From : Larry Scott

Problem: To Catch a Deer in the woods

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 woods. After that we introduce the following logical system:

Axiom 1: The set of deers in the woods is not empty.

Axiom 2: If there exists a deer in the woods, then there exists a deer 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 deer in the cage.

1.2 The geometrical inversion method

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We place a spherical cage in the woods, enter it and lock it from inside. We then perform an inversion with respect to the cage. Then the deer 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 woods as a plane surface. We project the surface onto a line and afterwards the line onto an interior point of the cage. Thereby the deer is mapped onto that same point.

1.4 The Bolzano-Weierstrass method

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Divide the woods by a line running from north to south. The deer 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.he deer 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 deer is caged into a fence of arbitrarily small diameter.

1.5 The set theoretical method

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We observe that the woods is a separable space. It therefore contains an enumerable dense set of points which constitutes a sequence with the deer as its limit. We silently approach the deer 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 woods. It has been proven [1] that such a curve can be traversed in arbitrarily short time. Now we traverse the curve, carrying a rifle, in a time less than what it takes the deer to move a distance equal to its own length.

1.7 A topological method

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We observe that the deer possesses the topological gender of a torus. We embed the woods in a four dimensional space. Then it is possible to apply a deformation [2] of such a kind that the deer 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 deer-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 woods. Its value is f(zeta), i.e.there is a deer in the cage [3].

1.9 The Wiener-Tauber method

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We obtain a tame deer, D_0, from the class D(-\infinity,\infinity),whose fourier transform vanishes nowhere. We put this deer somewhere in the woods. D_0 then converges toward our cage. According to the general Wiener-Tauber theorem [4] every other deer D will converge toward the same cage. (Alternatively we can approximate D arbitrarily close by translating D_0 through the woods [5].)

2 Theoretical Physics Methods

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2.1 The Dirac method

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We assert that wild deers can ipso facto not be observed in the woods.

Therefore, if there are any deers at all in the woods, they are tame. We leave catching a tame deer as an exercise to the reader.

2.2 The Schroedinger method

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

2.3 The nuclear physics method

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

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

2.4 A relativistic method

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All over the woods we distribute deer 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 woods. This will curl around the deer so it gets all confused and can be approached without being alerted to our presence.

2.5 The Newton method

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Neglect friction and the deer 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 deers pass through. This we drag through the woods.

3.2 The atomic fission method

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

[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 derFunktionentheorie, vol 1 (1928), p 178) it is possible to catch every deer 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 "

....lou.

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Changes were last made on 11-20-2001