Seminar final 12

Seminar final 12
拉康研讨班25:结论的时刻

Jacques Lacan

雅克、拉康

Seminar 5: Wednesday 18 January 1977

This is rather laboured, so there you are, in truth, here, it is more or less the testimony, the testimony of a failure, namely, that I have exhausted myself for 48 hours, in making what I would call, contrary to what is involved in a plait (tresse), I exhausted myself for 48 hours, in making what I would call a ‘four-stranded plait’ (‘quatresse’). There you are [ Fig. V-2]

这是相的费力的。所以你们在这里,事实上,它相当是这个证词,一种失败的证词。换句话说,我曾经让自己费尽力气两天两夜,来制作我所谓的「四个环圈的编织」。你们瞧这个图形。

The plait is at the principle of the Borromean knot. That is to say that after six times, one finds, provided one crosses these three threads in an appropriate fashion – good, so then, this means that at the end of six manoeuvres of the plait, you find an order, at the sixth manoeuvre, the 1, the 2 and the 3. This is what constitutes
这个是博罗米恩环结的原则。换句说,经过六次以后,我们发现,只要我们以一个适当的方式,越过这三条线,呵呵,这意味着,在这个编织的六次操弄结束之后,你们发现一种秩序,在第六次的操弄,第一,第二,及第三。这就是所组成的东西。

the Borromean knot [fig. V-3]. If you have, if you try it twelve times, you have likewise another Borromean knot, which Borromean knot is curiously not visualised immediately [Fig. V-4]. It has nevertheless this character that contrary to the first Borromean knot which, as you have seen just now, passes above the one that is underneath, since as you see, the red is above the green, underneath the one that is underneath: that is the principle from which the Borromean knot derives. It is in function of this operation that the Borromean knot holds up. Likewise, in a fourfold operation, you will put one above, the other underneath, and in the same way you will operate with underneath the one that is underneath, you will therefore have a new Borromean knot which represents the one with 12 crossovers.
What is to be thought of this plait?

博罗米恩环结(图形V-3), 假如你们尝试它十二次,你们同样拥有另外一个博罗米恩环结。耐人寻味地,这个博罗米恩环结并没有立即被构想(图xingV-4),可是它具有跟第一个博罗米恩环结相反的这个特性。如你们刚才看到的,它由底下的这个博罗米恩环结的上方通过。你们看到,红色这条在绿色这条的上方,在底下的这条的下方。那就是博罗米恩环结从那里获得的这个原则。以这个运作的功用,博罗米恩环结维持下来。同样地,以一种四个折叠的运作,你们将上方的这条,底下的另外一条。以同样的方式,你们将会运作,用底下的这个条,因此你们将会拥有一条新的博罗米恩环结。它代表拥有十二次跨越的这一条。这种编织应该如何被看待?

This plait can be in space. There is no reason, in any case at the level of the ‘fourfold’ (‘quatres-se’) that we cannot suppose it to be entirely suspended. The plait nevertheless can be visualised insofar as it is flattened out. I spent another period, one that was supposedly reserved for holidays, exhausting myself in the same way, in trying to make function another type of Borromean knot, namely, one that would be obligatorily made in space, since what I started from was not the circle as you
这种编织能够被放置在空间。无论如何,没有理由处于这「四个折叠」的层次。我们无法认为它完全地被悬置。可是,这种编织仅有处于被平面化时,始能够被构想。我花费另外一个时期,应该被保留给渡假的时期,同样让自己身心俱疲,尝试让另外一种博罗米恩环结运作。换句话说,这个环结将强制地在空间被形成。因为我开始地方,并不是跟你们一样的这个圆圈。

A tetrahedron is drawn like that. Thanks to that, there are 1, 2, 3, 4, 5, 6 edges (arêtes). I should say that the prejudices that I had – because it is a matter of nothing less – pushed me to operate with the four faces, and not with the six edges, and with the four faces it is quite difficult, it is impossible to make a plait. There must be six edges there to make a correct plaiting and I would like to see these balls carrying the outline of the schema, coming back [balls thrown into the audience].

一个拥有四个层面的多边形像那样被画。由于那样,有1,2,3,4,5,5 ,6 个边缘。我因该说,我曾经拥有的这些偏见逼迫我—确实是如此—使用这四个面相运作。不是用六个边缘,而是用四个面相。要制作一个编织,是相当困难,是不可能的。一定要有六个边缘在那里,才能制作一个正确的编织。我想要看到这些球具有这个基模的轮廓,回转过来(球被丢进听众那里)。

The fact is that you will note there that the plaiting, not six-fold but twelve-fold, is altogether fundamental. I mean that, what happens is that one cannot bring into play this knotting of tetrahedrons without starting, since there are only three tetrahedrons, without starting from the plait. It was a fact that was unveiled to me rather late, and which you will see here provided I pass you these balls which, I repeat, I would like to see coming back, because I have not, far from it, fully elucidated them,. I am going therefore, as I usually do, to throw them to you so that you can examine them.

事实上,你们将会注意到,这种编织不是六个折叠,而是十二个折叠。它完全是基本的,我的意思是,所发生的是,每当我们运作这个四层面的多边形,我们就会从这个编织开始,因此仅有三个四层面的多边形。我很迟才恍然大悟这一个事实,你们在此将会看出,只要我传递这些球给予你们。我重复一下,我想要看到这些球回来。因为我还没有充分地阐明它们,根本就没有。因此,像平常那样,我将把它们投掷给你们,让你们能够检视它们

I would like all four of them to be sent back. In effect, they are not similar. There are four of them, and there is a reason for that. It is a reason that I still have not mastered. It is preferable, even though of course that would take too much time, it would be preferable, that these balls should be compared one to the other, for they are effectively different. I would like that, from this threefold plait which is basic in the operation of these tetrahedric Borromean knots to which, I repeat, I applied myself without really completely managing them, I would like you to draw a conclusion.

我想要它们四个图形都被送回来。实际上,它们并不相同。有四个图形,是有一番道理。只是这个道理,我依旧没有参透。我宁可,即使当然那将会耗费许多时间,我宁可将这些球形互相作比较。因为它们实际上是有差异的。我想要,从这三个环结编织,在四层面的多边形的博罗米恩环结的运作,是基本的。我重复一遍,我并没有真正完全处理,就运用到我自己身上。我想要你们获得结论。

The fact is that, even for the tetrahedrons in question, one proceeds also to what I would call a flattening out for this to be clear. The flattening out which on this occasion is spherical is necessary for one to put one’s finger on the fact, as I might say, that the crossovers in question, the tetrahedric crossovers, are indeed of the same order, namely, that the tetrahedron which is underneath, the third tetrahedron, passes underneath, and that the tetrahedron which is above, the third tetrahedron passes above. It is indeed because of that that we are still here dealing with the Borromean knot.

事实上,甚至对于这个受到置疑的四层们多边形,我们也继续到我所谓的平面化,为了澄清这个。在这个场合,是球形的这个平面化是需要的,为了让我们理解这个事实。我不妨说,受到质疑的这个跨越,这个四层面的多边形的跨越,确实是属于相同的秩序。换句话说,在底下的这个四层面多边形,第三个四层面多边形,从底下经过。上方的这个四层面多边形,这第三个四层面多边形从上方经过。这确实是因为我们依旧在这里处理博罗米恩环结。

What is annoying nevertheless, is that even in space, even starting from a presupposed spatial, we should also be constrained in this case here to support – since when all is said and done, it is we who support it – to support the flattening out. Even starting from a spatial presupposition, we are forced to support this flattening out, very precisely in the form of something which presents itself as a sphere (Fig. V-5b).

可是,令人懊恼的是,即使在空间,甚至从一个被假设的空间,在这种情况,我们在此也应该受到约束,为了支持—当一切都说都做了,那是我们在支持它—为了支持这个平面化。甚至从一个空间的假设开始,我们就被迫支持这个平面化,所用的形式呈现它自己,作为一个图形(图形V-5b)

But what does that mean, if not, that even when we manipulate space, we have never seen anything but surfaces, surfaces no doubt which are not banal surfaces because we articulate them as flattened out. From that moment on, it is manifest on the balls that the fundamental plait, the one that crisscrosses itself 12 times, it is manifest that this fundamental plait forms part of a torus. Exactly this torus that we can materialise by the following, namely, the twelve-fold plait, and that we can also moreover materialise in terms of the following namely, the six-fold plait [Fig. V-3 and Fig. V-4].

但是那时什么意思,难道不就是,甚至当我们操控空间时,我们除了表面以为,从来没有看见别的东西。无可置疑地,这些表面并不是陈腐的表面,因为我们表达它们,作为平面化。从那个时刻开始,显而易见地,在这个球形上,这个基本的编织,交互跨越自己十二次的这个基本编织,显而易见地,这个基本的编织形成一个圆环面的部分。确实就是这个圆环面,我们能够根据以下具体化。换句话说,这十二折叠的编织,而且我们也能够让它具体化,使用以下的所谓的六个折叠的编织。( 图形V-3 及图形v-4)

In truth this function of torus is clearly manifest in the balls that I have just given you, because it is no less true that between the two little triangles, if we make – I would ask you to consider these balls – if we make a polar thread pass through, we will have exactly in the same way a torus; for it is enough to make one hole at the level of these two little triangles to constitute at the same time a torus. This indeed is why the situation is homogenous, in the case of the Borromean knot, as I have drawn it here, is homogenous between the Borromean knot and the tetrahedron.

事实上,圆环面的这个功用,在我刚刚给予你们的这些球形清楚地显而易见。因为这是同样地真实,在这两个小岛三角形之间,假如我们制作—我将要求你们考虑这些球形—假如我们制作一极端的线通过,我们将会同样地拥有一个圆环面,因为在这两个三角形的这个层次,制作一个空洞就足够了,同时也形成一个圆环面。这确实是为什么这个情况是同质性,在博罗米恩环结的这个情况。如同我在此所曾经画的。它在博罗米恩环结与这个四层面的多边形之间,是同质性的。

There is therefore something which ensures that it is no less true for a tetrahedron that the function of the torus governs here whatever is nodal in the Borromean knot. It is a fact, and it is a fact that has strictly never been glimpsed namely, that everything that concerns the Borromean knot is only articulated by being toric.

因此,有某件东西保证,对于一个四层面的多边形,这是同样地真实。圆环面的这个功用在此统辖博罗米恩环结的属于节点的东西。这一个事实,严格来说,从来没有被瞥见过。也就是说,跟博罗米恩环结有关的一切,仅是在成为圆环面时被表达。

A torus is characterised quite specifically as being one hole. What is annoying, is that this hole is difficult to define. The fact is that the knot of the hole with its flattening out is essential, it is the only principle of their counting – and that there is only one way, up to the present, in mathematics, of counting the holes: it is by going through, namely, by taking a path such that the holes are counted. This is what is called the fundamental group. This indeed is why mathematics does not fully master what is at stake.

圆环面的特性相当明确是作为一个空洞。令人懊恼的是,这个空洞很难定义。事实上,成为平面化的这个空洞的环结是基本的,这是它们计算的唯一原理。在数学方面,一直到现在,仅有一种方法计算这些空洞。以通过的方式,换句话说,以採取一条途径,这些空洞被计算。这就是所谓的基本的团体。这确实是为什么数学并没有充分地操控这岌岌可危的东西。

How many holes are there in a Borromean knot? This indeed is what is problematic since, as you see, flattened out, there are four of them [Fig. V-6]. There are four of them, namely, that there are not fewer than in the tetrahedron which has four faces in each of the faces of which one can make a hole. Except for the fact that one can make two holes, even three, even four, by making a hole in each of these faces and that, in this case, each face being combined with all the others and even repassing through itself, it is hard to see how to count these paths which would be constitutive of what is called the fundamental group. We are therefore reduced to the constancy of each of these holes which, by this very fact, vanishes in a quite tangible way, since a hole is no great thing.

在博罗米恩环结,有多少的空洞? 这确实是问题重重。从平面来看,你们看出,有四个空洞。换句话说,并没有少于四层面的多边形。后者有四个层面,每个层面,我们都能够制作一个空洞。除了我们能够制作两个空洞,甚至三个,甚至四个空洞的这个事实之外,我们在这些层面的每一个制作一个空洞。在这种情况,每个层面都跟其他的层面连接,甚至重新通过它们自己。我们很难看出,要如何计算这些途径。它们将会形成所谓的基本的团体。我们因此被沦为每一个这些空洞的常数,由于这个事实,以相当具体的方式消失,因为空洞让人无可奈何。

How then distinguish what makes a hole and what does not make a hole? Perhaps the quatresse can help us to grasp it.

因此,如何区别是什么形成一个空洞,跟什么没有形成空洞?或许这个「quatresse」能个帮助我们理解它。

What is here in this first drawing [Fig. V-1], these three circles form a Borromean knot. They form a Borromean knot, not that the first three form a Borromean knot since, as is implicated in the fact that the freed fourth, as I might say, the fourth element freed should leave each of the three free.

在这第一个图形(图形v-1) , 这三个圆圈形成一个博罗米恩环结。它们形成一个博罗米恩环结,并不是前面三个形成一个博罗米恩环结,如同这个事实所暗示的,这个被解放的第四个要素,我不妨说,这第四个被解放的要素,应该让这三个圆圈的每一个解放。

The quatresse binds nevertheless, starting from the one which is the highest (black), on condition of passing above the one that is highest, it will find itself by passing over the one which in the flattening out is intermediary (green), by passing beneath, it will find itself binding the three. This indeed in effect is what we see happening [Fig. V-7], namely, that, on condition that you see that as equivalent to the following, I think that you see here that it is a matter of a representation of the Real insofar as it is here that we have the apprehension of the Imaginary, of the Symptom and of the Symbolic, the Symbolic on this particular occasion being very precisely what we must think about as being the signifier. What does that mean?

可是,这个Quatresse 连接,从最高的这个黑色圆圈开始,只要它从最高点这个圆圈的上方通过,它将会发现它自己,由于通过处于平面化的这个圆圈,它是绿色圆圈的中介,由于从底下经过,它发现它自己连接这三个圆圈。实际上,这确实是我们看到发生的事情(图形V-7)。换句话说,只要你们看到,作为以下的相等物,我认为,你们看到,这是实在界的再现符号。因为在这里,我们理解到,想像界,病征,及符号界,在这个特别的场合。那确实是我们必须思考到,作为这个能知。那是什么意思?

The fact is that the signifier on this particular occasion is a symptom, a body, namely, the Imaginary being distinct from the signified. This way of making the chain questions us about the following: the fact is that the Real, namely, what on this particular occasion is marked here, the fact is that the Real would be very specially suspended on the body.

事实上,在这个特别的场合,这个能指是一个病征,一个身体。换句话说,跟所指不同的这个想像界。这种形成锁链的这个方式,质疑我们,关于以下:事实上,实在界,也就是在这个特别的场合被标示的东西,事实上,实在界将会被身体特别地悬置。

雄伯译
32hsiung@pchome.com.tw
Http://springhero.wordpress.com

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