A group of well-known scientists calling itself Science Debate 2008 (link on page 4) has just called for a presidential debate on scientific issues. Such a forum would be a most-welcome development, but I would supplement it with something more revealing of mental firepower -- garden-variety puzzles.
Big high-tech corporations such as Google and Microsoft as well as a host of smaller ones routinely utilize puzzles in their hiring practices. The rationale for this is the belief that an employee, say a programmer of some sort, is more likely to contribute in a creative, insightful way to the company if they're creative and insightful when presented with a complex puzzle.
Why then are candidates for the presidency never presented with a few simple puzzles to help the electorate gauge their cognitive agility? The same goes for interviewers who ask the same dreary, insipid questions time after time and accept the same dreary, insipid non-answers time after time.
These puzzles shouldn't be difficult since, after all, the primary job of the president is to enforce the Constitution, ensure an honest and open administration, and, in some generalized sense, make things better. For this task, judgment and wisdom are more essential than the ability to solve puzzles. Nevertheless, I think some non-standard questions like the following would help winnow, or at least chasten, some of the candidates.
1. Scaling. Imagine a small state or city with, let's say, a million people and an imaginative and efficient health care program. The program is not necessarily going to work in a vast country with a population that is 300 times as large. Similarly a flourishing small company that expands rapidly often becomes an unwieldy large one. Problems and surprises arise as we move from the small to the large since social phenomena generally do not scale upward in a regular or proportional manner.
A simple, yet abstract problem of this type? How about the following (answers on page 4): A model car, an exact replica of a real one in scale, weight, material, et cetera, is 6 inches (1/2 foot) long, and the real car is 15 feet long, 30 times as long. If the the circumference of a wheel on the model is 3 inches, what is the circumference of a wheel on the real car? If the hood of the model car has an area of 4 square inches, what is the area of the real car's hood? If the model car weighs 4 pounds, what does the real car weigh?
2. Estimating. Proposing any sort of legislation or any action at all requires at least a rough estimate of quantity, costs, benefits, other effects. An ability to gauge them is critical (as is an ability to listen to others' unbiased estimates).
A couple of simple, yet abstract problems of this type? How about the following (hint and answer on page 4): A classic problem: How many piano tuners are there in New York City? And how many times the death toll on Sept. 11 is the annual highway death toll?