Thursday, May 6, 2021

Aqualung's Paradox


Consider a hypothetical dart and target. The target is defined as a circle that encloses an infinite number of points. The dart is a line segment that pierces the circle at right angles at point P.


You pick point P to aim at and throw the dart at the target. What are your odds of hitting point P?

Point P exists as the intersection of a plane with no thickness and a line of no width. P is a single point out of an infinite number of points so the odds are:

1/ = 0

Surprisingly, you have no chance of ever hitting point P. This appears to be contradicted by the fact that the dart does, indeed, hit the target. This is what I call Aqualung's Paradox for historical reasons.

If we can add one to something, it makes it bigger. If we subtract one from something, it makes it smaller. A more flexible calculation of the odds might be:

1/( - 1) > 0

Thus, we end up with a result that is technically equal to zero, but not exactly equal to zero. Since the odds are not exactly zero, you might hit P on the very first try.

But I wouldn't bet on it.😉

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