Zeno and The Paradoxes of Motion. And why there's no such thing as movement.
Having sourced a picture of Zeno, which like all ancient Greeks mug shots is actually a bust that looks like every other bust of an ancient Greek (i.e. a bit like Charlton Heston in The Ten Commandments), I decided on a bow and arrow motif instead. For reasons that will become obvious, if they aren't already. Oh, and while this might be setting off all sorts of alarms in you along the lines of boring dissection of classical philosophy, it's heading somewhere very different.
Bear with me.
Zeno was said to subscribe to the philosophy of Parmenides. Parmendies is only known through one work (and bits of it are lost), which is mostly a poem, but then that was often the style employed even for works of science, in those days. For example Lucretius' On The Nature of the Universe is also largely poetry. In this scientistic age that relegates it to the realm of utter fiction, idiots that we are.
Parmenides was very big on oneness, he claimed that reality was always just one, unchanging, timeless thing. So that all change, including movement, is an illusion. Appearances are therefore basically false, and what is true is unchanging and timeless. If you have even the most rudimentary knowledge of philosophy it won't be an enormous surprise that Plato channelled all of this into his timeless forms, in the allegory of shadows on the walls of the cave representing reality outside the entrance. But really all philosophy revolves around this question of the nature of change and eternity, and in many ways philosophy and science today still gather around the same campfires as the old Greeks.
Zeno's paradoxes relating to movement are said to have been written to support Parmenides' philosophy. And they made a lot more inroads into popular consciousness than Parmenides ever did, so the moral is always dress it all up in a nice story (or undress it, for even better results). One of the paradoxes talks of an arrow never reaching its target, because (taken from Aristotle's Physics):
If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.
In other words, how can the arrow move if it always needs to be occupying some given space? Or maybe said in a clearer way, if at any given point in time the arrow is at point A, then during that moment it can only be at A, but it must also be on its way to the next point B. It can't be both of those things at once i.e. not moving and moving. So movement is an illusion.
[You can look at this same paradox in another way, with time itself. If time passes, and common sense says that it does, then each moment must be both 'now' AND on its way to the next moment. But how can it be both now and somehow not-now, on its way to somewhere else? Where does the 'passing' bit actually happen?]
Historically such paradoxes are nearly always answered using some sort of calculus i.e. using infinitesimals. Interestingly we think infinitesimal calculations only really started in a useful way with Leibniz and Newton, but Archimedes for example had already started the ball rolling. (Truly one of the greatest geniuses.) But the mathematical solutions don't always look at the basic assumptions behind what we mean by movement and rest, and space and time. Philosophers do that sort of thing, which is one reason the image philosophy took on as pointless abstract speculation is so ridiculous - philosophy does practical things, it solves practical problems. But maybe another day.
Let's fast-track this into the here and now and everyday life. Having been a keen self-taught student of various approaches of 'bodywork' in the past few years, mostly derived from The Alexander Technique, it's been a total revelation to discover that 'effort' i.e. that physical feeling of exertion we feel when we do things, is absolutely unnecessary. It's not what we think it is - effort is the feeling we have when we work against ourselves. So if you go to lift something, and it feels effortful, that feeling is some part or parts of you pulling against other parts of you, it has absolutely not one thing to do with the 'weight' of what you're lifting. Or if you strain to heave yourself out of a chair, or to hold a good posture when sitting, again that effort has nothing to do with you working against gravity, it's all the wasted energy of you straining with parts of you against other parts of you (gravity doesn't act 'down' as is popularly believed, it's a mutual force between two bodies - the force of you on the ground is exactly matched by the force of the ground up on you. So you should feel entirely weightless and effortless, and you will if you ever learn how to stop straining bits of you with other bits of you).
But again that's another topic.
You can move beyond even all of that work and think of it purely in terms of time and space and oneness i.e. like Zeno. If I'm standing or sitting here and want to 'move' over there, then normally we would take the me here and strain or use effort in some way to move there. But say you think of this like Zeno (for very different reasons mind you - overall I think Zeno proved something different to what he thought he did, of which more in a second), then at each moment and at each point in space between you here and you there, you just are at some point in space and time. At no point do you actually need to make an effort to get beyond where you are, you just are all the way from here to there. So you need absolutely no effort because effort is trying to get ahead of where you already are. Strain and effort are all about basically ignoring all of the spaces and moments between where you are and where you want to be.
Try it, try adding life back to all of those moments we usually rush away from, thinking of them as deadwood on the way to where we're going. Even if you're sitting still, don't leave the moment you're in to try to get to another moment or space, such as a more comfortable posture. Just let yourself be where you are in space and time, at each moment. All the strain and tension will disappear, because that strain is always about one thing only, namely trying to be in the next space or moment while you're still in the space and moment you're currently in. Watch how sublime, almost transcendental effortlessness enters your life.
What I think Zeno showed with his paradox isn't that the world of change and movement is illusory and debased from its pure, timeless form. Movement is not what we think it is, but it does exist. But it's not what we usually think of, as some separate body moving through or 'in' space and time. Space and time are not containers things sit inside. They're names given to relationships between things. When I get up to make a cup of tea, it's a whole series of events, with rising from the chair one event, moving through the room while hearing the TV another, arriving in the kitchen another, putting the jug on another, etc. It's a hopeless abstraction to reduce all of that to "me getting up and making a cup of tea", but you can try to live that abstraction, and that's when you'll feel strain. At each moment and at each point of space, we live a full event - reality and life are whole or full at each moment. My going to make a cup of tea is a series of unfolding events, each full and rich and whole, that I can choose to live or to ignore (why the Zen tea ceremonies make such a fuss about even the most basic activities).
And when you examine space and time as terms describing relationships between entities, rather than as containers, you notice that they define each other. They're not even separate things. Space gives the measure for time, and vice versa. So the notion of 'far away' for example expresses not just a distance but a time - the object is far away 'in space', and it would take a longer time for you to get there than for something that is 'closer'. It's one and the same relationship looked at from two different perspectives. Our usual mistake of saying something is in time and in space is exactly the same as if we described a person as 'in married'. It's mistaking a relationship for a thing.