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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]
This work is licenced under a creative commons licence.