A lot of learning is a dangerous thing

The well-known proverb “a little learning is a dangerous thing” is a typical elitist attitude to education, no less so today than it was in the 18th century. It expresses the arrogance of the learned towards “hoi polloi”, and conveys the intended meaning that education is wasted on ordinary people. My career in education has taught me that this proverb is as jejune, negative and false as it is possible to be. The real dangers of learning lie in doing too much of it.

An example: I had a PhD student once, who was obsessed with learning, and could never do enough of it. Despite my best efforts, he never understood that a PhD was about learning by doing, not about learning by reading. He never got his PhD. A lot of learning is a dangerous thing.

Another example: when I talk to physicists about new ideas, they always know so much that it is easy for them to find a reason why my ideas are wrong. They know so much that it is easy for them to prove that *all* new ideas are wrong. They know so much, therefore, that it is literally impossible for them to accept new ideas, and therefore it is literally impossible for them to make progress. A lot of learning is a dangerous thing.

The same has always been true. The use of epicycles to describe astronomical motions was a very difficult and erudite theory, requiring vast amounts of calculation and learning. Too much learning. A new idea comes along: have you tried using ellipses instead of circles? WHAT?!! ARE YOU MAD?!! You’ll be burnt at the stake! Well, history reveals that the simple idea of using ellipses instead of circles renders all of that learning about epicycles completely redundant. A lot of learning is a dangerous thing.

I have always lived by the maxim that a lot of learning is a dangerous thing. If a project requires a lot of learning, I generally eschew it. That is why I became a mathematician, which requires very little learning, especially if you are good at it. Mathematics is about learning as little as possible, as efficiently as possible.

That is why mathematics is properly regarded as an art, and not as a science. It is not about doing calculations (of epicycles, for example), it is about avoiding calculations. Most people don’t seem to understand that.


3 Responses to “A lot of learning is a dangerous thing”

  1. James Arathoon Says:

    Being philosophically minded I find that all the lies, deceit and deception occurs in the first few sentences of a physics paper or the first few pages of a physics book. Similar things happen in math books which try to hide dubious foundations, like the essential difference between finite entities (sets) and infinite entities (sets).

    At university students are hurried through the axioms and assumptions to avoid them learning how to question the material they are indoctrinated with.

    • Robert A. Wilson Says:

      Yes, I have to agree. Often, however, this deception is as much self-deception as anything else. When writing, one has to start by affirming the axioms, and the more dubious the axioms are, the more bluster is necessary to get through them without being found out. And the very worst is when you do the finding out yourself, and you suddenly realise you’ve been telling lies for years.

      It is more or less inevitable that this happens from time to time in a career spent in teaching, if you re-think your teaching every year as a good teacher would. I know, it’s happened to me many times! But if you don’t re-think, you can avoid this problem, if you’re lucky!

  2. Robert A. Wilson Says:

    All physicists know that the strength of gravity falls off with distance as 1/r^2. Except that astronomers have discovered that it doesn’t. There comes a point where this simple law of gravity needs some epicycles to rescue it from disaster. Epicycles upon epicycles have been piled onto this theory for decades. The calculations are so horrendous that no-one can do them themselves, no-one can even write their own computer programs to do it, but all they can do is write a tweak to someone else’s program, that is now so big that no-one understands what it does. And then they claim that these epicycles, that are deeply hidden inside computer programs that no-one really understands, actually explain astronomical observations. Poppycock.

    Forty years ago, Milgrom said, “Have you tried using 1/r?” WHAT?!! ARE YOU MAD?!! You’ll be burnt at the stake! Well, history relates that the simple idea of using 1/r when 1/r^2 gets too small renders all that scholasticism of dark matter and dark energy redundant. Or at least, it will do once history gets around to it. It may take a little while longer.

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