you addressed the classic example of non-Euclidean geometry paving the way for general relativity by saying that Einstein could have just invented non-Euclidean geometry on his own (!) when he needed it.
My claim was that Einstein explicitly considered gravity as curvature of space before being aware of any formal developments in non-Euclidean geometry. I inferred that, if Einstein had lived before any formal developments in non-Euclidean geometry occurred, then non-Euclidean geometry would have become an object of study not because it was interesting but because it was important. If you really want to have this argument, then you should describe where you think things would have broken down if non-Euclidean geometry had not already been developed. Would general relativity never have occurred to Einstein? Would the community have scoffed at the idea more than they did? Would the theory have stagnated before the math could catch up?
But lets count this as a point for the home team. Lets suppose that general relativity had been set back a hundred years, and that we had never considered the possibility of gravitational time dilation until we discovered the empirical formula for the time dilation experienced by satellites. I agree that this is worse than what really happened, but its not bad enough to convince me that I should support work on interesting problems. I would be interested in additional examples, even if they were much less compelling.
You’ve characterized my position as motivated cognition in defense of the status quo, but in my view that is both wrong and unfair
I don’t really care whether your position is motivated cognition. I realized my own beliefs were motivated cognition, and now I would like to replace them with beliefs that better reflect reality.
you think you have a good way of predicting the long-term impact of mathematical work,
We are both trying to predict the long-term impact of human activities. You don’t get to abstain from having beliefs. My claim is that concretely motivated problems are a significantly better use of the smartest researchers’ time than interesting abstract problems; your claim is that they aren’t. I came to my belief by observing the historical record, noting that important advances have at least been proximately due to smart people working on concrete problems, and suspecting that the causal connections drawn to more abstract problems are highly tenuous. If you think this reasoning is the explanation for the rate of human progress prior to the 17th century, then you should say so and I can describe at length why I believe you are almost certainly wrong.
My claim was that Einstein explicitly considered gravity as curvature of space before being aware of any formal developments in non-Euclidean geometry. I inferred that, if Einstein had lived before any formal developments in non-Euclidean geometry occurred, then non-Euclidean geometry would have become an object of study not because it was interesting but because it was important. If you really want to have this argument, then you should describe where you think things would have broken down if non-Euclidean geometry had not already been developed. Would general relativity never have occurred to Einstein? Would the community have scoffed at the idea more than they did? Would the theory have stagnated before the math could catch up?
But lets count this as a point for the home team. Lets suppose that general relativity had been set back a hundred years, and that we had never considered the possibility of gravitational time dilation until we discovered the empirical formula for the time dilation experienced by satellites. I agree that this is worse than what really happened, but its not bad enough to convince me that I should support work on interesting problems. I would be interested in additional examples, even if they were much less compelling.
I don’t really care whether your position is motivated cognition. I realized my own beliefs were motivated cognition, and now I would like to replace them with beliefs that better reflect reality.
We are both trying to predict the long-term impact of human activities. You don’t get to abstain from having beliefs. My claim is that concretely motivated problems are a significantly better use of the smartest researchers’ time than interesting abstract problems; your claim is that they aren’t. I came to my belief by observing the historical record, noting that important advances have at least been proximately due to smart people working on concrete problems, and suspecting that the causal connections drawn to more abstract problems are highly tenuous. If you think this reasoning is the explanation for the rate of human progress prior to the 17th century, then you should say so and I can describe at length why I believe you are almost certainly wrong.