The Dichotomy Paradox

As promised this is the begining of the philosopical journey into some of the craziest parodoxes ever created.


To go anywhere, you must go halfway first, and then you must go half of the remaining distance,
and half of the remaining distance and so forth to infinity: Thus motion is impossible.

This paradox has been attributed to ancient Greek philosopher Zeno, and it was supposedly created as a proof that the universe is singular and that change, including motion, is impossible (as posited by Zeno’s teacher, Parmenides).

People have intuitively rejected this paradox for years. From a mathematical perspective, the solution, formalized in the 19th century, is to accept that 1/2+1/4+1/8+1/16 … adds up to 1. This is similar situation to saying that 0.999… = 1.

But this theoretical solution doesn’t actually answer how an object can reach its destination. The solution to that question is more complex and still murky, relying on 20th century theories about matter, time, and space not being infinitely divisible.


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