Sometimes when you think really hard about something, you can reach a conclusion so contradictory to everyday experience, that it forces you to reexamine fundamental scientific and mathematical truths. That is exactly the predicament that Zeno of Elea, a Greek philosopher, reached almost two and a half thousand years ago. His famous Dichotomy paradox proposes that getting from point A to point B is impossible because it involves an infinite number of steps, which must take an infinite amount of time. As it turns out, the modern mathematics of calculus and infinite series is required to rigorously resolve this dilemma, but an intuitive explanation that captures the essence of the solution is possible. In his excellent animation, Colm Kelleher illustrates both the paradox and its resolution, and you don’t even need to know any calculus to understand the solution. This video is a good place to start when introducing the topic of infinite series and is also one more way to make a discussion of infinity more concrete.

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