Wednesday, November 29, 2017

It's Fun to use Fallacies on Undergraduates! (modified)

I absolutely love the humorous book A Random Walk in Science. One of the better contributions contained therein is a reprint of The Uses of Fallacy by Paul V. Dunmore, New Zealand Mathematics Magazine, 7, 15 (1970). In the article Dunmore explains some of the better fallacies employed by creative math teachers, but they can be adapted for use in any discipline. Here is an excerpt:
There is a whole class of methods which can be applied when a lecturer can get from his premises P to a statement A, and from another statement B to the desired conclusion C, but he cannot bridge the gap from A to B. A number of techniques are available to the aggressive lecturer in this emergency. He can write down A, and without any hesitation put "therefore B". If the theorem is dull enough, it is unlikely that anyone will question the "therefore". This is the method of Proof by Omission, and is remarkably easy to get away with (sorry, "remarkably easy to apply with success").
Alternatively, there is the Proof by Misdirection, where some statement that looks rather like "A, therefore B" is proved. A good bet is to prove the converse "B, therefore A": this will always satisfy a first-year class. The Proof by Misdirection has a countably infinite analog, if the lecturer is not pressed for time, in the method of Proof by Convergent Irrelevancies
Proof by Definition can sometimes be used: the lecturer defines a set S of whatever entities he is considering for which B is true, and announces that in future he will be concerned only with members of S. Even an Honours class will probably take this at face value, without enquiring whether the set S might not be empty.
Proof by Assertion is unanswerable. If some vague waffle about why B is true does not satisfy the class, the lecturer simply says, "This point should be intuitively obvious. I've explained it as clearly as I can. If you still cannot see it, you will just have to think very carefully about it yourselves, and then you will see how trivial and obvious it is."
The hallmark of a Proof by Admission of Ignorance is the statement, "None of the text-books makes this point clear. The result is certainly true, but I don't know why. We shall just have to accept it as it stands." This otherwise satisfactory method has the potential disadvantage that somebody in the class may know why the result is true (or, worse, know why it is false) and be prepared to say so.
A Proof by Non-Existent Reference will silence all but the most determined troublemaker. "You will find a proof of this given in Copson on page 445", which is in the middle of the index. An important variant of this technique can be used by lecturers in pairs. Dr. Jones assumes a result which Professor Smith will be proving later in the year--but Professor Smith, finding himself short of time, omits that theorem, since the class has already done it with Dr Jones...
If it were not too close to reality (and therefore not funny at all) I'd add Proof By Intimidation, which is something like this: "Only people who are [insert some undesirable group]  do not accept this theorem as correct."

The entire article is available here. Great stuff.

Anyway, here is another taste of A Random Walk in Science. A survey first published in Physicists continue to laugh, MIR publishing, Moscow, 1968. In appears in A Random Walk in Science on page 37.

What do Physicists Do?

In keeping with the spirits of the times the Editors of the wall newspaper 'Impulse' of the Physical Institute of the Academy of Science of the USSR have formed a Department of Sociological Investigations. Members of this department conducted a survey of the Moscow populace on the theme 'What do Physicists do?'

 Population Group Answers Writer-Realists They argue until hoarse in smoke-filled rooms. It is not known why they set up unintelligible dangerous experiments using huge apparatus. Writer-Visionaries They work on enormous electronic machines called electronic brains. They work mostly in the cosmos. First year college students They speculate a lot. They make discoveries no less than once a month. Graduate students They solder circuits. They ask the older ones to find the leak. They write articles. Young scientific staff members—experimenters They run to the equipment department. They scrub rotary vacuum pumps. They flap their ears at seminars. Young scientific staff members—theoreticians They converse in corridors helping to make great discoveries. They write formulae, mostly incorrect. Older scientific staff members They attend meetings. They help younger staff members find the leak. Members of the personnel department Experimenters must arrive at 8:25 so that at 8:30 they can sit silently next to apparatus that is running. Theoreticians do not work at all. Members of the guard force They walk back and forth. They present passes upside down. Representatives of the Ministry of Finance They spend money to no purpose

There are also great exam questions in the book. One I actually use on a quiz at some point in my Honor's class on the history of physics:  Design an experiment to measure Planck's Constant using the mose expensive equipment possible.