Logic of Phantasy 53 Jacques Lacan

Logic of Phantasy 53
Jacques Lacan
雅克 拉康

Lacan Seminar 14:
The Logic of Fantasy 13
幻见的逻辑

Seminar 13: Wednesday, March 1, 1967

(6) Such is this perfectly fixed relation, which has extremely important mathematical properties that I have neither the leisure nor the intention of developing for you today. You should know simply that its appearance in Greek mathematics coincides with the decisive step of putting order on what is involved in the commensurable and the incommensurable.

（第六）这个完全固定的关系就是这样。它具有极端重要的数学的属性，可是我今天没有这个时间，也没有这个意图要来发挥。你们只要应该知道，它出现在希腊的数学里，刚好巧合於，可约分数与不可约分数所牵涉的演算的关键步骤。

In effect, this relation is incommensurable. It is, in the search for the mode in which there can be defined – in the way in which there overlap – the succession of points given by the staggered series of two units of measure, incommensurable to one another. Namely, what is most difficult to imagine: the way in which they become confused, if they are incommensurable. What is proper to the commensurable, is that there is always a point where the two measures will come together on the same footing. Two commensurable values will always end up at a certain multiple, different for the one and for the other, constituting the same magnitude. Two incommensurable values, never. But how do they interfere with one another? It is along the line of this research that there was defined this procedure which consists in reducing (rabattre) the smaller into the field of the larger and asking oneself what happens – from the point of view of measure – to the remainder.

事实上，这个关系是不可约分的。在寻找能够下定义的模式时，测量的两个摇摆不定的单位，互相之间不可约分，它们所提供的连续的点，会有重叠的地方。换句话说，最难想像的是，假如他们是不可约分数，它们会以怎样的方式被混肴。至於可约分数的本体是，总是会有一点，两个单位的测量，会在同一个立足点，汇聚在一起。两个可约分的价值，总会以某个多重关系结束。这个多重关系，对於前者，或对於后者，都是不同的，它们组成相同的重要性。两个不可约分的价值，则永远没有办法以这种方式结束。但是它们如何互相干涉呢？沿着这条研究的途径，我们能够替这个程序下个定义。这个程序在於将较小的数，化简到较大的数的领域，然后问问自己，剩余的结果会是如何，从测量的观点来说。

For the remainder, which is here, which is obviously 1-o, we will proceed in the same way. We will reduce it within the larger one. And so on to infinity, I mean, without ever being able to arrive at the end of this process. It is in this that there consists precisely the incommensurability of a relation that is nevertheless so simple.

对於剩余的数目，显而易见是一减去零的结果，我们就照样演算下去。我们将它化简到这个较大的一的数目里。一直演算到无穷数，我的意思是，永远没有办法到达这个过程的终了。确实就是在这里，一个关系的不可约分，问题不是那麽单纯。

Of all the incommensurables, this one is the one that, as I might say, always leaves the greatest separation in the intervals that define the rationality of the commensurable. A simple indication that I cannot give any further commentary on here.

在所有的不可约分当中，这个数，我不妨这样说，总是在定义可约分数的合理数时，会留下最大的隔离。这简单地表明，我不可能在这里，再作任何详尽的评论。

In any case, you see that it is a matter, any way, of something which, in this order of the incommensurable, is specified by every special accentuation, as well as a purity of relation.

无论如何，你们看出，在不可约分数的这个秩序上，有某件东西，被每一个特别的强调，以及一个纯净的关系，明确指明。

(7) To my great regret – because I think that all the guts of occultism are going to tremble on this occasion – I am indeed obliged, for the sake of honesty, to say that this small o relation is what is called the golden number. After which, naturally, there is going vibrate, in the inner depths of your cultural acquisitions – especially as regards aesthetics – the evocation of anything you like: cathedrals … Albert Durer … alchemical crucibles and all the other similar fiddle faddles!

（第七）令我感到遗憾的，因为我认为，在这样的场合，所有神秘主义的本质即将动摇。坦诚地说，我确实不得不说，这个小客体的关系，就是所谓的「黄金数目」。当然，在你们文化的累积的内在深处，你们会有所共鸣，特别是关於美学方面。你们可以自由联想到，例如，「净化」的作用，或阿伯特、杜乐的化学的融合坩埚，或其它的类似的天方夜谭。

I hope nevertheless that the seriousness with which I introduced the strictly mathematical character of the matter – and very specifically its problematic nature, which in no way gives the idea of a measure that is easy to conceive of – made you sense that it is something different that is at stake.

可是，我希望，我认真地介绍这全然都是数学的特性，明确地，还会牵涉到它具有争议性的部分。这丝毫没有让测量的观念，变得容易构想。我的认真会使你们感觉到，岌岌可危的是某件不同的东西。

Let us see now some of the remarkable properties of this small o. I wrote them in black on the left. You can see already that the fact that 1+o is equal to the inverse of o, namely, to 1/o, was already sufficiently guaranteed in the premises given by the definition of this relation. Because the notion that it consists in the relation of the smaller to the greater, in so far as equal to that of the greater to the sum, already gives us this formula, which is the same as this fundamental one: o = 1/(1+o). Starting from this, it is extremely easy to see other equalities, whose obsolete and, in truth, for us, momentarily important character is marked by the fact that I wrote in red the following equalities.

现在，让我们看一看，这个小客体的一些显而易见的特性。我用黑色粉笔，将它们书写在左边黑板上。你们已经能够看出，一加零等於零的倒转，换句话说，就是等於零分之一。这个假设，在这个关系的定义，就已经可以得到足够的确认。因为观念上是，这个关系在於，较小的数要被化简到较大的数，这样它才会相等於是较大数目的和。我们从这里得到一个公式，跟这个基本的公式相同：零等於一加零分之一。从这里开始，其它的相等数，就极端容易看得出来。事实上，其它相等数的陶汰不用，对於我们目前的意义重大，它所标示的事实，我用红色粉笔，书写以下的平等式。

The only important thing to note being that the one minus small o which it here (1), can be equal to o squared, which is very easy to prove. And, on the other hand, that two plus small o which is here, and you can see – from the simple consideration of one plus small o over one minus o – how this two minus small o can be easily deduced. Which represents the following. Namely, what happens, when instead of involuting onto itself the reduction of segments, one develops them on the contrary towards the outside. Namely, that the one over 2 plus small o – namely, what corresponded earlier to our external segment in the anharmonic relation (it is equal to one, being obtained by the outside development of the one that the greater length represents) – the one over two o has the same value as this initial value that we started from, namely, small o, namely, one over one plus o. (cf. Appendix).

唯一要注意的重要的事情是，一减去这个小客体的零，在此这个「一」就等於是零的平方，要证明这一点是轻而易举。在另一方面，二加这个小客体的零，你们看到，从这个简单的推算：一加小客体的零，当一减零的分子，这个二减这个小客体的零，是多麽容易演算出来。这代表以下的结果。换句话说，发生的结果，非但没有将部分的化简，内捲到自己里面，相反地，我们发展它们朝向外面。换句话说，这个一充当二加小客体零，也就是说，早先对应於这个不和谐的关系，我们外在的部分（这个较大长度所代表的一，它的外在发展获的结果，等於一）。这个一充当两个零的分子，拥有跟原先我们开始时的价值相同的价值，换句话说，小客体的零，一充当一加零的分子。

Such are the properties of the mean and extreme ratio, in so far as they are going perhaps to allow us to
comprehend something about what is involved in genital satisfaction.

这就是这个黄金比率的特性。它们将会让我们理解，某件关於性器官的满足牵涉到的内涵。

As I told you, small o is one of the ordinary (quelconque) terms of this genital relation.

我告诉过你们，小客体的零，是性器官关系的普通术语之一。

(8) I am saying, one of the ordinary terms, whatever may be its sex. The girl, like the boy, in the sexual relation – the experience of the subjective relation in so far as analysis defines it as oedipal – the girl like the boy enters it first of all as a child. In other words, as already representing the product – and I am not giving this term at random, we will have to take it up again subsequently – in so far as it allows to situate, as different from what is called creation, what, in our day, circulates as you know, everywhere and even without rhyme or reason, under the name of production.

（第八）我是说，无论它的性别是男是女，它都是性器官的普通术语之一。女孩，在性的关系上，就像男孩一样，就生命主体的经验而言，精神分析学将它定义为伊底普斯情结。女孩，像男孩一样，首先进入这个世界时，身份是一个孩子。换句话说，它作为一个产品的代表。这个术语，我不是随便取的，随后我们还要运用到它。它使我们能够定位，在我们的时代，以「生产的名义」，没来由地到处流通的东西，不同於所谓「创造」的位置。

This relation of the subject as such to what is involved in production should be defined, and is indeed the most imminent, the most current problem proposed to thinking. Whatever may be advanced, I am saying, in a dialectic of the subject where it is not seen how the subject itself can be taken as a production, is entirely without value for us. Which does not mean that it is easy to guarantee, starting from this root, what is involved in production.

生命主体的本身，跟生产所牵涉到的关系，应该被定义。它确实是我们所建议的跟思想的问题当中，最咄咄逼人，最迫不及待的问题。我是说，在生命主体的辩证法里，不管我们提出什麽，对於我们完全都没有价值。因为在那里，生命的主体本身如何被看待为一个生产，其实无足轻重。这並不意味着，从这个根源开始，生产所牵涉的东西，就很容易得到确认。

It is so little easy to guarantee, that if there is anything an unprepared mind might well be astonished at, it is the remarkable silence – the silence of “Conrard” – that psychoanalysis maintains on this delicate question, which is nevertheless … I ought to say which plays its part, however little, in our journalistic, political, domestic, daily, and anything you wish, even commercial life, and which it called birth control. We have yet to see an analyst saying what he thinks about it! It is all the same curious, in a theory that claims to have something to say about sexual satisfaction!

要得到确认，並不太容易。假如有任何东西，会让一个毫无心理準备的人大吃一惊，那就是这个显而易见的沉默，这个「康拉德的小说黑暗之心」所描绘的沉默，精神分析学在这个微妙的问题上，所保持的沉默。我应该说，儘管是隐隐约约，这个沉默都会扮演它的角色，无论是在我们的新闻行业，政治领域、家庭、及日常生活里，任何你愿意看到的，甚至在商业的活动里，或它所谓的「节育生产」里。我们还没有听到哪一位精神分析师，大胆地说出他对於这个沉默的看法！同样耐人寻味的是，即使宣称对于性的满足振振有词的理论，同样是无言以对。

雄伯译
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