I found this fun to read, even years later. There is one case where Rohin updated you to accept a conclusion, where I’m not sure I agree:
As long as there exists an exponentially large tree explaining the concept, debate should find a linear path through it.
I think here and elsewhere, there seems to be a bit of conflation between “debate”, “explanation”, and “concept”.
My impression is that debate relies on the assumption that there are exponentially large explanations for true statements. If I’m a debater, I can make such an explanation by saying “A and B”, where A and B each have a whole tree of depth minus 1 below them. Then the debate picks out a linear path through that tree since the other debater tries to refute either A or B, after which I can answer by expanding the explanation of the one of them under attack. I agree with that argument.
However, I think this essentially relies on all concepts that I use in my arguments to already be understood by the judge. If I say “A”, and the judge doesn’t even understand what A means, then we could be in trouble, the reason being that I’m not sure the concepts in A can necessarily be explained efficiently, and possibly the concept is necessary to be understood for appreciating refutations of arguments of the second debater. For example, mathematics is full of concepts like “schemes” that just inherently take a long time to explain when the prerequisite concepts are not yet understood.
My hope would be that such complex abstractions usually have “interfaces” that make it easy to work with them. I.e., maybe the concept is complex, but it’s not necessary to explain the entire concept to the judge—maybe it’s enough to say “This scheme has the following property: [...]”, and maybe the property can be appreciated without understanding what a scheme is.
I found this fun to read, even years later. There is one case where Rohin updated you to accept a conclusion, where I’m not sure I agree:
I think here and elsewhere, there seems to be a bit of conflation between “debate”, “explanation”, and “concept”.
My impression is that debate relies on the assumption that there are exponentially large explanations for true statements. If I’m a debater, I can make such an explanation by saying “A and B”, where A and B each have a whole tree of depth minus 1 below them. Then the debate picks out a linear path through that tree since the other debater tries to refute either A or B, after which I can answer by expanding the explanation of the one of them under attack. I agree with that argument.
However, I think this essentially relies on all concepts that I use in my arguments to already be understood by the judge. If I say “A”, and the judge doesn’t even understand what A means, then we could be in trouble, the reason being that I’m not sure the concepts in A can necessarily be explained efficiently, and possibly the concept is necessary to be understood for appreciating refutations of arguments of the second debater. For example, mathematics is full of concepts like “schemes” that just inherently take a long time to explain when the prerequisite concepts are not yet understood.
My hope would be that such complex abstractions usually have “interfaces” that make it easy to work with them. I.e., maybe the concept is complex, but it’s not necessary to explain the entire concept to the judge—maybe it’s enough to say “This scheme has the following property: [...]”, and maybe the property can be appreciated without understanding what a scheme is.