15 December 1996
Understanding Sustainable Dialogue
the Secret within Bucky's Ball?
- / -
Bucky Balls: Yesterday evening the BBC announced that on 10th December 1996 a group
of people were to receive a Nobel Prize for the discovery of Carbon-60 -- a third form of carbon, structurally more complex than graphite or diamond.
The special characteristic of this new form is that it is a molecule of
60 carbon atoms forming a hollow sphere. Named as "fullerenes", such molecules
are also nicknamed "bucky balls" -- in each case after architect R. Buckminster
Fuller who studied and developed such structures, notably in the form of
geodesic domes. Since the discovery of bucky balls, chemists and physicists
have engaged in extensive study of what amounts to a new branch of chemistry
ans of materials with unique super-conducting properties..
These musings are neither a celebration of Fuller, nor of the recipients
of the Nobel Prize. Rather they are a celebration of the secrets that may
remain to be discovered through such structural patterns.
Whether at the architectural or the molecular level, the possibility
and significance of such structures were long denied. Research continues
into their significance in clarifying certain unexplained astronomical
phenomena. But these extremes only serve to highlight the relevance of
such structures in the case of material phenomena.
Psychosocial implications?: However the breakthrough
in structural thinking suggests that equivalent breathroughs may be possible
in human scale phenomena -- and especially in the understanding of psycho-social
structures, including communities and groups in dialogue.
But if such structures remain to be discovered in psycho-social phenomena,
how would evidence for them appear to us before their discovery? Presumably
we would be conscious of bits and pieces, but not be able to understand
how they formed a whole -- and the meaning of that whole would be especially
unclear to us.
So what do we have in the way of bits and pieces? C-60 is made up of
carbon atoms in 12 pentagonal and 20 hexagonal rings -- each carbon atom
being bonded to three others (with one valency left free). Much symbolism
is attached to pentagons in the psycho-social realms. Some is attached
to hexagons -- the Chinese have even attributed great significance to "hexagrams"
as in the I Ching. Indeed it is the Chinese who have built a vast system
on the theory of 5 elements. But in C-60, five hexagons are configured
around each pentagon. This forces the hexagons to curve into a bowl shape
rather than lying flat (as in the case of graphite sheets ofhexagonal rings).
This bowl-around-a-pentagon requires 20 carbon atoms. But already in
psycho-social terms we are stretched to understand what is going on. Small
groups have long been known to be stable up to 7 (plus or minus 1) participants.
In the bowl configuration, we could think in terms of 6 5-person groups
and 5 6-person groups, namely 11 groups clustered together with some common
members. Or we could think of the 11 as being one of the favoured sizes
for team games -- as in the case of soccer. A game with two teams, two
bowls, would only use up 40 of the atoms -- with 20 still to go.
Football and dialogue : Most ironically, those researching C-60 had to be informed by mathematicians
that what they were looking for was commonly represented by the stitching
of leather patches on a soccer ball -- otherwise known as a truncated icosahedron,
one of 12 semi-regular solids.
Maybe the "ball" that gets kicked around between positions in any dialogue
-- the topic -- needs to be understood as more complex. It is not just
a "point". It is only this complexity that accounts for its resilience
and ability to bounce back. Who would want a dialogue with a "ball" that
did not bounce, but just stuck where it landed? Would a dialogue then be
possible? What is the difference between games with a bouncing and a non-bouncing
"ball"? C-60 is remarkable for its resilience. Like a manufactured football,
it is a satisfactory approximation to a perfect sphere.
When we observe a soccer game, the ball moves unambiguously all over
the field --shifted onwards, or blocked and deflected, by players at different
positions. Runs and plays can be watched and remembered as a whole -- but
even then with some difficulty. For the game as a whole, the moves of the
ball -- and the corresponding positions -- could only be remembered by
those with photographic memory, or the mnemonic skills of a particular
form of autism. The ball is explicit, whilst the context -- the whole within
which it is set -- is implicit. We all have difficulty in understanding
what is going on in a dialogue. How come it took people so long to understand
the significance of C-60, having been exposed so long to footballs? What
is so well known to us in the psycho-social realm that is of similar significance?
Mapping complexity onto a ball in play: Suppose that the level of complexity associated with an ongoing dialogue
could be mapped on to something like C-60, assuming that structure has
the surprising degree of integrity that it does in nature. It would be
a cosmic joke if we were staring at a reflection of the structural dynamics
by which we were confused -- a joke with just the right twists to it that
give it some probability.
But the way the twist might work is that we, the participants in the
dialogue, in some way together constitute the C-60 type arrangement. We
are a configuration thatwe cannot grasp -- like confirmed flat-earthers.
But, like a resilient football, the configuration is constantly being subjected
to (extremely) violent stresses that distort its shape -- although it always
tends to revert to the spherical. It would be premature to over-define
just what is configured -- we cannot yet get our minds "around" it. We
need to be attentive to what happens in a dialogue. What flows where and
between what -- like stress flows in any physical structure? What happens
to our respective senses of identity? Do they merge and separate as we
agree and disagree?
Potentials to be explored?: More important, however, if we cease to observe the ball and instead
see how we and our context are reflected in it, we effectively become the
ball and the context. But what is it that then moves in the process of
the dialogue among us? What does move then mean? Strange too that what
we observe in football is the movement of a sphere of emptiness. And what
if we are reflected in that sphere? What then is the meaning of that emptiness?
There is a strange property to the C-60 structure. All the 12 constituent
pentagons are isolated from each other, embedded in a pattern of 20 (not
10) connecting hexagons. And the more organic 12 (according to our traditions
of number symbolism) are effectively insulated from each other in a continuum
of the 10 -- basic to the decimal organization of our man-made world. Is
that where the 12 tribes of Israel are hidden -- and the Knights of the
Round Table -- whatever they come to represent?
In experimenting with C-60, it was bombarded with laser beams that successively
removed two atoms at a time. Intriguing to think of a complex structure
that was stripped of its dualities in this way. The structure shrank after
each removal, through C-58, C-56, etc...down to C-32. Below that it simply
burst. How might we be thinking about the way in which the dualities which
divide us in a dialogue actually help to maintain the resilient context
for our community as a whole? Do some of our dialogues lack expression
of sufficent dualities -- especially in societies which seek to suppress
polarization of any kind?
Perhaps a final irony concerns the "perfection" of diamond -- a symbol
of accomplishment for many. Hard as a diamond for military tough guys.
Diamond awareness for those on a spiritual path. In diamond, all four carbon
valencies are "satisfied" and bonded -- the basis of its strength. But
in the case of graphite it is only three. Graphite is valued because its
sheets slides -- the fourth valencies are taken up by hydrogen atoms on
the molecular surface (just as on the surface of a diamond). In C-60 it
is also three, making it "less than perfect" according to the diamond criteria.
Do these valencies correspond to the functions of Jungian psychology
: sensation, feeling, thought and intuition? Individuation is about progressing
to freedom ofexpression of all four functions -- whereas one is usually
repressed in the average person. But perhaps a suitable configuration of
people can achieve much already without the need for all, or any, of them
to "complete" this individuation process. Does C-60 suggest the kind of
configuration that might be necessary?
It would of course be elegant if the hexagrams of the I Ching mapped
onto our C-60 psycho-social structure, since they supposedly represent
all the possible shifting patterns of transformation and change within
the whole. As a set they constitute a sufficiently complex pattern which
many struggle years to comprhend in the light of their experience. But
there are 64 of them, not 60. Is there some special reason why four of
them should be considered contextual to our immediate concern?
But there is another possibility. The C-60 structure has 32 faces --
half of 64. Other carbon structures, such as the benzene haxagonal ring,
are only stable because of resonance, namely alternation of bonding patterns
around the ring. Alternation of each ring between 2 configurations would
provide a C-60 structure onto which the hexagrams could be mapped.
Determining the nature of that mapping would certainly merit a veritable Noble
Prize. It would be the key to many structural discoveries of relevance to groups
and dialogue processes. But maybe one reason why the mapping remains undiscovered
and undetermined is precisely because it is incompatible with the "grasping"
process characteristic of our condition. As such it is the prize that cannot
be held -- it is beyond any conceptual "prise". Chinese philosophers have grappled
with this paradoxical notion for centuries -- alluding to its nature through
metaphor. Looking at a football, one of the few genuine universals, may prove
to be an appropriate catalyst for the much sort "paradigm shift".
Afterthought: Nicholas of Cusa (1401-1464), one of the most illustrious
figures of the fifteenth century, used a ball game as an imagistic container
for metaphysical insights: De ludo globi (1463) -- The Game of Spheres,
tr. P.M. Watts (New York, 1986), pp.251-319; Nicholas of Cusa, Metaphysical
Speculations, Volume 2, pp. 251-319. [see review]