Rings of string 03 绳之环

Encore 703
再来一次

By Jacques Lacan
雅克 拉岡

Rings of string 03
绳之环

What cuts a line is a point. Since a point has zero dimensions, a line is defined as having one dimension. Since what a line cuts is a surface, a surface is defined as having two dimensions. Since what a surface cuts is space, space has three dimensions.

切割线条的是一个点。因为一个点有零的向度,一条线就被定义为拥有一个向度。因为一条线切割的是一个表面,一个表面就被定义为拥有两个向度。因为一个表面所切割的是空间,空间拥有三个向度。

The little sign I wrote on the blackboard ( figure 1) derives its value therefrom.

我在黑板上所写的这个小标记(图形一),从它的本身得到价值。

It has all the characteristics of writing—it could be a letter. However, since you write cursively, you never think of stopping a line before it crosses another in order to make it pass underneath, or rather in order to assume that it passes underneath, because in writing something completely different than three-dimensional space is involved.

它拥有所有的书写的特色,它可以是一个字母。可是,你既然是潦草地写,你从来就没有想到要先停止一行,才跨越到下一行,为了让它从底下经过,或者为了认为它从底下经过,因为在书写中,会牵涉到跟三个向度完全不同的东西。

In this figure, when a line is cut by another, it means that the former passes under the latter. That is what happens here, except that there is only one line. But although there is one, it is distinguished from a simple ring, for this writing represents for you the flattening out of a knot. Thus, this line or string is something other than the line I defined earlier with respect to space as a cut and that constitutes a hole,, that is, separates an inside from an outside.

在这个图形里,当一条线被另一条线切过,它意味着,前者从后者底下经过。那是这里所发生的事情,除了只有一条线。虽然只有一条线,它跟一个简单的环截然不同,因为对你而言,这个书写代表一个结的摊开来。因此,这条线或环截然不同於我早先关於空间切割所定义的线,那会形成一个空洞,换句话说,它会隔开里面跟外面。

This new line is not so easily incarnated in space. The proof is that the ideal string, the simpliest string, would be a torus. And it took a long time for people to realize, thanks to topology, that what is enclosed in a torus has absolutely nothing to do with what is enclosed in a bubble.

这条新线不是那麽容易在空间具体显现出来。证据是,这条理想的绳子,这条最简单的绳子,将会是一个园形突起。由於地形学,人们要隔了很久才会体会到,这个园形突起里面所封闭的,跟气泡状里面所封闭的,绝对没有丝毫关系。

Regardless of what you do with the surface of a torus, you cannot make a knot. It is in this respect, allow me to tell you, that the torus is reason, since it is what allows for knot.

不管你如何处理园形突起状的表面,你无法制造一个结。就在这一方面,容我告诉你,这个园形突起状是理性,因为它考虑到结的问题。

It is in that respect that what I am showing you now, a twisted torus, is as neat an image as I can give you of the trinity, as I qualified it the other—one and three in a single stroke.

就在那一方面,我现在给你们看的,是一个扭曲的园形突起状,意象鲜明,就像我跟你们说的基督教的聖灵、聖父、聖子三位一体,三者的关系一气呵成。

Nevertheless, it is by making three toruses out of it, using a little thingamabob I already showed you called the Borromean knot, that we shall be able to operate on the first knot. Naturally, there are people here today who weren’t here last year in February when I spoke about the Borromean knot. I will try today to give you a sense of its importance and of how it is related to writing, inasmuch as I have defined writing as what languages leaves by way of a trace.

可是,将它制作成三个园形突起状,使用我已经显示过的波罗米安结,我们将能够运作第一个结。当然,今天在现场的人,去年二月未必在这里,当我提到波罗米安结,今天我将让你们感觉它的重要性,以及它如何跟书写有关,因为我已经将书写定义为语言遗留的痕迹。

With the Borromean knot, we are dealing with something that cannot be found anywhere,, namely, a true ring of string. You should realize that, when you lay out a string, you never manage to join the two ends together in the woof. In order to have a ring of string, you to make a knot, preferably a sailor’s knot. Let’s make a sailor’s knot with this string.

用这个波罗米安结,我们正在处理在别的地方找不到的东西,换句话说,一个真实的绳之环。你们应该体会到,当你安排一条绳时,你永远没有办法,将两端在纬线的部分连接起来。为了要有一个绳之环,你必须制作一个结,最好是一个水手结。让我们用这条绳制作一条水手结。

That’s it. Thanks to the sailor’s knot, we have here, as you see, a ring of string. I will make two more. The problem that is then raised by the Borromean knot is the following—once you have made your rings of string, how can you get these three rings of string to hang together in such a way that if you cut one, all three are set free?

就是这样。由於水手结,你们看到,我们在这里拥有一个绳之环。我再多做两个。波罗米安结所引起的问题如下:一但你已经制作了你的绳之环,你如何将这三个绳之环,悬挂在一起,然后,你切割一个结,其它三个结都会鬆开来。

Three is really nothing. The true problem, the general problem, is to work things out in such a way that, with any number of rings of string, when you cut one, every single one of the others becomes free and independent.

三个没有什麽困难。真正的问题,也是通常的问题是,如何将事情安排,将任何一个绳之环切开,其它每一个单一的绳之环,会变成自由与独立。

Here is the Borromean knot—I already put it up on the blackboard last year. It is easy for you see that no two rings of string are knotted to each other, and that it’s only thanks to the third that they hang together.

这就是波罗米安结,去年,我已经将它画在黑板上。你们很容易看出来,没有任何两个绳之环互相打成死结,只是由於有第三个绳之环,它们才悬挂在一起,

Pay close attention here—don’t let yourself remain captivated by this image. I’m going to show you another way to solve the problem.

请仔细看这里。不要让你们自己被这个意象所吸引住、我将告诉你们有另外一个方法,来解决这个问题。

Here is a ring of string. Here is another. You insert the second ring into the first, and you bend it ( see figure 4)

这里有一条绳之环。这里还有另一条。你们将第二条插入第一条,然后将弯曲过来。(见图四)

It suffices then to take up the second ring in a third for the three to be knotted together—knotted in such a way that it suffices for you to cut one for the other two to be set free ( see figure 5)

这样就足够将第二个绳之环插入第三个绳之环,为了让第三个绳之环打成一个结。它们互相结合在一起时,你只要将其中一个绳之环切开,其它两个绳之环就会鬆开来。(见图五)

After the first bending, you could also bend the third ring and take it up in a fourth. With four, as with three, it suffices to cut one of the rings for all the others to be set free. You can add an absolutely infinite number of rings and it will still be true. The solution is thus absolutely general, and the line of rings can be as long as you like.

在第一次弯曲后,你也能够弯曲第三个绳之环,然后再从事第四个绳之环。第四个绳之环,跟第三个绳之环一样,你只要切开其中一个绳之环,所有其它的绳之环都会鬆开。这种解决的方法绝对是大家都通用,环的线,你高兴想要玩多长,就可以有多长。

In this chain, whatever its length, the first and last links different from the others: while the intermediary rings, in other words, the bent ones, are all ear-shaped, as you see in figure 4, the extremes are simple rings.

在这个锁链中,不管它有多长,第一个跟最后一个链结不同於其它的链结:中间的绳之环,换句话说,那些弯曲的绳之环,都是像耳朵一般的形状,如你在圖四所看到,前后两端则是简单的绳之环。

Nothing stops us from making the first and last rings coincide, by bending the first and taking it up in the last. The chain is thereby closed ( see figure 6)

没有一样东西阻止我们将第一个及最后一个绳之环结合在一起,方法是将第一个绳之环弯曲,然后套上最后一个绳之环。这个锁链因此就封闭起来。

The collapse of the two extremes into one nevertheless leaves a trace: in the chain of intermediary links, the strands are juxtaposed two by two, whereas, when the chain closes on a simple, single ring, four strands on each side are juxtaposed to one strand, the circular ring.

可是,前后两端的崩塌成为一个,会留下一个痕迹:在中间的链接的锁链,链条会两个同时並列。当这个锁链在一个简单的单一绳之环打成封闭的死结,在每一边的四个链条会並列成一个链条,园形的链条。

That trace can certainly be effaced—you then obtain a homogeneous chain of bent rings.

那个痕迹确实能够被抹除掉,然后,你会得到一个同质性的弯曲的绳之环锁链。

雄伯译
sprigherohsiung@gmail.com

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