Chasing Leo

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In 1938, the American Mathematical Monthly published an unlikely paper: “A Contribution to the Mathematical Theory of Big Game Hunting.” In it, Ralph Boas and Frank Smithies presented 16 ways to catch a lion using techniques inspired by modern math and physics. Examples:

  • “The Method of Inversive Geometry. 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.”
  • “A Topological Method. We observe that a lion has at least the connectivity of the torus. We transport the desert into four-space. It is then possible to carry out such a deformation that the lion can be returned to three-space in a knotted condition. He is then helpless.”
  • “The Dirac Method. We 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.”
  • “A Relativistic Method. We distribute about the desert lion bait containing large portions of the Companion of Sirius. When enough bait has been taken, we project a beam of light across the desert. This will bend right round the lion, who will then become so dizzy that he can be approached with impunity.”

The article has inspired a tradition of updates by other mathematicians over the years:

  • “Let Q be the operator that encloses a word in quotation marks. Its square Q2 encloses a word in double quotes. The operator clearly satisfies the law of indices, QmQn = Qm + n. Write down the word ‘lion,’ without quotation marks. Apply to it the operator Q-1. Then a lion will appear on the page. It is advisable to enclose the page in a cage before applying the operator.” (I.J. Good, 1965)
  • “Game Theoretic Method. A lion is big game. Thus, a fortiori, he is a game. Therefore there exists an optimal strategy. Follow it.” (“Otto Morphy,” 1968)
  • “Method of Analytics Mechanics. Since the lion has nonzero mass it has moments of inertia. Grab it during one of them.” (Patricia Dudley et al., 1968)
  • “Method of Natural Functions. The 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.” (Dudley)
  • “Nonstandard Analysis. In a nonstandard universe (namely, the land of Oz), lions are cowardly and may be caught easily. By the transfer principle, this likewise holds in our (standard) universe.” (Houston Euler, et al., 1985)

Dudley also suggested a “method of moral philosophy”: “Construct a corral in the Sahara and wait until autumn. At that time the corral will contain a large number of lions, for it is well known that a pride cometh before the fall.”

“Another Paradox”

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If a cork ball about an inch in diameter be tied at the end of a thread about a foot in length, and then swung so that it enters a smooth stream of water flowing from a tap at about three inches from the mouth of the latter, it will be found that the ball will remain in the water, and that the thread will make an angle of about thirty degrees with a vertical line passing through the ball. The latter, it should be added, must be thoroughly wetted before this result is produced.

Strand, September 1908

Math Notes

20864448472975628947226005981267194447042584001 = (2 + 0 + 8 + 6 + 4 + 4 + 4 + 8 + 4 + 7 + 2 + 9 + 7 + 5 + 6 + 2 + 8 + 9 + 4 + 7 + 2 + 2 + 6 + 0 + 0 + 5 + 9 + 8 + 1 + 2 + 6 + 7 + 1 + 9 + 4 + 4 + 4 + 7 + 0 + 4 + 2 + 5 + 8 + 4 + 0 + 0 + 1)20

Moving Without Motion?

Achilles-weed is prostrate and grows along the ground at the amazing rate of 10 cm per hour. An exceeding slow tortoise munches one end of the Achilles-weed at the same rate as it grows at the other end. So the tortoise appears to chase the Achilles-weed round the garden. But, strictly speaking, the Achilles-weed does not move at all, it grows and is eaten. Yet its location changes, and it is made up of parts whose location changes (the left and right-hand halves of the Achilles-weed). Hence being made up of parts whose location changes is not sufficient for motion.

— Peter Forrest, “Is Motion Change of Location?”, Analysis, 1984

A Pretty Problem

In Longfellow’s novel Kavanagh, Mr. Churchill reads a word problem to his wife:

“In a lake the bud of a water-lily was observed, one span above the water, and when moved by the gentle breeze, it sunk in the water at two cubits’ distance. Required the depth of the water.”

“That is charming, but must be very difficult,” she says. “I could not answer it.”

Is it? If a span is 9 inches and a cubit is 18 inches, how deep is the water?

Click for Answer

Misc

  • SWEET-TOOTHED has three consecutive pairs of letters. SUBBOOKKEEPER has four.
  • Will you answer this question negatively?
  • 4624 = 44 + 46 + 42 + 44
  • The telephone number 278-7433 spells both ASTRIDE and CRUSHED.
  • “Nothing great was ever achieved without enthusiasm.” — Emerson

Beach Reading

Amazon reviews of A Million Random Digits with 100,000 Normal Deviates (1955), by the RAND Corporation:

  • “I had a hard time getting into this book. The profanity was jarring and stilted, not at all how people really talk.”
  • “Once you get about halfway in, the rest of the story is pretty predictable.”
  • “If you like this book, I highly recommend that you read it in the original binary.”
  • “I would have given it five stars, but sadly there were too many distracting typos. For example: 46453 13987.”
  • “I really liked the ‘10034 56429 234088’ part.”
  • “Frankly the sex scenes were awkward and clumsily written, adding very little of value to the plot.”
  • “For a supposedly serious reference work the omission of an index is a major impediment. I hope this will be corrected in the next edition.”

The average customer gives it four stars.

Misc

  • EVIAN, SEIKO, and STROH’S are all English words spelled backward.
  • Can “I apologize” be false?
  • 165033 = 163 + 503 + 333
  • Little Wymondley, in Hertfordshire, is bigger than Great Wymondley.
  • “How old would you be if you didn’t know how old you was?” — Satchel Paige