You surely have heard the quote misattributed to Einstein about explaining scientific ideas. It varies in wording, but the message is the same: if you can’t explain it in a simple way, you don’t understand it well enough yourself. Here’s a quote from the amazing book Cat’s Cradle by Kurt Vonnegut:
“Dr. Hoenikker used to say that any scientist who couldn’t explain to an eight-year-old what he was doing was a charlatan.”
Of course, some sources say a similar thought could be attributed to Rutherford, who used to state that “it should be possible to explain the laws of physics to a barmaid.” Then we have the majestic Mr. Feynman and his conclusion: if he couldn’t reduce a topic to the freshman level, this meant we [physicists] really don’t understand it.
I don’t want to further investigate who said what as people usually don’t care about the author anyway—they quote and feel victorious because a big brain shares their views. Or they use the quote as a vindication for their own ignorance. The quote above in particular is often used by people who don’t study maths or sciences. They ask a question and when their “science friend” finds it difficult to explain, they assume he/she is just lacking understanding.
And it bugs me. So even though I follow the logic behind the quotes above and agree on the importance of simple, clear answers, I’d like to argue in favour of the opposite view for a change.
Understanding a concept and being able to explain it clearly to someone who is ignorant of the whole field are two different and generally unrelated things. Imagine a man who has never seen an animal. He asks you what an elephant is. You could start describing it: it’s a huge living thing, but not a person, it has four legs and a trunk, etc. He paints a picture in his head, but since he’s never actually seen anything like an elephant, it will be severely distorted. Note that to make his mental image accurate, you have to add more specifics to your description—it won’t be simple anymore. In the course of explaining you are likely to use words he’s not familiar with, he’ll ask you about them and the process starts all over again.
Now imagine he’s a very special man and doesn’t even know what legs are or what a trunk is. Then you’ll grasp the difficulty of explaining things “simply”. Well, if it works for an elephant, why shouldn’t it be the same for, say, differential equations? First, the person must know what an equation is. Then you may tell him in these kinds of equations we are looking for a function that satisfies them, so the solutions are not numbers but functions (obviously, he has to know what a function is). Then you may add that the derivatives of the function are also part of the equation and you pray to God or Newton or Leibniz that he knows what a derivative is. And it’s not that simple a concept.
As a fellow classmate today said, “ask a mathematician what a derivative actually is, and you probably wouldn’t receive an answer”. Yes, we have a geometric representation of a derivative and to simplify you could say it’s the rate of change of something… But would that satisfy you?
Thing is, people just want to hear it in layman’s terms. And my experience shows it doesn’t satisfy them. At least if they really care and are genuinely curious. Other questions arise and you cannot run away forever from the real physics/maths definitions. It’s like a foreign language that has to be learned.
And it’s frustrating to disregard years of studying, hard work and contemplation just because someone can’t magically translate their knowledge into a digestible portion of information for your pleasure and convenience. That’s why good teachers are rare. It is unbelievably hard to strip something to its essence without losing most of its meaning. True, some simple analogies could be made for the sake of visualising things. If “a big dog without fur and ears like wings” works for you as a description of an elephant, then physics could be real easy and real fun for you. But not authentic.
What’s more, even if you do understand what an elephant is, that doesn’t mean you can ride one. Comprehension of the fundamental, sadly, doesn’t lead directly to solving practical problems and vice versa.
Isn’t this the tragedy of science?