Despite categorizing many of my posts as ‘educational content,’ I rarely set out to teach you something in a rigorous fashion; instead, I am usually attempting to explicate a specific concept or idea, without providing full context or progressing through an entire topic. It is therefore a different mindset, with a different decision space. When I was putting together a presentation about astronautics, intended as an introduction and overview approachable to anyone, I found myself confronting the question, not of what to include, but of what to exclude.
An article I read recently describes the staggering complexity of the proton, a particle that most people, if they think about it at all, likely consider to be a featureless sphere of uniform, positive charge. That is even how we treated it in our own post on nuclear physics, and for certain applications that is all you need to know about it. Except that the proton is not a uniform sphere of positive charge at all. It is a collection of three quarks, two with a charge of positive two thirds, and one with a charge of negative one third. No, it is a collection of quarks and gluons bonded together by the strong force. No, it is a cloud of quantum probabilities that includes up quarks, down quarks, charm quarks, and gluons that exist only transiently at high momentum collision points and have more mass than the proton itself.
Not all of these revelations about the proton’s complexity are recent – the first experiments that proved the proton is composed of smaller components occurred in the 1960s – so did your physics teacher lie to you? Is it a lie to say that the Earth is a sphere, when it is actually bulges at the center, no, it’s shaped like a pear, no, it’s a complex and rugged shape that only can be considered uniform at far remove? These questions are central to the educational quandary with which this post is concerned. With any topic, there is always another layer of nuance to peel back and thereby gain a deeper understanding, but unless you’re going to dedicate your life to the topic, at some point you have no choice but to stop peeling back layers and accept your present understanding as sufficient.
When pursuing autodidactism, that choice is yours, so long as you are able to find the resources to continue your explorations, but when you are attempting to educate someone else, deciding what layer is sufficient is your responsibility. You must decide how much detail to present, and where you make that choice will completely alter the nature and quality of the lesson you are attempting to convey. In my younger days, I naively would argue that to provide anything less than the maximum level of detail was lying, either directly or by omission. Indeed, I found a particular snippet from Neil DeGrasse Tyson about this very concept rather insulting, insinuating as it did that certain audiences would not be able to grasp the full complexity of a given topic. Now, I have come to recognize that it is not a judgement of capacity, but of time and interest.
Audience, therefore, becomes dominantly important in constructing a lesson. Say, like the example that helped to prompt this post, that you are crafting a lesson on astronautics. Knowing your audience will drastically impact how you format such a brief and what information you decide to present and emphasize. If I’m constructing a lesson for an audience of engineers, it will contain very different emphases from the lesson I would present to an audience of operators, which would again be different from an audience of writers, which is even a different presentation from what I would give to an audience of curious laypeople, and that’s an entirely different animal from what I might tell relatives who are feigning interest in my eccentricities.
To be more specific, let’s examine some of the headline changes that I will make for each of these audiences. Subtler, stylistic considerations, and differences in what I say and emphasize during the presentation are harder to capture, but, for instance, the presentation for engineers will include equations and diagrams that I would not bother showing to an audience of science fiction writers. In the reverse, I would dwell much more on theoretical and hypothetical technologies and capabilities with the science fiction writers than I would with the engineers or the operators.
Is it lying to do this? Is it a lie of omission to not tell every audience that I encounter how to derive the classic orbital elements from first principles, use differential equations to account for orbital perturbations, and that everything I’m teaching them is really just an approximation that is vastly surpassed in accuracy and precision by numerical methods, Kalman filter estimates, and applications of general relativity? It might be, but if it is, it is a necessary one. It comes down ultimately to opportunity cost. If I were teaching high schoolers about the proton, I could spend the entire year teaching them every nuance of its complexity, how it behaves on the quantum level, what probability collapse means, what all of the different types of quarks are, how all of the experiments are conducts that have taught us what we know about it, and the finer details of quantum chromodynamics, and by the end of the year those students would be able to speak on the proton on a caliber with professional quantum physicists. We would also have covered nothing at all about gravity, buoyancy, Newton’s Laws, or thousands of other topics.
There is no good, simple answer, and it is this that makes teaching such a challenge. I still maintain a skepticism of the kind of simplifications that Tyson advocates. Saying that the Earth is a uniform sphere is a precise application of verbiage that is blatantly wrong, and it would not add too much complexity to the discussion to admit the nuance of the Earth’s oblateness, the greater accumulation of mass in the northern hemisphere, and the irregularities of the surface. What makes the difference between an educational omission and a lie is how you frame your assertions. Saying that the proton is a uniform, positively charged sphere is a lie, because it’s not, but saying that the proton is a complex particle that can be thought of as a uniform, positively charged sphere is an educational omission. The words we use matter, especially when it comes to the ones we don’t use.