Zeno's presentation of this problem is limited to basic and intuitive geometry (the simplest of Euclidean geometry) and notions of physical materials derived from our daily life experiences.
If Zeno's paradox is to be taken as a problem of physics, then，
石凳說的衹是牛頓經典力學中的運動坐標問題: what is in motion in some reference frame (坐標)isn't necessarily so in some other reference frame.
In the Theory of Relativity, even the motion itself can not be uniquely defined because neither its temporal nor spatial factors can be uniquely defined. (Young Einstein's daydream of flying with a light beam). Neither the arrow itself can be uniquely defined due to the relativistic effect on the mass of the arrow. But still, each defined path in space-time (so called "worldline" 世界綫) is precise. It is just not unique.
In quantum mechanics, even the trajectory of the arrow in motion cannot be precisely defined due to restrictions by the so called wave function.
Therefore, as a problem of physics, Zeno's paradox is still unresolved and likely never will as seen below when treated as a problem of philosophy. And it is never truly purely a problem of mathematics. To be more specific, motion 運動 is not a problem of mathematics
Treated as a problem of philosophy, that is, assuming a world built of the simplest Euclidean geometry and physical materials consistent with the notions of which we derived from our daily life experiences as stated in the beginning of this post. Then I would provide the following response to Zeno: If the observation that the arrow holds still (stationary) in some position and in some instant during its flight is valid, then the same observation must be valid before the flight. Therefore the motion itself has nothing to do with this capability of being stationary in space in some instant. Hence it is something else that sets the arrow into motion. This very agency is the solution to this paradox. Of course, this response doesn't answer the fundamental question about what this agency is, but this is what should be expected in the first place: The original question is proposed in a world that is artificial and not real.
But all these do not take away the significance of zeno's paradox. The speculation itself is worthy.
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