Geometry

I’m walking and I’m thinking about Zeno, who lived two and a half thousand years ago, the Greek Zeno, who said motion is impossible, because to get anywhere you have to get somewhere else first, because if you set out to walk a mile, before you can walk a mile you have to walk a half a mile, but before you can walk a half a mile you have to walk a quarter of a mile, and before that an eighth, and before that a sixteenth, and so on to infinity, so you can never go anywhere because there is always somewhere else you have to go first, and I’m walking and I’m wondering what Zeno meant by this, whether he really believed movement is impossible and if he did believe this what he thought was happening when he sat down at table and dipped his spoon in his soup, and I don’t know because Zeno comes from an archaic time from which little has survived, so little is known of his work, so when we say his work we mean a few broken fragments embedded in the writings of others, like a beautiful statue which has fallen over and broken into pieces, and over the years all the pieces have been robbed to make the walls of other people’s houses, and one sees a few of the bits, a hand in a wall, isolated and in the wrong context, but one no longer understands the statue, so that we don’t know what Zeno was, our modern terms don’t fit, scientist, philosopher, intellectual, none of these existed then in the way we understand them now, so I think I don’t know what Zeno wanted to achieve with this and his other paradoxes, because seemingly he wrote about forty of them, and I know there are different ways to understand them and maybe all these ways are wrong, for example in modern times his arguments are commonly understood as part of an investigation into the form and possibility of reason, as if he were an academic in the philosophy department of a university, and perhaps it truly was something like this, even though there were no universities and no academics and nothing called philosophy in Zeno’s day, or then again perhaps he was playing, showing off even, duelling with other street teachers like in chess one grand master competes in a public tournament against another, or perhaps these dazzling and abrasive paradoxes were an advertisement, intended to capture attention, convince of his brilliance, and drive students to his teaching practice, if he had one, or then again maybe Zeno was a kind of Zen figure, perhaps he should be Zen-o, I laugh, and his paradoxes should affect me like Zen koans are meant to, like the sound of one hand clapping or the thought of your face before your parents were born, and it works like this, that when Zeno slaps you round the chops with a paradox he wants to stop you reasoning and he wants you to enter a kind of meditative state in which the distinctions reason tries to draw, like wanting there to be a beginning a middle and an end of a movement, dissolve into an inarticulable whole, inarticulable materially because the movement can’t be physically taken to bits and put back together, but verbally inarticulable too because the movement can’t be explained in words that make sense, and then I wonder about words and about thinking and how unsafe they seem when I think about Zeno, how unmoored from anything that could cleave right from wrong, and I think of the great Aristotle who, even he, could not disprove Zeno with logic but only in actu, only with experience, meaning that whatever Zeno’s logic might insist on I know movement is real because here I am walking and thinking and these are movements, and yet and yet when I think about Zeno I can’t understand what walking and thinking even are or how they are possible and I see a crow coasting down towards the roof of a house, doing that backwards flap a bird does as it lands, then hopping up the roof, peering from side to side, and I think of its busy brain, its beating heart, its flowing blood, its inexorable metabolism, its ten-times-recycled body and all the crow is movement and so all of it is impossible, and I wonder if there might be such a thing as a logic of the impossible, not of things which are impossible in experience like being in two places at once, but of things like movement, and isn’t everything movement? which are impossible in logic and yet exist in experience, but now I’m shaking my head and thinking how trivial is Zeno’s piece of abstract reasoning when laid against the vastness of experience, against the spinning world and the rising sun, and why really should I waste any time on something so contrary to the plainest realities, but at the same time I’m paying attention to my walking, how I move my legs, putting one foot in front of the other, and I realise that what I experience is not movement as a plain fact but the elusiveness of movement, even though it’s my own movement, because I don’t experience the bit-by-bit putting together of the movement, because sure my leg moves ahead but however short a step I take what I experience is a complete movement, never the parts that make up the movement, and if I try to concentrate on the instant when my leg starts to move I can’t because whatever I fix on is always a little movement, never the beginning of a movement but always already a movement, because I think taking a step is not like making a flipbook, where you draw a discrete image of a person on successive pages one after another and when you flip through the book quickly the person seems to walk, but you can single out the first image on the first page and look just at that, I think, and I think no, instead moving is a mystery and the experience of moving is the experience of a mystery, and maybe that mystery I feel in my legs and the mystery my thinking finds in Zeno’s paradoxes are one and the same, I think, and I wonder again why Zeno made his paradoxes and that’s another mystery and the crow is gone from the roof and the roof and the house and the lane are quiet and there is no movement and I wonder if Zeno ever thought about stillness, and I stand I stand unmoving in the lane and just rest and breathe and I’m past the big houses now and opposite the gates to the mansion house and I shift my gaze to look across the low wall that runs along the side of the lane, and I look over the wall into the field by the road, and the field is empty, meaning there are no animals or birds in it, it’s just grass stretching to some woods at the back, and I think about the field of grass and the field of vision which for me here and now is the field of grass and my eyes run over the field like a hare I think, only even faster than a hare, and I make my eyes a hare and I see the hare run many different lines over the field, left, right, up, down, zig-zag, curve, and I don’t move my head as I do this or even my eyes much, I only move the focus of my eyes, so my field of vision is still the field of grass, it’s just that I’m bringing different parts of the field into focus as I shift my attention, and I think if Zeno had written about seeing he would have said seeing is as impossible as moving, because my eye moving over the field is just like the hare running over the field, and if one is impossible then so is the other, I think, and yet here I am seeing the field, and I open the five bar gate and walk into the field, and I stop and I stand looking over the field at the broad sweep of grass and I ask myself why I think so much about these things, about Zeno and movement, because why does it matter if I can’t grasp movement? so what if it’s a mystery? I lost a hat once, put it down in the house, turned round and it was gone, no-one else there, it’s a mystery what happened to it, but it doesn’t matter because it was just a hat, things don’t matter just because they’re a mystery, but a mystery at the heart of things, at the heart of everything that moves, and everything does move, so a mystery at the heart of everything, doesn’t that matter, a mystery at the heart of the world? and I go on looking over the field, I stand and I look for a long time, and I think about the line you walk along and how it’s a mystery because you make the line when you move, you build it up little by little, and yet there is no first part of the line and so no way for the movement to begin, no way for it to be built up, so although we say a line is made of points it really can’t be made of points because a point has no length and no number of points can give a line its length, and I look at the field and I think it’s the same for a plain, that although we like to say a plain is made of lines it can’t be made of lines because a line has no width and so no number of lines can give a plain its width, and I think of the field of grass and my field of vision which is the same as the field of grass, and I close my eyes and open them again and the field of grass appears all at once in an instant without my witnessing how it is constructed, it’s not there and then blam it’s there, like my hat was there and then it wasn’t, and I think again about the hat and how it must have gone somewhere, there must be an explanation for what happened to it, I think, so the hat is only a mystery because I don’t know what happened to it, but with movement the mystery is real, or let’s suppose it’s real, let’s suppose no amount of extra information or understanding could eliminate the mystery, suppose movement just is a mysterious thing, suppose movement is mysterious even for God who is supposed to know everything, and I should say I’m not a practising believer, and I don’t know what God is or if God even exists, but if God did exist and were revealed by anything then God would surely be revealed by a mystery at the heart of all things, and here we have a mystery at the heart of things, and I set the hare running again in my head, through and through the field, and the hare is trying to exhaust every path across the field, but it can’t run every path because the paths are endless, there are straight paths, zig-zag paths, curved paths, paths that almost reach the field edge only to bend back on themselves and go another way, paths that differ from another path by only a yard, or a foot, or an inch and I feel like I’m trying to conquer the field with my mind but I can’t, I feel like I’m trying to take possession of the field, and I can’t because the field is pushing back, frustrating me, so I let the hare run off into the wood …