Sunday, June 22, 2008

Deceptive Numbers Used to Described Floods

Of all the deceptive numbers in circulation, the most ridiculous, expensive, and tragic are the numbers the U. S. Army Corp of Engineers use to describe the levees that they build. I saw an interview with General Michael J. Walsh on the NBC news this past week. In it he referred to the rainfall flooding Cedar Rapids as a “500-year storm.” The levees were not designed for such a rare event. According to General Walsh: “A lot of levees have over topped. We don’t consider that a failure.”

He is consistent with other officials I’ve seen interviewed, who refer to levees as having “100-year” or “500-year” designs. The terminology means that according to the statistical models used to predict floods, water should top a 100-year levee about once every 100 years and top a 500-year levee once every 500 years.

You wonder how engineers and government officials can quote these numbers with a straight face. Does the U. S. Army Corp of engineers understand anything about what they are doing along the Mississippi. Clearly once levees are constructed along the river all the flood statistics become meaningless.

Timothy Kusky, director of the Center for Environmental Sciences at St. Louis University, described in an interview on NPR how before levees were built, the Mississippi River was 4000 ft wide at St. Louis. Today the river is 1500 ft wide. As Kusky stated: “It is a simple concept; confine the river to a narrower channel and there is nowhere for the water to go but up.” The result according to Kusky is that we’ve had 15 hundred-year floods in the past hundred years, and many more 500-year floods in the past 150 years. Building structures changes all the statistics.

The other problem is that the flooding statistics are based on past events. Climate change models predict a 20% increase in rainfall in the coming decades for the Midwest. With that rainfall will come a 50% rise in the height of the rivers.

But, communities, developers, and home owners continue to invest large sums of money on the basis of the bogus statistical claims made by the Army Corp of Engineers. Chesterfield, Missouri now has the largest strip mall in the United States—3 miles long. The mall, along with 30,000 new homes, is built on land that was completely under 10 ft of water during the 1993 flood. The developer erected a “500-year” levee for protection and declared the area safe.

Robert E. Criss, Ph.D., professor of earth and planetary sciences at Washington University in St. Louis has strongly criticized such development as “ignoring geological reality.” On a Washington University news website, Criss describes as an "absurd exaggeration” the claim that a levee will withstand floods for 500 years. “If some private company were making claims that they'll sell you a car that will run for 500 years, they'd be in jail. Somehow, the government feels justified making absurd claims that have no basis."

It appears that little of substance was learned from the 1993 floods. The conclusion that higher levees need to be built ignores the reality that all of the water must have some place to go. A higher levee in one location will force water over the top in another location. The statistics that are the basis for the levee building and development become meaningless. But government officials and developers still rely on these absurd numbers and the result is heartbreaking for the people affected.

Joseph Ganem is a physicist and author of The Two Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy

Wednesday, June 18, 2008

A Question About the Monty Hall Problem

A reader forwarded me a link to an excerpt from a new book—The Drunkard’s Walk: How Randomness Rules Our Lives by Leonard Mlodinow. The excerpt discusses a widely misunderstood issue in probability theory that has become known as the “Monty Hall” problem. The reader asked me: “What is going on in this one? I looked through your book [The Two Headed Quarter] for a possible answer, but no luck.”

Coincidentally I just started reading Mlodinow’s book a few days ago and at least through the first two chapters I’m enjoying it. The book’s subject has always fascinated me and the author is a fellow physicist.

My book does not discuss the Monty Hall problem explicitly, but I do in the last chapter discuss how people become deceived by events that are conditionally probable. The Monty Hall problem is an extremely subtle example of how people are fooled by conditional probabilities. It is so subtle it has fooled professional mathematicians including Paul Erdos, one of the 20th century’s most prolific mathematicians.

Here is the problem. You are a contestant on the game show Let's Make a Deal. The host, Monty Hall, asks you to pick from one of three doors. Behind one is the grand prize and behind the other two are worthless consolation prizes. You choose door number one. Monty Hall, who knows what is behind all three doors and will not reveal the grand prize, opens door number two to reveal a consolation price and asks if you want to switch your choice to door number three. Should you switch or stay with door number one?

Many people argue that at this point your chances of winning are 50-50 and switching your choice to the other door will not improve your chances. But the reality is you should switch because you will win two-thirds of the time if you do. This fact is hard to believe. In his biography of Paul Erdos, The Man Who Loved Only Numbers, Paul Hoffman describes how Erdos, did not understand why switching improved the contestant’s chances. A friend wrote a computer program that simulated the Monty Hall problem and showed that switching does win two-thirds of the time, but Erdos still did not understand the reason why.

The reason you should switch is that once the all-knowing Monty Hall opened a door, he gave away information. His choice is not random; which means that your choice now has conditional probabilities associated with it. Had Hall acted first and then presented you with a choice of two doors, your chances would be 50-50. But he acted after you did and now you have a chance to respond. These are the three possible scenarios:

Prize behind door 1 – Hall opens either door 2 or 3, you switch to the one he doesn’t open and loose.
Prize behind door 2 – Hall must open door 3, you switch to door 2 and win.
Prize behind door 3 – Hall must open door 2, you switch to door 3 and win.

Switching wins two-thirds of the time and looses one-third of the time. But if you do not switch you have ignored the critical information that Hall provided. You win only the one-third of the time your original choice was correct.

That you do not even win half the time when you do not switch is another surprise. But if you ignore the information provided, the original odds cannot change. The mere act of opening another door has no effect on your original one out of three chance. You have to change your choice based on the new information. Notice the effect of the word “must” in the last two scenarios. Hall does not have a choice in these two scenarios but you do.

Note that you only lose by switching the one-third of the time your first choice was correct. The two-thirds of the time your first choice is wrong, switching guarantees a win. To understand this it helps to imagine an extreme example. Suppose there are 100 doors and you are asked to pick one. Your chances of being correct are 1%. Monty Hall then opens 98 doors revealing consolation prizes behind each. You are faced with a choice of two un-opened doors. I’d switch immediately to the one door he avoided opening. It will win 99% of the time. Only on the 1% chance that my first choice is correct will it be possible to lose.

The Monty Hall problem is subtle but people who play poker should recognize it as the entire premise of the game. In poker, players are dealt random cards, but they do not play random cards. Once the players act and additional cards are exposed it is not correct to say that someone vying for a pot could be holding any of the possible hands. In Texas Hold’em the odds against being dealt two pocket Aces are 220-1. But, if someone is betting and acting as if he or she has a great hand, the odds are much better than 220-1 that player has pocket Aces. The deal might be random but, like Monty Hall, a player’s actions are usually deliberate.

Joseph Ganem is a physicist and author of The Two Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy

Sunday, June 15, 2008

A Tax by Any Other Name

One of the most ludicrous debates of the never-ending election season is the one on tax policy. John McCain has changed his position on the Bush tax cuts and now says we should keep them. Congressional Democrats, who have argued for letting the tax cuts expire, quickly agreed to an economic stimulus package that includes mailing tax rebates to millions of American households. But it’s a sure bet that as November approaches, the “borrow and spend” Republicans will be saturating the airwaves with the “tax and spend” epithet hurled against the Democrats.

But what is lost in all in the election name-calling is that the government has two methods for taxing and it has been squeezing all of us financially while never using the word “tax.” The most familiar tax method is the one we all see with every paycheck; the method of subtraction. The government compels your employer to deduct money from your pay and send it to the U. S. Treasury. However, the government also controls the value of the currency you are paid in. Devaluing the currency is the second method of taxation.

As the U. S. government spends more and more dollars it doesn’t have, the world is being flooded with dollar-denominated IOU’s known as treasury bonds. These bonds are considered super-safe investments because the U. S. government has never defaulted on its debts. But why should it ever default? Unlike the rest of us, Uncle Sam has the power to print the dollars needed to pay its debts.

Federal debt is soaring into the trillions of dollars with no end in sight and no plan to pay it back. Foreign buyers of treasury bonds are losing confidence and the result is a steep slide in the value of the currency we are paid in. Eight years ago a Euro cost $0.82; today a Euro costs nearly twice that amount—over $1.50. The steep rise in the price of gas is only in part a change in the supply and demand equation for oil. The supply and demand equation for dollars is a significant part of the cost increase for gas, energy and food.

Politicians speak of their plans for “energy independence” or “food independence” as if the United States could wall itself off from the rest of the world and live only on its own resources. But independence is a myth. Oil is a global commodity and will always be sold on a worldwide market. Exxon-Mobil will always sell their product to highest bidder, wherever the bidder resides. The same is true for food companies.

If in the last election a politician had proposed a new substantial tax on gasoline to go towards federal debt he or she would have been voted out of office. But that has happened anyway without the word tax used as a label.

David T. King wrote in an op-ed article in the Wall Street Journal on May 23, 2008 that Oil is up because the dollar is down. A graphic that accompanied the article compared the price of oil in dollars with the price in Euros since 2002. In 2002 oil sold for $30 per barrel that at the time was equal to 30 Euros. Today oils sells for over $130 per barrel or just over 80 Euros. King concludes that we don’t need a gas tax holiday; we need an exchange rate policy.

In King's words: “Exchange rates can be managed.” But I don’t understand how exchange rates can be managed without the federal government first getting its own finances in order and wean itself away from reliance on debt.

Joseph Ganem is a physicist and author of The Two Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy