Comment on Soup of Theseus
protist@mander.xyz 2 days ago
Given that the soup and rainwater would mix together, the question of how long it would take to get that last molecule of soup out is one of probability. I’m not qualified to give you a calculated answer, but I can tell you the most likely outcome is that it’s going to take a lot of spoonfuls. The soup will begin tasting watered down very quickly and will basically be a bowl of >95% water for a long time before you get those last molecules
TranquilTurbulence@lemmy.zip 2 days ago
If you ignore the fact that soup consists of discrete molecules, the answer is infinite.
In real life though, you have to get probabilities involved. Haven’t done the math yet, but I can already tell you that it’s going to take a very long time until you get to the 50/50 point of the last soup molecule being gone. Prepare for geologic time scales.
Sabin10@lemmy.world 2 days ago
Well 14 spoonfuls wouldn’t finish the soup even if it wasn’t raining so that’s definitely wrong.
TranquilTurbulence@lemmy.zip 2 days ago
Ok, Now I’ve got some sort of estimate. Still didn’t do it “the proper way”, because writing a simulation was more fun and reading a few Wikipedia articles about mathematics would have taken… probably only a fraction of the time I spent on writing some horrible R code that produces suspicious results.
Anyway, here they are!
My simulation is based on keeping track of different kinds of molecules. First, I calculated how many water and soup molecules there are. I assumed that they both have the same molar mass. I also assumed that 500 ml = 500 g, which is close enough IRL. The number of each molecule type doesn’t have to be a whole number, so fractions are allowed. When the soup molecule count drops to 0.5, it means that there’s a 50% chance of 1 soup molecule being present. I’m not entirely satisfied with this implementation, but it felt reasonable at the time. Anyway, I set the threshold of a while loop to 0.5 soup molecules.
It took only 1146 spoons to scoop out the final molecule with 50% certainty. If you used a smaller 5 ml spoon, it would take 5848 spoons, which is still way smaller than I expected. I really thought it would be something totally absurd like the the number of atoms in the observable universe. I feel kinda skeptical about my code until I see a proper mathematical proof about this.
AwesomeLowlander@sh.itjust.works 2 days ago
Close enough, somebody mathed it out to 1144 in the comments