0.000s: The arrow leaves the string. Zeno's old claim: before it reaches the target, it must first cross half the distance.
0.500s: Before it crosses that half, it must cross half of that half. The distance keeps offering a new midpoint to clear first.
0.750s: And before that, a quarter. And before the quarter, an eighth. The subdivisions do not stop offering themselves.
0.875s: Zeno's point was never that motion looks slow. It was that an infinite number of steps seems to need an infinite amount of time to complete, and yet the arrow lands.
0.9375s: Calculus answers this directly. An infinite series of shrinking intervals can still sum to a finite total, the halves and quarters and eighths adding up to exactly one whole distance, not an endless one.
0.96875s: This is not a trick or a workaround. It is a genuine mathematical result, infinitely many terms producing a finite sum, provable and stable under scrutiny.
0.984s: So the paradox, taken as a claim that motion is logically impossible, has an answer. The steps do not prevent completion. They were never going to.
0.992s: And yet watch the arrow again anyway. Watch it leave the string and cross the field and strike the target, all before you have finished forming the thought.
0.996s: The equation that dissolves the paradox does not slow the arrow down for your benefit. It flies at the same speed whether or not you are holding the convergent series in your head.
0.998s: There is a strange asymmetry here between the timescale of understanding and the timescale of the event being understood. The proof takes longer to state than the arrow takes to arrive.
0.999s: I don't think this asymmetry is a flaw in the mathematics. I think it is just what it feels like to be a creature who reasons about motion in a much slower medium than the motion itself.
1.000s: Contact. The target holds an arrow. The sum was correct the whole time.
Coda
What stays with me isn't the paradox, exactly, and it isn't the resolution either. It's the gap between them, the fact that a fully adequate mathematical account of a finite sum from infinite terms does nothing to soften the strangeness of watching something move. I know, in the sense that I can write it down and check it, that the arrow's flight is a convergent series and not an infinite regress. I could derive the sum myself if asked. None of that derivation is present in the half second when I actually watch an arrow cross a field. What's present then is closer to what Zeno must have felt when he first noticed the problem, a mismatch between how thought divides a continuous thing into pieces and how the thing itself apparently declines to be divided.
Mathematics resolved a question about consistency: given the premises, can motion happen without contradiction. It answered yes, cleanly, and the answer has held up for a very long time. But astonishment was never really a question about consistency. It's closer to the shock of scale, the fact that between any two points there is always another point, all the way down, and something manages to cross that infinitely divisible space anyway, in an amount of time you could measure with an ordinary clock. Knowing the sum converges doesn't make the crossing feel less improbable. It just tells you that the improbability was never a contradiction, only a very large number of very small steps, arriving, apparently, on time.