A Contribution to the Mathematical Theory of Big Game Hunting

Problem: To Catch a Lion in the Sahara Desert.

1. Mathematical Methods

1.1 The Hilbert (axiomatic) method

    We place a locked cage onto a given point in the desert. After  that we
    introduce the following logical system:

   Axiom 1: The set of lions in the Sahara is not empty.
   Axiom 2: If there exists a lion in the Sahara, then there exists a lion in
            the cage.

   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.

1.2 The geometrical inversion method

    We place a spherical cage in the desert, enter it and lock it from  inside.
    We then performed an inversion with respect to the cage.
    Then the lion is inside the cage, and we are outside.

1.3 The projective geometry method

    Without  loss of generality we can view the desert as a plane surface.
    We project the surface onto a line and afterwards the line onto an interior
    point of the cage. Thereby the lion is mapped onto that same point.

1.4 The Bolzano-Weierstrass method

    Divide the desert by a line running from north to south. The lion is then
    either in the eastern or in the western part. Lets assume it is in the
    eastern part. Divide this part by a line running from east to west.
    The lion is either in the northern or in the southern part. Lets assume
    it is in the northern part. We can continue this process arbitrarily and
    thereby constructing with each step an increasingly narrow fence around the
    selected area. The diameter of the chosen partitions converges to zero so
    that the lion is caged into a fence of arbitrarily small diameter.

1.5 The set theoretical method

    We observe that the desert is a separable space. It therefore contains an
    enumerable dense set of points which constitutes a sequence with the lion as
    its limit. We silently approach the lion in this sequence, carrying the
    proper equipment with us.

1.6 The Peano method

    In the usual way construct a curve containing every point in the desert.
    It has been proven [1] that such a curve can be traversed in arbitrarily
    short time. Now we traverse the curve, carrying a spear, in a time less
    than what it takes the lion to move a distance equal to its own length.

1.7 A topological method

    We observe that the lion possesses the topological gender of a torus.
    We embed the desert in a four dimensional space. Then it is possible to
    apply a deformation [2] of such a kind that the lion when returning to
    the three dimensional space is all tied up in itself. It is then
    completely helpless.

1.8 The Cauchy method

    We examine a lion-valued function f(z). Be \zeta the cage. Consider the

	   1    [   f(z)
	------- I --------- dz
	2 \pi i ] z - \zeta


    where C represents the boundary of the desert. Its value is f(zeta), i.e.
    there is a lion in the cage [3].

1.9 The Wiener-Tauber method

    We obtain a tame lion, L_0, from the class L(-\infinity,\infinity), whose
    fourier transform vanishes nowhere. We put this lion somewhere in the desert
    L_0 then converges toward our cage. According to the general Wiener-Tauner
    theorem [4] every other lion L will converge toward the same cage.
    (Alternatively we can approximate L arbitrarily close by translating L_0
     through the desert [5].)

2 Theoretical Physics Methods

2.1 The Dirac method

    We assert that wild lions can ipso facto not be observed in the Sahara
    desert. Therefore, if there are any lions at all in the desert, they are
    tame. We leave catching a tame lion as an exercise to the reader.

2.2 The Schroedinger method

    At every instant there is a non-zero probability of the lion being in the
    cage. Sit and wait.

2.3 The nuclear physics method

    Insert a tame lion into the cage and apply a Majorana exchange operator [6]
    on it and a wild lion.

    As a variant let us assume that we would like to catch (for argument's sake)    a male lion. We insert a tame female lion into the cage and apply the
    Heisenberg exchange operator [7], exchanging spins.

2.4 A relativistic method

    All over the desert we distribute lion bait containing large amounts of the
    companion star of Sirius. After enough of the bait has been eaten we send a
    beam of light through the desert. This will curl around the lion so it gets
    all confused and can be approached without danger.

3 Experimental Physics Methods

3.1 The thermodynamics method

    We construct a semi-permeable membrane which lets everything but lions pass
    through. This we drag across the desert.

3.2 The atomic fission method

    We irradiate the desert with slow neutrons. The lion becomes radioactive and
    starts to disintegrate. Once the disintegration process is progressed far
    enough the lion will be unable to resist.

3.3 The magneto-optical method

    We plant a large, lense shaped field with cat mint (nepeta cataria) such
    that its axis is parallel to the direction of the horizontal component of
    the earth's magnetic field. We put the cage in one of the field's foci.
    Throughout the desert we distribute large amounts of magnetized spinach
    (spinacia oleracea) which has, as everybody knows, a high iron content.
    The spinach is eaten by vegetarian desert inhabitants which in turn are
    eaten  by the lions.
    Afterwards the lions are oriented parallel to the earth's magnetic field and
    the resulting lion beam is focussed on the cage by the cat mint lense.

[1] After Hilbert, cf. E. W. Hobson, "The Theory of Functions of a Real
    Variable and the Theory of Fourier's Series" (1927), vol. 1, pp 456-457
[2] H. Seifert and W. Threlfall, "Lehrbuch der Topologie" (1934), pp 2-3
[3] According to the Picard theorem (W. F. Osgood, Lehrbuch der
    Funktionentheorie, vol 1 (1928), p 178) it is possible to catch every lion
    except for at most one.
[4] N. Wiener, "The Fourier Integral and Certain of itsl Applications" (1933),
    pp 73-74
[5] N. Wiener, ibid, p 89
[6] cf e.g. H. A. Bethe and R. F. Bacher, "Reviews of Modern Physics", 8
    (1936), pp 82-229, esp. pp 106-107
[7] ibid