Identification219

Identification219
认同
Jacques Lacan
雅克 拉康

16.5.62 XX 1
Seminar 20: Wednesday 16 May 1962
(Edited from notes)

I am justifying the necessity of these lucubrations about the
surface. It is obvious that what I am telling you about it is
the result of a reflection. You have not forgotten that the
notion of surface in topology is not a self-evident one and it is
not given as an intuition. The surface is not something
self-evident.
我正在提有关这个表面的这润滑的必要性自圆其说。显而易见,我正在告诉你们关于它的东西,就是反思的结果。你们没有忘记,表面的观念在拓扑学并不是一个不证自明的表面,这个表面并不是作为直觉被给予。这个表面并不是某件不证自明的东西。

How can it be tackled? Starting from what introduces it into the
real, namely what would show that space is not this open and
contemptible extension that Bergson thought it was, space is not
as empty as he thought, it conceals many mysteries.
Let us pose certain terms at the beginning.

这个表面如何被克服呢?从表面被介绍进入实在界的东西开始,换句话说,从将会显示空间并不是这个开放与可轻视的延伸,柏格森认为它就是这个样子,空间并不像他认为的空无,空间隐藏许多的神秘。开始时,让我们提出某些的术语。

It is certain that a first essential thing in the notion of
surface is that of face: there are two faces or two sides in it.
This is obvious if we plunge this surface into space.

的确,一个最初的基本的东西,在表面的观念,就是脸孔的表面。在这个表面,有两个脸孔,或有两边。这是显而易见的,假如我们将这个表面投掷进入空间。

But to
appropriate to ourselves what the notion of surface can take on
for us, it is necessary that we should know what it presents us
with from its dimensions alone, indeed what it can give us qua
surface dividing space by its dimensions alone, suggests to us
that we should reconstruct space in a different way to the
intuition we believe we have of it. In other words, I propose to
you to consider it as more obvious (imaginary capture), much more
certain (linked to action), more structural to start from the
surface to define space – which I hold we have few guarantees
about – let us say rather to define the locus (lieu), than to
start from the locus to define the surface – cf the locus in
philosophy.

但是为了将表面的观念对于我们能够形成的东西,适用于我们,我们应该知道,它呈现给我们什么东西,光是从它的维度。的确,它能够给予我们的东西,作为作为分开空间的表面,光是凭借它的维度,就跟我们暗示:我们应该重建空间,用不同的方式,针对我们对于它拥有的直觉。换句话说,我跟你们建议,要将它认为是更加明显(想像的补捉),更加确定(跟行动连接一块),更加具有结构,从表面开始定义空间—关于这个空间,我认为我们拥有的保证很少。我们不妨说,为了定义这个轨迹,而不是从轨迹开始定义这个表面—譬如,哲学的轨迹。

The locus of the Other already has its place in our
seminar. To define the face of a surface, it is not enough to
say that it is on one side and on the other, all the more so
because that has nothing satisfying about it, and if something
(2) gives us a Pascalian vertigo, it is indeed these two regions
into which an infinite plane is supposed to divide the whole of
space.

大他者的这个轨迹在我们的研讨班已经具有它的一席之地。为了定义表面的脸孔,光是这样说并不足够,说表面的脸孔是在一边与另外一边。它更加是如此,因为关于表面的脸孔,这丝毫并不令人满意。假如某件东西给予我们一个巴斯卡的晕眩,那确实就是这两个地区,无限的平米被认为将整个空间区分成为两个地区。

How define this notion of face? It is the field on which a line,
a path can be extended without having to meet an edge. But there
are surfaces without edges: the plane to infinity, the sphere,
the torus and several others which are surfaces without edge
being reduced practically to a single one: the cross-cap or mitre
or bonnet pictured here (1).

我们如何定义表面对这个观念?在这个领域,一个线条,一个途径能够被延伸,而不需要会见一个边缘。但是有很多没有边缘的表面,进入无限的平面,这个球形,圆环面与好几个其他的圆环面。它们都是没有边缘的表面,几乎被化简成为单一的表面:在此被画出的这个交叉帽,或软帽。

In learned books this is what the cross-cap is: cut in order to
be inserted onto another surface (2).
These three surfaces, sphere,
torus, cross-cap are
elementary closed surfaces to
the composition of which all
the other closed surfaces can
be reduced.

在学习书籍,这就是交叉帽的样子:被切割,为了被插入进入另外一个表面。具有这三个表面,球形,圆环面,交叉帽是基本的封闭的表面,所有的其他的封闭的表面能够被化简成为这些基本的封闭的表面的组成。

16.5.62 XX 2

I will nevertheless call
figure 1 the cross-cap. Its
real name is the projective
plane of Riemann’s theory of
surfaces whose plane is the
base. It brings into play at
least the fourth dimension.
Already, for us depth psychologists, the
third dimension creates
problem enough for us to consider it as not very assured.
Nevertheless in this simple figure, the cross-cap, the fourth is
already necessarily implied.

可是,我将称图形1,为交叉帽。它的真实的名字是列曼的表面理论的投射的平面。这些表面的平面就是基础。它运作至少有四个维度。对于我们深度新理学家而言,这第三个维度已经是问题重重,让我们将它认为是并不确定。可是,在这个简单的图形,这个交叉帽,第四个维度已经必然被暗示出了。

The elementary knot made the other day with a piece of string
already presentifies the fourth dimension. There is no valid
topological theory unless we make intervene something which will
lead us to the fourth dimension.

前天,我制作的这个基本的环结,用一条绳子,它已经让第四维度具体表现。没有确实的拓扑图形的理论,除非我们用某件东西介入,这个东西将会引导我们到第四维度。

(3) If you want to try to reproduce this knot using the torus by
following the circuits and the detours that you can make on the
surface of a torus, you could after several circuits return to a
line which closes on itself like the knot above.

假如你们想要尝试复杂这个环结,使用这个圆环面,遵循这些迴圈与迂迴,你们能够在圆环面的表面,形成这些迴圈与迂迴。经过好几个迴圈之后,你们能够回到一个线条,它就像以上的环结,依靠自己封闭起来。

You cannot do
it unless the line cuts itself; since [on] the surface of the
torus you will not be able to mark that the line passes above or
below, there is no means of making this knot on the torus. It is
on the contrary perfectly makeable on the cross-cap. If this
surface implies the presence of the fourth dimension, it is a
beginning of the proofs that the most simple knot implies the
fourth dimension.

你们无法做它,除非这个线条切割它自己。因为在圆环面的表面,你们将不能够标示,这个线条从上面或从底下通过。没有任何工具在圆环面上做这个环结。相反地,在交叉帽,它形成得非常完美。假如这个表面暗示第四维度的存在,那是各种证据的开始,即使是最简单的环结暗示着第四维度。

I am going to tell you how you can imagine
this surface, the cross-cap. It will not impose its necessity by
that even, for us, its manoeuvre. It is not unrelated to the
torus, it even has the most profound relationship to the torus.

我将要告诉你们,你们如何想像这个表面,这个交叉帽。它并没有赋加它的必要性,凭借那样,甚至,对于我们而言,它甚至没有赋加它的谋略。它跟这个圆环面并非不相关。它甚至拥有最深的关系,跟这个圆环面。

The simplest fashion to show you this relationship is to recall
to you how a torus is constructed when it is decomposed in a
polyhedric shape, namely by bringing it back to its fundamental
polygon. Here this fundamental polygon, is a quadrilateral. If
you fold this quadrilateral onto itself, you will get a tube by
joining the edges. If you
vectorize these edges by
agreeing that only the vectors
which go in the same direction
can be stuck to one another,
the beginning of one vector
being applied to the point
where the other vector
terminates, from then on you
have all the coordinates for
defining the structure of the
torus.

最简单的方式,跟你们显示这个关系,就是跟你们提醒,一个圆环面如何被建构,当它被瓦解成为是多边形的形状。换句话说,凭借将它带回它的基本的多边形。在此,这个基本的多边形是一个四边形。假如你们折叠这个四边形到它自己,你们将会获得一个管子,凭借连接这些边缘。假如你们将这些边缘形成向量,凭借同意:只有朝相同方向的这些向量,才能够互相聚集。一个向量的开始被运用到这点。在这点,另外一个向量终止。从那时开始,你们拥有所有的座标,用来定义圆环面的结构的座标。

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

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