interfacial boundaries). Here there is no transactional severance between 'subject' and 'object', which introduces a 'time-delay' or 'intervening thought' in the 'feedback' between the 'action' of 'one' and the 'reaction' of the 'other'. The 'local' and 'non-local' are inescapably and simultaneously included in one another: 'somewhere' is a dynamic inclusion of 'everywhere' in the same sense that 'local self-identity' is a dynamic inclusion of 'non-local neighbourhood'. Amongst other 'things', this understanding gives rise to a new 'transfigural mathematics' in which the intrinsic discontinuity of both classical and modern mathematics, embedded in discrete numbers and 3-dimensional geometry is solved.
The river system illustrates innate, receptive-responsive reflexivity, which is not active-reactive in a Newtonian sense. On the other hand, the conditioned reflex (which I erroneously referred to as 'knee-jerk' in my response to Sarah) arises from the reinforced mental association (thought connection) between one phenomenon or idea and another. The aim of cognitive behavioural therapy (CBT) is to recognise and question the validity of this thought connection in cases where it engenders addictive/recurrent patterns of behaviour that are problematic for the sufferer. In a sense, I (as an OCD sufferer and beneficiary) have been trying to recognise and question the thought connection that engenders cultural and personal conflict. And the thought-connection is ironically a dislocation: 'I, me, myself and I, AM an exception from my natural neighbourhood (habitat)'. It is this thought, re-inforced by the paradoxical, space-excluding logic of the excluded middle for millennia, that leads us to believe, and act upon the belief, that there is a definable gap (an absence of presence or discontinuity) between subject and object. So habitual has this thought become in many situations (especially 'workplaces'), that we have to stop ourselves, suspend judgement, step back and THINK, to recognise its invalidity, and allow our natural receptive-responsiveness space for expression. Conversely, our natural receptive-responsiveness is often allowed expression when we let go of the paralysis of analysis and can just be our natural complex selves.
Warmest
Alan
----------------------------------------------------------
Psychology
Brief Introduction
Deep in the heart of much human psychological distress is an oppressively singular rationalization of the individual 'self', analogous to a cardboard cutout model. This 'free agency' is a paradoxical artefact of the objective abstraction of the material 'content' of nature out of spatial context. It is dislocated from the receptive space of its natural neighbourhood, and so held to be 'independent' and fully responsible and culpable for its own behaviour. But at the same time it is confined within an imaginary 3-dimensional structural frame, where it is embroiled in a relentless 'struggle for existence'. This artefact is sustained in human cultures by the desire for power over sources of fear, which leads to the imposition of definitive 'barriers to love' that provide a false sense of security and control.
All movement is thereby reduced to the translocation of independent bodies in discrete numerical intervals of distance and time, as a reaction to or effect of the imposition of causal force or action. In life forms, this causal force must be situated on one side or other of a fixed bodily boundary, either within some internal executive control centre or in the external environment: the so-called 'nature or nurture' dichotomy.
In natural fluid flow, however, boundaries are transitional, ever-forming and reforming places of dynamically coupled relationship and distinction - not places of severance, which isolate subject from object. Here, self-identity forms from the complex dynamic involvement of local and non-local realms and so cannot be extricated from its natural evolutionary neighbourhood.
-------------------------------------------------------------------------------------
Hence we can appreciate - as the four of us did in the process of writing - the profound literal confusion that can be made in rationalistic theory between contiguity and continuity, and between interconnectedness and communion. Such confusion arises from the treatment of space as a physical 'absence', 'gap' or 'vacuum'. In an inclusional view, contiguity, as instantaneous informational interconnectedness does not mean the same as dynamic continuity. The latter arises from the communion of information within a dynamic spatial continuum. Whereas contiguity is a feature of the informational envelope of a distinct natural flow-form as a simultaneous receiver of and responder to energy flow - a local 'convection cell' or 'soliton' - this form is in a spatial continuum with all others.
Hence natural flow forms are inclusionally distinguishable but not discontinuous - 'distinct but not discrete'. They can be non-contiguous, but inescapably both include and are pooled together in space. Non-contiguity is natural; discontinuity is unnatural. Correspondingly, we cannot restore natural spatial continuity to what we have mentally abstracted as informational 'bits', simply by making these bits contiguous (placing them in alignment) as in Newton and Liebniz's 'calculus'. We cannot, without including receptive space, restore inclusionality from objective rationality, but can always derive the latter from the former by excluding space. Inclusionality is to objective rationality as water is to ice: a transformation through which to understand and melt what gets in the way of understanding natural flow, not a competitive replacement.
------------------------------------------------------------------------------------------------
----- Original Message -----
From: Jack Whitehead
To: [log in to unmask]
Sent: Sunday, October 07, 2007 10:12 PM
Subject: Re: A question of values?
On 7 Oct 2007, at 20:45, Dianne Allen wrote:
"Terminology:
I am using the term 'reflexive' to convey the relationship where the subject conducting the activity is also to some extent the object of the activity - thinkers exploring their thinking.
I use the term 'reflective' to refer to the careful thinking which has the characteristics identified by Dewey in How we think (Dewey, 1933).
Other authors use 'reflexive' to speak of an action which is a reflex action - virtually automatic, without any evidence of any space for conscious thought. When that is the meaning I want to convey I will use the term 'reactive', and I distinguish that from 'responsive' where the action responds to the situation or actions of others, but intentionally: that is, where some thought, or rationale, is informing the action."
Hi Dianne - I like the way you distinguish between 'reflexive', 'reflective' and 'reactive'. I hadn't realised 'reflexive' was sometimes used to describe a reflex action and I'll now use 'reactive' to describe this kind of action. In his 1989 book on Learning from Experience, Richard Winter distinguished 6 principles of rigour for action research. One of these was 'reflexive critique'. I just put into Google - richard winter reflexive critique learning from experience - and came up with the following for reflexive critique - This is what I understand Richard Winter to mean by Reflexive critique:
"Reflexive critique
An account of a situation, such as notes, transcripts or official documents, will make implicit claims to be authoritative, i.e., it implies that it is factual and true. Truth in a social setting, however, is relative to the teller. The principle of reflexive critique ensures people reflect on issues and processes and make explicit the interpretations, biases, assumptions and concerns upon which judgments are made. In this way, practical accounts can give rise to theoretical considerations."
I think it goes a little further than the relationship where the subject conducting the activity is also to some extent the object of the activity. I like the way it emphasises the importance of making explicit the normative assumptions upon which judgments are made.
Love Jack.
