Stories tagged math

Feb
26
2007

Are life and death just a game?: Mathematics says they follow the same rules. Photo from the National Park Service.
Are life and death just a game?: Mathematics says they follow the same rules. Photo from the National Park Service.

Game theory is a branch of mathematics that attempts to explain how people make choices by weighing costs and benefits. It can be applied not just to games, but to all kinds of serious situations – business, politics, even war.

This report (abstract free; $ to download complete report) argues that even terrorists use classic game theory to maximize the impacts of their attacks:

We find that more educated and older suicide bombers are less likely to fail in their mission, and are more likely to cause increased casualties when they attack.

Knowing this, I wonder if anti-terrorist efforts are focusing more on those older, educated operatives, to minimize the threat of attack.

*(It's also the name of an '80s band, but that's neither here nor there.)

Webmath is a site that explains a wide variety of equations. In most cases, they don't just give you the answer, but also walk you through the explanation step-by-step so you can see how it works.

Nov
30
2006

Digging dinosaurs in Utah: Courtesy Bureau of Land Management
Digging dinosaurs in Utah: Courtesy Bureau of Land Management

That’s how many types of dinosaurs remain to be discovered. According to Steve Wang, a statistician at Swarthmore College, Pennsylvania, and Peter Dodson, a palaeontologist at the University of Pennsylvania, Philadelphia, at least 70% of the dinosaurs that once existed have yet to be found. They arrived at this figure by taking the known dino discoveries and plugging them in to a mathematical model that has proven successful in extrapolating data.

The scientists estimate that about half of the missing dinos will probably never be found. They lived in upland areas where fossilization is rare. Or the rocks that held their bones have been destroyed by glaciers or other Earth processes. But that leaves some 700 types of dinosaurs yet to be discovered.

Dinosaur discovery has accelerated in recent years. Nearly half of all dinosaurs known today have been dug up in just the last 20 years. Countries like China and Argentina – long inaccessible to paleontologists – have been producing many new finds. But there are plenty of other countries, particularly in Africa, that have yet to be fully explored. Wang and Dodson figure that most of the remaining dinosaur discoveries should come to light in the next 100 to 140 years.

Oct
17
2006

Sucked in: Will this harm your development?
Sucked in: Will this harm your development?

Autism is a serious concern in our country today, with 1 out of every 166 children diagnosed with some form of the disorder. But could the sharp rise in Autism (it was only 1 in 2500 30 years ago) be linked to the increased prevalence of TV in our homes? Economists from Cornell University say that the data shows a pretty strong correlation.

Michael Waldman and Sean Nicholson looked at populations in California, Oregon, and Washington using the Department of Labor's American Time Use Survey. They compared this information with clinical autism data and found a statistically significant correlation between and increase in early childhood hours spent watching TV and autism rates.

Is that science?

Well, the authors of the study will be the first to say that this isn't definitive proof that TV causes autism (or that autism causes TV...sorry, bad joke). And these guys are economists looking at population data not medical scientists studying individuals with autism. But that doesn't mean this study is without merit. Something in our environment causes autism and we don't really know what it is. I support any unique thought on the subject that gives us new research questions to evaluate.

Do you have a story or thought on autism? Have you heard of other possible causes of autism?

Aug
09
2006

Comparison of body temperatures: A plot of the relationship between average body temperature (°C) and the logarithm of body mass for dinosaurs and modern crocodiles.  This graph potentially shows the accuracy of the formula by applying it to modern crocodiles. Chart  courtesy Gillooly JF Allen AP, Charnov EL (2006) Dinosaur Fossils Predict Body Temperatures. PLoS Biol 4(8): e248.
Comparison of body temperatures: A plot of the relationship between average body temperature (°C) and the logarithm of body mass for dinosaurs and modern crocodiles. This graph potentially shows the accuracy of the formula by applying it to modern crocodiles. Chart courtesy Gillooly JF Allen AP, Charnov EL (2006) Dinosaur Fossils Predict Body Temperatures. PLoS Biol 4(8): e248.
The question regarding whether dinosaurs were warm-blooded or cold-blooded has been debated for decades. Currently, most scientists believe that dinosaurs were warm-blooded and used internal mechanisms to maintain a constant body temperature. However, what that internal body temperature was could have fluctuated depending on the size of the dinosaur, making it possible for dinosaurs to have been both.
The bigger the hotter
Researchers at the University of Florida devised a mathematical formula that describes the connection between temperature, growth rate and biomass across a wide range of modern creatures. They then applied this formula to newly available fossil data on the growth rates of eight dinosaur species.
The equation showed that the bigger a dinosaur was the hotter is was. Smaller dinosaurs had internal body temperatures of around 77º Fahrenheit, which was close to the average air temperature of their time, so could have regulated their body temperatures much like modern cold-blooded reptiles. As dinosaurs grew larger, and the ratio of their surface area to volume fell, they became less efficient as dissipating their own metabolic heat. Because of this increased internal body temperature, dinosaurs probably had to develop behavioral or other adaptations to avoid overheating.
Body temperature influenced dinosaur size
One of the larger dinosaurs studied, Sauroposeidon proteles, weighed nearly 120,000 pounds. Applying the mathematical formula reveals that it may have had a body temperature close to 118º Fahrenheit, which is about as hot as most living creatures can get before the proteins in their bodies begin to break down. Because of this, the size of the largest dinosaurs may have been limited by their internal body temperatures.

Jul
01
2006

Hourglass: from Wikimedia Commons  Life is a gift. Use it wisely.
Hourglass: from Wikimedia Commons Life is a gift. Use it wisely.

How many seconds are in a day?

Can you picture how many seconds are in a day? One day equals 86,400 seconds. Here is a link to a clock that has a dot for every second in the day. You can watch them change color one by one. Unless, of course, you can think a better way to use your gift of life.

Life is a gift.

We all receive this gift equally, second by second, day after day, until we die. Use this gift wisely.

We've been thinking about different ways that the resurgent craft movement has links to science (trust me there are tons). So while doing some origami this weekend I was psyched to find this cool math resource on how to fold a square into thirds, fifths, and all those other hard to eyeball fractions.

What would a billion (or a trillion) pennies look like? The Megapennie project shows you.

May
17
2006


Keeper: Image courtesy various visual stuff.

Earlier I wrote a blog post where mathematicians had determined that soccer was the most exciting sport to watch because the probability for an upset was higher than in other sports. In recent soccer related science research, Ken Bray, a theoretical physicist from the University of bath in England has conducted research to show that the areas near the top corners of the net are what he calls an “unsaveable zone”. To find this zone, Bray studied games from the past 50 years and applied his knowledge of physics, biology, and psychology to calculate the reach of a goalkeeper attempting to save a penalty kick. His advice for the goalkeepers? Move before the ball is kicked…which I think is cheating, so that would not be my advice! Bray also says that in 85% of penalty kicks, the direction in which the plant foot is the direction of the shot.

Dr. Bray has written a book on the science of soccer titled, “How to Score”.

Jan
09
2006


A goaltender: Diving for the ball.

I play soccer. I can frequently run and kick the ball without falling on my face, so I enjoy it. In fact, it is my most favorite sport to play. However, I think that watching soccer on TV is like watching paint dry — I find it to be very dull.

However, researchers at the Los Alamos National Laboratory have found that soccer is the most unpredictable sport, as it more likely that a team with a worse record can defeat a team with a better record. The researchers looked at the results of over 300,000 soccer, baseball, basketball, hockey and football games, and found that the likelihood for an upset was greatest in soccer.

So, it should be more exciting to watch a soccer game because the results are not as predicated on the records of the two teams as other sports.

This research is an interesting way to combine an interest in sports and an interest in math!