LETTERS: METHOD OF PROOF FOR THE IMPOSSIBLE

To the editor:

Someone contacted Speak Out to voice agreement with a letter of mine which was published in this space Jan. 2. This region being the way it is, I thank the person for what will no doubt turn out to be a rare instance of approval of my probably unpopular opinion. I would like to correct one thing in the person's comment, if I may. The comment ended, "You cannot prove something to be impossible." The "something" in my letter was the classical mathematical task of constructing, with compus and unmarked straightedge, a square equal in area to a circle of a given radius.

If I were trying to be humorous, I would respond to this person's assertion of the impossibility of proving something to be impossible by demanding, "Prove it." But I think the person was serious and deserves a serious answer, so here goes.

One way of proving a task to be impossible (or an assertion to be false) to the satisfaction of mathematicians, who are very hard to satisfy on such matters, is to start off by assuming that the task is possible (or the assertion is true) and seeing what the logical consequences of the assumption is. If the consequence is an absurdity, tht absurdness is deemed to be proof of the impossibility of the task (or the falsity of the assertion). This method of proof is called, in Latin, reductio ad absurdem (reduction to the absurd).

DONN S. MILLER

Tamms, Ill.