While I was in the shower, I thought of a brilliant idea! Let’s trigger several smaller volcanic eruptions that release a semi-controlled amount of volcanic ash into other atmosphere. That will cool down the atmosphere, which should buy us some time to fix our carbon emissions.
Then I realized, that doing so would block visible light. Plants need the light to grow, and we need the plants to breathe and eat. Obviously, this is not going to be a long term solution. Oh, and how do you even make sure the volcanic eruption doesn’t spiral out of control and suddenly spew out 50 times the ash we were aiming for. Oh, and volcanoes also spew CO2 and even nastier gases, so… It sounded so good while I was still in the shower. The more I think about it, the worse it gets.
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.