CONFERENCEAgustín García Calvo

[La Casa Encendida, Madrid, September 1st, 2007]

Either line or dotby Agustín García Calvo

[extract]

As a kind of language trying to deal with ideal entities with certain purity, Geometry cannot help being invaded by the notion of what EXISTS, like God; the notion that he is what he is and at the same time, that he exists. This is the most usual way in which deception creates reality: through theology, physics or geometry.

At first sight it seems that we're gathered here to discuss things, but...

...a dot, for instance, ISN'T properly a thing. And what I am telling you here must serve us not only to clarify the notion of what "dot" means, but also of what "thing" means, the latter trying to encompass all things in reality. Dot is not a thing; in that sense, it doesn't pertain to reality. It is inexistent, it is ideal (nowhere in the realms of reality will you ever find a pure dot), and I should also add that it is a geometrical entity. But at this point we must be cautious because, as we have seen, geometry is already taking a step into reality.

Apparently, there ARE dots; any Euclidean geometry rests on the fact that there are dots. And not only there are dots, but each of these dots are particular, each is the one it is. You can name them A, B, C...

A name, like a person's or a place's name in reality, ascribes -on the one hand- to the entity (in this case, to a particular dot) and at the same time, it determines that this entity is being made, produced, taught in certain context (like this blackboard, this room, this particular occasion where I am talking to you, because otherwise, the dots wouldn't be worthy of a name).

Ok. Thus, geometry is already taking a step into reality. And see how:

It could have been sufficient that we have identified the dots with a name, but now it is almost inevitable the following:

The fact that A and C are different entails that they are distant. And this step is huge, because distance (even though Euclidean geometry has adopted it as something you can work with) is something completely real.

Difference has become distance.

This is expressed in abstract terms, but very simply. The fact that there are various dots (A, B and C) required that these dots, in order to be diverse, must be separated by some distance susceptible to measurement one way or another. You surely remember from school that this was the same method that traditional geometry uses to determine a "straight line": the shortest distance. And this implies the inclusion of a quantification, quantity in geometry. "The shortest distance between two dots".But naturally, you can already see the catch in this, because we'd be admitting that the dots EXIST, and that we can derive all other entities from them. But as I showed you before, the dot DOES NOT EXIST, in the sense that it cannot appear anywhere or anywhen in reality. It is completely alien to things, IT IS NOT a thing.

The expression THERE ARE belongs to common language. "There are things, there are people"... but EXISTS is a term imposed from above; imposed by the schools to create that trap invented for God: a way to COMPATIBILIZAR the fact that THERE IS a God and that he EXISTS. We all fall into this trap.

To fight against this, 30 years ago I proposed in my book "On numbers" a way to rethink geometry which wouldn't imply a quantification, which wouldn't be derived from such immediate realization as the one we've just seen. At school, on the contrary, it was taught that this entity...

... (which, of course, does not exist, I could only paint it there by cheating, same as the dots), was supposed to be a representation of perseverance, of fidelity. In this sense, I would say that the STRAIGHT LINE is the idea of all ideas.This, as you can see, makes us step into reality in a different way as the dots do, because "perseverance", "the idea's fidelity to itself” implies an attempt at dominating the real time. “Perseverance”, “fidelity” is through time. And time is, indeed, a condition of reality.As I said, through this different path, a straight line is also taking us into the realm of reality. A line that has no beginning or end, of course, because I haven't drawn any dot there. This line doesn't need to have any dots because we started from it as the primordial thing. It is the continuous permanence, the continuous fidelity, the perseverance. And this would be the first appearance of a eometrical entity. Unreal, of course, as in actuality there are no straight lines.

The non-existence of straight lines in reality is different to the non-existence of dots. In actuality there are no straight lines, there are only curves; any attempt at representing something perfectly rectilinear will automatically put it out of reality. And in this sense, "straight line" belongs to those IDEALS that rule reality -as we'll soon see- even though they don't exist. The world, all things, we ourselves are constantly accosted by ideals of this kind.

In actuality there is no such thing as a body at rest. It is purely ideal, as reality is subject to movement and change. But in practice and for physics sake, it is necessary to start from there to explain the laws of inertia and movement: "body at rest".

The same way, neither is there any uniform rectilinear motion in reality. But we equally need to coin this notion to try to explain the deviations and approximations with respect to that notion.

Reality is inexact in essence. It is inexact, it is approximative and actually, the use of numbers to explain reality had to end up in probabilistic calculations. This is a way to admit the triumph of probabilistics and chance factors, though most of the time scientists don't see it as such.

Well, in the school game I mentioned earlier, it was assumed that THERE ARE many straight lines, not just one.

Straight lines coming from any point in the world and, for example, intersecting like this [as the lines are infinite, they would have to intersect at certain point]. They are diverse and their diversity is very different to the one we have seen before: it is a difference of angulations, of directions. This is also a way to step into the realm of reality, but not through the notion of distance.In this game, the dot emerged at the inevitable intersection between the lines. We had to represent the dot right there. It is quite ridiculous that, in order to draw a dot, what teachers often did was:

Trying to draw a dot is extremely difficult, and that is why it was represented like the intersection between two straight lines.

Ok, these are some school games I wanted to introduce here to start uncovering reality's deception. Naturally, we will have to talk about our reality, about the ways of reality which are closer to us: the horrors of power, of politics, of submission.

In the first place, FAITH. The need to believe that our own death has a meaning. All this is part of reality, all this is part of the deception.

But it is convenient to keep in mind that this deceptive set-up is already uncovered in the logic of physics.

Physics must always propose an explanation, so if Epicurean atoms, electrodes or photons are used to express reality, it is thanks to the fact that they themselves have become real, and therefore, are now completely useless. They cannot explain reality because they are already within the realm of reality, just like the dreams, the expectations -more or less fantastic-, the utopias, etc. We can only fight reality by saying "NO" to it. That's it, by uncovering its deception, like I'm doing here with you.

One of us is never completely who he is, but he exists. And to exist he must be suffused by this ideal: that he is what he is, that he is who he is, like the dots I named A, B and C earlier: "John Doe". It is a lie. Anyone who's capable of listening to his own heart knows that it is a lie. That we are not what we are, we don't know who we are. But the need to believe that we do is truly compelling, overwhelming. And that is what makes us collaborate submissively with all other forms reality, like the States, money and such; their case is the same: they aren't true, but they have to exist. And they must change to survive.

We humans are constituted by our own deaths. Our death is never here; it doesn't exist, it isn't part of reality, but it can certainly rule all which is here, all we could call "life" and such, the passing of things.

Naturally, “punto y raya” [dot and line] cannot be taken in the sense that the first can be the second and the second, the first; but that one comes AFTER the other, there's no other way. Like in the Morse alphabet, for instance. The conjunction Y [AND] doesn't imply in this case that the dot is a line AND the line is a dot and therefore, the engendered creature is at the same time dot AND line. You can follow that idea easily, using mere common sense. This AND, on the contrary, is a sequential AND. It means that first there's the dot AND THEN, the line; first there's a line AND THEN a dot. You can now understand why I proposed a closed disjunctive with my title EITHER LINE OR DOT, placing myself in another logical moment where it is necessary to enquire about the being: either it is a dot or it is a line. A thing like this, for instance... what is it? Is it a dot or a line? Either it is a line or a dot, but it cannot be both at the same time. And heretofore, the conjunction OR doesn't refer to the temporal sequence but to the mere logical opposition, which also means an ontological perspective: one's need to be who he is.

The case of a person's death -always in the future- is evidently a case of a DOT. And his life, a case of a LINE.

The dots and the lines do not exist, but they rule existence. They are ideal entities, like "body at rest", "uniform rectilinear motion", "everything", "nothing"... All these are ideals: they don't exist, but they rule reality.