UUCP Gernot jokes Math Jokes Jun

Article 343 of eunet.jokes:

From: heiser@ethz.UUCP (Gernot Heiser)

Newsgroups: rec.humor,sci.math,eunet.jokes

Subject: Re: Math Jokes

Message-ID: <464@ethz.UUCP>

Date: 4 Jun 88 12:08:44 GMT

References: <3440@pasteur.Berkeley.Edu> <2932@phoenix.Princeton.EDU> <1155@bentley.UUCP> <1156@bentley.UUCP> <546@osupyr.mast.ohio-state.edu> <583@picuxa.UUCP>

Reply-To: heiser@iis.UUCP (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

German translations  of   books  on Einstein   which also usually  re-translate

Einstein's words :-) ).

A Contribution to the Mathematical Theory of Big Game Hunting

=============================================================

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

ntroduce 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.

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.

Without  loss of  generality  we  can view the   desert as a  plane surface. We

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

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

n the northern or  in the southern part. Lets   assume it is  in the  northern

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.

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

ts limit. We silently approach the lion  in this sequence, carrying the proper

equipment with us.

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.

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

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

s a lion in the cage [3].

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].)

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.

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

Sit and wait.

t 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.

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.

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

through. This we drag across the desert.

We irradiate the desert  with  slow neutrons. The  lion becomes radioactive and

the lion will be unable to resist.

We plant a large, lense  shaped field with cat mint  (nepeta cataria) such that

ts  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  Phone:       +41 1/256 23 48

ETH Zuerich                     EARN/BITNET: GRIDFILE@CZHETH5A

CH-8092 Zuerich, Switzerland    EUNET/UUCP:  {uunet,...}!mcvax!ethz!iis!heiser

Article 426 of eunet.jokes:

From: steven@cwi.nl (Steven Pemberton)

Newsgroups: eunet.jokes

Subject: Re: Catching a Lion with computer science

Message-ID: <388@piring.cwi.nl>

Date: 6 Jul 88 11:24:18 GMT

References: <2024@sics.se>

Reply-To: steven@cwi.nl (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

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))

Establishing C initially is trivially accomplished with the statement

	;cage := {}

Note 0.

This is easily implemented by opening the door to the cage and

(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 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

(End of note 3.)

(End of approach.)

Steven Pemberton, CWI, Amsterdam; steven@cwi.nl

Article 426 of eunet.jokes:

From: steven@cwi.nl (Steven Pemberton)

Newsgroups: eunet.jokes

Subject: Re: Catching a Lion with computer science

Message-ID: <388@piring.cwi.nl>

Date: 6 Jul 88 11:24:18 GMT

References: <2024@sics.se>

Reply-To: steven@cwi.nl (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

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))

Establishing C initially is trivially accomplished with the statement

	;cage := {}

Note 0.

This is easily implemented by opening the door to the cage and

(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 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

(End of note 3.)

(End of approach.)

Steven Pemberton, CWI, Amsterdam; steven@cwi.nl