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#5596·Dennis HackethalOP, 3 days agoOk so let’s put ourselves in the shoes of someone who genuinely thinks different decimal numbers lead to different variants for both competing explanations, and that, as a result, there are infinitely many variants for each. Walk me through how that person would use your program?
In short, the question is: how can we use the program when we genuinely think both explanations have infinitely many variants?
Okay, so you're thinking of an edge case where two competing explanations genuinely both have infinitely many working variations.
For example, one explanation says some amount X of grass cures the disease, another says some amount Y of wheat cures it, and neither explanation constrains what X or Y should be. Both can just keep being varied indefinitely.
If that's the kind of case you have in mind, then yes, I agree it's an interesting edge case. If these were the only two competing explanations, my current program would have an awkward time representing the fact that both have infinitely many variations. But also, in this example they're genuinely both extremely easy to vary, so ranking them equally doesn't seem obviously wrong to me.
I don't think we need to get into comparing different sizes of infinity here. If a third explanation had only a finite number of working variations, it would clearly be harder to vary than either of the infinite ones.
As for the implementation, one simple extension would be to let the user indicate that a submitted variation represents an infinite family of working variations, rather than requiring them to enumerate individual examples. Something like a checkbox for "this can be varied indefinitely." That would let the program represent this edge case without changing the basic idea.