According to Leucippus some of the atoms darting about in the universe collide and thus give rise to new substances. He also believed that the atoms followed whirling or circular paths and that such rotary motions drew in neighboring atoms, and that as these movements continued indefinitely within the atoms the constituents were being constantly rearranged, the lighter elements being grouped around the periphery; the heavier ones around the center. These changes were due to pressure and impact. These conceptions about atoms were carried into cosmological discussions and it was taught that there are various worlds and planets within the boundless universe, each one moving freely according to physical laws, unless fractured by collision with another.
Zeno challenged these doctrines because of the importance attached to the whirling motion. He attempted to show that such atomic motions are impossible. His proofs of the impossibility of atomic motion were designed with the object of sustaining his own theory of an ultimate principle of unity. His mental trend was toward negation. Whenever his rival Parmenides argued affirmatively regarding a scientific principle, Zeno would invariably maintain the negative side of the question.
Zeno's first proof of the impossibility of motion referred to the impossibility of passing through a fixed space. He showed that by dividing a line into an infinite number of parts an infinite number of points would be obtained and these permitted no beginning of motion.
His second proof tried to show the impossibility of passing through space having movable boundaries. The story of Achilles and the tortoise illustrates this. A pursuer in a race at every interval must reach a point from which the pursued starts simultaneously. But the latter is always in advance.
The third, or "resting arrow," argument showed that a moving arrow is at every instant in some one point of its track. Its movement at such instant is then equal to zero. Its track is a group of zeros. No magnitude could be framed from these.
Zeno also anticipated much later philosophical discussions, like Einstein's, relating to the relativity of motion. He took for an example a moving wagon. Its movement would appear different to observers on other moving bodies going in various directions. They would see changes in rates of speed as well as in direction.