Recognizing, knowing, understanding.

The future needs people who really understand technical material, but I fear what now passes for technical education (including self-education) lacks depth.

Reusing my example of the Heisenberg (physics, not cristal meth) joke, namely,

Police officer: "Sir, do you realize you were going 67.58 MPH?
Werner Heisenberg: "Oh great. Now I'm lost."

there's a number of levels at which we can understand it.

At the recognition level, Alex associates "Heisenberg" with "science reference" and decides to laugh to appear educated. I find that most people who "love" science are like Alex. I also find people like this in my field of work, effectively LARPing at being experts.

At the knowing level, Blake has some idea that Heisenberg said that you can't measure speed and position together with arbitrary precision. Blake also knows that Heisenberg was talking about electrons or other particles, so applying his "rule" to a car must be hilarious.

At the understanding level, Chris can do what I did and spoil a joke by making calculations. From the linked post:

A simplified form of Heisenberg's inequality, good enough for our purposes, is 

$\qquad \Delta p \, \Delta x \ge h $ 

Going by orders of magnitude alone, assuming that the mass of Heisenberg plus car is in the order of 1000 kg, and noting that the speed is given to a precision of 0.01 mi/h, an order of magnitude of 10 m/s, with $h \approx 10^{-34}$ Js, we get a $\Delta x$ of the order of 

$\qquad \Delta x  \approx \frac{ 10^{-34} }{10 000} = 10^{-38}$ m.

There are degrees of understanding, from the ability to make use of the uncertainty principle, as above, to deeper understanding of what that means for what the universe is like. But at the most basic level of understanding, you should be able to operationalize knowledge into decision, calculation, program, etc.




I think that there's some merit in trying to improve from recognition to knowledge and from knowledge to understanting. So here are a couple of observations on that:

Recognition to knowledge

The main problem in most cases, as I see it, is not of ability or opportunity but rather of motivation: if Alex gets social cachet for "loving" science just by recognizing a "science situation," why put in the effort to learn some science (or other technical material)?

There's a trap, however, for people who decide that they want knowledge: because of the identity problem in science popularization, most of the more popular sources are designed for recognition only, not understanding.

I find that books, lectures, etc. from active researchers or practitioners in the technical field (say Leonard Susskind instead of Neil deGrasse Tyson) generally mean better chance of knowledge rather than recognition. Even when non-researchers and non-practitioners are better at showmanship (mistaken for communication skils), it's worth a little effort to get real knowledge from those who understand it and don't treat their readers or audiences as an echo chamber.

(As for television shows, except for a few that are based on books by active researchers, they are to be avoided: they are not reliable sources, not even for the recognition level.)

Knowledge to understanding

Problem sets. That's the solution.

Well, to be precise, the step from basic knowledge to understanding has two parts: first, learn the concepts, principles, and tools of the field; second, practice them with incrementally difficult problems.

For the Heisenberg example, some of the elements needed for understanding are:

Concepts: speed, mass, momentum;
Principles: uncertainty principle;
Tools: order-of-magnitude reasoning.

My rule-of-thumb for learning technical material is $1\%$ from being a passive member of an audience (to a lecture or a video) or a passive reader (reading but not thinking); $9\%$ from actively studying the material (say, working through solved problems, making sure you understand all the steps in an example); and $90\%$ is practicing, in the lingo of academe solving problem sets.

It then becomes a matter of how much practice and how much effort you're willing to put in: at this level, the difference between amateurs and professionals is that amateurs practice something until they get it right, professionals practice until they can't get it wrong.

Understanding something is so much better than just knowing it, and knowing it so much better than just recognizing it. It worth the effort and the change in attitude required. At least for me it is.