Zeno (c. 495 BCE) was a Stoic philosopher best known for his nine surviving paradoxes.¹
The two most popular paradoxes are:
1 – Zeno asks how many grains of millet must fall before a sound is heard. One fallen grain makes no sound on impact, therefore it accounts for “nothing.” A second grain (a second “nothing”) might also make no sound. But suppose a third grain (a third “nothing”) is added to the two grains and this does make a sound. This would result in a “something” (audible sound) being made out of three “nothings.”
2 – The great runner Achilles can never catch a slower tortoise in a race if the tortoise begins ahead of Achilles. By the time Achilles reaches the tortoise’s starting point, the tortoise has moved to a new position. And by the time Achilles reaches the tortoise’s new position, the tortoise has moved on to another position. The distances between the two may become increasingly small but the tortoise always remains a fraction ahead of Achilles.
Philosophers still debate the import of the Achilles paradox but its solution might be simple. The problem seem to arise from Zeno’s use of logic divorced from actual observation.
The student of vectors will observe that a higher-velocity object gaining on and moving in the same direction as a lower-velocity object will at some point overtake the slower moving object. Not so complicated.
But Zeno imaginatively ‘stops motion’ to observe the competitors in a series of equally imaginative points to say that Achilles will never reach the tortoise’s position. And this act of imagination doesn’t correspond to what actually happens in observable reality.
Among other things, Zeno’s paradoxes illustrate how thinking about problems and their apparent solutions can be influenced, limited and distorted by our use of symbol systems like language, logic or mathematics—especially when divorced from empiricism.
Still, he remains significant in the history of ideas because he was thinking out of the box and imagining new scenarios. Sometimes this works well, as with Einstein. But the difference is that with Zeno, we find limited conceptualizations and a lack of empirical support for his ideas.
With the first paradox, for instance, we might say that a grain of millet makes no audible sound but, in actual fact, it does create a disturbance in the air (a wave pattern) when it hits the ground. Today, this could be measured, amplified, and thus demonstrated to actually make some sound. So it’s not a “nothing” as Zeno would have thought in the ancient world.
¹ Scholars actually debate just how many paradoxes Zeno authored. But for the sake of simplicity I’ll go along with the Wikipedia entry. http://en.wikipedia.org/wiki/Zeno%27s_paradoxes