STRANGE BUT TRUE- Counting sheep: Numbers not what they appear


Q. "I see you've got 3 fine sheep in the field there," you say to the farmer. "Actually," he replies, "there might be 2, 2.5, 3, 3.5 or 4, depending." Depending on what? What's this wiseacre thinking? –B. Peep

A. Maybe wise thoughts, as he explains that 1 of the 3 is a lamb, say Michael Blastland and Andrew Dilnot in The Tiger that Isn't: Seeing Through a World of Numbers. So does a lamb still count as a full sheep, or is it half a sheep? Also, one is a pregnant ewe in advanced labor, he continues. Would that one be 1, 1.5, or 2? (Assuming no multiple sheep births.) 

"Therefore, depending on how the units are defined, the sheep total could be any of the numbers I gave initially," says the farmer. Thus, suggest the authors, the farmer did successfully parlay "the laughably simple example of 3 sheep into 5 answers, which is quite a spread, one of them twice the size of another, and counting to 4 just became ridiculous."

Moral: You can count on many things in life to be not quite what they first seem.

Q. It's a central event of every football game, lasting barely 8 milliseconds (.008 second), or a lot less than an eyeblink while involving a ton of force– literally. What is getting bent out of shape here? –A. Vinatieri

A. That's roughly the duration of the collision between the kicker's foot and the ball on a kickoff,

averaging about 450 pounds of force but spiking up for an instant to maybe 2,000 pounds, says Timothy Gay in Football Physics: The Science of the Game. Here, the football– under high-speed stroboscopic photography– can be seen to deform dramatically, squashing in very briefly by several inches. "No wonder a ball so pictured looks a little like it's made of foam rubber!" says Gay.

Q. Can you envision the next space food frontier? –D. McNair

A. The Space Agriculture Task Force is looking toward the day when long-term space travelers "grow" their own food, though not vegetables or grains since these don't supply the needed fats and amino acids, says Wynne Parry in Discover Magazine. Even a small on-board farm would be sufficient to produce a steady stream of edible bugs that rapidly reproduce and efficiently convert materials inedible to humans– mulberry leaves, wood, waste, etc.– into their own body mass. 

"So bugs like silkworms, termites, drugstore beetles could help fill in the astronauts' nutritional gaps. Japanese researchers have already made cookies from a commonly domesticated silkworm species," says Parry. Out-of-this-world entomophagy up on the farm.

Q. It's hard to swallow, but a circus performer helped bring about modern medical esophagoscopy? How so? –L. Lovelace 

A. Here a viewing device of optical fibers is extended down the patient's throat and into the stomach, says Jearl Walker in The Flying Circus of Physics. The curved tube follows the path from mouth to esophagus, with light projected down and then back to a video camera. The doctor looks for signs of cancer or an ulcer or maybe even illicit packages of smuggled drugs (called "body packing").

As for the circus performer, originally the procedure was performed with a crude straight tube, but this proved too short to reach the stomach. So a pioneering doctor experimented with using a longer one: he called in a sword swallower who was able to tilt his head back, relax certain muscles along the esophagus, and make a fairly straight passage from pharynx to stomach. "When the doctor illuminated the free end of the inserted tube, he saw the stomach's interior, and modern esophagoscopy began."

Q. Never seen a UFO? Are you in the mood for seeing one tonight? –D. Kucinich 

A. Try this: In a dark room, stare at the glowing tip of a cigarette in an ashtray a distance from you. Within seconds, it will begin moving around– or seem to– as your eye muscles grow tired from fixating too long on one spot. 

"It will appear to wander around erratically, swooping in different directions or oscillating back and forth," says Ronald K. Siegel in Fire in the Brain: Clinical Tales of Hallucination. "With proper suggestions, the light can appear to move several feet. Despite such movements, the light always comes back to its original position."

Now go outdoors and stare a while at a solitary star and watch it begin to move around (the "wandering star illusion"). Or pick out an unidentified colored light far off near the dark horizon. In a suitably suggestible mood, you may soon witness your own UFO "visitation."

Send Strange questions to brothers Bill and Rich at