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"Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy." Reasoning by anal

by 99_00 6y ago

"Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy." Reasoning by analogy sounds dodgy to me.

dls2016 6y ago
Dodgy how? 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.
- 99_00 6y ago
  Using analogy to teach people something new makes sense and it's done all the time with positive effect. 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.
conistonwater 6y ago
I read the book and it's pretty solid, you can read more about how he introduces reasoning by analogy in the book itself.
henron 6y ago
Often people find it easier to reason about real life situations than equivalent formal abstractions. This passage from a novel I read recently demonstrated this principle well. No idea if the statistics are correct, but for me at least the first formulation required some reasoning and the second was immediately obvious. https://books.google.com/books?id=_zQsDwAAQBAJ&lpg=PT54&ots=-BxTWmpzSI&pg=PT53#v=onepage&f=false https://books.google.com/books?id=_zQsDwAAQBAJ&lpg=PT54&ots=...
randcraw 6y ago
Reasoning by analogy is akin to modeling. A model is presumed to capture a sufficient number of principal components that by permuting those, you can usefully predict the behavior of the target system. 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.

by 99_00 6y ago

"Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy." Reasoning by analogy sounds dodgy to me.

dls2016 6y ago

Dodgy how? 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.

99_00 6y ago
Using analogy to teach people something new makes sense and it's done all the time with positive effect. 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.

conistonwater 6y ago

I read the book and it's pretty solid, you can read more about how he introduces reasoning by analogy in the book itself.

henron 6y ago

Often people find it easier to reason about real life situations than equivalent formal abstractions. This passage from a novel I read recently demonstrated this principle well. No idea if the statistics are correct, but for me at least the first formulation required some reasoning and the second was immediately obvious. https://books.google.com/books?id=_zQsDwAAQBAJ&lpg=PT54&ots=-BxTWmpzSI&pg=PT53#v=onepage&f=false https://books.google.com/books?id=_zQsDwAAQBAJ&lpg=PT54&ots=...

randcraw 6y ago

Reasoning by analogy is akin to modeling. A model is presumed to capture a sufficient number of principal components that by permuting those, you can usefully predict the behavior of the target system. 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.