Cosimah2o
Active Member
Accurate title < A Contribution to the Mathematical and Physical Theory of Big Game Hunting >
Ralph Philip Boas was a fine mathematician, also shares with the reader a much broader profile of a man who contributed to the mathematics community as editor, teacher, administrator, and insightful humorist.
The reading starts with a problem: How to catch a lion in the Sahara desert? or How does an unarmed person capture a lion using only the weapons of mathematical thought?
There are more ways than you would think. It seems that every area of mathematics & physics can be used to construct a way to capture a lion. Of course, some are more efficient than others. Over thirty different "proven" methods are given.
To give you an idea, here some methods:
1. The Hilbert, or axiomatic, method.
Sometimes mathematicians has been characterized as lacking in humor, abstract or eccentric and considered to be brillant. Ralph P. Boas Jr. is a fascinating counterexample to most of these inaccurate stereotypes. A reading filled with humor and mathematics. At times amusing, other times profound, but at all times interesting, they are simple notes describing how the mathematical world works.
Ralph Philip Boas was a fine mathematician, also shares with the reader a much broader profile of a man who contributed to the mathematics community as editor, teacher, administrator, and insightful humorist.
The reading starts with a problem: How to catch a lion in the Sahara desert? or How does an unarmed person capture a lion using only the weapons of mathematical thought?
There are more ways than you would think. It seems that every area of mathematics & physics can be used to construct a way to capture a lion. Of course, some are more efficient than others. Over thirty different "proven" methods are given.
To give you an idea, here some methods:
1. The Hilbert, or axiomatic, method.
We place a locked cage at a given point of the desert. We then introduce the following logical system.
Axiom 1: The class of lions in the Sahara Desert is non-void.
Axiom 2: If there is a lion in the Sahara Desert, there is a lion in the cage.
Rule of procedure: If p is a theorem, and 'p implies q' is a theorem, then q is a theorem.
Theorem 1: There exists a lion in the cage.
2. The method of inversive geometryAxiom 1: The class of lions in the Sahara Desert is non-void.
Axiom 2: If there is a lion in the Sahara Desert, there is a lion in the cage.
Rule of procedure: If p is a theorem, and 'p implies q' is a theorem, 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. We perform an inversion with respect to the cage. The lion is then in the interior of the cage, and we are outside.
3. The Peano method.
Construct, by standard methods, a continuous curve passing through every point of the desert. It has been remarked that it is possible to traverse such a curve in an arbitrarily short time. Armed with a spear, we traverse the curve in a time shorter than that in which a lion can move his own length.
4. Mittag-Leffler method The number of lions in the Sahara Desert is finite, so the collection of such lions has no cluster point. Use Mittag-Leffler's theorem to construct a meromorphic function with a pole at each lion.. Being a tropical animal a lion will freeze if placed at a pole, and may then be easily taken.
5. Steenrod algebra method
Consider the mod p cohomology ring of the lion. We may regard this as a module over the mod p Steenrod algebra. Doing this requires the use of the table of Steenrod cohomology operations. Every element must be killed by some of these operations. Thus the lion will die on the operating table.
6. The Dirac methodWe observe that wild lions are, ipso facto, not observable in the Sahara Desert. Consequently, if there are any lions in the Sahara, they are tame. The capture of a tame lion may be left as an exercise for the reader.
7. The Schrödinger method
At any given moment there is a positive probability that there is a lion in the cage. Sit down and wait.
8. The Einstein method
Run in the direction opposite to that of the lion. The relative velocity makes the lion run faster, and hence it feels heavier.
9. Logical methodA lion is a continuum. According to Cohen's theorem he is undecidable (especially when he must make choices). Let two men approach him simultaneously. The lion, unable to decide upon which man to attack, is then easily captured.
10. Method of natural functionsThe lion, having spent his life under the Sahara sun, will surely have a tan. Induce him to lie on his back; he can then, by virtue of his reciprocal tan, be cot.
11. Method of differential topology or REIMANN Geometry.The lion is a three-manifold embedded in Euclidean 3-space. This implies that he is a handlebody. However, a lion which can be handled is tame and will enter the cage upon request.
Sometimes mathematicians has been characterized as lacking in humor, abstract or eccentric and considered to be brillant. Ralph P. Boas Jr. is a fascinating counterexample to most of these inaccurate stereotypes. A reading filled with humor and mathematics. At times amusing, other times profound, but at all times interesting, they are simple notes describing how the mathematical world works.