They said they ate 8 times and got diarrhea 8 times, the only way to be sure it’s one of them is to eat at least once without those ingredients and not get diarrhea
They said they got diarrhea 8 times over 8 bowls, but they never said how many ingredients they used. (Edit: Fuck)
Assume nine ingredients exist: a, b, c, d, e, f, g, h, i
Bowl 1: a + b + c + d + e + f + g + h + i: Diarrhea
Bowl 2: a: No diarrhea
Bowl 3: b: No diarrhea
Bowl 4: c: No diarrhea
Bowl 5: d: No diarrhea
Bowl 6: e: No diarrhea
Bowl 7: f: No diarrhea
Bowl 8: g: No diarrhea
Bowl 9: The one the OP is referring to “tomorrow”, which could have h, i, or h + i
That’s a perfectly feasible if disgusting way to have a bowl from a poke truck if you’re doing it solely for an experiment. And that’s just one setup; there are more convoluted ones you could do that have fewer ingredients but mixed together so your bowls aren’t just one combination. I just chose the counterexample that’s easiest to construct mathematically and which logically uses the fewest steps to eliminate each ingredient.
Edit: Wait, sorry, I misconstructed this because I misread it even while quoting it. Fuck, if they got diarrhea each time, then yeah, they’ve properly eliminated nothing.
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.
They said they ate 8 times and got diarrhea 8 times, the only way to be sure it’s one of them is to eat at least once without those ingredients and not get diarrhea
They said they got diarrhea 8 times over 8 bowls, but they never said how many ingredients they used.(Edit: Fuck)Assume nine ingredients exist: a, b, c, d, e, f, g, h, i
That’s a perfectly feasible if disgusting way to have a bowl from a poke truck if you’re doing it solely for an experiment. And that’s just one setup; there are more convoluted ones you could do that have fewer ingredients but mixed together so your bowls aren’t just one combination. I just chose the counterexample that’s easiest to construct mathematically and which logically uses the fewest steps to eliminate each ingredient.
Edit: Wait, sorry, I misconstructed this because I misread it even while quoting it. Fuck, if they got diarrhea each time, then yeah, they’ve properly eliminated nothing.
Yeah that’s what I meant, 100% diarrhea means they eliminated nothing. Sorry I should have phrased that better.
I take exception to this phrasing, whenever i have 100% diarrhea I eliminate the the contents of my guts and a half roll of toilet paper at least.
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.