Comments on “Fake insights”

I am just wondering, why choose to specifically call ‘fake’ insight for lack of understanding a problem as a whole. You can call it something else right?

My thought on reading this is that good therapy teaches you to generate insights yourself (small or large). Methods I have found useful include Focusing (a la Gendlin), dream analysis, and holotropic breathing. Beginning therapy, or therapy that keeps you hooked on doing if forever, is therapy in which you get insights, but only with the help of the therapist; you never learn methods to get them outside of therapy on your own. Maybe a good way to figure out whether your therapy is “good” or not.

Avinash, I like the name “fake insight”. It seems like it’s going to be a (broad and useful) insight, and poses as one or is offered as if it is one; but upon deeper reflection it is not.

This reminds me of numerous math and physics exercises I did as an undergraduate. It was quite rare to have any genuine ambiguity in the weekly exercises. While such exercises can help in learning the basic subject matter, they do not teach some of the essential research skills. I mean, in a real physics study you have to try out different things and look at the question from different angles, and perhaps something works out - or it does not. For example, there is no known generalized analytical solution to Navier-Stokes equation of fluid dynamics, but you have the deal with that beast anyway.

An exercise idea:

Instead of having to solve a pre-determined problem, one could give instructions for the student to “play” with a set of physical equations. Put stuff in and see what happens, like trying different boundary and initial conditions or approximation. However, instead of asking a specific pre-determined answer, give the student a task of considering the implications of the assumptions. Do they make sense? Why or why not?

It seems like a reasonable pedagogical technique to present a student with toy problems that have simple canned solutions. But you are right, too often everybody involved forgets that that is what is going on, and the toy problems displace the real subject.

In retrospect, now that you’ve raised this distinction, I can classify most of the teachers I’ve had as mediocre (focused on the toys) vs good (aware that the toys are just a bridge to something deeper and more important and difficult).

Sure, toy problems are mandatory to have with math/physics education - especially when basic concepts require learning. The idea I presented above would technically work best with people at master’s studies level where there is some sense of the basics.

You have to first love the nabla operator; before you can make love with it.

This seems like one specific way that insights can be ‘fake’, but even if it is a common one, surely there are others. For instance, some people feel like things are insightful due to particular mental states, but when they try to explain the insight, or review it when they are more sober, it doesn’t work out. So I do not want to use the general term ‘fake insight’ for this specific thing.

I have long thought that this would be the right way to teach differential equations (and physics). It seems like an excitingly powerful idea. However, I gather that many people have tried it, and results appear to have been disappointing, unfortunately. I’m not sure what to make of that. Maybe their implementations were lame. I remain enthusiastic about the possibility!

This might be just a matter university education being often very fragmentary, so ideas and know-how in that regard do not transfer well. Most of the university teachers are not education specialists, and in my experience just repeat a safe, common approach. Almost nobody reads about any new findings in teaching methodology etc. I am not personally free of this either (though I never been in a position design my own course), though I am an unusual case of having received at least a bit of pedagogical learning intended for university teachers. Most do not bother.

I am not sure how well the idea I stated have been tried somewhere else, but I know that “problem-based learning” is a thing nowadays, and the idea of playing with equations is aligned with that sort of approach. It is also based on my personal experience of having a weirdly working brain, where the most conventional approach is not the best, and how I actually learned to work with i.e. mathematical descriptions of turbulence (after of course covering the basics otherwise).

(Also, I am curious about a sort of Dzogchen Long-dé approach to mathematics/physics, but that is bit too cryptical stuff to be explained here.)