The mathematical theory of big game hunting
1. Mathematical methods
1. The Hilbert, or axiomatic, method. We place a locked cage onto a given point in the desert. After that we introduce the following logical system:
Axiom I. The set of lions in the Sahara is not empty.
Axiom II. If there exists a lion in the Sahara, then there exists a lion in the cage.
Rule of procedure. If P is a theorem, and if the following is holds: "P implies Q", then Q is a theorem.
Theorem 1. There exists a lion in the cage.
2. The method of inversive geometry. We place a spherical cage in the desert, enter it and lock it from inside. We then perform an inversion with respect to the cage. Then the lion is inside the cage, and we are outside.
3. The method of projective geometry. Without loss of generality, we can view the desert as a plane. We project the surface onto a line, and then project the line onto an interior point of the cage. Thereby the lion is projected onto that same point.
4. The Bolzano-Weierstrass method. Divide the desert by a line running from N-S. The lion is then either in the E portion or in the W portion; let us assume him to be in the W portion. Bisect this portion by a line running from E-W. The lion is either in the N portion or in the S portion; let us assume him to be in the N portion. We continue this process indefinitely, constructing a sufficiently strong fence about the chosen portion at each step. The diameter of the chosen portions approaches zero, so that the lion ultimately surrounded by a fence of arbitrarily small perimeter.
5. The "Mengentheoretisch" method. We observe that the desert is a separable space. It therefore contains an enumerable dense set of points, from which can be extracted a sequence having the lion as limit. We then approach the lion stealthily along this sequence, bearing with us suitable equipment.
6. The Peano method. Construct, by standard methods, a continuous curve passing through every point of the desert. It has been remarked [1]that it is possible to traverse such a curve in an arbitrarily short time. Armed with a spear, we traverse the curve in a time shorter than that in which a lion to move a distance equal to its own length.
7. A topological method. We observe that a lion has at least the connectivity of a torus. We transport the desert into four-space. Then it is possible [2] to carry out such a deformation that the lion can be returned to three-space in a knotted condition. He is then completely helpless.
8. The Cauchy, for function theoretical, method. We examine a lion-valued function f(z). Let ζ be the cage. Consider the integral
where C represents the boundary of the desert. Its value is f(ζ), i.e. there is a lion in the cage [3].
9. The Wiener-Tauberian method. We obtain a tame lion, L0, from the class L(-¥, ¥), whose Fourier transform vanishes nowhere, and release it in the desert. L0 then converges toward our cage. By Wiener's General Tauberian Theorem [4], any other lion, L (say), will converge to the same cage. Alternatively we can approximate arbitrarily closely to L by translating L0 through the desert [5].)
10. The Eratosthenian method. Enumerate all the objects in the desert. Examine them one by one, and discard all those that are not lions. A refinement will capture only prime lions.
2. Methods from theoretical physics
11. The Dirac method. We observe that wild lions are, ipso facto, not be observable in the Sahara desert. Consequently, if there are any lions at all in the Sahara, they are tame. We leave catching a tame lion as an exercise to the reader.
12. The Schroedinger method. At any given moment there is a positive probability that there is a lion in the cage. Sit down and wait.
13. The nuclear physics method. Place a tame lion into the cage, and apply a Majorana exchange operator [6] on it and a wild lion.
As a variant, let us suppose, to fix ideas, that we require a male lion. We place a tame lioness into the cage, and apply the Heisenberg exchange operator [7] which exchanges spins.
14. A relativistic method. We distribute about the deser lion bait containing large portions of the Companion of Sirius. When enough bait has been taken, we project a beam of light across the desert. This will bend right around the lion, who will hen become so dizzy that he can be approahced with impunity.
3. Experimental physics methods
15. The thermodynamics method. We construct a semi-permeable membrane, permeable to everything except lions, and sweep it across the desert.
16. The atom-splitting method. We irradiate the desert with slow neutrons. The lion becomes radioactive, and a process of disintegration set in. When the decay has proceeded sufficiently far, he will become incapable of showing fight.
17. The magneto-optical method. We plant a large lenticular bed of catnip (Nepeta cataria), whose axis lies along the direction of the horizontal component of the earth's magnetic field, and place a cage at one of its foci. We distribute over the desert large quantities of magnetized spinach (Spinacia oleracea), which, as is well known, has a high ferric content. The spinach is eaten by herbivorous denizens of the desert, which in turn are eaten by lions. The lions are then oriented parallel to the earth's magnetic field, and the resulting beam of lions is focus by the catnip upon the cage.
