this post was submitted on 17 Jul 2025
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When I was a kid I encountered this problem when I wondered what would happen if I half-empty a bottle of soda, re-fill it with water, and repeat. Will it eventually become just water or will there always be some soda left? It boggled my mind for a while, then I forgot about it until I reached university calculus haha
The answer is that eventually all trace of the soda would be gone because there are only a finite number of atoms of "soda-stuff" and eventually you'll end up with a situation where there's only one molecule left, which - assuming that wasn't the water part of soda in the first place - will have a 50% chance of being in the half that's removed before the next dilution step. Theoretically it could survive infinitely many rounds of this, but the chance of that is basically zero.
How many times is that though? For a litre of soda, the lower bound is about 85. A hundred ought to be more than enough. (And 300 times would be enough to dilute the entire observable universe assuming it was soluble in water, so that's a reasonable upper bound.)
You'd almost certainly stop tasting the soda quite a while before that though. After 20 dilutions you're into parts per million soda to water.
Things become more complicated if you replace the soda in this experiment with holy water. It seems to be agreed that 50/50 holy to regular water remains holy, but after that, some believe that dilution can be repeated forever (presumably being left to sit for a while after that step) while others claim the holiness disappears once the dilution goes beyond 51%, regardless.
It's easy to test for water holiness. If you drop the bottle and it bursts into flame molotov-cocktail style, it is still holy water.
Source : Belmont et al., Wallachia, 1986
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