How to catch a lion:
- THE HILBERT METHOD. Place a locked cage in the desert.
Set up the following axiomatic system.
(i) The set of lions is non-empty
(ii) If there is a lion in the desert, then there is a lion in the cage.
Theorem. There is a lion in the cage
- THE PEANO METHOD. There is a space-filling curve passing through every
point of the desert. Such a curve may be traversed in as short a time as
we please. Armed with a spear, traverse the curve faster than the
lion can move his own length.
- THE TOPOLOGICAL METHOD. The lion has a least the connectivity of a torus.
Transport the desert into 4-space. It can now be deformed in such a way as
to knot the lion. He is now helples.
- THE SURGERGY METHOD. The lion is an orientable 3-manifold with boundary
and so may be rendered contractible by surgery.
- THE UNIVERSAL COVERING METHOD. Cover the lion by his simply-connected
covering space. Since this has no holes, he is trapped.
- THE GAME THEORY METHOD. The lion is a big game, hence certainly a game.
There exists an optimal strategy. Follow it.
- THE SCHROEDINGER METHOD. At any instant there is a non-zero probability
that the lion is in the cage. Wait.
- THE ERASTOSHENIAN METHOD. Enumerate all objects in the desert: examine
them one by one; discard all those that are not lions. A refinement
will capture only prime lions.
- THE PROJECTIVE GEOMETRY METHOD. The desert is a plane. Project
this to a line, then project the line to a point inside the cage. The
lion goes to the same point.
- THE INVERSION METHOD. Take a cylindrical cage. First case: the lion
is in the cage: Trivial. Second case: the lion is outside the cage.
Go inside the cage. Invert at the boundary of the cage. The lion is
caught. Caution: Don't stand in the middle of the cage during the