Popularizing STEM? Bring the math!
Trying to get STEM popularizers to motivate their audiences towards a more operational understanding of the material, by using numbers.
STEM (Science, Technology, Engineering, and Math) popularizers are great! They are. This post is an exhortation for them to be even better, in a specific way.
STEM popularizers keep their audiences up-to-date with current developments in science; they explain the basics, which even those who have been educated in STEM may have already forgotten; they motivate the younglings to become scientists or, even better, engineers; they show everyone how science can be fun, useful, and though-provoking; and many of them do all this for little more than the pleasure of sharing their love of STEM and against a relentless torrent of nonsense.
These are all good things, so let’s make them better, by bringing the math!
Let’s get quantitative!
In STEM, numbers (quantitative thinking) are one of the main differences between someone having a descriptive level of knowledge (how things work, roughly; the two cases on the left below) and an operational level of knowledge (solving problems; the third case below).
For example, it’s good that we know, descriptively, that water is H2O, a molecule with two atoms of hydrogen combined with one atom of oxygen, and that if we burn hydrogen we get water; but if we level-up with numbers, we will be able to compute how much oxygen is needed to fully burn an amount of hydrogen (say one kilogram) into water.
(This “turning into water” part happens, for example, in rocket engines running on LOX-LH2, i.e. liquid oxygen and liquid hydrogen, and generally not precisely at the proportions that yield just water [vapor]: by having more hydrogen than needed, the engine efficiency in the use of mass for propulsion is a little better than with full combustion — look up “specific impulse” for more details.)
We get the answer by looking up the atomic masses in a periodic table (like this one on the interwebs): hydrogen 1, oxygen 16. H2O means that for each 2 atoms, i.e. 2 mass units, of hydrogen we need one atom, i.e. 16 mass units, of oxygen, i.e. the mass ratio of H to O is 1 to 8; so for 1 kg of hydrogen we need 8 kg of oxygen.1
The fancy name for this arithmetic is stoichiometry.
Another example, to solidify the difference: descriptively we know that — on Earth, but ignoring the atmosphere — a dropped object accelerates at a constant rate called “one gee,” and some of us even know that it's 9.8 “units.”
Operationally we can calculate how far an object falls in a time period T: it's one-half gee times T-squared. So in one second it's 4.9 m, two seconds 19.6 m, etc. We can do that, because if the acceleration is 9.8 meter per second-squared, then the velocity is 9.8 times T meter per second and the distance is 4.9 times T-squared meter.2
The causality explanation (discovered by Galileo but formalized with calculus by Newton) is as follows:
(Note that at T = 2 seconds both the speed and the distance are 19.6, but they’re not the same: the speed is 19.6 meter per second, the distance is 19.6 meter. The equal numbers are just a coincidence.)
The point here is that the use of numbers (and the ability to check their precise predictions against experimental results) is a jump in the quality of the audience’s understanding of the material in STEM.
Which is why it's so discouraging when otherwise excellent and generally well-liked STEM popularizers forgo using numbers, missing opportunities to nudge their audiences into a deeper understanding, or — much worse — get their numbers wrong.3
One recent missed opportunity
With the DART mission success on September 26, there were many videos, posts, and other forms of online celebration. Some of those made reference to the [excruciatingly bad, scientifically speaking, but highly entertaining and well-paced] 1998 movie Armageddon, where a crew of misfits led by Bruce Willis drills a hole in an incoming asteroid and drops a tactical nuke inside it.
Armageddon (1998)
Sadly, none of these posts or videos — the ones I, JCS, saw and read, that is — used readily available information from NASA to compute the energy of the DART impact. Here it is:
Now, obviously the purpose of the impactor was not to destroy Dimorphos, just to change its orbit; but taking this opportunity to make the calculation would have told the audiences of those videos and the readers of those blog posts that:
(a) numbers are nothing to be afraid of (many people develop a form of number-phobia that increases as they age away from their formal learning; this should be countered, and who better to do so than STEM popularizers?); and
(b) numbers let us make comparisons: for example, between a tactical nuke like the one used in Armageddon and the DART impactor there are between four and five orders of magnitude of energy.
It would have taken one line in the main text of a post (just the three numbers: speed, mass, energy) to drive these points across; similarly it would take a moment in a video, possibly with the calculations on screen for that moment. (It took about one minute to locate the information, including the specific energy of TNT, and less than ten seconds to do the calculations; took longer to format that table to make it pretty.)
These were missed opportunities. A bit like when people take the a Uber across a park to go watch a presentation about the need for regular activity like walking.
All it takes is the will to do it.
And two positive examples from fiction
In the science fiction novel Torchship Trilogy by Karl K Gallagher,4 we find a simple example of operational knowledge: KKG has a warring faction send a kinetic kill vehicle against another planet, but puts numbers in the book and does the math.
Building on that, we can also compute the specific energy (the energy per unit mass) of that impactor (we don’t have the mass to figure out the total energy), and compare that to the specific energy of the Little Boy atomic bomb.
Readers can use this extra step (playing with the numbers beyond their use in the text) to gamify novels: take the experience of reading and turn it into a game of fact-checking the authors’ dedication to accuracy. Warning: in regards to the STEM in novels, not many authors are as accurate as KKG; one could even suggest that in science fiction, STEM accuracy is a custom more honored in the breach than the observance.5
And from Breaking Bad, season 5 and episode 5, the great methylamine train heist.
Walter and Jesse need methylamine (CH3NH2 = CH3 methyl + NH2 amine) to cook their blue meth, so they get some by stopping a train and removing it from a tank car.
Because the tank car is weighed at both ends of the trip, they must replace the methylamine with water, and Walter computes the necessary volume to replace 1000 gallons of [aqueous; we’ll use the industrial concentration of 40% by mass] methylamine as 900 gallons of water. (He then does an engineering adjustment for spillage and water remaining in the hoses, but we’ll ignore that.)
Jesse then asks whether the owners of the methylamine will notice the robbery and Walter quickly calculates the changes in concentration and says they will… and will blame the manufacturers for shipping a marginally worse batch.
And the numbers work:
It says something that the producers of a TV show, who could easily have skipped the whole discussion between Walter White and Jesse Pinkman about the methylamine-to-water ratio and the detectability, decided to have someone knowledgeable do the calculations and then even mentioned the engineering adjustment of accounting for spillage and what’s in the hoses.6
It’s not that difficult. It’s all a matter of attitude.
Typical LOX-LH2 rocket engines use 5 to 7 kg of oxygen per kg of hydrogen (according to the interwebs) to maximize specific impulse (efficient use of mass for propulsion).
Proper scientists and engineers always read the units in the singular.
Note that this post applied to real science popularizers. There are plenty of people pretending to be science popularizers whose entire schtick is monetizing an echo chamber by attacking people (Elon Musk is a common target, as his social media profile guarantees an audience; research scientists with poor public speaking skills and reporters who oversell what those research scientists say are also common targets).
Some of those pseudo-popularizers have real STEM degrees, but their behaviors is that of an intellectual swindler, and in many cases they get numbers “wrong,” but always in the direction that supports their argument, i.e. they use numbers for deception.
The anonymized tweet in the figure above is from a real science popularizer, though its numbers could have used a little more care. More’s the pity.
Highly recommended for readers who like hard science fiction, as is obvious from its use as an example of good science popularization. It describes a future multi-planetary human civilization with conflicts among humans and between humans and AI-controlled planets.
Yes, it’s Shakespeare; Hamlet, to be precise. But like many people in the TV age I first got the reference from a Yes Prime Minister episode.
Compare for example with this scene from The Orville (season 3, episode 6), where they get things half right (you do need a 400 light-year roundtrip at close to the speed of light to go 400 years into the future of a still reference frame, and Alpha Tucanae is indeed 200 light-years from Earth), but miss out on the more difficult part (the Special Relativity calculation of how close to the speed of light you must be for the trip to last a few minutes in your reference frame):
Breaking Bad producers again FTW!