Stories tagged math

A new book, The General Rule, A Guide to Customary Weights by Vivian Linacre examines the origin of the English system of measurement – the inch, foot, yard, mile, etc. By examining ancient stone monuments such as Stonehenge, she finds our modern measurements date back thousands of years, and that prehistoric Britons understood advanced mathematical concepts such as the Fibonacci series and the golden ratio.

A story on CBS news claims that military veterans commit suicide at a much higher rate than the general population. However, blogger Bill Sweetman argues that the report is flawed. It fails to account for the fact that the vast majority of veterans are men, who have a higher suicide rate than average. Most veterans are also young, and young people commit suicide far more often than older people. Once you account for these two factors, the supposed difference in veterans’ suicide rates disappears.

Nov
19
2007

Surfing the cosmic waves

Garrett Lisi, a 39-year-old surfer, hiking guide and construction worker (with a PhD in theoretical physics), believes he may have solved the biggest problem in all of science – how are all the particles of matter and forces of nature related to one another? Scientists since Einstein have been trying to figure it out, with little success. (The current theory involves outrageously tiny “strings” vibrating in 11-dimensional space. The mathematics, they say, is beautiful, but it cannot be tested or verified.) Lisi’s breakthrough came when he noticed that the formulas that describe something called the E8 pattern -- a complex, geometrical design with 248 points – also describe many of the fundamental forces and particles. His theory is that nature follows the same formulas as E8, and that the figure can be used to predict particles that have not yet been discovered. If he's right, he will have finally shown that everything in the universe is related, and basically just different manifestations of the same essence.

Nov
06
2007

Health care by the numbers

Providing health care for all is no easy task.: Photo by Neimster at Flickr.com

There’s been a lot of talk about the American health care system of late. And there’s going to be a lot more talk in the months ahead, as it becomes a campaign issue in the 2008 Presidential election. Gregory Mankiw, a professor of economics at Harvard, has crunched the numbers on health care, and found that some of the issues aren’t quite what they seem.

Lower life expectancy

Demographically and economically, the United States and Canada are fairly similar. Yet Americans, on average, die about two-and-a-half years sooner than our neighbors to the north. So health care in the US must be worse, right?

Not necessarily. Mankiw found that Americans, especially younger ones, are far more likely to die in an accident or a homicide than a similar Canadian. Take that away, and the difference virtually disappears. As Mankiw states, “Maybe these differences have lessons for traffic laws and gun control, but they teach us nothing about our system of health care.”

Infant mortality

In America, a higher percentage of babies die during infancy than in other countries. Ironically, this is not a sign that American health care is worse, but rather, that it is better.

In many countries, low-weight babies who are born not breathing are considered stillborn—doctors do not try to save them. American doctors do. In fact, America has the best rate of success with low-weight babies, simply because we are willing to take on these high-risk cases. But high risk also means high failure rate: despite the doctors’ best efforts, many of these babies die anyway, raising our infant mortality rate. In other countries, the baby is not counted as ever having been alive at all, making their rate appear low.

Also, Mankiw notes that low birth weight is associated with teen pregnancy, and America has a higher teen pregnancy rate than many other countries. While there are steps we can take to reduce that phenomenon, overhauling the way we pay for health care is not going to have any effect on teenagers’ behavior.

Millions of uninsured

Many politicians have noted that some 47 million Americans – nearly one in six – has no health insurance. Some of these people want health insurance, but can’t afford it, or can’t get it through their jobs. This is a real problem.

However, Mankiw notes that this 47 million includes a lot of other groups. Millions of poor people are already eligible for Medicaid, but have simply never enrolled. Millions more have been offered health insurance through their jobs, but declined. We could reduce the 47 million substantially, without changing a thing, just by getting these folks to sign up.

Mankiw notes that a large number of uninsured are illegal immigrants. Getting these people covered is a matter of immigration reform, not health care reform.

So, when you hear politicians throwing numbers around in the health care debate, remember: the story behind the numbers is often a lot different than the sound bites make it appear.

Meanwhile, here’s a possible solution to providing health care to the uninsured.

Aug
06
2007

Here are some of the most interesting perspectives on the 35W bridge collapse that I have run across in the last few days:

Cell phone network sends ominous signals - Engineers at T-Mobile were alerted that something had gone wrong right after the bridge collapse. They hadn't heard the new yet but saw a sharp change in cell phone activity on their network.

Government spending collapsed as well - A graph of US government spending on infrastructure over the last 55 years.

Historians and engineers have a thing or two to learn from each other - An editorial from 2006 of the history of engineering disasters.

Bridges made from glass - A prescient report from the National Science Foundation on poor infrastructure and the future of bridge technology.

Jul
30
2007

World Series math: How many games to crown a true champ?

True trophy: Under a statisical analysis of the past 30 years of baseball seasons, the true champion of the game would be crowned following a 265-game season and a best-of-11 World Series. (Photo by madmolecule)
The New York Yankees have had a hard time winning the World Series in recent years, despite having the largest payroll and brightest array of all-star players. What owner George Steinbrenner might need to do next to turn his team’s luck is get more games on the regular and post-season schedules.

That’s the finding a new study that analyzed Major League baseball’s statistical leaders vs. the team the ultimately won the year’s championship. Using this methodology, the study found that in 2003, the Florida Marlins had no statistical right to be in the same ballpark as the Yankees.

“The world of sports provides an ideal laboratory for modeling competition because game data are accurate, abundant, and accessible," answers the study in the journal Physical Review E. "Even after a long series of competitions, the best team does not always finish first.”

The Yankees found that out in 2003, when underdog Florida beat them out for the championship in six games. The study, through its statistical analysis identified the Marlins as the worst team in the past 30 years to win the World Series.

Baseball has, by far, the longest season and largest number of games at 162. But the study found that in order to ensure the best teams win the championship each year the regular season should stretch for 265 games and the World Series should be a best-of-11 affair.

Lower-seeded teams have a 44-percent chance of winning baseball games over the past 100 years. Using that data along into a mathematical model, the study came up with these ideal numbers of games to identify a true champion.

Baseball does have the longest season of any other sport. Football, on the other hand, has just 16 games in a season. In playoffs, especially, the more games involved in getting to the finish line lead to the better teams winning the title more often.

On the other hand, the single-elimination nature of the NCAA’s mens’ basketball tournament makes it hugely popular just because of its Cinderella nature. Fans love to cheer on the underdogs who emerge through its unpredictability.

I have to admit that I’m haven’t run the numbers myself. And while they look good and logical, I wonder how they really stand up. The last several World Series champions have been wild-card entries. But the shorter, single-elimination football playoffs seem to more often put the crown on the league’s top-winning team.

What do you think? Should seasons be set up to have the best shot of identifying the best team? Or do you like things to be unpredictable in sports? Share your thoughts here with other Science Buzz readers.

Jul
11
2007

Interplanetary warming

Venus and Mars are alright tonight: They may not teach us much about conditions on Earth, but they provide hours of entertaining temperature conversion! Photo of Venus (left) from NASA; photo of Mars (other guy) from the Library of Congress.

As Science Buzz's resident global warming skeptic, I've taken a lot of shots at Al Gore over the years. Today, however, I find myself in the unusual position of having to defend him against unfair attacks. Somewhat.

In an editorial last Sunday, Gore stated:

“Consider this tale of two planets. Earth and Venus are almost exactly the same size, and have almost exactly the same amount of carbon. The difference is that most of the carbon on Earth is in the ground - having been deposited there by various forms of life over the last 600 million years - and most of the carbon on Venus is in the atmosphere.

As a result, while the average temperature on Earth is a pleasant 59 degrees, the average temperature on Venus is 867 degrees. True, Venus is closer to the Sun than we are, but the fault is not in our star; Venus is three times hotter on average than Mercury, which is right next to the Sun. It's the carbon dioxide.”

This got a bunch of bloggers to thinking. George Reisman went to a NASA website and found an interesting comparison:

 PLANET Venus Earth Mars CO2 IN ATMOSPHERE 96% 0%* 95% AVERAGE TEMPERATURE 867˚F 59˚F -81˚F

*Not quite true: Earth’s atmosphere is 0.035% CO2.

So, planets with lots of carbon in their atmosphere can be either broiling hot or icy cold.

(Another writer, Evan Kayne, complained (seventh item) the comparison isn't fair; Reisman didn’t take into account the fact that the atmosphere on Mars is only 1.3% as thick as Earth’s. James Taranto of the Wall Street Journal re-did the calculations, and concluded that frigid Mars still has 34x as much CO2 per cubic foot of atmosphere as the Earth does.)

So far, Al isn't looking too good. But then, blogger David Downing thought he'd discovered another problem. According to the NASA site, Mercury has an average temperature of 452˚ Kelvin, while Venus has an average temp of 726˚ Kelvin. That’s only 1.6 times hotter, a far cry from what Gore had claimed!

Wait a minute. What’s this “Kelvin” scale and why is Downing using it? Well, all temperature scales measure energy. And on the Kelvin scale, 0 degrees means “no energy AT ALL.”

This makes it very easy to compare the energy in different systems. In Celsius, 0 degrees doesn’t mean “zero energy;” it means “the amount of energy in frozen water” -- which may seem chilly to you and me, but at a molecular scale, it’s got plenty of heat. (0 degrees Fahrenheit is apparently the amount of energy in a mix of ice, water, and ammonium chloride.) Comparing 25˚F to 50˚F is tricky, because the scale doesn't stop at 0. As any Minnesotan knows, it goes wayyyyy lower than that!

(It’s kind of like saying “Mike is five years older than me; Vic is 10 years older than me; therefore, Vic is twice as old as Mike.” That would only be true if I were 0 years old. If I were, say, 47, then Mike would be 52 and Vic would be 57, and the differences would be much less impressive.)

So, Downing assumed Gore must have been working in Fahrenheit, and believed that if Venus is 867˚F and Mercury is 289˚F, then Venus is three times hotter. Ha ha, what a silly mistake! I was all prepared to poke fun at Al for this glaring error, until I realized – Mercury isn’t 289˚F. According to NASA, it’s a toasty 354˚F.

So, where did Al get 289˚F? I looked in a bunch of sources -- no one was even close. Wikipedia listed Mercury at a mere 26˚F. (The side facing the Sun broils; the side turned away freezes; this is an average.)

But then I noticed -- 26˚F is 270˚K. And Wikipedia lists Venus at 735˚K . Using the proper Kelvin scale, that works out to 2.7 times hotter than Mercury. Not quite 3 times, but in the ballpark. And, to be fair, Wikipedia gives Mercury a range of temperatures, and “3x hotter” fits comfortably within that range.

So, it turns out Gore was closer to being right than he’s given credit for. He WAS working in the proper Kelvin scale. He was just relying on figures from Wikipedia rather than from NASA.

I don’t know if all this has taught us anything about global warming. But man, have I learned a lot about planetary atmospheres, temperature scales, and math! Thanks, Al!

UPDATE: Evan Kaye had claimed that the atmosphere on Mars is only 2% as thick as Earth's. James Taranto, using figures from the NASA site linked to above, calculated that it is actually 1.3% as thick as Earth's. We have corrected the figure.

Jul
10
2007

“Making predictions is very difficult, especially about the future”

So said Yogi Berra, and science is proving him right. It turns out that making accurate predictions entails more than taking current conditions and extrapolating them into the future. It’s a specialized sub-field of mathematics, with lots of rules to ensure that predictions have a reasonable chance of being accurate.

Scott Armstrong of the University of Pennsylvania and Kesten Green of Monash University, Australia, examined the forecasts recently made by the UN’s Intergovernmental Panel on Climate Change.

Armstrong and Green rated the methodology used by the panel against 89 principles of good forecasting derived from years of research. They found that the panel report breached 72 of those principles. They concluded that the forecasts the weather was likely to change in many negative ways were worthless.

Now, this doesn’t mean that the Earth isn’t getting warmer—that’s a well-established fact. But, most of the predictions we’ve heard of climate catastrophe due to this warming are based on bad math.

(Freeman Dyson, physics professor at Princeton, makes a similar point in this video. He argues there’s been too much focus on building computer models of climate, and not enough emphasis on collecting actual data to see if the models hold up.)

Jun
29
2007