seminar final 35

Jacques Lacan

雅克、拉康

Moment to conclude

结论的时刻

13.12.77 (CG Draft 2) 1

Seminar 2: Wednesday 13 December 1977

That is to indicate to you that it is a torus. That is why I wrote hole. In principle, it is a fourfold torus. It is a fourfold torus, such that anyone of the four may be reversed.

Here is the fourfold torus that is at stake [II-1].

那是要跟你们指示，这是一个圆环面。那就是为什么我书写这个空洞。原则上，这是一个四个折叠的圆环面，这四个圆环面可能被倒转。在此，这四个折叠的拓扑图形岌岌可危。

It is Soury who noticed that by reversing any one of the four that one obtains what I am showing you, what I am showing you in the figure on the left [II-2]. By reversing any one of the four, one obtains this figure which consists in a torus except for the fact that inside the torus, we only do what is presented there on the board, namely, rings of string, but each one, each one of what you see there, each one of these rings of string is itself a torus.

邵瑞注意到，以倒转四个圆环面的其中一个，我们获得我正在跟你们显示的，我正在跟你们显示，以左边的这个图形。以倒转四个的其中一个，我们获得组成这个圆环面的这个图形，除了这个事实： 在圆环面的里面，我们仅是做黑板上所被呈现的东西。换句话说，绳之环圈，但是每一个环圈，你们在那里看到的每一环圈，这些绳之环圈本身就是一个圆环面。

And this ring of string reversed as torus gives the same result, the same result, namely, that inside the torus which envelopes everything, each of the rings of string which is nevertheless a torus, each of the rings of string, which I repeat is also a torus, each of these rings of string functions in the way that Soury has formulated in the form of this drawing. This implies an asymmetry, I mean that he has chosen a particular torus to make of it the torus such as I have drawn it: it is the torus that he has reversed – I would ask you to be careful – and, in this respect, he has given it a privilege over the other tori which only figure here as rings of string.

当圆环面给予相同的结果时，这种绳之环圈会倒转，这个相同的结果。换句话说，在涵盖一切的圆环面里面，可是，每一个绳之环圈都是一个圆环面，每一个绳之环圈，我重复一下，也是一个圆环面。每一个这些绳之环圈发挥功用，邵瑞以绘图的方式解释。这暗示着一种不均称，我的意思是，他曾经选择一个特别的圆环面，来将它解释成为譬如我所绘制它的这个圆环面。他倒转这个圆环面—我想要要求你们小心—在这方面，他曾经给予它一个特权，甚过于另外一个圆环面，在这里它仅是作为绳之环圈的图形。

Nevertheless [II-1], it is quite obvious that the torus that he has chosen, the torus that he has chosen and which could be designated by 1,2,3,4, starting from the back towards what is in front.

可是，图形（II-1）这是显而易见的，他曾经选择的圆环面，他曾经选择的这个圆环面，能够用1，2，3，4，来指明。它们从后面开始，朝向前面。

This is the one which is in front (1). 13.12.77 (CG Draft 2) 2 This is the one which is most in front and this one which is a little more in front – that is why I give it no.3 – this one is completely in front.

这是一个前面的圆环面。这是最前面的圆环面，这个稍微前面一点。那是为什么我给予它编号3，这一个完全在前面。

Moreover, as you see, provided that you have a bit of imagination, as you see, there are four of them and it is by choosing one and reversing it that one obtains the figure that you see on the left [II-2] and this figure is equivalent for any one of the rings, I mean of the tori.

而且，如你们所见，只要你们拥有一点想象，如你们所见，它们有四个。凭借着选择一个，倒转它，我们获的这个图形，你们在左边看到的这个图形（II-2）。这个图形相等于任何的一个环圈，我的意思是圆环面的任何一个环圈。

Nevertheless I pose the objection to Soury something which is not any less true, which is that by reversing any one whatsoever of what is called the Borromean knot, one obtains the following figure, [II-3]. The 2 and 3 being unimportant, it is by reversing what I designated here as 1, namely, 1 of the elements of the Borromean knot, and you know how it is drawn [II-4].

可是，我提出某件同样的真实的东西，反对邵瑞。凭借着倒转任何所谓的博罗米恩环结，我们获得以下的图形（II-3）。这个2与3的环圈并不重要，凭借着倒转我在此指明作为第一环圈，换句话说，博罗米恩环结的这些要素的第一环圈，你们知道它在此如何被画。

In the figure on the left, this one [II-2], it is quite clear that the rings of string which are inside, inside the torus, and which in a way equivalent to what I said just now can be depicted as tori, each one of these reversed tori envelopes the two other tori, just as what is designated in 1 [II-3] here is a torus which has the property of enveloping the two others, on condition that it is reversed. Therefore what is in the figure on the right [II-4} becomes what is in the figure on the left [II-3], on condition that each of these tori is reversed. 13.12.77 (CG Draft 2) 3 It is obvious that the two figures on the left [II-2 and [II-3] are more complex than the two figures on the right [II-1] and [II-4]. Besides, what makes the third figure appear is the following: that once reversed, the torus that I designated by 1 on the figure, by going from left to right on the third figure…

在左边的这个图形，这个图形，显而易见地，在里面的这个绳之环圈，在圆环面里面，以某种的方式，它相等于我刚才所说的。这些绳之环圈能够被描述为圆环面。这些倒转的圆环面，每一个都涵盖另外两个圆环面，正如在（II-3）的图形所被指明的东西，是一个圆环面，它具有涵盖另外其他两个圆环面对特性，只要它被倒转。因此，在右边的（II-4）图形变成在左边的（II-3）的图形，只要这些圆环面，其中有一个被倒转。显而易见地，左边的（II-2）跟（II-3）的两个图形更加复杂，比起右边的(II-1)跟（II-4）的两个图形。除外，让这个第三图形出现的东西如下： 一旦被倒转，我根据图形的1 指明的这个圆环面，从左边到右边，这第三图形、、、

Left Right

II-2 II-1

II-3 II-4

II-5

Something comes to me, comes to my mind in connection with these tori: suppose that what I called ‘privileging a torus’ happens at the level of torus 2 for example, can you imagine what torus 2 becomes by privileging it as compared to torus 3, namely, by reversing it inside, inside of the torus that I designated by the name of 1, namely, by privileging the 2 with respect to torus 3?

某件东西来到我这里，来到我的心里，有关这些圆环面：假设为所谓的「具有特权的圆环面」发生在圆环面的层次，譬如，你们能够想象第二圆环面变成什么吗？凭借让它拥有特权，跟第三圆环面相比较。换句话说，凭借从里面倒转它，我指明的圆环面的里面，以这个1的名字，换句话说，凭借着给予这个2的圆环面，关于第三圆环面？

In one case, the reversal will change nothing to the relationship of torus 2 with respect to torus 3. In the other, it will amount to a rupture of the Borromean knot. This comes from the fact that the Borromean knot behaves differently according as the rupture happens in a different way on the reversed torus. I am going to indicate on the left hand figure [II.3] something which is obvious:

在某个意义上，这个倒转将不会改变第二圆环面跟第三圆环面的关系。在另一方面，那将等于是博罗米恩环结的断裂。这来自于这个事实：博罗米恩环结行为不同，当这个断裂以不同的方式发生，在被倒转的圆环面。我将要在左边的图形（II.3）指示明显的东西。

Concentric section 1

同心圆的区隔 1

Perpendicular section 2

垂直的区隔 2

The fact is that by sectioning (2) the reversed torus in the way that I have just done, the Borromean knot is undone. On the contrary by sectioning in this other way (1) which is, I suppose, evident to all of you as being equivalent to what I am drawing here [II-5], that it is equivalent, the Borromean knot is not dissolved, while in the present case the cut (2) that I have just made dissolves the Borromean knot. Therefore the privilege that is at stake is not something univocal.

事实上，凭借区隔 2， 这个被倒转的圆环面，以我刚刚做的，这部博罗米恩环结被解开。相反地，凭借另外一种方式的区隔 1， 我认为这是对于你们大家都是显而易见的，它相当等于是我正在这里所画的（II-5）。这是相当的，这个博罗米恩环结没有被解开，而在目前的情况，我刚刚所做的这个切割，解开这个博罗米恩环结。因此，岌岌可危的这个特权，并不是某件一致性的东西。

The reversal of any one at all of what ends up at the first figure, the reversal does not give the same result according as the cut is presented on the torus in such a way that it is, as I might say, concentric to the hole or according to whether it is perpendicular to the hole. 13.12.77 (CG Draft 2) 4

在第一个图形结果的任何东西的倒转，这种倒转并没有给予相同的结果，依照这个切割被呈现在圆环面上，以这样一种方式，跟这个空洞是同心圆，我不妨这样说，或是依照它跟这个空洞是垂直。

It is quite clear – this can be seen on the second figure [II-3] – it is quite clear that it is the same thing, I mean that by breaking according a tracing out which is this one (concentric), the threefold Borromean knot is dissolved; for it is quite clear that even in the state of torus, the two figures that you see there dissolve, I mean are separated if the reversed torus, cut in the sense that I have called longitudinal (2), while I can call the other sense transversal (1). 、

这是相当显见的—在第二个图形（II-3），能够被看得出来—这是相当显见得，这个相同的东西，我的意思是，凭借着突破，依照一种追踪，这是这个同心圆的追踪，这个三重的博罗米恩环结被解开。因为这是相当显见的，即使在圆环面的状态，你们在那里看到的这两个图形被解开。我指的是，它们被分开，假如这些倒转的圆环面被切割，用我所谓的纵长的切割意义，而另外一个意义的切割来说，那是跨越的切割。

The transversal does not free the threefold torus but on the other hand the longitudinal frees it. There is therefore the same choice to be made on the reversed torus, the same choice to the made according to the case that one wants or does not want to dissolve the Borromean knot.

这个跨越的切割并没有解放三重折叠的圆环面，但是在另一方面，这个纵长的切割解放它。因此，在倒转的圆环面，有这个相同的选择能够被做。这个相同的选择能够被做，依照我们想要或是不想要解开博罗米恩环结的情况。

The figure on the right [II-5], the one that materialises the way in which the surrounding torus must be cut in order – I think that you see this to free the three, the three that remain – it is quite clear that, by drawing things like that, you see that what I designate on occasion as (2), that this is freed from (3) and that secondarily the (3) is freed from the (4), [II-1 and II-2].

在右边的这个图形（II-5），这个图形具体表现这个围绕的圆环面必须被切割的方式，为了—我认为你们看出这一点，为了要解放这三个圆环面，始终在的这三个圆环面—显而易见的是，凭借像那样的绘图，你们看出，我有时指明作为，这个从图形（3）解放出来，其次，这个图形（3）被解放从这个图形（4）。（II-1）跟（II-2）

I propose the following, the following which is initiated by the fact that in the way of dividing up the figuration of (4), Soury had a preference, I mean that he prefers to mark that the (4) is to be drawn like that. 13.12.77 (CG Draft 2) 5

我建议以下，以下被开启的东西，根据这个事实：以区隔（4）的图形的方式，邵瑞拥有一个偏好。我的意思是，图偏好标示，这个（4）的图形，应该像那样被画。

This is equally a Borromean knot but I suggest that there is a six-fold Borromean knot, six-fold which is not the same as the Borromean knot which, as I might say, would follow in single file, it is a more complex Borromean knot and I am showing you the way in which it is organised, namely, that, as compared to the 2 that I drew first, these two are equivalent to what happens from the fact that one is on the other; and in this case, the Borromean knot must be inscribed by being over this one which is above and under this one which is below. This is what you see here: it is under the one that is below and over the one that is above.

这确实是一个博罗米恩环结，但是我建议，有一个六重折叠的环结。这个六重折叠的环结，跟博罗米恩环结并不相同。我不妨说，后者将会遵照单一的行列。这是更加复杂的博罗米恩环结。我正在跟你们显示这个方式，它被组织，换句话说，跟我最初所画的这个2 的图形比较起来，这两个相等于所发生的事情，根据这个事实： 以上的这个跟着底下的这个博罗米恩环结。

It is not easy to draw. Here is the one that is below… You have in connection with these two couples, of these 2 couples which are depicted here, you have only to notice that this one is above, the third couple therefore comes above and underneath the one that is below.

要这样画并不容易。在此是你们拥有的底下的这个博罗米恩环结。关于这两对，这两对在这里被描述的博罗米恩环结，你们只需要注意到，这一个博罗米恩环结在上面，这第三对因此，出现在上面，及底下的这个环结的下面。

I pose the question: does reversing one of those which are here, give the same result as what I called the single file figure, namely, thus, the one which is presented thus 1,2,3,4,5,6, all ending in the ring here, would reversing the 6 fabricated in this way give the same result as the reversal of any one at all of these three sixes. We already have an indication of response: which is that the result will be different.

我提出这个问题：倒转在那里的那些环结，给予这个相同的结果，如同我所谓的相同行列的图形。这个图形因此在此被呈现为1，2，3，4，5，6，一切都在这个环圈里结束。倒转以这个方式建构的6的图形，将会给予这个相同的结果，跟所有的这三个 6 的任何一个的倒转。我们已经拥有一个回应的指示, 结果将会是不同的。

It will different because the fact of reversing any one at all of these six that I call single file will give something analogous to what is depicted here [II-2]. On the contrary, the way in which the figure [[II-7] is reversed will give something different.

这将是不同的，因为事实上，倒转我所谓的单一行列的这六个环结的任何一个，都会给予某件类同时在图形（II-2） 所被描绘的东西。相反地，图形(II-7) 被倒转的方式，将会给出不同的东西。

I apologise for having directly implicated Soury. He is certainly very valuable for having introduced what I am stating today. The distinction between what I called the longitudinal cut and the transversal cut is essential. I think I have given you a sufficient indication of this by this cut here. The way in which the cut is made is quite decisive. What happens by the reversal of one of the six, as I designated it here, this is what is important to know and it is by putting it in your hands that I desire to have the final word on it.

There you are, I will stay with that for today.

我很抱歉没有直接引用邵瑞的拓扑图形。他确实是非常有价值，因为他曾经介绍我今天正在陈述的东西。在我所谓的纵长的切割跟横跨越的切割之间的区别，是很重要的。我认为我曾经凭借这里的这个切割，给予你们一个充分的有关它的指示。这个切割被从事的方式是相当决定性的。根据这个六的环结的其中之一的倒转，所发生的事情，如同我在此指明它，这是非常重要的，要知道的事情。凭借将它放置在你们的手里，我渴望拥有对于它的最后的论断。

就这样，今天我在此告一段落。

雄伯译

32hsiung@pchome.com.tw

https://springhero.wordpress.com

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