Retorts

Splitting Cigarettes

I cannot accept that the shorter piece of Russell Dear's broken cigarette [Neurobics, November 1992] is to be expected to measure a quarter the original length. The assumption that it is equally likely to have any value between zero and half is false, because it is almost impossible to break off a piece that is shorter than a few millimetres -- all you'll do is fray the end. Your mind is set upon the breaking off of a finite piece, so it won't allow you to break off an unmanageably short length. Thus, values of one, two or three mm for the length of the shorter piece are less likely that 15, 16 or 17 mm, for example. In other words, true randomness does not exist. The workings of the human mind don't obey the rigid theories of the mathematician -- thank goodness. But keep those puzzles coming; they are great fun!

Mike Bradstock, Christchurch