"Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy."
Reasoning by analogy sounds dodgy to me.
Reasoning by analogy sounds dodgy to me.
I've always found that it's difficult to get a student to even venture a guess about the answer to a problem. If they do make a guess then they probably have a mental model about how the situation should work... and then teaching becomes easy: either their model is good or it needs tweaking.
You gotta have the confidence to be wrong.
But using an analogy to infer something that hasn't been observed? Unless the analogy is very close to the subject, it doesn't make much sense to me.
That said, I agree with you. IMO, systems that can't be factored into quantifiable components can't be modeled accurately -- i.e. analogies.
Like the field of economics, where too often, analogies that are based qualitatively on only one or two factors are often proposed as sufficient to explain the behavior of diverse international economies, IMO analogies have proven to be insufficient bases for larger theories.
Same goes for philosophy and science. Analogistic thinking too often leads down garden paths. Too untestable.
https://books.google.com/books?id=_zQsDwAAQBAJ&lpg=PT54&ots=...