A CONTRIBUTION TO THE MATHEMATICAL THEORY OF
BIG GAME HUNTING
H. PETARD, Princeton, New Jersey
This little known mathematical discipline has not, of recent
years, received in the literature the attention which, in our
opinion, it deserves.
In the present paper we present some algorithms which, it is
hoped, may be of interest to other workers in the field.
Neglecting the more obvious trivial methods, we shall confine our
attention to those which involve significant applications of
ideas familiar to mathematicians and physicists.
The present time is particularly fitting for the
preparation of an account of the subject, since recent advances
both in pure mathematics and in theoretical physics have made
available powerful tools whose very existence was unsuspected by
earlier investigators. At the same time, some of the more
elegant classical methods acquire new significance in the light
of modern discoveries. Like many other branches of knowledge to
which mathematical techniques have been applied in recent years,
the Mathematical Theory of Big Game Hunting has a singularly
happy unifying effect on the most diverse branches of the exact
sciences.
For the sake of simplicity of statement, we shall confine
our attention to Lions (Felis leo) whose habitat is the Sahara
Desert. The methods which we shall enumerate will easily be seen
to be applicable, with obvious formal modifications, to other
carnivores and to other portions of the globe. The paper is
divided into three parts, which draw their material respectively
from mathematics, theoretical physics, and experimental physics.
The author desires to acknowledge his indebtedness to the
Trivial Club of St. John's College, Cambridge, England; to the
M. I. T. chapter of the Society for Falicy Research; to the F.
o. P., of Princeton University and to numberous (sic) individual
contributors, known and unknown, conscious and unconscious.
1. MATHEMATICAL METHODS
1. The Hilbert, or Axiomatic Method. We place a locked cage
at a given point of the desert. We then introduce the following
logical system.
Axiom I. The class of lions in the Sahara Desert is non-void.
Axiom II. If there is a lion in the Sahara Desert, there is a
lion in the cage.
Rules of Procedure. If p is a theorem, and "p implies q" is a
theorem, then q is a theorem.
Theorem I. There is a Lion in the cage.
2. The Method of Inversive Geometry. We place a spherical
cage in the desert, enter it, and lock it. We perform an
inversion with respect to the cage. The lion is then in the
interior of the cage, and we are outside.
3. The Method of Projective Geometry. Without loss of
generality, we may regard the Sahara Desert as a plane. Project
the plane into a line, and the line into an interior point
of the cage. The lion is projected into the same point.
4. The Bolzano-Weierstrass Method. Bisect the desert by a
line running N-S. The lion is either in the E portion or in the
W portion. Bisect this portion by a line running E-W. The lion
is either in the N portion or in the S 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 is 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 dessert. It
has been remarked (1) that is 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
can move his own length.
7. A Topological Method. We observe that a lion has at least
the connectivity of the torus. We transport the desert into
four-space. It is then possible (2) to carry out such a
deformation that the lion can be returned to three-space in a
knotted condition. He is then helpless.
8. The Cauchy, or Functiontheoretical, Method. We consider
an analytic lion-valued function f(z). Let z1 be the cage.
Consider the integral:
( f(z)
1/(2*pi*i) \ -------- dz
) z - z1
C
where C is the boundary of the desert; its value is f(z1), ie.,
a lion in the cage (3).
9. The Wiener Tauberian Method. We procure a tame lion, Lo,
of class L(-oo,oo), whose Fourier transform nowhere vanishes, and
release it in the desert. L then converges to our cage. By
Wiener's General Tauberian Theorem, any other lion, L (say) will
then converge to the same cage. Alternatively, we can
approximate arbitrarily closely to L by translating Lo about the
desert (5).
2. METHODS FROM THEORETICAL PHYSICS
10. The Dirac Method. We observe that wild lions are, ipso
facto, not observable in the Sahara Desert. Consequently, if
there are any lions in the desert, they are tame. The capture of
a tame lion may be left as an exercise for the reader.
11. The Schrodinger Method. At any given moment there is a
positive probability that there is a lion in the cage. Sit down
and wait.
12. The Method of Nuclear Physics. Place a tame lion in the
cage, and apply a Major and exchange operator (6) between 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 in the cage, and
apply a Heisenberg exchange operator (7) which exchanges the
spins.
13. A Relativistic Method. We distribute about the desert
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 then become so dizzy that he can be approached with
impunity.
14. The Thermodynamical Method. We construct a
semi-permeable membrane, permeable to everything except lions,
and sweep it across the desert.
15. The Atom-Splitting Method. We irradiate the desert with
slow neutrons. The lion becomes radioactive, and a process of
disintegration sets in. When the decay has proceded sufficiently
far, he will become incapable of showing fight.
16. The Magneto-optical Method. We plant a large lanticular
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
oleracia), which, as is well known, has a high ferric content.
The spinach is eaten by the herbivorous denizens of the desert,
which are in turn eaten by lions. The lions are then oriented
parallel to the earth's magnetic field, and the resulting beam of
lions is focussed by the catnip upon the cage.
(Contributed to Ground Zero Publications by Lee R. Bradley, SYSOP
of Mouse House Software Computer Facility, 24 East Cedar Street,
Newington, CT 06111, (203) 665-1100, an RCP/M RBBS interested
in many things, among which is putting a smile on your face.
August 23, 1986.)
