Comment on Soup of Theseus

• TranquilTurbulence@lemmy.zip ⁨1⁩ ⁨week⁩ 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.

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  • AwesomeLowlander@sh.itjust.works ⁨1⁩ ⁨week⁩ ago

    Close enough, somebody mathed it out to 1144 in the comments

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