The Strip of Möbius
Requiéscat In Pace[1]
Beginning with the classic definitions of the geometry,
we obtain: first, the point. Which lacks dimension; it is a dimensionless;
second, the line. Element that possesses one dimension; third, the surface.
Which is constituted, in turn, for two dimensions; fourth, the volume. That it
implies three dimensions.
Among the above elements, the definition of point,
line and surface –be about Euclidean or not Euclidean geometries - it doesn't
change. We can deny the fifth postulate of Euclides
and to build new spaces, hyperbolic or elliptic, but they are not deniable the
primitive geometric concepts of point, straight line and surface.
An imaginary error that is usually made would be to
argue in the following way: 1) that if I displace a point I obtain a line.
False, a point cannot move because it is dimensionless; 2) that if I displace a
line I obtain a surface. False, the line lacks thickness and of wide… anything.
That is to say that is not valid to displace something definable as a geometric
line. We would rot yes to transfer, to make run, a line -because has thickness-
toward some of their lateral borders. To enlarge a line is possible, to port or
starboard. Then, I reiterate, it could never get wider something that lacks
that dimension that we understand as the width. 3) In the third place - and
lastly - to affirm that transferring in the space - Euclidean or not - a
surface, a volume is obtained, it is the height of the illusory thing. False,
false and false; three times reinforcement. For what we already exposed
regarding the point, the line and the surface: a surface, let us reiterate it
has two and only two dimensions. How could it move and to add something lacking
of thickness? It’s impossible.
With these basic considerations we pass to the matter,
regarding which we seek to not point out an error noticed so far. Not noticed,
not only for the psychoanalysts followers of the teachings of Lacan but inclusive for the mathematicians.
"Band of Möbius."
Nominative, possessor itself of a charm. It summarizes rich associations
referred to the world of the paradoxes. Let’s remember that Möbius,
who first described it, but he wasn't the only. It was
a certain Johann Benedict Listing that in 1847 published "Vorstudien zur Topologie." In 1858, independently of Möbius, he discovers the properties of the band.
A strip of Möbius-Listing
we can build it in this way: we start with of a surface, rectangular, with four
corners that we choose to designate A, B, C, D
STOP HERE
Congruent to the surface definition, the "step" of
the figure 1 to the figure 2, shows sample flat and flatly, something that,
without inhibitions, we should understand as a fizzle. According
with Mr. Descartes, neither God could turn round a surface!
Reiterating it: the figures 1 and 2 show that way
falls in the trap of a false premise: pass from the figure 1 -right- to the
figure 2 -wrong- that graph the effectuation of a turn of 180° to a rectangle!
Pretending with this torsion in a rectangle, to arrive to the "other face
of the surface!"
In the way of a synthesis of all that has been written
so far by the mathematicians, that they have not noted this gross error, we
will get some expressions of someone mathematical -which we respect -, Rey Pastor: band of Möbius which
is obtained by linking the opposite faces (of the rectangle) after rotating one
of them investing their faces”.
It
is hard to believe in -denying? - (be
worth the redundancy) such a denying: to say "faces" when it has only
one. To seek to "give turn." when we know that the surface doesn't
possess more than two dimensions.
If a surface has another
side or another face, it would
not
be a surface but a volume, that we know as a:
Parallelepiped
Honestly, to make a
torsion in a parallelepiped and later to hit the ends doesn't have anything of
incredible, neither paradoxical. Except when it is operated in no-Euclidean
spaces. Not we will develop the geometric properties here of the one mentioned object
but, speaking of sides, it has the trifle of possessing six, and not two that
would be made one. The borders, better, it would be necessary to count them,
but they never decrease at two that would be made one in the supposed band of Möbius.
Galileo Galilei said that the truths are easy to understand once
discovered and that in science questions, the authority of thousand is not
worth the humble reasoning of one. One that is not without the others
(exception of psychosis) Peirce said in 1905: "I
call not science to the solitary studies of an isolated man. Only when a group
of men, more or less in intercommunication, they are helped and each other are
stimulated when understanding a group peculiar of studies like no stranger
could.
Cristoforo Colombo discovered that
we could arrive to the east going toward the west. Previous him they existed
important mathematicals and geometricians. He reach,
without knowing it, a new continent,
We say that
sun rises or goes down. That the things fall, error sensed for Galileo and
interpreted by Albert Einstein, whom developing their theory of the relativity,
where he demonstrates that the things don't fall. In a same way "Other
face of a surface" is said only for our erroneous perception, it happens
that we not utter the statement we "give turn over a surface" because
it’s impossible. The space it is not something that pre-existing that you full
with things, but rather is the surface that create it.
We
know that there isn't metalanguage, significant isn't
meant itself and there isn't sexual relationship. In that analysis Gödel, Peirce and Frege attend us, among
others. To look for something whole and perfect it is a condition that
renounces of the castration (Freud dixit) It is like
to think in a surface with two faces: an impermissible operation.
Lacan outlines the cut of the strip to speak of the subject
and of the same band. Good intuition, as
long as this court undoes it. It undoes it because it
is an ERROR; as it was the idea of a flat and not
spherical Earth and, in the same way, the "all
the roads lead to
the above thing regarding Lacan when cutting the band.
To cut the band? –as Like Lacan said- or rather, to cut with the band? With this
synthetic sentence - to deploy - we make allusion to another way of thinking
the concept of narcissism.
The lacanian notion of court
in a surface is a gross error: first, because it cannot intersect something
that doesn't have body; second, because the same surface is the cut: there is
not court of the cut like there is not castration of the castration, neither
another of the Other one. The castration of the castration would be equivalent
to annul it like in the perversions.
The censor cuts the movie
or film that it is a parallelepiped and don't unite surface, the one which, in
this example it would correspond to the projection: we call it
"movie" to indicate something very thin, but a surface is not a
movie, rather it would be like a shade: we can see it in a screen but it is
impossible to cut it. Who would be happened to cut a shade? They can only
intersect dimension objects three, that is to say bodies.
I not seek to invalidate
the topology, or the utility that can have in psychoanalysis. But alert about
the fascinating consequence of the foolish, sedative story, of the "small
ant that travels without knowing that it strolls for a stranger space"
Dr. Carlos Norberto
Mugrabi