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Rich GSP Digest Jul EST Gene

Found at: 0x1bi.net:70/textfiles/file?humor/lion.jok

To: humourous-backbone@rascal.ics.utexas.edu
Subject: [Rich Kulawiec: GSP Digest #186]
Date: Tue, 25 Jul 89 00:34:23 EST
From: Gene Spafford 

The classic bit about how to catch a lion.  Added to the end are some
new ways for physicists & computer scientists.  I especially like
Dijkstra's method...

--spaf
------- Forwarded Message


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From: ji@walkuere.altair.fr (John Ioannidis)
Date: 19 Jul 89 10:30:04 GMT
Subject: how to catch a lion

origins, but it's a good one. It looks like something that might have
appeared in the JIR (Journal of Irreproducible Results) but I don't

A Contribution to the Mathematical Theory of Big Game Hunting





We place a locked cage onto a given point in the desert.  After that
   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.


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


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
nteriour point of the cage. Thereby the lion is mapped onto that same


Divide the desert by a line running from north to south. The lion is
then either in the eastern or in the western part. Let's assume it is
n the eastern part. Divide this part by a line running from east to
Let's 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
arbitrarily small diameter.


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


arbitrarily short time.  Now we traverse the curve, carrying a spear,
n a time less than what it takes the lion to move a distance equal to
ts own length.


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.


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

.e. there is a lion in the cage [3].


We obtain a tame lion, L_0, from the class L(-\infinity,\infinity),
n the desert.  L_0 then converges toward our cage.  According to the
toward the same cage.  (Alternatively we can approximate L arbitrarily
close by translating L_0 through the desert [5].)



We assert that wild lions can ipso facto not be observed in the Sahara
are tame. We leave catching a tame lion as an execise to the reader.


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


operator [6] on it and a wild lion.

As a variant let us assume that we would like to catch (for argument's
apply the Heisenberg exchange operator [7], exchanging spins.


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



We construct a semi-permeable membrane which lets everything but lions


We irradiate the desert with slow neutrons. The lion becomes


We plant a large, lense shaped field with cat mint (nepeta cataria)
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
nhabitants which in turn are eaten by the lions.  Afterwards the
lions are oriented parallel to the earth's magnetic field and the

[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
- -- 



We assume that the lion is most likely to be found in the direction to
the north of the point where we are standing. Therefore the REAL


By using parallelism we will be able to search in the direction to the
north much faster than earlier.


We pick a random number indexing the space we search. By excluding
neighboring points in the search, we can drastically reduce the number
of points we need to consider. The lion will according to probability
appear sooner or later.


We see a rabbit very close to us. Since it is already dead, it is


trivial to solve.


We know what a Lion is from ISO 4711/X.123. Since CCITT have specified
a Lion to be a particular option of a cat we will have to wait for a
nitial investigastions into this standard development.


Stand in the top left hand corner of the Sahara Desert.  Take one step
east.  Repeat until you have found the lion, or you reach the right
before you manage to get it in the cage, press the reset button, and
try again.


The way the problem reached me was: catch a wild lion in the Sahara
Desert. Another way of stating the problem is:

	Axiom 1: Sahara elem deserts
	Axiom 2: Lion elem Sahara
	Axiom 3: NOT(Lion elem cage)

We observe the following invariant:
	
	P1:	C(L) v not(C(L))


Establishing C initially is trivially accomplished with the statement

	;cage := {}

Note 0:	
This is easily implemented by opening the door to the cage and shaking
out any lions that happen to be there initially.
(End of note 0.)

The obvious program structure is then:

	;cage:={}
	;do NOT (C(L)) ->
		;"approach lion under invariance of P1"
		;if P(L) ->
			;"insert lion in cage"
		 [] not P(L) ->
			;skip
		;fi
	;od


Note 1:	
Axiom 2 esnures that the loop terminates.
(End of note 1.)

Exercise 0:
Refine the step "Approach lion under invariance of P1".
(End of exercise 0.)

Note 2: 
The program is robust in the sense that it will lead to
abortion if the value of L is "lioness".
(End of note 2.)

Remark 0: This may be a new sense of the word "robust" for you.
(End of remark 0.)

Note 3: 

>From observation we can see that the above program leads to the
(End of note 3.)  
(End of approach.)




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