CEPA eprint 2094 (FJV-1981f)

“Your inside is out and your outside is in” (Beatles 1968)

Glanville R. & Varela F. J. (1981) “Your inside is out and your outside is in” (Beatles 1968). In: Lasker G. E. (ed.) Applied Systems and Cybernetics: Proceedings of the International Congress on Applied Systems Research and Cybernetics, Volume 2. Pergamon, New York: 638–641. Available at http://cepa.info/2094
This paper examines the grounding of George Spencer Brown’s notion of a distinct­ion, particularly the ultimate distinctions in intension (the elementary) and ex­tension (the universal). It discusses the consequent notions of inside and out­side, and discovers that they are apparent, the consequence of the difference between the self and the external observer. The necessity for the constant re­drawing of the distinction is shown to create “things”. The form of all things is identical and continuous. This is reflected in the distinction’s similarity to the Möbius strip rather than the circle. There is no inside, no outside except through the notion of the external observer. At the extremes, the edges dissolve. The elementary and the universal thus re-enter each other. “Your inside is out and your outside is in.”
Key words: Circle; distinction; elementary; hierarchy; inside; last distinction; Nöbius strip; outside; universal; re-entry; self.
A distinction (in the sense of Spencer Brown (1969)) is a form. It is drawn in a space. This implies that such a distinction is characterised as having both an inside and an outside (which correspond to the conventional pair, system/environ­ment).
If all depends, as Spencer Brown claims, on distinctions being drawn, it is reason­able to enquire about the distinctions at the extremes of intension and extension: the distinctions that correspond to what we will call the “elementary” and the “universal”.
The elementary is that which cannot be further reduced: it is only itself: it has no properties. Thus it can have no inside separate from its distinction. Its distinction may have no content.
The universal is that which cannot be further expanded: it is everything: nothing may be excluded. Thus it may have no outside separate from its distinction. Its distinction must contain all content.
It is clear that these two – the elementary, and the universal – have at least some sort of similarity, which is what we shall explore in this paper.
Each of the two involves the assertion that they may not have one of the major features of distinctions: they may not have, in the case of the elementary, an inside, in the case of the universal, an outside.
The side which is excluded is the side that would be next in the direction of exploration: an inside, in intension, an outside, in extension.
This seems to require, in at least these two cases, some re-design of the notion of’ distinction, or of some of the concepts surrounding it.
And yet, both these two distinctions do, in a certain sense, have insides and out­sides. For, in. drawing the last distinction (in either intension or extension), we are drawing not only one distinction: the distinction that is meant to be last (the elementary, the universal) in fact is not. A consequence of this distinction being “final” is, in both cases, a further distinction: that the elementary/univer­sal distinction is distinguished as the last distinction to be drawn.
Clearly this is an impossible state of affairs. We require distinctions that are missing some (normal) essentials, and then we require that they also simultaneously have these essentials and thus that they are not what they are!
Which is to say that in the case of the elementary – the last distinction in inten­sion – we require that its distinction has no inside and, at the same time we place, in this non-existent inside a further distinction which asserts that the distinction of the fundamental was the last distinction! And, of course, an argument of the same form applies in extension.
Clearly, we are in an apparent mess. So the question arises: is our picture a good picture of the state of affairs?
Then we should consider how this series of paradoxes comes about, in order to find another picture in which the paradoxes dissolve.
Remember that a distinction is a form: and the paradoxes are all concerned with the intuitions of the inside and outside that are connected with such forms. These notions are grounded in a particular (Euclidean) geometrical preference, namely that of a circle drawn in a plane. However, we may think of another form which is equally simple as that form which generates an inside and an outside. This form – in terms of a 2-dimensional plane – is a Möbius strip, as opposed to a circle, and we will use these two forms as diagrammatic analogues. (Viewed from “above”, they are very hard to tell apart.) A Möbius strip, as opposed to a circle, has no in and out side. If we can remove the sense of in and out side, our paradoxes, of course, vanish, for they only occur as a consequence. And since Spencer Brown is explicitly putting forward a calculus based on the single primitive act (Draw a distinction”!) we might assume that the use of a Möbius strip like form, as opposed to a circular form, would appeal if only on the basis of its comparative simplicity (i.e. primitiveness).
Is there any other basis for this position? A distinction is supposed to be a mark (“1’) with some value (“p”) – such that “0” – which is distinguished (contained) by the mark. Drawing the distinction (by making the mark) brings the value into being. But then, if everything’s being depends on a distinction being drawn, what distinguishes between the mark of distinction and its value? Another distinction, surely. And between the mark and value of that other distinction? Yet another dis­tinction, surely. And so on, in an infinite regress of distinctions being, each to validate the other but none ever providing the grounding of the value.
Thus, the idea of the value contained in the mark reveals, when one examines it, a loop (to the observer’s point of view). This complication is clarified when the distinction is considered as a self-mark of a self-value – that is, as containing nothing, only being itself. Then it has a form akin to what is, in 2 dimensions, a Möbius strip, as opposed to a circle, and it has no inside or outside. This self-value demarkated by the self-mark is not, of course, directly accessible to the (external) observer, who, in terms of the analogue used here, sees the distinction projected as if it were a circle (i.e., from outside), not as a Möbius strip. By doing this, he does indeed separate the mark from the value and hence also brings into being not only that which is distinguished, but also its very’ inaccessibility (the value is never reached since there is always another distinction to be drawn), together with the concepts of process and time, since there is always another distinction being drawn: i.e., that which is distinguished is seen as going on and on being distinguished (process) by distinction drawn after distinction (time).
Now the role of the further distinction implied in the ultimate distinction drawn in intension and extension becomes clear. From the point of view of the external observer the separation of mark and value requires the drawing of another distinct­ion to be forever drawn. Thus the process of distinguishing (as far as the exter­nal observer is concerned) necessarily implies there is another distinction to be drawn and therefore that nothing is really ultimate (i.e., the last), for there is never a fundamental grounding.
And simultaneously, from the point-of-view of the self (in as far as we others can necessarily imperfectly understand it), there can be no hierarchy, for the self (should there be one) is distinct ONLY IN ITSELF as a self-distinction, without in­side or outside – that is as a self-point in what is otherwise a continuity, a tangle, a Möbius strip.
But can a continuity end? What does such continuity imply for the ultimate intens­ion and extension which we persist in talking of (as external observers) in spite of now knowing that the ultimate, the last, will always be superseded? What is (apparently) outside extension? What is (apparently) inside intension?
Consideration of this is the necessary next step, which is a formal consequence of the form of making the form (of the distinction). Thus, at the extremes we find there are no extremes. The edges dissolve BECAUSE the forms are themselves contin­uous – they re-enter and loop around themselves.
So the assertion of ultimate extension and intension requires the continuity of re-­entry. And so, “Your Inside is Out, and your Outside is In”, for there are, for selves, no in and out sides, in the selves themselves, while for external observers the appearance of in and out sides necessitates the continuity of re-entry just because the act of distinguishing always implies just-one-more distinction. In terms of forms (and Spencer Brown insists that his distinction is a form), just as in intension the ultimate distinction can not have an inside – and yet must have – so in extension the ultimate extension cannot and yet must have an outside: so from the external observer’s point of view they are formally equivalent and therefore the forms are identical and so indistinguishable. So, once again, the inside of one is the outside of the other, and vice versa.
Thus is the continuity of all things and of no thing necessitated. In as far as we (external observers) can see there is no hierarchy, nor are there properties, but only perfect continence. The space we construct to inhabit is limitless, continuous and boundless. What Spencer Brown claims is a consequence of his calculus and not (as he makes it) an assumption.
But the external observer, in making his distinctions as a result of which these arguments arise also creates hierarchy, not in the continuum, but in his manner of distinguishing the “things” he distinguishes. For in distinguishing the mark and the value he requires the constant re-drawing of the distinction – a process of the boundary’s self-reproduction – that makes that which is distinguished distinguishable as constant, and allows the apparent perpetuation. Thus there come into being “things”, and thus they acquire, in our minds, in and outsides: and hence hierarchy.
Things are brought into being out of no thing by distinctions being drawn which insist on boundaries. That these are, in as far as we, external observers, can tell, illusions does not make them any less real or necessary. Such illusion­ness – ephemerality – ungraspably shimmering quality we often forget, especially in laying down laws of the bounds of the imagination.
Truly the poet has said;
“Everybody’s got something to hide,Except me and my monkey.” (Beatles (1968)).
Beatles (1968). “Everybody’s got Something-to-Hide,. except.me and my Monkey”. from The White Double Album, Apple-EMI, Hayes, Middx.
Spencer Brown, G. (1969). “The Laws of Form”, George Allen & Unwin, London.
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