Sure Finance has inspired from MATH THEORY OF BIG GAME HUNTING :D

Discussion in 'Psychology' started by harrytrader, Mar 7, 2003.


    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

    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. 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.

    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


    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

    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 disintegrate. 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

    4 Contributions from Computer Science.

    4.1 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.

    4.2 The parallel search method.

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

    4.3 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.

    4.4 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.

    4.5 The common language approach.

    If only everyone used ADA/Common Lisp/Prolog, this problem would be
    trivial to solve.

    4.6 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 investigastions into this standard development.

    4.7 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.

    4.8 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))

    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:

    ;do NOT (C(L)) ->
    ;"approach lion under invariance of P1"
    ;if P(L) ->
    ;"insert lion in cage"
    [] not P(L) ->

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

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

    In-Real-Life: John Ioannidis
  2. U need 2 get out more, dude!
  3. balda


    I agree

  4. Damn Harry,

    You've got way too much time on your hands..

  5. It's not from me (see the signature at the end) but perhaps you're right: astrologically I'm a Lion and I should have been captured by a mathematical cage :D

    As for financial world sometimes their method is as laughable as this:

    4.4 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."

    The example is Fibonacci justification when the only argument is "Leonardo Fibonacci has discovered it that's why it is scientific proof that it can be used as natural Order Law for stocks market " :D