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Philip Koop's avatar

There is a lot of question-begging going in all this analogizing to the technological advances of the past. Oh yes, to be sure *if* AI functioned as a nail gun does to a hammer, as a compiler does to an assembler, or as a calculator does to pencil and paper, then indeed the problem would be to master the new, higher level of abstraction. But in actuality, in order to integrate AI "similar to the way calculators have been integrated into math and science", we mainly have to account for the fact that the calculator gets a completely wrong answer about 15% of the time. The compensating skill to be developed would not be abstraction but rather estimation, being able to check whether the calculator's answer is in the right ballpark. But this is an advanced skill!

Once your students understand this point, will they really be so enthusiastic about AI? Will they be happy to leave the interesting bits to automation and take on the dull drudgery of copy-editing and correction themselves? It seems unlikely. I would remind you that you yourself, with your remarkably open and flexible mind, have publicly made several attempts to coax useful output from AI without any notable success so far.

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EMANUEL DERMAN's avatar

In terms of teaching, in fields where you have knowledge to transfer, one should put oneself imaginatively in the position of the student, understand where they are coming from, and then figure out how to analytically continue them from their state to the state of knowledge you'd like them to be in. This cannot be done by teaching axiomatically the first time around.

From Barenblatt's book on scaling:

"Of special importance is the following fact: the construction of models, like any genuine art, cannot be taught by reading books and/or journal articles (I assume that there could be exceptions, but they are not known to me). The reason is that in articles and especially in books the 'scaffolding' is removed, and the presentation of results is shown not in the way that they were actually obtained but in a different, perhaps more elegant way. Therefore it is very difficult, if not impossible, to understand the real 'strings of the work: how the author really came to certain results and how to learn to obtain results on your OWn."

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