Seminar XXIV Final Sessions 1 - Lacan in Ireland

proceeds also to what I would call a flattening out for this to be clear. Theflattening out which on this occasion is spherical is necessary for one to put one’sfinger on the fact, as I might say, that the crossovers in question, the tetrahedriccrossovers, are indeed of the same order, namely, that the tetrahedron which isunderneath, the third tetrahedron, passes underneath, and that the tetrahedronwhich is above, the third tetrahedron passes above. It is indeed because of thatthat we are still here dealing with the Borromean knot.What is annoying nevertheless, is that even in space, even starting from apresupposed spatial, we should also be constrained in this case here to support –since when all is said and done, it is we who support it – to support the flatteningout. Even starting from a spatial presupposition, we are forced to support thisflattening out, very precisely in the form of something which presents itself as asphere (Fig. V-5b). But what does that mean, if not, that even when wemanipulate space, we have never seen anything but surfaces, surfaces no doubtwhich are not banal surfaces because we articulate them as flattened out. Fromthat moment on, it is manifest on the balls that the fundamental plait, the onethat crisscrosses itself 12 times, it is manifest that this fundamental plait formspart of a torus. Exactly this torus that we can materialise by the following,namely, the twelve-fold plait, and that we can also moreover materialise in termsof the following namely, the six-fold plait [Fig. V-3 and Fig. V-4].In truth this function of torus is clearly manifest in the balls that I have just givenyou, because it is no less true that between the two little triangles, if we make – Iwould ask you to consider these balls – if we make a polar thread pass through,we will have exactly in the same way a torus; for it is enough to make one hole atthe level of these two little triangles to constitute at the same time a torus. Thisindeed is why the situation is homogenous, in the case of the Borromean knot, asI have drawn it here, is homogenous between the Borromean knot and thetetrahedron.There is therefore something which ensures that it is no less true for atetrahedron that the function of the torus governs here whatever is nodal in theBorromean knot. It is a fact, and it is a fact that has strictly never been glimpsed,52