I'll Give You 15 Minutes


Answer Me!

There is a country in Europe where multiple-choice tests are illegal.

- Sigfried Hulzer

Source: Funny Times September 2000

Source: The Dominion 28 August 2000

Intelligent Politicians?!?

Should Potential Presidents Know Math?

A List of Proposed Quiz Questions

by John Allen Paulos

Watching political debates, I sometimes find myself hoping that the moderators will pose a simple arithmetical question or two.  Queries about the war, taxes, and cultural issues usually elicit rhetoric and canned answers that most of the candidates could recite in their sleep, but even very simple arithmetical questions would require a bit of thought and calculation that they couldn't easily evade.

Professional myopia may be part of the reason for my writing about this topic again, perhaps, but I do believe that some feel for mathematics (not algebraic topology or partial differential equations, but arithmetic) is essential to being an effective president.  After all, almost every political issue has a large quantitative aspect: medicare and social security, the environment, military spending, tax and service cuts, social security, crime, and education, to name a few.  A candidate who could answer, or at least reasonably respond to most of the following questions would, I think, be sufficiently numerate to hold the job.

To help insure this end, I hereby urge future debate moderators (both during the primaries and the general election) to announce that no candidate will be left behind, that each will be asked at least one basic numerical question during each debate.  The answers the candidates provide might be more telling than their latest "bold new program" or inconsequential anecdote.  They might even be amusing.

The Quiz

Below are just 10 of the many politically neutral questions that might be asked.  The answers follow.

  1. A crucial number to know is the population of the country of which you want to be president.  What is the approximate population of the United States?  of the world?  What percentage of the latter is the former?
  2. A news article claims that 15% of all strokes occur sometime between noon and midnight on either Friday or Saturday, perhaps because of increased celebrating on the weekends.  Do you check with the Centers for Disease Control?  Do you stop campaigning on weekends?  What's your reaction to this statistic?
  3. You must understand the electoral process, of course, so given the way the Electoral College is set up, what is the theoretically smallest number of actual votes (not electoral votes) a candidate can receive and still be elected president?
  4. Approximately how many Americans died in the attacks on 9/11?  There's no moral comparison, of course, but approximately how many die in auto accidents annually?  from heart disease annually?
  5. You're campaigning in a state in which the percentage of employees who subscribe to a particular drug plan has risen 1 percentage point, from 1.5% to 2.5%.  By what percent has this figure risen?  By what percent must it fall to return to its former level?
  6. In Disproportia, a small Midwestern town, the average tax cut per household is $2,200, but the median tax cut is $150.  What does this say about the distribution of taxable incomes in the town?  If the founder of a high-tech company were to move into the community, which is more likely to rise, the mean or the median tax cut?
  7. Roughly how big is the federal budget?  What fraction of it is discretionary and non-military?  By contrast, what is the gross domestic product (to the nearest trillion dollars)?
  8. If the government spends $1,000 per second, it will take approximately 17 minutes to spend $1 million.  At this rate, about how long will it take to spend $1 billion?  How long to spend $1 trillion?  One comparison: the $87 billion supplementary budget for Iraq is approximately how many times the annual US contribution to the UN?
  9. An ace pollster on your staff claims that 63.86% of 100 Americans surveyed support your foreign policy.  What's your reaction to these numbers?
  10. If FAWUA, the federal agency with an unpronounceable acronym, deposits $1 billion in an escrow fund at 7%, how long until the deposit is worth $2 billion?  $4 billion?  Alternatively, if the agency borrows $1 billion at 7% and makes no payments on it, how long until it owes $2 billion?  $4 billion?

The bottom line: a president should be able to put 2 and 2 together, both numerically (the easy part) and otherwise.

The Answers

  1. About 290 million.  A bit more than 6 billion.  A little less than 5%.
  2. By itself that's not very impressive evidence.  The time period after 12pm on Fridays and Saturdays constitutes 1/7 or 14.3% of the week so, as a first approximation, you'd expect roughly that percentage of strokes over any two days after 12pm.
  3. Candidate X could receive as few as 11 votes and his opponent, candidate Y, tens of millions.  Specifically, if California, New York, Texas, Florida, and the 7 other states with the most electoral votes each had a turnout of 1 voter who voted for X, and the other 39 states voted unanimously in the millions for Y, X would win.
  4. Approximately 3,000, 40,000, and 700,000, respectively.
  5. It's risen by 67% but must be cut by only 40% to reach its former level.
  6. By the definition of "median," half the households receive less than $150 in tax cuts, half more, so there are some very wealthy people in town.  These people, like the new company founder, drag up the average tax cut much more than they do the median cut.
  7. About $2 trillion, 20%, and a bit more than $11 trillion, respectively.
  8. About 11.5 days for $1 billion, 32 years for $1 trillion, and roughly 250 times as much, respectively.
  9. The question at issue is impossibly vague, the number surveyed is relatively small, and the precision of the figure is entirely bogus.  Fire the pollster.
  10. About 10 years and 20 years, respectively.  It's important to know that the length of time it takes money to double at an annual interest rate of r percent is roughly 70/r.  In this case 70/7 equals 10 years, and a second doubling requires another 10 years.

Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy, and the just released A Mathematician Plays the Stock Market.  His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.

Source: abcnews.go.com 4 January 2004

Also see:

bulletBrain Games (in the Animation section) - requires a fast connection and Flash (it contains this Mensa quiz - plus lots more).
bulletIQ Test - for an example of the cultural assumptions involved in assessing someone else.
bulletCan This Be True? - short visual test of an area problem (also contained in Brain Games, above).
bulletAre You a Professional? - test of creative thinking.
bulletPassing the 8th Grade, 1895 - and includes history and world affairs questions drawn from The Economist (the latter are also included in Brain Games, above).

The bottom four sites above are all located elsewhere in this section if you really like taking tests.  In other sections are:

bullet100 Facts (in the section on Oddities) - I'll bet you don't know most of them...
bulletThanks, Mom, for the Brains (in the section on Men) - articles which discuss the genetic basis for IQ

Memory Bottleneck Limits Intelligence

by Tanguy Chouard

A single spot in brain determines size of visual scratch pad.  The number of things you can hold in your mind at once has been traced to one penny-sized part of the brain.  The finding surprises researchers who assumed this aspect of our intelligence would be distributed over many parts of the brain.  Instead, the area appears to form a bottleneck that might limit our cognitive abilities, researchers say.

"This is a striking discovery," says John Duncan, an intelligence researcher at the Cognition and Brain Sciences Unit in Cambridge, UK.

Most people can hold 3 or 4 things in their minds at once when given a quick glimpse of an image such as a collection of coloured dots, or lines in different orientations.  If shown a similar image a second later, they will be able to recognise whether 3 or 4 of these spots and lines are identical to the first set or not.  But some people can only catch 1 or 2 things in a glance, while others can capture up to 5.

This very short-term memory capacity is thought to be related to intelligence.  In the same way that a computer with a larger working memory can crank through problems more quickly, people with a greater capacity for holding images in their heads are expected to have better reasoning and problem-solving skills.  A person's working memory capacity can be determined using simple psychological tests.  But now two teams of researchers report in Nature that they can see it in brain scans too.  One of the teams, led by Edward Vogel of the University of Oregon in Eugene, found that the electrical activity in a single section of the brain, as detected through electrodes attached to the scalp, is directly related to short-term working memory1.

The team first tested subjects with an image of 2 coloured dots, waiting a second between flashes and asking the subjects if the image had changed.  They then ramped up the test to 4 dots.  A large increase in the subject's brain activity on the 4-dot test indicated that his or her memory capacity had not been pushed to its limit.  No increase in electrical activity indicated that his or her working memory had topped out on the 2-dot test.  By graphing these responses, the team worked out the exact size of each subject's working memory.

A second team, led by René Marois of Vanderbilt University in Nashville, Tennessee, used functional magnetic resonance imaging during similar tasks to accurately locate the part of the brain being used for short-term visual memory2.  Both teams concluded that everything depended on the same tiny spot in the posterior parietal cortex.  "It is amazing that both groups should converge on the same area in the end," says Duncan.  Since the task involves remembering many different aspects of each object, including spatial position, orientation and colour, most people thought that several parts of the brain would be involved, he says.

There are still many other aspects to human intelligence that are governed by other parts of the brain, the authors of both studies warn.  But the capacity of one's working memory may form a bottleneck for certain kinds of intelligence, they say.

Tanguy Chouard is a senior biological sciences editor at Nature


  1.  Vogel, E K & Machizawa, M G.  Nature, 428, 748 - 751, doi:10.1038/nature02447 (2004).
  2. Todd, J J & Marois, R.  Nature, 428, 751 - 754, doi:10.1038/nature02466 (2004).

Source: www.nature.com 15 April 2004 © Nature News Service / Macmillan Magazines Ltd 2004

How's That?

bulletCoca-Cola was originally green.
bulletIt is impossible to lick your elbow.
bulletThe state with the highest percentage of people who walk to work: Alaska
bulletThe percentage of Africa that is wilderness: 28%
bulletThe percentage of North America that is wilderness: 38%
bulletThe cost of raising a medium-size dog to the age of eleven: $6,400
bulletThe average number of people airborne over the US any given hour: 61,000
bulletThe first novel ever written on a typewriter: Tom Sawyer.
bulletThose San Francisco Cable cars are the only mobile National Monuments.
bulletIf a statue in the park of a person on a horse has both front legs in the air, the person died in battle.  If the horse has one front leg in the air, the person died as a result of wounds received in battle.  If the horse has all four legs on the ground, the person died of natural causes.
bulletHershey's Kisses are called that because the machine that makes them looks like it's kissing the conveyor belt.
bulletQ. Half of all Americans live within 50 miles of what?
A. Their birthplace
bulletQ. Most boat owners name their boats.  What is the most popular boat name requested?
A. Obsession
bulletQ. If you were to spell out numbers, how far would you have to go until you would find the letter "A"?
A. One thousand
bulletQ. What do bulletproof vests, fire escapes, windshield wipers, and laser printers all have in common?
A. All invented by women.
bulletQ. What is the only food that doesn't spoil?
A. Honey
bulletQ. What is an activity performed by 40% of all people at a party?
A. Snoop in your medicine cabinet.
And Finally
bulletAt least 75% of people who read this will try to lick their elbow.  [I don't believe that.]

Source: avolites.org.uk

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