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Fuzzy Math: The Wine-Dark Seas

A simple math problem has a surprising answer.

By Alex Stone
Jun 25, 2006 5:00 AMNov 12, 2019 5:10 AM


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Take a magnum of wine and dump it in the ocean, wait until it has mixed completely with the waters around the world, then refill the bottle. What is the chance that the bottle now contains one of the original wine molecules? Answer: The odds are 100 percent. This surprising answer is the result of a simple consequence of statistics. The odds of randomly picking a wine molecule from the ocean is tiny—about 10^-21—because the volume of the bottle is so small relative to the volume of the ocean. But the bottle holds 10^25 molecules, which means you get 10^25 "tries" to nab one molecule of wine. After that many attempts, the highly improbable becomes destiny. By the same logic, every breath you take contains air molecules you have breathed before—guaranteed.

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