Algodoo

Zeno of Elea, a Greek philosopher from the 5th century BCE, formulated several paradoxes concerning the physics of motion and the concept of infinity. In one of those paradoxes, he claimed that any object in motion cannot reach its destination because before it can reach its destination it must travel to the halfway point. After it reached the first halfway point it then must travel to the next halfway point of the remaining distance.... and so on forever, never actually reaching its destination! The motion of the rabbit shown in the scene is just one example of this paradox. The number units shown along the horizontal (X) axis can be meters, feet, miles, or any other unit of distance. After you run the simulation, click the "Click to Move Rabbit" button and watch the rabbit run halfway to the number 4 unit at the end of the track. Then you must click that button each time to tell the rabbit to run another halfway point.... again, and again and again. Eventually, after you reach some value such as 3.999999 the next click will allow the rabbit to reach the 4 unit. That's because of the fact that the math calculations in Algodoo have limited precision. If you had a calculator that has infinite precision (physically impossible), then the rabbit will never reach the 4 unit! Well, to prevent that from happening, we smart humans have invented a math concept (used mainly with Calculus) known as "limits" which allows us to get very close to the result of a calculation that, without it would cause an infinite series of calculations which would never end! That is the basis of Zeno's argument that an object can never reach its destination because it must move an infinite number of halfway points which, if truly were possible, would take more time than the lifetime of our universe!


Update: Adjusted size of thumbnail image.