You’re eating apples with your friend Dr. Psychic Psycho, a talented biochemist who fancies himself a clairvoyant and has made many accurate oddball predictions.

“I have interesting news for you,” he says. “You must seriously consider taking this pill. As you know (since we have recently determined it together), it contains substance X, which (as you also know — but consult this pharmacopeia if in doubt) is fatally poisonous by itself, while nevertheless furnishing unfailing antidote to poison Z — though it does have some minorly unpleasant side effects. Now the apple I gave to you, which you have just finished eating, was poisoned by me with Z — or not — in line with my prediction as to your taking or not taking the antidote pill. Benign old me, of course, only poisoned the apple if I foresaw that you were indeed going to take the antidote. And not to worry — I’m a very good predictor.”

He rushes off. What should you do?

(By University of Pittsburgh philosopher Nicholas Rescher.)

In 1958, B.F. Skinner and Erich Fromm attended the same California symposium. Skinner found that Fromm “proved to have something to say about almost everything, but with little enlightenment,” and “when he began to argue that people were not pigeons, I decided that something had to be done”:

On a scrap of paper I wrote ‘Watch Fromm’s left hand. I am going to shape a chopping motion’ and passed it down the table to [Halleck Hoffman]. Fromm was sitting directly across from the table and speaking mainly to me. I turned my chair slightly so that I could see him out of the corner of my eye. He gesticulated a great deal as he talked, and whenever his left hand came up, I looked straight at him. If he brought the hand down, I nodded and smiled. Within five minutes he was chopping the air so vigorously that his wristwatch kept slipping out over his hand.

“William Lederer had seen my note, and he whispered to Halleck. The note came back with an addendum: ‘Let’s see you extinguish it.’ I stopped looking directly across the table, but the chopping went on for a long time. It was an unfair trick, but Fromm had angered me — first with his unsupported generalizations about human behavior and then with the implication that nothing better could be done if ‘people were regarded as pigeons.'”

(From Skinner’s 1983 memoir A Matter of Consequences.)

4³ + 18³ + 33³ = 41833
16³ + 50³ + 33³ = 165033
22³ + 18³ + 59³ = 221859
44³ + 46³ + 64³ = 444664
48³ + 72³ + 15³ = 487215
98³ + 28³ + 27³ = 982827

There is a legend that after Buddha died, his shadow lingered in a cave. It actually is possible for a shadow to persist without any sustaining object. Light travels at 299,792,458 meters per second in a vacuum. The moon is about 384,400,000 meters away from Earth. Hence, if the moon were instantly obliterated during a solar eclipse, its shadow would linger for more than a second on the surface of Earth. If the moon were farther away, its shadow could last several minutes. We can extrapolate to posthumous shadows that postdate their objects by millions of years. We can also speculate about an infinite past in which a shadow is sustained by a beginningless sequence of objects. As one object is destroyed, an object of the same shape and size seamlessly replaces it. This shadow antedates any object in the sequence and so refutes the principle that every shadow is caused by an object. Shadows are not dedicated dependents. Although slaves to some object or other, they can switch masters.

— Roy Sorensen, Seeing Dark Things, 2008

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, Q^mQⁿ = Q^{m + 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.”