Oh, no, you phrased it fine; I read 8 bowls and 8 bouts multiple times and somehow still misinterpreted the experiment. It was only after I wrote down and submitted an example setup that I snapped out of my own illiteracy. I realized every possible counterexample was assuming “no diarrhea” trials.
If we’re taking them at their word (and not the silly joke it is) technically they could have removed 7 ingredients so far, with only 2 left, while still having diarrhea each time. In that context, say next time they try the dish with only 1 ingredient and the don’t have diarrhea, then they have the likely suspect. They could then try the dish with every ingredient except the suspected allergen to confirm it
That’s the logic I was avoiding, because although it’s heuristically likely in real life that there’s only one culprit – and that you could get Bowl 9 with ingredients a, b, c, d, e, f, and g to show it’s definitely h or i if you don’t get sick – there’s also a chance you have diarrhea on that Bowl 9 and gain very little information. There’s no conclusiveness to the variable isolation, so it’s not sound from an information theoretic perspective.
Actually, if you assume a comically unlikely worst-case scenario where all of the ingredients cause diarrhea, that sort of recursive algorithm might be the most amount of diarrhea you can get while still gaining information on each bowl.
By neither, I meant the cause could be out of the scope of the variables being tested. Eg. It could be something the cook does, or a particular spice, or the subject may have an ongoing condition they’re unaware of, or be doing something before or after lunch which causes it.
Oh, no, you phrased it fine; I read 8 bowls and 8 bouts multiple times and somehow still misinterpreted the experiment. It was only after I wrote down and submitted an example setup that I snapped out of my own illiteracy. I realized every possible counterexample was assuming “no diarrhea” trials.
If we’re taking them at their word (and not the silly joke it is) technically they could have removed 7 ingredients so far, with only 2 left, while still having diarrhea each time. In that context, say next time they try the dish with only 1 ingredient and the don’t have diarrhea, then they have the likely suspect. They could then try the dish with every ingredient except the suspected allergen to confirm it
That’s the logic I was avoiding, because although it’s heuristically likely in real life that there’s only one culprit – and that you could get Bowl 9 with ingredients a, b, c, d, e, f, and g to show it’s definitely h or i if you don’t get sick – there’s also a chance you have diarrhea on that Bowl 9 and gain very little information. There’s no conclusiveness to the variable isolation, so it’s not sound from an information theoretic perspective.
Actually, if you assume a comically unlikely worst-case scenario where all of the ingredients cause diarrhea, that sort of recursive algorithm might be the most amount of diarrhea you can get while still gaining information on each bowl.
I love this thread
By neither, I meant the cause could be out of the scope of the variables being tested. Eg. It could be something the cook does, or a particular spice, or the subject may have an ongoing condition they’re unaware of, or be doing something before or after lunch which causes it.