Two volumes of Pushkin, the first and the second, are side-by-side on
a bookshelf. The pages of each volume are 2 cm thick, and the cover – front
and back each – is 2 mm. A bookworm has gnawed through (perpendicular to
the pages) from the first page of volume 1 to the last page of volume 2. How
long is the bookworm’s track?
[This topological problem with an incredible answer – 4 mm – is absolutely
impossible for academicians, but some preschoolers handle it with ease.]
I tried to illustrate with this problem the difference in approaches to tasks by mathematicians and physicists, in my invited paper in the journal “Physics – Uspekhi” for the 2000 Christmas jubilee. My success surpassed by far what I intended: the editors, unlike preschoolers, on whom I had been basing my experience, failed to solve the problem, and therefore altered it to match my 4mm answer as follows: instead of from the first page of volume 1 to the last page of volume 2″ they typeset from the last page of volume 1 to the rst page of volume 2. This true story is so implausible that I am including it here: the proof is the editors’ version published by the journal.
If you still can’t figure out why that holds and the “obvious” answer is incorrect, then as hint: the first book is on the left and the second book is on the right.