In article <
d6rnefhppafsn1lmm...@4ax.com>,
How to put a lion in a cage.
Build an empty cage in the Sahara. Step into it. Invert your
definition of cage interior and exterior.
http://gksoft.com/a/fun/catch-lion.html
How To Catch A Lion
Problem: To Catch a Lion in the Sahara Desert.
1. Mathematical Methods
2. 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.
3. 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.
4. 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.
5. 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. Let's 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. 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 partitions converges to zero so that the lion is
caged into a fence of arbitrarily small diameter.
6. 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.
7. 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.
8. 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.
9. The Cauchy method We examine a lion-valued function f(z).
Be \zeta the cage. Consider the integral
1 [ f(z)
10. ------- | --------- dz
11. 2 \pi i ] z - \zeta
12.
13. C
14.
where C represents the boundary of the desert. Its value is
f(zeta), i.e. there is a lion in the cage [3].
15. 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-Tauber 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].)
3. Theoretical Physics Methods
2. 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 exercise to the reader.
3. The Schrodinger method At every instant there is a
non-zero probability of the lion being in the cage. Sit and wait.
4. 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.
5. 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.
4.
5. Experimental Physics Methods
1.
2. The thermodynamics method We construct a semi-permeable
membrane which lets everything but lions pass through. This we
drag across the desert.
3. The atomic fission method We irradiate the desert with
slow neutrons. The lion becomes radioactive and starts to
disintegrate. Once the disintegration process is progressed far
enough the lion will be unable to resist.
4. 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.
6.
7. Contributions from Computer Science
1.
2. The search method 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 problem we have is that of
speed, since we are only using a PC to solve the problem.
3. The parallel search method By using parallelism we will
be able to search in the direction to the north much faster than
earlier.
4. The Monte-Carlo method 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.
5. The practical approach We see a rabbit very close to us.
Since it is already dead, it is particularly easy to catch. We
therefore catch it and call it a lion.
6. The common language approach If only everyone used
ADA/Common Lisp/Prolog, this problem would be trivial to solve.
7. The standard approach 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 harmonized standard to
appear. $20,000,000 have been funded for initial investigations
into this standard development.
8. 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.
9. The 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))
10.
where C(L) means: the value of "L" is in the cage. Establishing C
initially is trivially accomplished with the statement
;cage := {}
11.
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 := {}
12. ;do NOT (C(L)) ->
13. ;"approach lion under invariance of P1"
14. ;if P(L) ->
15. ;"insert lion in cage"
16. [] not P(L) ->
17. ;skip
18. ;fi
19. ;od
20.
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.)
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