Stepping on the Gas And Decoding the Bible

Old challenge

You are out driving your gas-powered or perhaps new electric battery-powered car. At a freeway entrance, you need to accelerate from 0 to 60 m.p.h. within 20 seconds. What do you think is the best way to do this to use the least amount of energy?

Answer

Charles Sullivan reports that engines are more efficient at full throttle at high gears, so at least with a stick shift you should give it plenty of gas but shift up as quickly as possible. Marc Abel reports that batteries are more efficient at low power, so that it is better to apply more thrust at lower speeds. Robert Rein and Erik Randolph point out the opposite advantage of accelerating at the last minute to minimize total air friction (despite the sacrifice of safety and distance traveled). John Morrison duly notes the first, most obvious rule: Don't step on the brake! Search the Web for more fuel-saving tips.

'The Bible Code'

Readers have asked about the recent bestseller, "The Bible Code" by Michael Drosnin. (See book review, Sept. 4, Page 14.) The book reports how computer analysis of the original Hebrew Bible found interspaced spellings of "assassinate" and "Yitzhak Rabin," for example. My inclination is to attribute such hidden patterns to coincidence, not only because deliberate encoding sounds incredible, but also because the mathematics of coincidence can be very subtle.

Suppose your new phone number happened to be identical with the first seven digits of your US Social Security number. You would have every right to be astonished. If either number were completely random, the odds of such a coincidence would be 1 in 10 million. Now suppose 100 million of us compare our phone and Social Security numbers. With probability of more than 99.99 percent, someone will have identical numbers.

The point is that in a large context, some coincidences are bound to occur, and it is sometimes difficult to identify the appropriate context. If you look long and hard enough, you will find a big coincidence.

New challenge

Send in a true personal coincidence with an estimate of its mathematical probability of occurring. The least likely will be the winner.

* Send answers, comments, and new questions to:

Math Chat

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Princeton, NJ 08540

or by e-mail to:

Frank.Morgan@williams.edu