When Greek Athenians mastered the social, political challenge of moving from a subsistence based farming economy to an economy based on exports, a political economy that mastered the challenge of colonial maritime trade, Athenians experienced a level of leisure, excellence and achievement whose impact is still felt today.
The Greek maritime colony in Sicily is where the great predecessors of Plato and Aristotle lived, they were thinkers who established schools of thought that demonstrated profound complexity, especially mathematically. It was in the realm of philosophical rationalism that a man named Zeno (of Elea, because people's last names where assigned to them after great achievements which usually took the name of one's home city).
Zeno's paradox is a conception, a pure idea of infinity that cannot be empirically reconciled. It is thought divorced from the created order, it is numerical denotation to infinity. For Zeno and his followers applying it empirically demonstrates an unsolvable realm, a paradox. Let's examine it. Keep in mind that Zeno and his followers thought of dividing every conceivable number, measurement or digit by half, effectively demonstrating that space and its numerical equivalent are infinite.
Zeno's paradox is explained as involving a fast runner and slow tortoise (turtle), if you place the tortoise ahead at the runner, the runner cannot ever catch up because the runner continually needs to reach half the remaining distance infinitely.
For modern people space, time and measurement are discrete and definite so we don't experience Zeno's paradox. Non-Eucledian mathematics, especially prime numbers (a methodical approach of mathematical thought similar to Zeno's school) is applied by government agencies today as encryption.
Although Aristotle and his followers conceived of applied mathematics empirically, his predecessor Zeno applied mathematics as a 'thought experiment', of mathematical ideas, relations, angles conceived in thought without experiment. Zeno's school of thought provided ample cover for numerous philosophies in Athens, especially cynicism and Epicureanism.