The Trick of Predicting the 'Random'

THE trick in the box below has been circulating by e-mail lately, and came to us via Mary Lee. Your answer was 7, was it not? Try it on your friends.

Why do most folks pick 7? It would be a bit extreme to pick 12 or 5, or even 11 or 6. That leaves 7, 8, 9, and 10.

Seven has great appeal. It is the number of days in the week, for example. Seven is special.

The other numbers factor: 8 = 2 x 4, 9 = 3 x 3, 10 = 2 x 5; but 7 is a prime number and cannot be factored into other numbers. Furthermore, the phrase "between 12 and 5" might somehow suggest 12 - 5 = 7.

The preliminary addition questions in the trick are not important, except to put the respondent on edge and discourage concocting a deliberately unusual answer.

A similar old trick ends with "Name a vegetable," and invariably evokes the response, "Carrot!"

These tricks show that what appear to be random actions often follow hidden patterns or habits. The mathematical theory of chaos, popularized by beautiful pictures of fractals and by the mathematician in the movie "Jurassic Park," explains how some structure often underlies apparent disorder.

If you try these tricks on friends, first hand them a sealed envelope with the answer, in order to produce the appropriate amazement when they open it after their response.

Old challenge

What causes the irregularities on the order of 10 minutes in the time from one arrival of spring to the next?

Answer

Mike Bevan explains that the moon (and other planets), although much smaller than the sun, perturb the earth's orbit around the sun slightly. Although we think of the moon as circling the earth, actually both circle their mutual "center of mass," which lies in between their two centers. The earth is so much heavier than the moon that the center of mass lies inside the earth.

Still, depending on which side of the earth the moon is on, the center of the earth can be either a bit ahead or behind the common center of mass, and spring arrives early or late. Also, as pointed out by George Dillard, Bill Hasek, and Erik Randolph, the axis of the earth wobbles a little ("nutation"), causing the moment when the axis is at a right angle to the sun ("spring equinox") to vary fractionally.

Bob Swanson and Stanley Wales point out that at spring equinox, day (sunrise to sunset) is longer than night for two reasons. First, dawn comes before the center of the sun reaches the horizon when just the top of the sun clears the horizon. Second, the earth's atmosphere bends sunlight so that we can see the sun even earlier. This all assumes no mountains get in the way!

New weighing challenge (Joe Shipman)

A balance scale tells which of two objects is heavier. How many weighings does it take to put three objects in order from heaviest to lightest? What about four objects? What about five objects?

Send answers and new questions by e-mail to:

fmorgan@princeton.edu

http://www.williams.edu/Mathematics/fmorgan