To make an archer's bow, we bend a piece of wood by binding both ends together with a band. The band is kept taut and straight under the strain of the wood, which itself is bent but aims to return to the original straighter shape. A straight arrow is notched against the band and pulled backwards. The archer's one arm is stretched out straight, holding the wood, the other arm is bent backwards, pulling at the band and bending it. The bent finger holding the band is suddenly straightened, the arrow is released and flies away, further than the archer's hands could ever reach, and the band becomes straight again. Maybe it snaps. Then the wood returns to its straight shape and the band drops away, bent up in a curl. The straight arrow flies on, bent only by the winds, until it hits a target that it bends and deforms in turn.

In this example of archery we can uncover a paradigm of reflexion, in the sense of Edgar Morin who defined a paradigm as made up of a certain type of an extremely tight logical relation between some master notions, key concepts or key principles. Of such a paradigm it is sometimes possible to find a distant echo, itself possibly a reflexion, in the origin of the words that are logically tied up in it. There appear to be four word families within this particular paradigm of reflexion. First, the words bending, band and binding have the common indo-germanic root bhendh-, where bending is caused directly by binding something together. In German, the equivalent of bending is beugen or biegen which together with the English word bow are based on the second word family here: bheugh-. Un-binding, or de-fending if we use the same root in its Latin variant, allows what is bowed to stretch and become straight again. These last two words point to the third common root within this paradigm. Finally, there is the arqu- family of the arrow that is shot from the bow, or arc. The possible deeper origin of this last word family is unclear. Some have argued that it may be derived from the ar- family to which belong the modern words art and harmony. The four master notions in our paradigm are therefore binding, bowing, stretching and arching.

We now see how two things are joined together by the antonym pair of bowing and stretching: a band, with a tendency to curl up or bow, that here is stretched; and an arc, with a tendency to stretch and straighten out, that here is bowed. The band bows the arc that wants to be straight. The arc stretches the band that wants to be bowed. The formal pattern is this: We start with an antonym pair of behaviours, labelled say A and B, which is not-A. In the above example, this is bowing and stretching. We add one more general distinction in the form of tendency versus capacity. Out of these two distinctions we then build two formal objects: one with a tendency for A and a capacity for B, the other with a tendency for B and a capacity for A. In the above example, these two objects are the band and the wooden arc, or bow, respectively. If not joined or bound up, both objects behave according to their tendency. But once they are joined and bound up, they both behave according to their respective capacity and maintain one another in this, with behaviours A and B looped and interlocking. A brand new third object emerges in this way, a proper archer's bow, with behaviours A and B working internally, reflexively and simultaneously, to maintain it.

A physicist might say that each object can be in a ground or in an excited state, corresponding to tendency and capacity, respectively. If uncoupled, each object relapses to its ground state on a fast time scale. Through appropriate coupling, however, new composite objects emerge where each component is maintain in its excited state on comparatively longer time scales. Binding as coupling, stretching and bowing as the transitions between two states: these take up three of the four master notions of the paradigm.

More generally, on reflexion, we really do not need two distinctions for our formal construction. We can say that the behaviour A is bowed and that behaviour B is stretched. The move from B to A is bowing, and from A to B to stretching. State and transition can be identified. From now, we therefore refer to any shift of behaviour from tendency to capacity as bowing; while stretching happens when the behaviour falls back in line with its tendency. In the brand new composite object, bowing then maintains bowing, and it is maintained by it reciprocally. This is how I understand reflexion to operate its ways: the linked bowing of bowing in self-maintaining loops, making new things in its wake. The Latin flectere of course means bowing; it is probably related to the word for sickle, falx, with its bowed shape. The prefix re- is commonly interpreted as indicating a direction back to where something came from or back in the opposite direction, as when something recoils. I read it in a more logical sense of pointing back, not necessarily directly, but in ultimately closed and self-maintaining loops, recursively. These loops of reflexion require linking, or binding, and through looped linkage the conjoint shift happens away from tendency to create new things, with reflexive internal structure. The linkage of reflexion is never just simple concatenation.

In the poem, the flow between heaven and earth is reflected in the eyes, then in turn in the mind as the sight is tied, then in word and then bent out again in one loop, reflexion upon reflexion, bowing on bowing. The passenger in the window seat is one link in this loop of reflexion; he has a capacity to be linked up in such loops of reflexion; and with it completely new things make their appearances in this world, such as the poem itself. The expression bent out again is the last line of the poem and key for the passenger to achieve the closure of the reflexive loop. What can it mean?

There is a setting sun reflected in the ocean water. The artwork by Erwin Brahe reflects this reflexion in turn. Via this website, his reflexion reaches out to others. In some who view it, this reflexion grows pale and the loop remains incomplete. In others, as with this editor, it finds reflexion in an editorial text. Yet others, occasionally, may find themselves at an ocean's edge in front of a setting sun and then see it as a reflexion of what Erwin Brahe has shown. They recognise it, they recall it. There it is: the loop is closed. This is what I take the expression bent out again to mean here. With this, the whole reflexive loop then takes on for the passenger a significance; it literally becomes sign making. The new thing that makes its appearance in this world, when the passenger stands in the loop as one of the reflexive links, is apparently the sign. This word, too, has an old echo, through the indo-germanic root sekw-, of seeing or sehen, and of saying or sagen. This echo of course tells us again that seeing and saying rely on, and are relied on by, signs that apparently emerge in this world when the passenger, mysteriously, stands in a closed sequence of reflexions. One could attempt to unfold the sekq- word family a little differently by saying that a given sign points us in a certain direction, bending our way and telling us to follow where it points, hence making us see where it points to. But this is not enough. It must be possible to go round from any one unfolded word of the family to another, with each word reflecting the entire unfolding. Hence the insistence here on the closure of the sequence of reflexions, like the band and the wood in the archer's bow. We see and say what has been signposted; and we signpost by seeing and saying, bent out again in such loops of reflexion.

We commonly say that the passenger, or man, has a capacity for reflexion and also a tendency for non-reflexion, for dullness. This, too, can now be read in a nested and recursive sense as follows. When man bows in reflexion, uniquely, the bowing behaviour itself is a closed reflexive loop of activity in his mind. The passenger's capacity to reflect, his mindfulness, which is always an effort and may snap back to stretch out in dullness, is the capacity of his mind for its own closed reflexive loops, where there were none before. His mind is flexible in this sense. The more ways there are for man's mind to bow and evoke its own loops of reflexion, then literally the more flexible it becomes. As a result, man can stand, bowed and bowing, in more and more different chains of reflexion with the world, and when they close, more and more things emerge that were not there before without his reflexion; and new signs, new seeing and new saying emerge with it.

In the course of our discussion thus far, we have made explicit and repeated use of only three of the four master notions of the original paradigm: the bowing and stretching of complementary elements, and the binding or linking that has to take place between them. The missing notion is the closure of reflexion in loops. Now, in a movement of bending from this discussion back onto the four word families, we are led to an understanding that arching refers to the closure of bowing on bowing in loops. In this reading, the arch, or arc, is not a bridge between two points, but it is the closing element of a loop, pointing to this circularity as a whole. Indeed, the arch always completes the surround of a more or less circular void that provides passage through it and that allows the passenger to go further than he can reach without it, arrow-like. This perspective would be consistent with the view of a closer proximity between the arqu- and the broader ar- families, between the arch and art. Art, here, would then be the span of looped reflexion.

The famous fragment B3 by Parmenides says according to one reading of it:

For the same is thinking and being.

Our reflexion on reflexion thus leads to this specific model for Parmenides' thought: that thinking and being are alike as loops of reflexion, that the reflexive loops of thinking can themselves be links in the reflexive loops of being, that in this way being is reflected in thinking and thinking in being. The sun and the sea bent out again.

Valete, Amici.

William A. Wayman
Chief Editor
JUL 2011