Great essay! And clearly you put your elbow grease in to make it flow and feel right rhetorically. Mwah. That catalogue of hurdles was very well thought out.
I have one comment on the following:
“If it were, say, a millwright, he would have to learn enough about machines to go beyond the kinds that he had been taught to make through apprenticeship, and invent something entirely new. Where would this knowledge have come from?”
I was just listening to Esther Duflo talk about mathematics ability and difference between street kids who sell produce and students in school. The 10 year old math practitioner in the streets can solve very complex practical problems involving two divisions, an additions, and a subtraction quickly with a high degree of accuracy. But in the study which ratcheted up the abstraction layers of the question to the practitioners, they quickly fell off as the questions became more abstracted out (even when given monetary incentive to solve the problem!).
Similarly students in school weren’t able to climb down the ladder from abstraction to application. And when they tried, they needed pen and paper and took 10 minutes to figure it out.
This study once again indicates the difficulty of transfer. What is learned in one area only with conscious and deliberate practice can be applied to another.
But another more subtle takeaway is possible, namely that the vast majority of millwrights don’t engage in philosophical abstraction of the art of millwrighting, hunting for foundational and transferable principles to other fields. You present it as a ‘knowledge problem’. Perhaps we can get even more precise. It’s that millwrights don’t teach their apprentices general principles, because they themselves never did formulate explicit general principles about machines. Until there are general principles, there are few inventors. It’s a science problem. Technique without science is sterile.
The Hamming Principle: Archimedes requires Euclids, not Euclids Archimedes.
Great essay! And clearly you put your elbow grease in to make it flow and feel right rhetorically. Mwah. That catalogue of hurdles was very well thought out.
I have one comment on the following:
“If it were, say, a millwright, he would have to learn enough about machines to go beyond the kinds that he had been taught to make through apprenticeship, and invent something entirely new. Where would this knowledge have come from?”
I was just listening to Esther Duflo talk about mathematics ability and difference between street kids who sell produce and students in school. The 10 year old math practitioner in the streets can solve very complex practical problems involving two divisions, an additions, and a subtraction quickly with a high degree of accuracy. But in the study which ratcheted up the abstraction layers of the question to the practitioners, they quickly fell off as the questions became more abstracted out (even when given monetary incentive to solve the problem!).
Similarly students in school weren’t able to climb down the ladder from abstraction to application. And when they tried, they needed pen and paper and took 10 minutes to figure it out.
This study once again indicates the difficulty of transfer. What is learned in one area only with conscious and deliberate practice can be applied to another.
But another more subtle takeaway is possible, namely that the vast majority of millwrights don’t engage in philosophical abstraction of the art of millwrighting, hunting for foundational and transferable principles to other fields. You present it as a ‘knowledge problem’. Perhaps we can get even more precise. It’s that millwrights don’t teach their apprentices general principles, because they themselves never did formulate explicit general principles about machines. Until there are general principles, there are few inventors. It’s a science problem. Technique without science is sterile.
The Hamming Principle: Archimedes requires Euclids, not Euclids Archimedes.