[RossBencina]

Indeed everything has an opportunity cost, and every life has its own priorities.

Since you mention Feynman, I would like to observe that many expositors who target the lay audience have the skill of making the audience believe that they have comprehended(1) something of an intellectual world that they have no technical grounding to truly comprehend(2). In my view these are two distinct types of comprehension/understanding. So long as the audience is clear on which type of understanding they are getting, and is not wasting time unwittingly pursuing one type at the expense of the other then I see no harm.

There is a risk however, that the pop expositors will put you in a headspace where even if you are faced with accessible, but type 2, material you will not be familiar with what really constitutes understanding. As a mature age student it took me quite a few years of maths exams to switch from 1 to 2. Nowadays I am more comfortable with admitting that I don't understand some piece of math (for that is the first step on the path to learning) than being satisfied with a pop-expository gist.

[mlyle]

I've thought a lot about this exact topic. You need both to do well.

You need handwavy and vague versions of things to understand the shape of them and to build intuition.

Then you need to test the intuition and build up levels of rigor.

Especially in the context of the Kalman Filter. I just helped a bunch of middle school students build a system for field localization and position tracking. They don't have all kinds of knowledge. They don't have linear algebra or a real understanding of something being gaussian and have to have a bazillion variables. They understand that their estimates and the quality of stuff coming off their sensors have different qualities based on circumstances, and that gain needs to vary. They'll never hit the optimum parameters.

But: their system works. They understand how it works (even if they don't know how to quantify how well it works). They understand how changing parameters changes its behavior. When they learn tracking filters and control by root locus and all kinds of things later, they'll have an edge in understanding what things mean and how it actually works. I expect their intuition will give them an easier time in tackling harder problems.

Conversely, I've encountered a bunch of students who know what "multimodal" means but couldn't name a single example in the real world of such a thing. I would argue that they don't even know what they're talking about, even if they can calculate a mixture coefficient under ideal conditions.