I take the dog out in the morning, and he conscientiously pees on the four corners of a block: there you go, the birth of private property, and of the tool we use to measure it: geometry, the brute of sciences. Because he (you’ll excuse me the personification) loves a precise perimeter and the correct covering of all surfaces (and he carefully calculates the volume of urine he is to keep until the path is shielded). Just like me and you, creatures with an outer shell and a clear-cut perception of an inside and an outside, projecting it to everything around us, drawing borders around our small patches, and putting limits where there are none, and finally pissing onto them. It’s all a matter of stench and corporal fluids, and last but not least a war on all the other urine producers. That’s what rough geometry’s for: marking territories, showing our possessions, proving where is the beginning and the end of what belongs to us.
Daniela wishes to build a square fence with an area of 121 square yards. What is the perimeter of the fence, in yards?
Geometry’s also our way to lay a rational design upon the endless continuum offered to our senses – a journey is a segment, a dull, predictable chap is square, your friends are a circle, infinity is a lemniscate and unfaithfulness… well, unfaithfulness is a triangle. I like to imagine it as a right triangle, with its two catheti and hypotenuse. The catheti are concurring, one depends on the other, like the two legs of a body. They’d like to prevail in the eternal war for the hegemony on the hypotenuse. And yet, they stand opposite each other and can’t help keeping the other cathetus under close observation. For the minor cathetus, especially, the perspective on the major cathetus is so predominant that it can’t help looking at it all the time. In this hypothetical human geometry, the catheti are the loving ones. In the same hypothetical structure, hypotenuses are the beloved ones.
But, in a retrospective, the real, geometrical problem here is and has always been my almost medieval conception of this sort of correspondence in things – and now that I can see things distinct from their geometries, I can also see that the hypotenuse is not mine alone and doesn’t answer to my directives. That it has self-governing movement, direction, feelings. That I have no right at that rancorous disappointment at every small shift in weight. Geometries change, they must change, and there’s no point in guarding them with your grandpa’s popgun.
“Comme jaloux, je souffre quatre fois : parce que je suis jaloux, parce que je me reproche de l’être, parce que je crains que ma jalousie ne blesse l’autre, parce que je me laisse asujettir à une banalité. Je souffre d’être exclu, d’être agressif, d’être fou, et d’être commun.”
Roland Barthes, Fragments d’un discours amoreux