The infinity of Asterion — Part IV
In this fourth part of the work dedicated to the story "The house of Asterion" by Jorge Luis Borges, the spatial aspect of it is analyzed in detail. The way in which the space is treated by the narrator will be analyzed in detail, as we will see vital importance for its interpretation.
THE INFINITE HOUSE AND THE INFINITE UNIVERSE
The treatment that is made of the space is the key of the story. The importance of the house that houses the protagonist is evident from the title itself: "The House of Asterion". We see that the title is a nominal construction in which house is the nucleus and Asterion appears as an indirect modifier. That is to say that guided by the title would be in the house and not in Asterión where we should pay more attention. And, in fact, it can be seen in the text how Asterion is defining himself according to his house.
Recurrent references to the house
He begins his monologue defending himself against the accusations of arrogance, misanthropy and madness that he says fall on him and for this he refers to his house: "It is true that I do not leave my house, but it is also true that its doors (whose numbers are infinite) are open day and night to men and to animals as well. Anyone may enter. He will find here no female pomp nor gallant court formality, but he will find quiet and solitude. And he will also find a house like no other on the face of this earth. " It is worth noting that at no time is the word labyrinth used to describe the place inhabited by Asterion; even, after mentioning that "there is not a single piece of furniture in the house", he contradicts those who say that he is a prisoner: "Another ridiculous falsehood has it that I, Asterion, am a prisoner. Shall I repeat that there are no locked doors, shall I add that there are no locks?"
The house is present in each part of Asterion's monologue, with the exception of the second paragraph in which it seems to forget about it in order to talk about its relationship with language and knowledge. But in the next three paragraphs, which complete the five of which his parliament is composed, the house is once again the center of his musings.
In the third he relates the games he imagines to distract his solitude, all games in which the house appears in the foreground: "I run through the stone galleries until I fall dizzy to the floor", " I crouch in the shadow of a pool or around a corner and pretend I am being followed"," There are roofs from which I let myself fall until I am bloody"," of all the games, I prefer the one about the other Asterion. I pretend that he comes to visit me and that I show him my house".
The fourth paragraph is devoted frankly to the house, in which Asterion transmits his reflections about it: "... I have also meditated on the house". Finally, in the fifth paragraph (last of the monologue), Asterion reveals that every nine years nine men enter who he kills; also here the references to the house are significant: " I hear their steps or their voices in the depths of the stone galleries…", "They remain where they fell and their bodies help distinguish one gallery from another"; and, when he thinks of the redeemer that one of those men killed by him prophesied, he says: " I hope he will take me to a place with fewer galleries fewer doors".
The infinite house
That is to say that the house is always present as the center of a narrative that goes around it. But how is that house? We are told that it is as unique as its inhabitant: "a house like no other on the face of the earth." It is now necessary to ask ourselves what makes it unique.
As we noted above, throughout the story it is not indicated that it is a labyrinth, this we can recognize from the perspective of the myth, but not from that of Asterion. It is not the intricacy of the corridors that Asterion highlights when he meditates on the house, but its infinity: "... I have also meditated on the house. All parts of the house are repeated many times, any place is another place. There is no one pool, courtyard, drinking trough, manger; the mangers, drinking troughs, courtyards pools are fourteen (infinite) in number ".
Note that the text does not simply say of each part of the house that they are infinite, but first it is mentioned that the parts are fourteen and then put in a relationship of equality to this number with infinity. We must go to the beginning of the story to see that the first time reference is made to the house is indicated: "its doors (whose numbers are infinite) ..." and, with a footnote that refers to the infinite term, clarifies: " The original says fourteen, but there is ample reason to infer that, as used by Asterion, this numeral stands for infinite."
In this paratextual clarification, which may seem somewhat ironic, perhaps is implicit that controversy between nominalists and realists about the two kinds of infinities: the potential and the actual, to which we refer in the second part of this paper. The fourteen, like every finite number, is presented to us without discussion as actual; which, as we saw, is not so simple for the case of infinity. But we are told that fourteen for Asterion is infinity; in this way the reader is made to vacillate between the clear and total notion he has of the finite number and the idea of the infinity, whose complete vision is not possible.
This proposed equivalence can be explained in two different ways depending on whether one wants to think about it from the side of nominalism, which rejects the actual infinity, or from the side of realism, which accepts it.
From the nominalist point of view, it will be said that for Asterion the fourteen is as for us an unimaginably large number, as for example a Googol (a one followed by a hundred zeros) to which, although we can always add one more, we can find as unattainable as infinity. Consider, for example, the amount of grains of sand on a beach or the number of stars that populate the universe; that although we know that it is a finite quantity, given its immensity it can be understood that the effect it produces on us is the same as that which causes us the infinity (whether he is in front of an infinite or in front of a finite but unattainable number, the nominalist will say, Asterion will also feel his loneliness).
Defending the realist position, on the other hand, we can say that equivalence is given because the infinity is as actual, as real, as a finite number. So, as we understand it, the controversy is raised, but in principle it is not resolved.
An infinity inside another
A complete analysis of this aspect of the story can not ignore that in the monologue of Asterion a beyond the house is mentioned. Asterion tells that he has crossed the limits of the house; This is mentioned in the first paragraph: " … one afternoon I did step into the street" and repeated in the fourth: "… by dint of exhausting the courtyards with pools and dusty gray stone galleries I have reached the streetand seen the temple of the Axes and the sea". The existence of something outside the house for Asterion is incomprehensible until it is also revealed infinitely: " I did not understand this until a night vision revealed to me that the seas and temples are also fourteen (infinite) in number".
That is to say that the infinite house is contained in turn in an infinite universe. This idea of an infinite within another seems to refer us to the set theory that we mentioned in the introduction. And if we look at this other enigmatic phrase that Asterion says shortly before: "The house is the same size as the world; or rather it is the world", we see there raised the paradox of Galileo, according to which according to which when we speak of infinities the part can be equal to the whole.
Loneliness
Everything is infinite times for Asterion, everything except him and the sun. As Marta Gallo explains, in the story two spatial planes are presented: the horizontal in which everything is repeated infinitely, both in the house and in the world outside it; and the vertical, in which only two things are found that are only once: " above, the intricate sun; below Asterion". And Marta Gallo goes further and suggests the possibility that Asterion and the sun are really one:
But «Asterion» is also the name, or one of the names (because language also speculates), of the sun. Who then is the true Asterion? Or is Asterion not once, and below, as Asterion-me says, but twice, "above" and "below"? Or just "above", and then "below" is not Asterion? Who is, what is, then, Asterion-me? Perhaps, I suggest, an image (speculate?) of the true Asterion-sun.[13]
When these two individualities (which could now be understood as one) appear immersed in the infinity of the horizontal plane, the solitude in which they find themselves is highlighted and, likewise, they stand out as what remains unchanged through time.
[13] Marta Gallo, “Asterión, o el divino Narciso”, Revista iberoamericana, 687.