Eight Lessons on Infinity by Haim Shapira

Author:Haim Shapira
Language: eng
Format: epub
Publisher: Watkins Media

We subtract the first equation from the second, and get:

Hence,

½ S = 1 and S = 2.

In other words, it will take precisely two minutes to travel infinite half points to get from A to B.

Frankly, this solution is not so surprising. We began by assuming that it takes one minute to get from A to C, which is exactly half the distance, and therefore one cannot be surprised that the entire distance will take two minutes.

Zeno would most certainly have objected vociferously to this solution, because we assumed what needed to be proven. When we said, “If we assume that it takes a minute to get from A to C”, we assumed that motion is possible and that we can get from A to C. However, that assumption is what needs to be proven, and this leads to what is called a circular proof.

Zeno would have probably clarified his standing by saying something similar to this: “How and on what grounds do you assume that you can get from point A to point C? It is totally obvious to me that you are making a monumental error. It’s as clear as the sun on a summer day on a beautiful Greek island, that before arriving at point C from point A, one must travel half that distance and reach point X. He then must travel another half of the remaining distance to C to reach point Y, and so on and so forth. You certainly realize that it is impossible to pass infinite halfway points in finite time. Therefore it is impossible to get from point A to point C, which is in contradiction of what you just said. I trust that you understand that it is also impossible to get from A to X, because here, too one must pass half the distance, and blah, blah, blah. The truth is that it is impossible to get from any point to any other point. In other words, it is impossible to even begin any sort of motion whatsoever.”

It seems that Zeno has won the day. Doesn’t it?

What do you think?

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