Seno and the Bakery
The human mind, wherever it sits inside or outside the brain, is a remarkable piece of machinery. We use it constantly when awake, and subconsciously when dreaming. I find it remarkable that our mind can recognize a given dilemma or a predicament as extremely logical, but at the same time, it senses a disturbing unreasonableness about the problem and simply leaps beyond it.
An example of this unreasonable logic is the flight of Zeno’s arrow. Zeno (ca. 490 B.C. – ca. 430 B.C.) was an early Greek philosopher from a place called Elea. His paradoxes have puzzled and troubled and boggled the minds of both mathematicians and scientists for over 2000 years (Physics, Aristotle).
Applying Zeno’s reasoning about the arrow to a real life paradox, let’s suppose a man, Seno, wants to go to a bakery which is about one mile away. He decides to walk for the exercise. As he puts on his tennis shoes, in his mind Seno thinks, there will be a halfway point between his house and the bakery.
As he ties his shoes, Seno thinks, but there will be a halfway point between here and the half mile point. He starts for the front door and opens it. A frown crosses his face. Good grief, he thinks, there will be a halfway point between here and the quarter mile point! He appears befuddled.
With the front door open, Seno stands contemplating. There will be a halfway point between my front steps and the quarter mile point. Now his mind is reeling. There will be a halfway point between my steps and the one eighth mile point, too. Seno continues to obsess—faster and faster. There will always be another halfway point I have to reach before I get started: 1/16th, 1/32nd, 1/64th, 1/128th, 1/256th, ad infinitum.
Frustrated, Seno decides that since there are an infinite number of points he must cross before starting out for the bakery, it is impossible to get there; he will give up and stay home. Logic tells him he cannot cross an infinite number of points in finite time.
“Haven't you gone yet?” asks his wife coming to the door.
“No,” Seno answers. Before he can explain, his wife opens the door and walks toward the bakery in a huff.
As silly as it seems, this is a good example of the human mind’s ability to see something that appears in every way logical (to Seno) but is also recognized as unreasonable (to Seno’s wife). In philosophy courses, one typically hears about Zeno’s arrow that can never reach its target for the same reason Seno felt he could never reach the bakery.