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In search of the golden section
There is a place in Volume 20 of Lacan's Seminar which ties the objet a to the function of urgency, or pressure for time. In other words, the passage in question hints at the relation between the short session and the objet a. Here, Lacan says that the objet a can be understood as the "golden mean". Now, on the one hand, the objet a shows itself inescapably in the analysis in such base forms as the breast, feces, the voice, the gaze, and so on. On the other, the golden mean could almost be called the patron saint of Beauty itself. What possible connection can there be between two such seemingly opposed quantities ?
Let us return to the well known parable of the three prisoners, described in Lacan's article of 1945 (Le temps logique et lassertion de certitude anticipée). "I" that is, one of the three prisoners, was looking at the cards on the back of the other two. And "I" attempt to extract, from the way the backs of "my" two fellows look to "me", knowledge of what sort of thing ""I"" myself am.
Let us express notion of "how things look" by means of a ratio, that is to say, a set of propositions : but also by means of ratio in "ratiocination" and "rationality", that is "reason" and "calculation". For instance, in relation to 2, 5 is 5/2, that is, 2.5. In similar fashion, we will say that, in relation to "I" (x) , the other (y) is y/x.
Now, how should we think about the question of what "I" myself am ? We can be sure that the same "I" assumes a different significance for the people of "my" nation as a whole, to what it has to, say, my blood relatives. We can see, then, that the question of what "I" am must be asked in the following form : what am "I", from the perspective of a whole which satisfies certain fixed criteria ?
Returning to the perspective of the prisoner "I", the problem for "me" is, what am "I" as "I" am whithin the whole formed by myself and the other prisoners (assuming that such a thing exist) ? If we notate the line of sight common to "I" (x) and the other (y) as x+y, then we can write "I" as
This is the "I" that we should properly seek. This is the "I" as it appears in the perspective of the whole, and it is an image of "I" that is originally and forever beyond our grasp. In fact, this is precisely the essence of that which is known as the objet a. In other words
It my be true to say that this image of the "I" as it is for the whole is originally and permanently unobtainable for "me". But what if this image of the "I" were to appear in the midst of the way the others appear to "me" ? That is to say, would it not be a stroke of luck if, just when "I" want to know what "I" am to the whole, this mode of "my" being were inscribed in the others "I" am seeing ? In a sense, this would make it possible for "me" to access the view of myself from the back, even as "I" remain just as "I" am the whole while.
As it so happens, this is precisely what did in fact occur for the prisoner "I". From the midst of the way "I" saw the others, emerged what "I" was for the whole, inclusive of myself. Of course, this could happen only on the condition that "I" had already taken flight from the place where this happend (having rushed out to see the superintendent) . We can notate the state of affairs at this point in time as follows :
(1)
Since the right hand side of this equation is identical to a, we arrive at
From this we can discover that y = ax, and by substituting this into (1), we obtain
(2)
If we solve this, taking the positive solution, we derive the following value :
This value is the golden mean (the golden section).
When "the way I see the other" is equal to "what I am within the whole" like this, the other is the golden mean for the "I". The golden section is "the proportion of the two divisions of a line segment such that the longer is to the whole as the shorter is to the longer".
Taking a rectangle as an example, how long ought the short side be, in termes of the long side, for us to feel that this rectangle is a beautiful as possible ? It is said that the proportion of the short side to the long must be the same as the proportion of the long side to the sum of the two lengths, and this proportion is the golden mean. In the calculations we just performed, then the "I" corresponded to the long side, and the "other" to the short. Incidentally, if we calculate the value of our answer,
(5-1) / 2 is approximately 0.618, and in the case of the Parthenon in Greece, for instance, the ratio of the height of the building to the breadth of the main face is extremely close to this value.
Let us now have another look at equation (1) above. Here, the other is to "me" as "I" am to the whole comprised of both myself and the other. Let us remove this formulation from the context of the parable of the three prisoners and consider it in a more general manner. This formula tells us that the other is to "me" as "I" appear from the perspective of a universal, God-like viewpoint made up of both the "I" and the other. It is a case of, "Love thy neighbor, because God sees thee from behind thy back even as thou seest thy neighbor". That is, when "I" regard my neighbor with the same regard that God has for "me", "I" will be able to see myself as "I" appear to God, in my neighbor. At that point, my neighbor will be the golden mean to "me", "I".e. the objet a. The importance of this is perhaps clearest only if we consider the state of affairs in reverse. That is to say, at the moment when "I" perceive the objet a in my neigbor, "I" myself am seeing my "I" with the eyes of God.
"I" think that "I" am human. The human species has both male and female, and there is no way for "me" to change my gender ; on top of this, there are many different races and "I" am locked within my blood and heredity. Despite all this, however, "I" determine myself to be human, just as if it were possible for "me" to experience all conceivable human standpoints. Ultimately, this means that, unawares, "I" have all along been in possession of a God-like viewpoint, comprised of the amalgam of other people and "me". It also means that as the support for this viewpoint, we have all, likewise all along and unawares, been seeing in one another the objet a, which is nothing other than our self. In all likelihood, the reason that the golden mean is considered beautiful is also to be found somewhere here.
Some time ago, there was a pop song called
x + y = Love (3) If we consider this formula in the Greek sense, "love" is Eros, god of love, a transcendent viewpoint that knows the hearts of both lovers.
"How do 'I' see her ? Do 'I' feel love or lust ? Oh, 'I' dont know !" When we get to worrying like this, alle we need to do is think as fallows : "When 'I' can see her just as God sees me, then 'I' love her." Then, if "I" am x, and she is y, we can have the transcendent perspective be borne for us by the god of love given in formula (3) above, and make the following equation to solve my emotional problem. We arrive at
Of course, this is identical to equation (1) above. To "me", she is a, the golden mean. And, to God, "I" also am a, the golden mean. A happy identity between Agape and Eros. It is a little worrying that (
"I" think the meaning of the notion that the objet a is the golden mean should be fairly clear by this point. The objet a is the support that is necessitated when "I" come to see myself from a transcendental perspective. This support appears in the people and objects aroud "me", and helps "me" as "I" steal away, unbeknownst even to myself to the transcendent viewpoint. Were it not for this support, "I" would never be able to see myself from outside myself at all.The impossible relation between individual and universal
In this way, whenever "I" enter into a relation with an other, and that relation is equal to the relation that this "we", as the set of both the other and "I", enters into with "me", then the objet a appears. Here the objet a shows itself as the ratio of the other to the "I", an aspect of itself more relation than positive entity.
When "I" feel myself to be somthing with identity (identity with itself, that is), "I" am, in a manner of speaking, one or 1. At that point the objet a, which is best notated as (
If we look closely, we will see at this point that the objet a and the value of the transcendent are inverses of one another. We see that (
The support of my self-identity is objet a, as the ratio of the other to the "I". Naturally, the objet a, if it is a ratio, cannot be seen. As with all things, however, problems with this ratio become obvious only when things do not go right : When the ratio is even slightly disturbed, the objet a appears not as a ratio, but as the gaze, the feces, or in other concrete forms. The relation between "I" and other, as when "I" see the other in terms of the golden mean, is from the first an unstable one. This is because the golden mean is an irrational number. Love, so to speak, is a numerically "irrational relation" its constant is an irrational number, and just as irrational numbers contain "irreducible radicals", love is also radically irreducible. It oscillates forever about a radical core of ultimately indeterminable value, and like its value, our hearts too are never quite clear.
In fact, although we at first notated the other as it is for the "I" in the form of the fraction (ratio) y/x, the answer that ultimately presented itself was this sort of irrational number. Irrational numbers cannot really be written as fractions. For this reason, the relation between "I" and other is something beyond the fraction (ratio), that is to say, beyond reason (ratio).
In using equations to consider our problem, we approached the equivalence of the viewpoint of the "I" seeing the other, and of the "we" as it looks at the "I". In this sense, it is possible to say that we have been treating the identity of individual and unieversal. In the Rome Discourse (The function and field of speech and language in psychoanalysis), Lacan is attempting to look at the human relation to language from the perspective of the essential difficulty of the identity between individual and universal. What might make it possible for "me" to see myself as "I" truly am, from the universal viewpoint of language ? Lacan was to gradually prepare an answer to this question in the form of the subject in relation to the objet a, which thus takes the place of the Hegelian Absolute Spirit emergent from the synthesis of subjective and objective.
Perhaps the equation we have been using might make a Eastern reader think of the Confucian dictum, "Be able to follow what your heart desires, without transgressing what is right". But in Lacans case, it is rather precisely when the relation of the subject to the other (object) is congruent with the relation of the whole to the subject itself, that the appearence of the objet a within that congruency exposes the subject to an intense temptation from the Other side to transgress. For the subject then runs the risk of reducing itself to a mere utensil of the desire of the Other, and forgetting its own desire in stupefaction. In this sense, the relation of the subject to the objet a is, for the subject at least, conflictual enough.
In fact, the sense of the "numerically irrational relation" is missing from notions like "Absolute Spirit" and Confucian formulations. We find rather more of an affinity to this feeling in Descarte's cogito ("I think, therefore I am"), and in the Seminar of 1969-1970 (Seminar Vol. 17), Lacan experimented with expressing the cogito by means of a formula which utilized the golden mean. There, he uses the formula given as (2) above. However, let us turn now to the concept of Eastern Nature and try to formulate the relation of the human subject to it.The desire of Eastern nature
The desire of the Other as found in Lacan smacks strongly of a religious background. This religious overtone ranges right across the religious field, from the Christian "bearing witness to the self" to Zen freedom. And the path that leads from freedom of desire to becoming the object of the desire of the Other might well lead us still further, to recall the Eastern conception of nature.
As is evident from the statement, "Non-contrivance on our side is called 'naturalness'", when we become one with nature and relinquish self, salvation comes to us from Amida Buddha. Desire reaches the point where it is the desire of the Other, in the form of "Amida's vow", and it is complete. We will not enter into whether the path to this point is one of being helped by Buddha (tariki) or helping oneself (jiriki). The point is that be the Buddhism Pure Land or be it Zen, freedom is still sought in a return to nature.
It seems to "me" that Lacan's concept of "the desire of the Other" is interchangeable with the "desire of nature" found in Japanese thought. In so saying, I am not reducing Lacan to Buddhism, nor vice versa. Rigorous comparison of Lacanian and Buddhist thought would no doubt require careful work to prepare the ground. But I think it not meaningless at this point to compare the concept of shizen to Lacan's Other. To put it another way, "nature" (shizen) is not "nature" as the object of science, but the Eastern "nature" as that to which self returns, and with which it becomes one. I think the idea that this "nature" possesses "desire" in the Lacanian sense is one well worth entertaining.
The "desire of nature" thus becomes a question of what humanity is as far as nature is concerned. We often hear that "Man is part of nature". Even if we concede that this is a self-evident truth, the question remains: What sort of a part does that make humanity, in nature's eyes? In what manner does nature desire man?The objet a in the hand of the chimpanzee
If we posit an opposition between creationism and evolutionism, Lacan is an unequivocal creationist. While Freud attempted to take into consideration Darwin's discoveries and their implications for his own psychoanalytic theories, there is absolutely nothing of the sort in Lacan. For him, there is no evolutionary continuum between animal languages and human language.
However, there are times when Lacanian truths appear in the startling context of research conducted from an evolutionary perspective. Television once carried cover of a Japanese research team investigating chimpanzees in Africa. The research team established themselves in the midst of a troupe of chimpanzees, and patiently filmed all that went on around them. They confirmed that use of tools could already be seen among the group. Similarities existed between the chimpanzees' use of stones to split fruit, and human use of stone tools.
However, in the midst of these observations, and quite likely by chance, a baby in the troupe gradually weakened and died. The camera strayed from its intended observations and took to following the fate of the young chimp. Even after the baby died, its mother would not stop humping it around. She turned up every day at the observation site, piggy-backing the corpse. The camera faithfully recorded the gradual decomposition and mummification of the corpse, until it wasted away to a mere thing, glistening darkly. One day, as the camera followed the corpse, its father picked it up from where the mother had left it and charged the camera, brandishing the corpse with bared teeth and flailing fists.
How are we to read this series of incidents? Somewhere in the title of the program, or in captions superimposed on the screen, were the words a "mother's love". In my opinion, however, this is not nearly explanation enough.
Let us recall the original motive for the observations. This was to verify the hypothesis that humanity exists as part of nature, as an evolutionary development from the chimpanzee. This objective was achieved with the discovery of continuity in the use of tools. However, the question of what sort of thing humanity is, as a part of nature, still remained. We must still ask whether nature really views humanity as fit to be a part of itself, or not.
Let us consider the notion that this sort of question motivated the teams practical observations. The formula found in the previous chapter once again applies. In the fact that the humans observe the troupe of chimpanzees, the nature of humans for nature is inexorably brought out in relief. We arrive at
where x is the humans, and y the chimpanzees. x + y is the evolutionary continuum of nature as a whole, reached by adding humans and chimpanzees together. The Golden Section, "I".e. the objet a, appears once more, just as in the previous chapter.
We can find the answer to this problem as follows. Humanity is to nature exactly what the humans find in the chimpanzees ? the mummified corpse of the baby chimp. The mummy in question was the objet a.
If humanity is to nature something like the mummified infant chimp, then Kojeve's reading of Hegel, studied by the early Lacan, fits perfectly. Kojeve held that humanity is a fatal illness at natures heart. The observation of the chimpanzees may well have empirically proven humanity a part of nature, as a user of tools. On the other hand, though, we can also see in these images that there is only one way for humanity to be part of nature ? precisely as this malady that does nature to death.
Here we must mention that the Eastern notion that the return to nature itself was identical with death, and setting out for the Other side. This conception of the return to nature, formulated so long ago, speaks volumes in our current context.
It is highly probable that many viewers overlaid a psychoanalytic experience onto this series of images. The troupe of chimpanzees corresponds to the analyst, and the cameras line of sight corresponds to the gaze of the analyzed subject. During analysis, we get the feeling there is something strange uncanny within the analyst, and this something ultimately appears before us as no less than what we are as a subject.
Lacan's psychoanalysis lays emphasis on the heterogeneity of the analyst and the subject under analysis. The two are not of a kind, as we might expect of two human beings, and they are therefore not related symmetrically, like an object and its reflection in a mirror. The analyst is so far separated from the human realm that he or she might indeed, in passing, be less of a person than a chimpanzee ? in one case actually appearing in an analysand's dream like the simians in Planet of the Apes. Note, however, that the objet a as it appears in analysis is an unmistakable guise of the subject.
The Other in Lacan is the Other as language, and this Other is also interpretable as the Other as nature. Long before nature was ever the nature of evolution, it was always-already articulated by language to an almost hopeless degree, transformed into language-nature; we can thus say that, from the Lacanian perspective, the Eastern concept of nature indicates the structure of language qua that prior to any subject.* This paper is an extract from : K. SHINGU "Lacan's Psychoanalysis", Kodansha, Tokyo, 1995. We owe this English translation to Mr. Michael RADICH in Matsumoto.
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