The solution to your April Brain Bogglers states that "if two percentages are to multiply out to 100 percent, one of the percentages must be greater than 100 percent and one must be less." But I must point out that it is also impossible to generate an exact copy using only the 125 percent and 10 percent keys, or only the 128 percent and 10 percent keys. For example, using the 125 percent key 31 times and the 10 percent key 3 times, or the 128 percent key 28 times and the 10 percent key 3 times, will lead to copies between 100 and 101 percent of the original but will not generate an exact copy. It will also lead to illegible copies, an irritated secretary, and a broken machine.
John L. Drost
Huntington, W. Va.
Assuming a standard 8.5-by-11-inch original document, could a copier output a single sheet of paper ten times the original's size (requirement of problems two and three)? And if this restriction could be overcome, how could they copy such large intermediate reproductions? Finally, how readable would the last copy be?
Maybe the mathematics department should have taken their originals next door to the English department. I'm sure they could have whipped out a copy in no time.
North Bergen, N.J.
If you insist on realism, assume that the math professors were trying to make a 100 percent copy of a postage stamp. Though legally suspect, this scenario would fit entirely within the capabilities of a standard photocopier.
Fat as We Wanna Be?
Fat people are quick to seize on any excuse for their obesity other than their own self-indulgence. It is certainly true that people who are fat are so because they eat more than their bodies require. Physicians spend many hours, usually unsuccessfully, in the effort to persuade patients to control their intake of food and drink. We don't need help like your April article "Why We Get Fat."
Daniel H. Cannon, M.D.
New Albany, Ind.
Be Fruitful, Die Young
Having had four children, I read "Be Fruitful, Die Young" in the April issue thinking I was doomed. However, if "nearly half" the women who survived past 81 were childless, doesn't that mean more than half the survivors did have children? Unless there is a third category, it seems that having children improves your chances of surviving past 81. Did I miss something?
Our short article required readers to fill in some information. In the data analyzed, which spanned a period from 740 to 1875, more than two-thirds of the women had children, but only about half the women who lived beyond 81 had children. Childless women were disproportionately well represented in the long-lived pool. Those women who had children and lived to a ripe old age tended to have had fewer children than those who died younger. But take heart: while the study indicates that the body's resources may make trade-offs between longevity and reproduction, we can't use such data to determine individual outcomes, much less life decisions. In life, as in car mileage, actual results may vary.
The Rocket Men Weigh In
"Private Rockets" [April] neglects to mention that there are several ways to beat the rocket equation by attacking its assumptions. First, there is no need for an orbital launcher to contain its own fuel. Many proposals have been made, including launching a capsule using mass accelerators in the same way a bullet is launched from a firearm, or beaming launch energy to the vehicle in the form of microwave or laser beams.
Second, even if we are resigned to fueling the launcher, the rocket equation is problematic if we restrict ourselves to chemical fuels. Chemical reactions lack the energy density to efficiently fuel a launcher. Even if we envision tremendous breakthroughs in materials science permitting lighter structures and hotter, more efficient engines, this basic truth remains.
There is another alternative. A nuclear-powered launcher would show vast improvement in fuel density. Even if designs required a massive amount of shielding or other structures for nuclear fuel, they would not be as wasteful and inefficient as current chemical-power designs.
Perhaps the millions being spent to reinvent the chemical rocket launcher would be better invested on investigating nuclear sources. With a suitable energy source, inexpensive orbital launchers would be at hand.
Although Kelly Space may be serious about using a highly modified Lockheed L1011 as a second-stage vehicle, the sight of this being towed aloft by a 747 would be quite remarkable. And if the 747 in question is the one shown in the picture on page 91, my confidence in the mission would be reduced by orders of magnitude, for it appears in need of at least a wash to remove the hydraulic fluid from the underside of the fuselage.
Francis E. Tarzian, Jr.
You claim that Burt Rutan's Voyager "set a record by becoming the first single-engine airplane to fly around the world nonstop." Voyager had two engines, one in the front and one in the back. And you imply that other multiengine aircraft have accomplished nonstop around-the-world flights. Excluding orbiting vehicles, no other heavier-than-air craft of any design has successfully flown around the world nonstop without refueling. In fact, Voyager's flight is more than double the next longest airplane flight.
Matthew R. Sleeter
Voyager had an engine in front of the cockpit and one behind. It used the rear engine while in flight but required two for its fuel-heavy takeoff.
Birds of a Feather?
We got a kick out of your article in the April issue on zebra finches and their ersatz crests ["Hot Headgear," R&D;]. Only one problem: the bird pictured on the left is an Australian long-tailed grassfinch, commonly known as a shafttail. We know because we have the last offspring of our breeding pair (Fibber and Molly) still thriving in our living room aviary. Its parents had 17 successful offspring and were quite wonderful to watch as they performed their mating dances and pair-bonding rituals. The other bird in the photo is indeed a zebra finch, which is a prolific breeder as well. Wonderful pictures in any case and a real grin for small-bird fans.
Carl and Maret Hutchinson
The photograph, as well as the study on which the article was based, included both zebra finches and long-tailed finches, a fact we did not have space to mention.