At the end of May, Microsoft gave up in the race with Google to digitize all the world’s printed books and magazines. The motivation for these ambitious projects is to allow search engine technology to reach inside the pages of every book in print. These corporations envision a future with no need to actually thumb through a book at a store or library in search of information. Search engines will perform the task much faster and return the exact location inside of any book for any text or keyword a user is seeking.
Whether such a future is a good or bad one for writer and publishers remains to be seen. Publishers have been less than enthusiastic about these digitization projects because of fears of copyright infringement and potential loss of sales. My own view as a writer is that exposure is a good thing. Obscurity is a greater threat to a writer’s livelihood than copyright infringement.
The Microsoft explanation provided for the decision to abandon the project came in classic corporate-speak. On a Microsoft blog, Satya Nadella, Senior vice president for search portal and advertising, wrote:
“Given the evolution of the Web and our strategy, we believe the next generation of search is about the development of an underlying, sustainable business model for the search engine, consumer, and content partner. For example, this past Wednesday we announced our strategy to focus on verticals with high commercial intent, such as travel, and offer users cash back on their purchases from our advertisers.”
If I ever need to write a parody of a corporate memo these sentences are a good starting point. Just how many buzzwords—evolution, development, strategy, sustainable, verticals, model, etc—are packed into just these two sentences with 65 words of prose? Actually with digitized books, questions such as that can be answered. In fact Google and Microsoft have been playing catch up with Amazon’s “Search Inside the Book” program launched in 2004. Publishers are now encouraged to submit electronic copies of printed books for Amazon to digitize and make searchable.
But, Amazon’s “Search Inside The Book” program allows for more than just keyword searches. You can now look at statistics about the writing style of a book before you purchase it. I checked Amazon’s listing for my book—The Two Headed Quarter—and discovered all sorts of numerical facts that I did not know. My book has 672, 289 characters arranged into 99,104 words. As expected in a book about deceptive numbers, the word “number” appears frequently—567 times, but it is the second most frequently occurring word. I had no idea that the most frequently used word in my book, appearing 709 times, is “years.”
But most fascinating is the statistical summary of my writing style that Amazon provides. Potential buyers can view the “readability” and “complexity” analysis of the text. My book rates as highly readable with a Flesch-Kincaid index of 7.2, meaning that you only need a 7th grade education to read it. According to Amazon 77% of all the other books are harder to read and in the category of personal finance books, 93% are more difficult to read. The easy reading arises in large part because the complexity analysis reveals that I have a simple writing style averaging only 8.6 words per sentence.
Now that last number threw me. I opened my book to some random pages and I found myself hard pressed to find sentences as short as 8 to 9 words, let alone enough sentences less than 8 words that would allow 8.6 to be the average. Amazon’s number for my average words per sentence just didn’t seem reasonable to me. I decided to run my own check using Microsoft Word’s analysis tools on some chapters from the original manuscript. I had never done that kind of analysis on my writing before, which shows you how much I think about readability statistics when I’m writing. The results:
For Chapter 1:18.0 words per sentence, Flesch-Kincaid index —10.1
For Chapter 2: 17.2 words per sentence, Flesch-Kincaid index —10.7
For Chapter 5: 18.9 words per sentence, Flesch-Kincaid index —11.4
For Chapter 8: 19.3 words per sentence, Flesch-Kincaid index —10.8
This means the readability of my writing is consistently at a 10th to 11th grade level (not 7th grade) and about average in complexity (according to Rudolf Flesch, co-inventor of the Flesch-Kincaid scale, the average words per sentence found in reading material is 17).
So how can Amazon’s statistics be so skewed? I don’t know but I have a good idea. Again, my book is about numbers and there are many numbers in the book. There are figures and tables with numbers along with worked examples containing numbers that allow readers to figure out numerical answers to many common financial questions. Many of the numbers in the book contain decimal points. My hypothesis is that the software Amazon uses to perform readability analysis cannot tell the difference between a period and a decimal point. After all, there is no difference between the two characters. Only an actual reader who can interpret the meaning of a sentence knows that a decimal point inside a number does not terminate a sentence.
I find it ironic that a book about deceptive numbers has an Amazon listing with a bunch of deceptive numbers to characterize its readability. Another example of companies spending time and resources to compile and publish useless numerical information. By the way, according to Amazon’s site my book has 3348 words per ounce and if you buy it you will receive 4715 words for each dollar you spend.
Joseph Ganem is a physicist and author of the award-winning The Two Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy
Thursday, July 31, 2008
Tuesday, July 15, 2008
Does showing up for work cost more than you earn?
The Sunday (July 13, 2008) Baltimore Sun this week had a front-page article about mothers: “Back to Work, Like it or Not” with the subtitle that “Women who left jobs for children find economy reverses the trade.” Reporter Jill Rosen writes “The soured economy—with its ever-increasing gas, food and utility prices, its sinking home values and its corporate downsizing—is forcing mothers who have traded careers for families to think about trading back.”
I can relate to the article because my wife will change from part-time to full-time work this fall. Energy and food prices have increased so much in the past year our budget no longer works as it once did. But our three children are teenagers and our current financial goal is getting them all through college. The Baltimore Sun article profiled women in much more difficult circumstances—mothers of toddlers and infants who planned on being stay-at-home moms. But, the article left me wondering if working for a paycheck outside the home is a financially viable option for many these women.
Women who can work professional salaried jobs will come out ahead financially by working outside the home. But women who work part-time or for lower wages might find that the same financial pressures forcing them outside the home might also make it impossible to realize any financial benefit.
How much money will these women have left after paying for commuting costs, daycare, work expenses, Social Security, and state and federal taxes? I’ve already seen television news reports about men with commutes so long it no longer pays to drive to work. I can imagine many common circumstances where stay-at-home moms would be hard pressed to increase the family income by working outside the home.
To assist families in figuring out how much additional income can be generated by working outside the home, I’ve teamed with my publisher to create a new calculator for the Compute Gas Savings Website. The calculator, at http://www.computegassavings.com/earningscalc.html, computes daily take home pay after subtracting all of the costs associated with showing up for work.
Consider a married mom in the suburbs with one child who finds a job in a city that pays $12 per hour. She must commute 25 miles each way in a family SUV that gets 20 miles per gallon. She manages to find daycare for $25 per day and finds herself spending an additional $5 per day on average for other work-related costs—coffee, snacks, clothes, car maintenance etc. Because she is married her additional income is not completely sheltered by deductions and exemptions. For this example we will assume a net federal tax rate of 10% and state tax rate of 3%. After entering all these numbers in the calculator it shows that she will take home just $36.17 per day out of her $96 per day net earnings or about $4.50 per hour.
Where did the money go? The combined cost of Social Security, federal, and state taxes takes one-quarter and the combined cost of daycare and gas takes one-third. That means it costs more than one half of her pay just to show up for work. This assumes she has only one child. Add the cost of daycare for a second child and daily earnings come to $11.17.
In fact it is easy to construct plausible scenarios where real earnings per day become negative. Keep the same tax rates, lower her hourly pay to $10, or $80 per day, give her two children so that daycare becomes $50 per day, make the distance to work 30 miles and the gas mileage 15 miles per gallon, and the real earnings per day becomes a negative $7.52. Going to work will cost her more than she makes.
I urge women looking to increase family income by working outside the home to test out different scenarios before deciding on a job. The hourly pay offered might not be the relevant number to compare when making a decision.
Joseph Ganem is a physicist and author of the award-winning The Two Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy
I can relate to the article because my wife will change from part-time to full-time work this fall. Energy and food prices have increased so much in the past year our budget no longer works as it once did. But our three children are teenagers and our current financial goal is getting them all through college. The Baltimore Sun article profiled women in much more difficult circumstances—mothers of toddlers and infants who planned on being stay-at-home moms. But, the article left me wondering if working for a paycheck outside the home is a financially viable option for many these women.
Women who can work professional salaried jobs will come out ahead financially by working outside the home. But women who work part-time or for lower wages might find that the same financial pressures forcing them outside the home might also make it impossible to realize any financial benefit.
How much money will these women have left after paying for commuting costs, daycare, work expenses, Social Security, and state and federal taxes? I’ve already seen television news reports about men with commutes so long it no longer pays to drive to work. I can imagine many common circumstances where stay-at-home moms would be hard pressed to increase the family income by working outside the home.
To assist families in figuring out how much additional income can be generated by working outside the home, I’ve teamed with my publisher to create a new calculator for the Compute Gas Savings Website. The calculator, at http://www.computegassavings.com/earningscalc.html, computes daily take home pay after subtracting all of the costs associated with showing up for work.
Consider a married mom in the suburbs with one child who finds a job in a city that pays $12 per hour. She must commute 25 miles each way in a family SUV that gets 20 miles per gallon. She manages to find daycare for $25 per day and finds herself spending an additional $5 per day on average for other work-related costs—coffee, snacks, clothes, car maintenance etc. Because she is married her additional income is not completely sheltered by deductions and exemptions. For this example we will assume a net federal tax rate of 10% and state tax rate of 3%. After entering all these numbers in the calculator it shows that she will take home just $36.17 per day out of her $96 per day net earnings or about $4.50 per hour.
Where did the money go? The combined cost of Social Security, federal, and state taxes takes one-quarter and the combined cost of daycare and gas takes one-third. That means it costs more than one half of her pay just to show up for work. This assumes she has only one child. Add the cost of daycare for a second child and daily earnings come to $11.17.
In fact it is easy to construct plausible scenarios where real earnings per day become negative. Keep the same tax rates, lower her hourly pay to $10, or $80 per day, give her two children so that daycare becomes $50 per day, make the distance to work 30 miles and the gas mileage 15 miles per gallon, and the real earnings per day becomes a negative $7.52. Going to work will cost her more than she makes.
I urge women looking to increase family income by working outside the home to test out different scenarios before deciding on a job. The hourly pay offered might not be the relevant number to compare when making a decision.
Joseph Ganem is a physicist and author of the award-winning The Two Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy
Thursday, July 3, 2008
Oil Prices Are Not Dependent on Oil Sources
A reader of my post “A Tax By Any Other Name” felt that I was naïve to suggest that supply and demand sets oil prices. The reader believes that oil pricing is driven more by speculation than anything else.
I agree with the reader that speculation is a large part of the reason we are paying $4 per gallon for gas at the moment. In my post I stated the supply and demand for oil is only a part of what sets the price for gas. I was mostly writing on how the increasing supply and decreasing demand for dollars is contributing to oil price increases. But in the last six months the falling dollar and increased oil consumption cannot account for the sudden 50% price rise for a barrel of oil. Speculation is clearly part of the problem.
It is no secret that the banks, investment houses, hedge funds, and oil companies now conduct most the trading in oil futures on all electronic foreign exchanges (such as the InterContinental Exchange or ICE) that are out of reach of U. S. regulators. A CBS news story quoted Michael Greenberger, a former top staffer at the Commodities Futures Trading Commission, as saying that 25% -50% of the price per barrel might be due to speculation. Greenberger believes that “If you can trade out of the sight of U.S. regulators, you can manipulate these markets."
What is especially disturbing about “foreign exchanges” like the ICE is that it is not actually foreign. Among its founding partners are Goldman Sachs and Morgan Stanley, its headquarters is in Atlanta, its primary data center is in Chicago, and it settles most trades in U. S. dollars. Despite all of its U. S. ties, the ICE claims that because its energy futures business is conducted in London—whatever that means—U. S. laws or regulations do not apply to it.
But all this supports the crux of my earlier argument that the energy independence that politicians speak of achieving is a myth because oil companies “will always sell their product to highest bidder, wherever the bidder resides.” The price of oil has no relationship to its origin.
In 2007 the U. S. imported about 10 million barrels of oil per day and produced about 5 million barrels per day. According to the Energy Information Administration, the top three countries of origin for imported oil in 2007 were Canada (1.85 million barrels per day), Mexico 1.47 million barrels per day) and Saudi Arabia (1.36 million barrels per day). Canada and Mexico actually supply more oil to the United States than Saudi Arabia.
If the U. S. decides to increase its domestic production of oil through offshore drilling or other means, it will contribute to the world supply of oil and that additional supply will be factored into the world price. Any politician who claims we can be more energy independent by drilling for more oil in the U. S. is being disingenuous. A far more relevant question to ask our political leadership is: Why are U. S. investment banks allowed to manipulate energy futures markets with no government oversight? I don’t think there is going to be a straight answer for that question.
Joseph Ganem is a physicist and author of the award-winning The Two Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy
I agree with the reader that speculation is a large part of the reason we are paying $4 per gallon for gas at the moment. In my post I stated the supply and demand for oil is only a part of what sets the price for gas. I was mostly writing on how the increasing supply and decreasing demand for dollars is contributing to oil price increases. But in the last six months the falling dollar and increased oil consumption cannot account for the sudden 50% price rise for a barrel of oil. Speculation is clearly part of the problem.
It is no secret that the banks, investment houses, hedge funds, and oil companies now conduct most the trading in oil futures on all electronic foreign exchanges (such as the InterContinental Exchange or ICE) that are out of reach of U. S. regulators. A CBS news story quoted Michael Greenberger, a former top staffer at the Commodities Futures Trading Commission, as saying that 25% -50% of the price per barrel might be due to speculation. Greenberger believes that “If you can trade out of the sight of U.S. regulators, you can manipulate these markets."
What is especially disturbing about “foreign exchanges” like the ICE is that it is not actually foreign. Among its founding partners are Goldman Sachs and Morgan Stanley, its headquarters is in Atlanta, its primary data center is in Chicago, and it settles most trades in U. S. dollars. Despite all of its U. S. ties, the ICE claims that because its energy futures business is conducted in London—whatever that means—U. S. laws or regulations do not apply to it.
But all this supports the crux of my earlier argument that the energy independence that politicians speak of achieving is a myth because oil companies “will always sell their product to highest bidder, wherever the bidder resides.” The price of oil has no relationship to its origin.
In 2007 the U. S. imported about 10 million barrels of oil per day and produced about 5 million barrels per day. According to the Energy Information Administration, the top three countries of origin for imported oil in 2007 were Canada (1.85 million barrels per day), Mexico 1.47 million barrels per day) and Saudi Arabia (1.36 million barrels per day). Canada and Mexico actually supply more oil to the United States than Saudi Arabia.
If the U. S. decides to increase its domestic production of oil through offshore drilling or other means, it will contribute to the world supply of oil and that additional supply will be factored into the world price. Any politician who claims we can be more energy independent by drilling for more oil in the U. S. is being disingenuous. A far more relevant question to ask our political leadership is: Why are U. S. investment banks allowed to manipulate energy futures markets with no government oversight? I don’t think there is going to be a straight answer for that question.
Joseph Ganem is a physicist and author of the award-winning The Two Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy
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
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
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
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
Monday, May 19, 2008
Who Will Bail Out The U. S. Government?
My “stimulus” payment from the federal government arrived on the same day that a front-page article in USA Today reported that federal deficit is far greater than the government admits. While the politicians struggle to bailout the housing crisis and head off a recession, they are also rigging the budget numbers to hide the fact that there is no money to give away.
The reported deficits of hundreds of billions of dollars sound bad. But, USA Today found that federal deficits would be trillions of dollars if the government used the accounting rules that are required of corporations when issuing financial reports to shareholders. The reason for the discrepancy is that trillions of dollars in unfunded liabilities to Medicare and Social Security do not show up on the government’s balance sheet. A corporation would have to report future financial obligations as a liability unless it had the funds set aside to make the payments.
But the federal government avoids reporting unfunded liabilities. It collects Social Security and Medicare taxes to supposedly set aside in trust funds to pay for future financial obligations. That allows the government to claim its future obligations are funded. The ruse is that the money never remains in the trust funds. Instead money is “borrowed” from the trust funds to pay for present day obligations. Because the money is “borrowed” from funds the government controls, it never reports that obligation as part of the deficit.
What the practice means is that a mathematically equivalent expression for “borrowed from the trust fund” would be “spent the trust fund.” But the government never admits that it has spent the trust funds because that would undermine the entire rationale for collecting separate Social Security and Medicare taxes.
None of this is a secret. When I wrote The Two Headed Quarter I included a chart that showed that projected indebtedness to the Social Security trust fund was expected to increase from $1.5 trillion to $4.0 trillion between the years 2003 to 2014. The Congressional Budget Office (CBO) made the projection. I simply made a chart of data taken off the CBO Website. The chart makes clear that the government has no plans to every pay back the money it is “borrowing” from the trust fund.
Even though these trust funds exist on paper, the fact is money is not in them.
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
The reported deficits of hundreds of billions of dollars sound bad. But, USA Today found that federal deficits would be trillions of dollars if the government used the accounting rules that are required of corporations when issuing financial reports to shareholders. The reason for the discrepancy is that trillions of dollars in unfunded liabilities to Medicare and Social Security do not show up on the government’s balance sheet. A corporation would have to report future financial obligations as a liability unless it had the funds set aside to make the payments.
But the federal government avoids reporting unfunded liabilities. It collects Social Security and Medicare taxes to supposedly set aside in trust funds to pay for future financial obligations. That allows the government to claim its future obligations are funded. The ruse is that the money never remains in the trust funds. Instead money is “borrowed” from the trust funds to pay for present day obligations. Because the money is “borrowed” from funds the government controls, it never reports that obligation as part of the deficit.
What the practice means is that a mathematically equivalent expression for “borrowed from the trust fund” would be “spent the trust fund.” But the government never admits that it has spent the trust funds because that would undermine the entire rationale for collecting separate Social Security and Medicare taxes.
None of this is a secret. When I wrote The Two Headed Quarter I included a chart that showed that projected indebtedness to the Social Security trust fund was expected to increase from $1.5 trillion to $4.0 trillion between the years 2003 to 2014. The Congressional Budget Office (CBO) made the projection. I simply made a chart of data taken off the CBO Website. The chart makes clear that the government has no plans to every pay back the money it is “borrowing” from the trust fund.
Even though these trust funds exist on paper, the fact is money is not in them.
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
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