"Well, invent the principle then."

"There's at least two lessons here.  The first lesson is noticing that you have no idea why a set of rules has to be the way it is, and couldn't give a strong solid answer about what goes wrong, if somebody asks you, well, how about if the rules were different, how about if we break those rules?  It's closely related to the art of making sure that your beliefs mean anything.  The way of having math mean anything, if you are using that math for something and not just admiring it, is to say what ill fate would befall you if you used different math."

"And the second lesson is, Civilization didn't get to learn the principle that, yes, I haven't covered yet, by successfully noticing they didn't know it, and then sitting back in class waiting for a teacher or a god to tell them.  Having noticed the gap in their knowledge, they tried to fill it in.  You try.  Come up with some bad thing that happens to people who assign a 300/100 chance that something happens.  I'm not going to answer until I see somebody try, even if they fail, because I'd rather teach people to try and fail, then to teach them to wait for the teacher to answer."

"Well, invent the principle then."

"There's at least two lessons here.  The first lesson is noticing that you have no idea why a set of rules has to be the way it is, and couldn't give a strong solid answer about what goes wrong, if somebody asks you, well, how about if the rules were different, how about if we break those rules?  It's closely related to the art of making sure that your beliefs mean anything.  The way of having math mean anything, if you are using that math for something and not just admiring it, is to say what ill fate would befall you if you used different math."

"And the second lesson is, Civilization didn't get to learn the principle that, yes, I haven't covered yet, by successfully noticing they didn't know it, and then sitting back in class waiting for a teacher or a god to tell them.  The ancestors of Civilization noticed the gap in their knowledge, some people tried to fill it in, somebody eventually succeeded, and that's why Civilization now knows.  You try.  Come up with some bad thing that happens to people who assign a 300/100 chance that something happens.  I'm not going to answer until I see somebody try, even if they fail, because I'd rather teach people to try and fail, then to teach them to wait for the teacher to answer."

"Well, invent the principle then."

"There's at least two lessons here.  The first lesson is noticing when you have no explicit idea why a set of rules has to be the way it is, and couldn't give a strong solid answer about what goes wrong, if somebody asks you, well, how about if the rules were different, how about if we break those rules?  It's closely related to the art of making sure that your beliefs mean anything.  The way of having math mean anything, if you are using that math for something and not just admiring it, is to say what ill fate would befall you if you used different math."

"And the second lesson is, Civilization didn't get to learn the principle that, yes, I haven't covered yet, by successfully noticing they didn't know it, and then sitting back in class waiting for a teacher or a god to tell them.  The ancestors of Civilization noticed the gap in their knowledge, some people tried to fill it in, somebody eventually succeeded, and that's why Civilization now knows.  You try.  Come up with some bad thing that happens to people who assign a 300/100 chance that something happens.  I'm not going to answer until I see somebody try, even if they fail, because I'd rather teach people to try and fail, then to teach them to wait for the teacher to answer."