Here is an interesting phenomenon I have observed! It takes place over several generations, so you have to take it for what it’s worth.
A teacher explains a certain phenomenon to her students. She understands it perfectly, at least to whatever extent it is possible to understand a thing. For the sake of clarity, suppose it is about the phases of the Moon. “So, you see,” she says, “if the Moon happens to be exactly overhead at 6:00 PM, when you can assume the Sun is just setting, the line from the Moon to the Earth will be at 90 degrees to the line from the Sun to the Earth!”
The majority of the students, of course, will see where this is going, and while the Sun may not be just setting, in principle the Moon-Earth-Sun angle is going to be roughly a right angle, as close as makes no difference. Now, since the line from the Sun to the Moon, and from the Sun to the Earth are nearly parallel (that’s probably a tough sell, too; some of the slower kids will get hung up on the fact that if the Sun lies on both lines, how can they be parallel? They cannot understand that they’re never going to experience more parallel lines than these two, since the Sun is so far away. (Oddly enough, kids will not have any problem regarding two sides of a street as being parallel, though in theory they’re actually little bits of enormous circles, and as such the term ‘parallel’ does not even apply to them.)
Anyway, the point is, that if it so happens that the Moon is dead overhead at 6:00 PM, it will have to be a half-moon. Throughout the night, both the Sun and the Moon will drift Eastwards, but they will essentially maintain the right angle, since it is the Earth that is rotating, while the Sun and the Moon are moving far too slowly to make much of a difference to the angles.
You can imagine that the teacher explains the phases of the Moon in greater detail, and some of the students get it, but others will not. However, if the teacher is to be considered a good teacher, by the standards that have come down to us, she will give the class some rules of thumb whereby even the students who have not understood the phenomenon can make predictions about the phases of the Moon.
Unfortunately for us, and for humanity at large, you can imagine that it is some of those kids who just didn’t get it, but who were able to use the rules of thumb effectively, who go on to take up the profession of teaching. Many teachers teach for the love of it. The rest do it because it is the most convenient thing to do.
Teachers, by and large, are a conscientious lot, and one can imagine that, in advance of having to teach about the phases of the Moon, a teacher will put in a fair attempt at trying to understand the whole business, and what eluded her as a student might easily be within her grasp as an adult, and her students may be so lucky as to have the opportunity to understand the geometry of the phenomenon. But over several generations, it is quite possible that only the rule of thumb survives.
Years later, it is possible that the principles of a particular phenomenon still hold, but whatever condition allowed the creation of Rules of Thumb no longer applies. For example, the rules of thumb governing health insurance are probably no longer valid, especially in light of the changed situation regarding pre-existing conditions. Insurance analysts who relied on Rules of Thumb must make up a whole new set of RoT's to use when they’re not in a mood to really think, on a morning after a night of heavy drinking. (Actuaries drink like fish. I’ve seen them. There’s a rule of thumb for you!)
So if the assumptions on which a Rule of Thumb is based change enough, people will be puzzled, and lose faith in the entire education they have received, which in most cases is just the entire body of Rules of Thumb on which they operate. Kids these days actually think that the teacher’s entire responsibility is to pass along some rules of thumb (and some professors have bought into this idea), and are puzzled and frustrated when anyone tries to give them the Big Picture. We have an entire population of kids saying: “Just the facts, Ma'am.” They mean: Just the rules of thumb, please; I don’t have time for anything else.
The phenomenon of only the rule of thumb surviving is, of course, not by any means restricted to astronomy. All around us we see examples of people relying on rules of thumb:
- Buy low, sell high.
- Charge whatever the Traffic Will Allow.
- Cheating the Government is OK, because it’s Our Money, Anyway.
- Righty Tighty, Lefty Loosey. (Unless you’re working with certain plumbing fixtures or bicycle pedals!)
- Red Sky In The Morning, Take Warning.
- Taxes are bad for Small Business.
- Government is bad for Health Care.
Rules of Thumb for responding to Economic Conditions are pretty interesting, and suspicious, too. Economists have a myriad ways of advising whether or not to raise taxes, whether or not to raise interest rates, whether or not the Fed should tighten the money supply, whether or not investors should buy stocks versus bonds. The very fact that these superstitions are so widespread—and make no mistake: they’re superstitions—means that when something unexpected happens, all economists react the same way, just like panic-stricken people in a burning cinema, and of course all the nervous investors on Wall Street are watching each other, just so they can make the same lame-brain move as everyone else.
I used to have a rule of thumb, borrowed from a famous mathematician in Cambridge of the 1920's: give easy exams, but grade hard. You quickly learn which students know what they’re doing, and which do not.
This really works, provided the kids do not do detailed postmortems of the final examinations for the benefit of their juniors. Can you imagine the conversation?
“I got a B! I sort of knew a little of what was going on, but I just didn’t have the time to put in much work all semester, but I must have nailed the final! He gives easy finals, y’all!”
So of course the next class doesn’t do a stroke of work, anticipating an easy final.
So I give really difficult finals. They certainly are harder to grade, but with a lot of work, it is possible to decide which students really know what they’re doing, and which ones are just applying Rules of Thumb.
[Added later:
I’ve seen much the same phenomenon even among my close friends, when we go to a seminar or an informational meeting. It is almost the expected thing to do, to ignore almost everything except what is known as the Takeaway. What is the Takeaway? It is the whole event condensed into a Rule of Thumb. Distilling everything into trivial niblets is a way of life, for those of us who just can’t bother to deal with, or can’t handle, the subtleties of modern life. It is certainly true that people whose job is giving information have lost the knack of delivering the information tellingly and succinctly. But even if the speaker was a genius, there is always that executive summary that everyone demands. Executives are people who do not have a lot of brains, but have a lot of responsibility, and most of the time they work with rules of thumb (more’s the pity). But once everybody wants to Takeaway only the Rule of Thumb, we are in deep trouble.]
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