Family Fun/Family Fun.iso/joke1/jokes_l/lions.cat

Text File | 1992-01-07 | 12KB | 362 lines

Article 343 of eunet.jokes:
Xref: puukko junk:7310 sci.math:1574 eunet.jokes:343
Path: puukko!santra!tut!enea!mcvax!cernvax!ethz!heiser
From: [e-mail] (Gernot Heiser)
Newsgroups: rec.humor,sci.math,eunet.jokes
Subject: Re: Math Jokes
Message-ID: <[e-mail]>
Date: 4 Jun 88 12:08:44 GMT
References: <[e-mail]> <[e-mail]> <[e-mail]> <[e-mail]> <[e-mail]> <[e-mail]>
Reply-To: [e-mail] (Gernot Heiser)
Organization: ETH Zuerich, Switzerland
Lines: 184


The following is from a book whose title I don't recall. The  book is in German
but the article is actually a translation from  the original by H. Petard which
appared in  the American Monthly  54,  466 (1938). Unfortunately our library is
lacking some  years of this journal  around WW 2,  so I had to re-translate the
stuff into English.  (That will make you people share the experience of reading
German translations  of   books  on Einstein   which also usually  re-translate
Einstein's words :-) ).



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 performe 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 interiour 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 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

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 execise 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 diintegrate. 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
--
Gernot Heiser <[e-mail]> Phone:       [phone]
Integrated Systems Laboratory   CSNET/ARPA:  [e-mail]
ETH Zuerich                     EARN/BITNET: GRIDFILE@CZHETH5A
CH-8092 Zuerich, Switzerland    EUNET/UUCP:  {uunet,...}!mcvax!ethz!iis!heiser


Article 426 of eunet.jokes:
Path: puukko!santra!tut!enea!mcvax!steven
From: [e-mail] (Steven Pemberton)
Newsgroups: eunet.jokes
Subject: Re: Catching a Lion with computer science
Message-ID: <[e-mail]>
Date: 6 Jul 88 11:24:18 GMT
References: <[e-mail]>
Reply-To: [e-mail] (mcvax!steven.uucp)
Distribution: eunet
Organization: CWI, Amsterdam
Lines: 66

Linear search:

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
hand edge.  If you reach the right hand edge, take one step
southwards, and proceed towards the left hand edge.  When you finally
reach the lion, put it the cage.  If the lion should happen to eat you
before you manage to get it in the cage, press the reset button, and
try again.

Dijkstra approach:
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))
where C(L) means: the value of "L" is in the cage.

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
where P(L) means: the value of L is within arm's reach.

Note 1.
Axiom 2 ensures 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
desired goal. It goes without saying that we therefore do not have to
run it.
(End of note 3.)
(End of approach.)

Steven Pemberton, CWI, Amsterdam; [e-mail]


Article 426 of eunet.jokes:
Path: puukko!santra!tut!enea!mcvax!steven
From: [e-mail] (Steven Pemberton)
Newsgroups: eunet.jokes
Subject: Re: Catching a Lion with computer science
Message-ID: <[e-mail]>
Date: 6 Jul 88 11:24:18 GMT
References: <[e-mail]>
Reply-To: [e-mail] (mcvax!steven.uucp)
Distribution: eunet
Organization: CWI, Amsterdam
Lines: 66

Linear search:

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
hand edge.  If you reach the right hand edge, take one step
southwards, and proceed towards the left hand edge.  When you finally
reach the lion, put it the cage.  If the lion should happen to eat you
before you manage to get it in the cage, press the reset button, and
try again.

Dijkstra approach:
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))
where C(L) means: the value of "L" is in the cage.

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
where P(L) means: the value of L is within arm's reach.

Note 1.
Axiom 2 ensures 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
desired goal. It goes without saying that we therefore do not have to
run it.
(End of note 3.)
(End of approach.)

Steven Pemberton, CWI, Amsterdam; [e-mail]