Dear Joan and all,

For all that I sympathize with what you say here, as you know, I don't think 
conventional holism goes anywhere near far enough or deep enough to take 
adequate account of intangible presence. At best it engenders inconsistent 
reasoning (self-contradiction), at worst it becomes an oppressive form of 
colonization that is disrespectful of local identity through imposing 
complete definition upon natural energy flow and 'tying all up as one'.

Your mountain top metaphor illustrates the 'point' very well. It reminds me 
of a dream I once had, and a painting I made about this. I have attached the 
painting and pasted a description (taken from the attached chapter of 
'Inclusional Nature') of what led me to make it below.

When One knows that the mountain has no discrete limit, One is no longer 
Alone (All One), a singularity without neighbourhood. A dimensionless 
mountain top 'point' with no room to breathe is the singular starting point 
of the logic of conflict, and all classical and modern mathematics and 
objectivistic frameworks. It is what excludes loving presence.

Warmest

Alan

--------------------------------

On September 15th, 2000, I made a desperate journey of around 130 miles, 
through stormy weather and in the midst of a fuel-shortage crisis, with a 
warning light flickering on my car's dashboard. I stopped to pick up my 
sister, Joy, from her home in Woking, Surrey, and continued to the nursing 
home near Bognor Regis, W. Sussex, where my mother lay dying. When my sister 
and I entered the room, we found my mother speechless, wild-eyed and greyish 
yellow. She had lost the swallowing reflex and her breathing was laboured 
and noisy. She kept tugging at the sheets like a child desperate for a 
security blanket. Every now and then, a nurse would come in to suck out the 
gooey saliva that was accumulating in her mouth and try to make her more 
comfortable.



I didn't know what to do or say. What could I do or say? Perhaps I could 
only be lovingly present with her as she expired.



I described a dream to her that I had experienced a few weeks previously in 
which I was on a plane that landed at Anchorage in Alaska. It was a 
brilliantly clear day, so I looked out of the Airport window to see if I 
could see Mt McKinley, the highest mountain in North America. Sure enough, I 
could see a range of mountains and in the far distance was one that was 
clearly higher than all the others. That must be it, I thought. But then, as 
I continued to stare into the distance, I realized that what I had taken to 
be clouds above the mountains were actually snow patches on an enormous, 
summitless, barely visible peak that lay behind and beyond all the others.



As I reached the climax of this description, my mother let out a long, loud 
sigh. I don't know whether this was just a reflex, or whether perhaps my 
description had registered with her, but somehow it seemed to let loose of 
all the pent up anxieties of her long and far from painless life. My sister 
simply said, 'go and find that mountain, Mum!'



Some months later, I painted the picture shown in Figure 10.





INSERT PICTURE HERE





Figure 10. 'View from Anchorage' (Oil painting on canvas by Alan Rayner, 
2001). The clear perspective of explicit landscape features grounded within 
a fixed reference frame, is dwarfed by the implicit view taken in from 
encircling flights of Snow Goose imagination, where cloud-dappled sky 
becomes summitless, snow-patched mountainside, far beyond the peaks and 
troughs, light and shadow, of rational consciousness.





This dream and painting seems to me now to relate very strongly to that most 
mysterious of mathematical concepts, that of 'infinity', which had to be 
developed in order to quantify curved structures using abstract linear 
methods of analysis (the 'irrational' number, ?, is a product of such 
imposition). But it also implies that to look for understanding of this 
concept in limitless material terms makes nonsense. No matter how high we 
try to pile the material quantities that we define as discrete numerical 
units - isolated bodies - we will always fall far short in our comprehension 
of fathomless depths and summitless peaks. Like it or not, to comprehend 
infinity, we have to take a fearful leap of imagination, and in making this 
leap, we have to shift our focus from material to immaterial presence. This 
is the leap that conventional mathematical abstraction of content out of 
context fails to make, leading it to make a meal out of the simultaneous 
distinction and common identity of One and Many.



Shakunlean, Transfigural Mathematics, as I have slowly come to understand it 
for myself, is based on making sense of One and Many simultaneously as both 
the same and different, without contradiction, rather than giving rise to 
the nonsensical paradox that comes from one-sided abstraction. It has the 
following ternary or inclusional features, which distinguish it radically 
from orthodox mathematics:



1.      Implicit space, as a vital presence of material absence is 
inextricably included within, around and through the explicit linings that 
give dynamic form (i.e. flow-form) to distinct features or 'configurations' 
of all kinds.

2.      This space is where 'infinity', far from being an expression of 
limitless material presence (content), is located as a realm of indefinite 
inductive potential or 'receptivity' applied via its linings, which fold 
inwardly and outwardly over all scales of magnitude.

3.      Spaces on either side of a lining attract in opposite/complementary 
directions, which can be represented as positive and negative (omega and 
alpha) depending on their relative situation.

4.      These complementary attractions are mediated and dynamically 
balanced through the space of the lining itself, which hence lies at the 
heart of inner-outer relationship and cannot be reduced to a finite 
Euclidean point-centre.

5.      All numerical features formed through this dynamic balancing process 
have both local (finite) and non-local (infinite) aspects combined via their 
intermediary linings.

6.      Zero is the condition where complementary attractions are exactly 
balanced, rather than an absence of material presence (content).

7.      All 'contents' are locally lined expressions of non-local spatial 
'context' and cannot be separated therefrom.



This purely mathematical description correspondingly relates to the implicit 
physical presence of gravitational space informed/stiffened explicitly with 
electromagnetic linings to produce the dynamic flow-form features of nature. 
It also corresponds with the light-lined space of the giant, beckoning 
figure in my 'dark angel' dream. In terms of numbers, it replaces the idea 
of these as singular 'units', with that of 'threesome-onesome couples' of 
inner with outer through intermediary domains - the latter being the 
locations of the 'zeroids' or 'self-identities'. Correspondingly, the 
conventional number, 2, is identified transfigurally in terms of its nearest 
neighbours (which it respectfully emerges from and is in the process of 
becoming) as '1,2,3'. Similarly, the conventional number, 3, is identified 
as '2,3,4' (which includes 2).



In this way, all numbers are included together in fluid relationship, as 
aspects of one another, distinct, but all of the same fundamental form, 
unlike binary systems, where 0, 1 and infinity are fundamentally different 
and inaccessible to or from one another. The symbol of the cross, (+) is 
seen as the loving inclusion of receptivity (-) with informational lining 
(I), so that (+) and (-) no longer cancel one another out, but are like 
solute and solvent combined in solution. I is transfigured through love (-).



The geometry that emerges from and underlies this numerical representation 
is full of inwardly and outwardly flowing spirals. 'Male' receptive 
responsiveness combines with 'female' responsive receptivity in forming an 
inner zeroid. This coupling has the form of Lennon and McCartney's phrasing: 
all you need is love, love, love is all you need.  Perhaps this is the 
mathematics of love, the mathematics of the included middle that liberates 
us from the loveless contradiction of the excluded middle and false 
positivism.



---------------------------------

----- Original Message ----- 
From: "Joan Lucy Conolly" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Sunday, October 31, 2010 6:35 AM
Subject: Re: Journeys and Love in teaching


Dear Sara

Thank you for your generous and open hearted response. I really like 
'transitional'. Thank you. I shall use that if I may and work at changing 
the view of both the learners and us ... as 'transitional' teachers and 
learners. Actually I belong/lead the Self Study for Transformative Higher 
Education and Social Action project at the Durban University of Technology 
and so our focus is on our own transformation and that of the learners and 
everything that, and everyone else who, is transformable! People, 
curriculum, policies, timetables, assessment, worldviews, structures, and 
the list goes on and on. This is very exciting. It is an holistic process in 
that everything is linked and connected to everything else, so as any one 
element changes, then it is predictable that something else will change, but 
the intriguing part is that, as I watch and experience this change, I can 
never be sure WHICH or WHAT or WHO will change at that point in the process. 
All I can be very sure of is that SOMETHING or SOMEONE WILL CHANGE. And it 
is this absolute certainty that the process of holism is unstoppable that 
assures me that even when it SEEMS that everything is 'going wrong' 
SOMETHING/SOMEONE I CANNOT NECESSARILY SEE IS CHANGING, and all I have to do 
is hang in there and wait for it to become apparent. 'Hanging in there' 
means continuing to do what is right and doing it with the love that it 
deserves. This is very hard. When things appear to be going wrong (as you so 
aptly describe in your mail ... I recognize your situation well!) ... when 
things APPEAR to be going wrong, I find it very hard to keep 'hanging in 
there'... so I sympathise. I have come to think of this situation to be like 
climbing mountains. The mountains where I live present the perfect 
challenge. As I puff and pant up the hill I am facing, I look up and see the 
'top', but when I get to the 'top', I see another hill in front of me, with 
a 'top', ... and so on and on. Why then do I keep climbing the mountain????? 
Because I know that there is a REAL TOP ... and if I just keep putting one 
foot in front of the other, I WILL GET THERE. Of course it helps enormously 
when there are other hillclimbers with me and together we encourage each 
other, to keep putting one foot in front of the other. In the business of 
transformation, the putting one foot in front of the other, is simply doing 
what needs to be done with love.....

I hope you will forgive the simplicity of this analogy ...

Thank you for allowing the sharing of your situation. I sent it to many, and 
in exactly ONE MINUTE I had a response from a friend in England applauding 
your courage ... here it is....

"Dear Joanie

How do I get permission to use this in my own loved class of fellow 
lecturers and collegues so that they can discuss what Sara said?  I applaud 
Sara with my heart and my mind for her sprit and courage, and you for your 
wisdom in sending it further.

Charl"

And so I have told Charl how to join the listserve ... and she will, and she 
will be another lovefilled hill climber, and who knows what Charl will bring 
to the mix in the fullness of time.....

And so the process of holism goes on and on and on and on changing changing 
changing ...

I send wishes for a love filled day ... believing that all is happening as 
it should ...
Joan

-----Original Message-----
From: Practitioner-Researcher 
[mailto:[log in to unmask]] On Behalf Of Salyers, Sara M
Sent: Saturday, October 30, 2010 11:08 PM
To: [log in to unmask]
Subject: Re: Journeys and Love in teaching

Dear Pip, Joan, Alan and Brian (and all)
I'm very, very grateful to you for your responses to something I wrote out 
of a feeling of desperation and for the practical purpose of saving my 
husband's sanity! (I've been a difficult, short tempered, distant and 
downright prickly person at home for the past couple of weeks.) It felt like 
a very selfish act, to thrust my own - lengthy - situation at everyone when 
I know perfectly well that we are *all* facing our own difficulties - 
especially Geisha. So it's very humbling indeed to be thanked for that. I'm 
still learning about AR and while I can clearly see how the dynamics of 
relationship supersede every other factor in terms of what kinds of 
practice, growth, empowerment, achievement etc. happen in a classroom, it's 
harder for me to see how or where to fit that into the AR model. I think I 
would have responded to my own story by identifying with the experience and 
perhaps by clarifying what I already understood. I wouldn't know how to 
begin share it with anyone else in a way that made it useful. (Just as I 
wouldn't know how to even find the things that Jack discovers in the 
teaching videos, let alone extrapolate from them. But I love it when he 
points them out!)

So, dear Pip, thank you so much, and please use anything I wrote in any way 
that you see fit. I'm just an adjunct. I teach developmental writing (and 
this semester, reading and writing), at Pellissippi State Community College 
in Tennessee within an extraordinary department - the Tranistional Studies 
Department. I do seem to remember that Jack recommended that paper by Moira 
Laidlaw to me and it is high time I got hold of it. Thank you.

Joan, thank you also for your loving support and of *course* I don't mind 
your sharing my story with whomever you wish. I absolutely agree that the 
under-preparedness is even more (and more critically), a feature of us, the 
teachers than of these students. I like 'underprepared' as a term much more 
than the term 'developmental' but I like my own Dept's, rare epithet 
'Transitional' students even better for the following reason: A student who 
had not had the opportunity to learn how to read and write or do math would 
be underprepared. It would be our job to help that student fill in the gaps 
and prepare for the rigors of college. A student who has been through 
thirteen years of a vertical, (colonizing) compulsory education system has 
not simply lacked the opportunity to acquire the necessary skills. He has 
undergone actual neurological damage. (That means you and me, too, I'm 
afraid!) The ones *we* see in our classrooms have sustained the greatest 
damage. So, before we can even begin to 'fill in the gaps' (at least 
successfully), we have to reverse the damage. Thus, we help them to 
transition from "learned helplessness" to empowered, from damaged to whole 
and from programmed to be programmable, to independent thinkers. That means 
developing programs whose primary function is this healing, (manifest in 
re-engagament, 'alert relaxation', focus, reflection, self awareness et 
alia) and which address the mechanical skills of language and, mathematics 
as a *means to that end* rather than the other way around. In a nice irony, 
the outcomes in terms of required benchmarks are satisfyingly higher, and 
often quite a *lot* higher, than the norm. Teaching something other than, or 
beyond, Math and English for their own sakes causes controversy and has 
already put my own department into conflict with other, traditional 
departments at my college. I won't bore you with the miserable details of 
the war but it is reflected, of course, at State Board level. (I spent 
months writing a kind of 'manifesto' for our department in order to help 
raise awareness - among our own faculty as well as the rest of the college - 
of what the Dept. is really taking on because, of course, when I became 
fierce about my students I became fierce about a department that is actually 
willing to rewrite the whole 'rule book' to help them.) I am just 
overwhelmed right now at the odds stacked against us and the chances that 
the light can prevail against the darkness, which seem very small. It feels 
as if we're destined to 'go under'. At the instigation of the traditional 
departments, full time jobs are currently being denied to those with 
advanced degrees in anything other Literaure or Math, on the grounds that, 
when our department folds and the individual courses return to control of 
the English and Math Depts., they will no longer be qualified to teach our 
students. The smug and delighted certainty of our removal, in the face of 
the miracles coming out of this department, is infamous and utterly 
debilitating. I'm just holding on tight to the names and faces of individual 
students for whom I have been important. A single human soul matters as much 
as a whole world - As Pip  reminded me, what Mother Teresa said to a novice 
who was in tears because she felt that all her efforts were just a 'drop in 
the ocean', was, "Yes, but the ocean is made of drops." (I'm really, 
*really* trying to remember that, Pip!)

Alan, forgive me but I intend, not to forsake but to ignore the vertical as 
much as I possibly can, beyond acknowledging its importance! I *do* of 
course, acknowledge it. I maintain, however, that if balance is an x/y axis 
between which effective and powerful 'oscillation' can take place, then we 
have a job in front of us to construct any kind of y axis at all. (Indeed, I 
doubt we have a true appreciation of the vertical anyway, since we have no 
working, established horizontal from which to look at it!) At least, that's 
my intent if there remains any point in doing so when the multitude of 
excuses for social engineering (and lobotomizing), under the dissembling 
guise of education - with the backing of the Rockefellers, Carnegies and 
their NGO offspring - seem set to sweep us, and everything I do and believe, 
into historical footnotes.

Brian, thanks also. The strange thing is that I am only just *truly* coming 
to see that the most important thing we can articulate isn't what works for 
our students  (as huge and revolutionary as that might be) it's the love 
that gives rise to what works. That's quite a big step for me - the ideas, 
articulation person!

Much love to all,
Sara
________________________________________
From: Practitioner-Researcher [[log in to unmask]] On 
Behalf Of Brian wakeman [[log in to unmask]]
Sent: Saturday, October 30, 2010 5:09 AM
To: [log in to unmask]
Subject: Re: Love in teaching

Sarah,

You say:
something extraordinary happened. I fell in love with my classes: fiercely 
and deeply in love with them.  I have a fallen in love again each semester 
and with every class, so far. I've never had any equivalent experience and I 
know no adequate way to describe it. I can no more explain or define it than 
I can explain the beauty of a baby's smile. One week I am with a bunch of 
strangers towards whom I  am well disposed and, I suppose, committed. The 
next... they possess my soul. Though I cannot explain how or why this 
happens, it is the only elegant explanation for what has taken place since 
that first 'fall'. (I know that I am by no means alone in this teaching 
experience, by the way, but I suppose we each respond to love in our own 
ways.)
I've never seen these thoughts written before...... but it is something I 
have felt so important in teaching, indeed in management of a school too.
Education has strong elements of the 'relational', of seeking the good of 
students, affection, agape love, and the human chemistry of interaction
.
When students see the regard, when they feel the warmth of acceptance, the 
genuine interest of the teacher in their world, their learning.....then the 
hard shell bud cases can open to the sun.
I've observed it in 15 year olds, and in adult education.
.... and seen the 'joy' in the face of the teacher.

Thank you for expressing this.

Brian

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