Seminar XXIV Final Sessions 1 - Lacan in Ireland

namely, that everything that concerns the Borromean knot is only articulated bybeing toric.A torus is characterised quite specifically as being one hole. What is annoying, isthat this hole is difficult to define. The fact is that the knot of the hole with itsflattening out is essential, it is the only principle of their counting – and that thereis only one way, up to the present, in mathematics, of counting the holes: it is bygoing through, namely, by taking a path such that the holes are counted. This iswhat is called the fundamental group. This indeed is why mathematics does notfully master what is at stake.How many holes are there in a Borromean knot? This indeed is what isproblematic since, as you see, flattened out, there are four of them [Fig. V-6].There are four of them, namely, that there are not fewer than in the tetrahedronwhich has four faces in each of the faces of which one can make a hole. Exceptfor the fact that one can make two holes, even three, even four, by making a holein each of these faces and that, in this case, each face being combined with all theothers and even repassing through itself, it is hard to see how to count thesepaths which would be constitutive of what is called the fundamental group. Weare therefore reduced to the constancy of each of these holes which, by this veryfact, vanishes in a quite tangible way, since a hole is no great thing.How then distinguish what makes a hole and what does not make a hole?Perhaps the quatresse can help us to grasp it.What is involved in this quatresse is something which solidarises what is found,that by which it happens that I qualified three circles, namely, that, as you see53