Stories tagged math

Jul
10
2007

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
26
2007

Americans with diabetes nears 21 million and is growing 5% per year.

One out of every eight U.S. federal health care dollars is spent treating people with diabetes. A report by Medco Health Solutions Inc. issued last month found that the growing diabetes epidemic and more aggressive treatment could result in soaring costs to treat the disease over the next three years.

An analysis of Medco's 2007 Drug Trend Report found that, by 2009, spending just on medicines to treat diabetes could soar 60 percent to 68 percent from 2006 levels. The sales of diabetes drugs in the United States reached $9.88 billion in 2005, according to data from IMS Health Inc. Yahoo News

Diabetes is deadly.

Over the next 30 years, diabetes is expected to claim the lives of 62 million Americans. Uncontrolled diabetes can result in heart disease, stroke, vision loss, amputation of extremities and kidney disease.

Obesity blamed.

Using data from an ongoing federal health survey of U.S. adults, researchers found that, on average, obese 18-year-old men had a 50.1-percent lifetime risk of developing diabetes, while obese women had a 57.3-percent risk. Diabetes Care, June 2007.

Overweight? Do something.

If we are going to stem the growing burden of diabetes, we must improve our prevention efforts. You can start by reading about diabetes(World Health Organization fact sheet).

Apr
17
2007

Friday nights at 9 pm.

"Numb3rs" is currently the most-watched program on Friday nights, attracting nearly 12 million viewers. Now in its third season, Numb3rs, along with the program's co-creators, Nick Falacci and Cheryl Heuton, will receive a National Science Board group Public Service Award for 2007 "for their contributions toward increasing scientific and mathematical literacy on a broad scale".

The annual Public Service Award recognizes individuals and organizations for their extraordinary contributions to increase public understanding of science. Recipients are chosen for their contributions to public service in areas such as: increasing the public's understanding of the scientific process and its communication; contributing to the development of broad science and engineering policy; promoting the engagement of scientists and engineers in public outreach; and fostering awareness of science and technology among broad segments of the population. NSF

Mathematical CSI

Cryptanalysis, probability theory, game theory, decision theory, principal components analysis, multivariate time series analysis and astrophysics are just some of the many disciplines employed in the series thus far. If you have not seen this show I recommend that you check it out.

Mar
23
2007


Math: Image courtesy Lodri.
I’m not good at math. Math and I are not friends. We’ll nod hello in the hallway, but we don’t hang out. So, when I read stories about researchers solving a century old math problem that when written out would cover the island of Manhattan, I am more than a little blown away. Seriously, can you even imagine a math problem that long? I can just hear Mr. Rambo, my 7th grade math teacher admonishing me to, “show your work!”

It took an 18-member international team four years to solve the theoretical puzzle known as the “Lie group E8”, which was discovered in 1887 and is the most complicated Lie group. What is a Lie group? Well, let’s ask Wikipedia:

In mathematics, a Lie group, named after Norwegian mathematician Sophus Lie, is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups represent the best developed theory of continuous symmetry of mathematical objects and structures. This makes Lie groups tools for nearly all parts of contemporary mathematics, as well as for modern theoretical physics, especially particle physics.

Since Lie groups are manifolds, they can be studied using differential calculus, in contrast with the case of more general topological groups. One of the key ideas in the theory of Lie groups, due to Sophus Lie, is to replace the global object, the group, with its local or linearized version, which Lie himself called an infinitesimal group and which has since become known as its Lie algebra.

Lie groups provide a natural framework to analyse continuous symmetries of differential equations (Picard-Vessiot theory), much in the same way as permutation groups are used in Galois theory to analyse discrete symmetries of algebraic equations.

I have tried, sitting here with my little brain, to make this explanation simpler, to make it more understandable. I think, perhaps, that the author of the Wikipedia article did that, and this is as simple as it gets.

"To say what precisely it is is something even many mathematicians can't understand," said Jeffrey Adams, the project's leader and a math professor at the University of Maryland.

So, I obviously have no chance.

But hey, I think this is cool none the less. It boggles my mind to think that there are problems like this to be solved – that seem impossible, and have remained unsolved for over 100 years – yet they are being solved today, and whose proof consists of more than 205 billion entries. Amazing.

Congratulations.

...now here's your chance to do something about it! Here's a cool traffic simulator that allows you to play what-if scenarios with different traffic conditions.

Mar
11
2007

That's how lotteries are often described. The odds of winning the top prize in the Mega Millions lottery is more than 600 times worse than your odds of getting hit by lightning. Yet people continue to play. Why?

Professor Lloyd Cohen suggests people aren't paying for the chance so much as they are paying for the dream. They enjoy fantasizing about winning, the same way people enjoy reading lifestyle magazines or watching movies of the rich and famous. And at one dollar a pop, a lottery ticket is not only cheaper than these other forms of entertainment, it actually has a chance -- no matter how infinitesimally tiny -- of actually paying off.

Mar
05
2007

It seems like every week there’s another medical breakthrough announced in the press – only later to fizzle when additional studies show it didn’t really hold up. Why are there so many false starts?

Dr. Peter Austin of the Institute for Clinical Evaluative Sciences in Toronto says it has to do with the way researchers use statistics. All statistical studies rely on “confidence intervals” – if an event has only a 5% chance of happening at random, then doctors can be 95% confident that it isn’t a random fluke. They assume they’ve discovered a real phenomenon, and start looking for a cause.

(For instance, a coin has about a 3% chance of landing heads five times in a row. If you had a coin that did that the first time you tried it, you’d have good reason to suspect something funny was going on, and conduct more tests.)

But Dr. Austin notes that many studies run multiple tests simultaneously. When you do that, the odds of at least one test giving an unusual result, just by chance, is very high. In our coin-flipping example, if you tested 100 identical coins by tossing each 5 times, it would be perfectly normal for at least one, and probably a few, to land all heads, without anything “funny” about them at all.

The point is, you have to look at the whole test, not just selected parts of it. And doctors – and journalists – need to be more careful when presenting the results of studies, so they don’t report false relationships.

Feb
28
2007

They call Economics “the dismal science” because it pays no attention to questions of right and wrong, good and evil, but only looks at supply and demand, profit and loss. But even with that limitation, it still helps illuminate certain moral precepts.

Take for instance the old adage “crime doesn't pay.” According to economist Steven Levitt (WARNING: 22-minute video, with occasional objectionable language), the worst job in America is drug dealer. Not only does it ruin lives; not only does it bring crime and violence that destroys entire neighborhoods; it simply doesn't pay well:

  • The average dealer earns $3.50 an hour – well under minimum wage.
  • There is little opportunity for advancement.
  • The death rate is extremely high. Not only is a dealer more likely to die on the job than a soldier on active duty; a dealer is seven times more likely to die in a given year than an inmate on death row!

Even without considering legality or morality, the math shows: dealing drugs is a pretty dumb way to make a living.