A Contribution to the Mathematical Theory of Big Game Hunting
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Problem: To Catch a Lion in the Sahara Desert.
1. Mathematical Methods
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1.1 The Hilbert (axiomatic) method
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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
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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.
1.3 The projective geometry method
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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 interiour point of the cage. Thereby the lion is mapped onto that same
point.
1.4 The Bolzano-Weierstrass method
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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
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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
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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
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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
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We examine a lion-valued function f(z). Be \zeta the cage. Consider the
integral
1 [ f(z)
------- I --------- dz
2 \pi i ] z - \zeta
C
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
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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
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2.1 The Dirac method
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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 execise to the reader.
2.2 The Schroedinger method
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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
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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
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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.
2.5 The Newton method
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Neglect friction and the lion and the cage will attract each other.
3 Experimental Physics Methods
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3.1 The thermodynamics method
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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
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We irradiate the desert with slow neutrons. The lion becomes
radioactive and starts to diintegrate. Once the disintegration process is
progressed far enough the lion will be unable to resist.
3.3 The magneto-optical method
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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.
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USEFUL PHRASES TO KNOW WHEN TRAVELLING IN THE MIDDLE EAST:
AKBAR KHALI_KILI HAFTIR LOTFAN
Thank you for showing me your marvelous gun.
FEKR GABUL ORADAN DAVAT PAEH CUSH DIVAR
I am delighted to accept your kind invitation to lie on
the floor with my arms above my head and my legs apart.
SHOMAEH FEKR TAMOMEH DEH GOFTEH BANDE
I agree with everything you have ever said or thought in your life.
AUTO ARREREGH DAVATEMAN MANO SEPAHEH HAST
It is exceptionally kind of you to allow me to travel in the trunk
of your car.
FASHAL-EH TUPEHMAN NA DEGAT MANO GOFTAM CHEESHAYEH MOHEMARA
JEBEHKESHVAREHMAN
If you will do me the kindness of not harming by genitel appendages
I will gladly reciprocate by betraying my country in public.
MATERNIER GHERMEZ AHLEIEH, GHORBAN
The red blindfold will be lovely, excellency.
TIEKH NUNEH OB KHREELEH BEZORG VA KHRUBE BOYAST INO BEGERAM
The water-soaked bread crumbs are delicious, thank you. I really must
have the recipe.