Stories tagged Math
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.)
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The white male law professor -- an endangered species?: Photo from Rep. Jim Cooper, US House of RepresentativesThe Science Museum of Minnesota is hosting a new exhibit Race: Are We So Different? A lot of racial topics are emotionally charged and hard to talk about. So, when we can find a scientific study, it gives us something a little more objective to discus.
This study shows that, over the last 14 years, white males have had a harder time getting jobs as law professors than minorities or female candidates:
Candidate Type Success Rate (%) Minority Women 18.5 Minority Men 17.5 Non-Minority Women 15.0 Non-Minority Men 11.3
The study looks at success rate -- that is, what percentage of white candidates get hired, what percentage of black candidates get hired, etc. It does not look at what percentage of a law school's faculty is black, white, green, purple, etc.
The large amount of data in the study makes it pretty unlikely that this is a fluke -- the pattern has held steady for 13 of the past 14 years. It's hard to avoid drawing the conclusion that women and minorities enjoy an advantage in getting hired as law school teachers. Some people would say that's discrimination. Some would say it's justified to make up for the decades these groups were barred from the profession. Some would say it's necessary to give today's students a well-rounded education with many perspectives.
What do you say? Leave a comment.
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.
Storm chasers know that puffy cumulus clouds often cause sudden rainstorms, while storms associated with stratus clouds form more slowly. Now physicists at England’s Open University have finally found an explanation.
They propose that neighboring water droplets in a stable stratus cloud don’t crash into each other because they’re all moving at about the same speed. But fast-forming, turbulent cumulous clouds contain water droplets moving at many different speeds. They crash into each other and form larger drops. As the turbulence grows, the drops grow quickly and fall as rain within a few minutes.
Cumulous cloud: These puffy clouds are associated with sudden rainstorms. Scientists are beginning to understand why.
Sun and rain
Ever noticed the bright, moving lines on the bottom of a stream, bathtub, or swimming pool? They’re called caustics, and they’re caused when ripples on the water’s surface focus sunlight. (Caustics form whenever light rays are bent by a curved surface or object and then projected onto another surface.
Caustics have a characteristic shape. Physicists can graph the phenomenon mathematically, and the graph also describes other phenomena, such as particle motion or the movement of raindrops within a cumulus cloud.
Caustics: What do the rippling patterns on the bottom of a swimming pool and cumulous clouds have in common? (Photo by R. Motti)
Atmosphere to outer space
The researchers say their finding won’t have any impact on weather forecasting. But particle collisions in turbulent gases must have been involved in planet formation. Perhaps the same theory can be applied?
If you're at the museum on Saturday afternoon (11/18), the MakeIt team can help you play with caustics. Does bending mylar in a different direction produce a new pattern? Does using a different color flashlight or a brighter or dimmer light affect the design?
You can also play with caustics at home.
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?
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.
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.
Whale speak
Humpback Whale: A Humpback Whale dives beneath the surface Courtesy NOAA
Scientists Ryuji Suzuki, John Buck, and Peter Tyack used information theory to prove that humpback whale songs have syntax--rules that govern the structure of language.
Like humans, the whales use a hierarchy of communication: they make sounds to build phrases that they can combine in different ways to create songs that last for hours.
The scientists wrote a computer program that breaks down the elements of the whales' songs (moans, cries, and chirps) and assigns a symbol to each one. Then they analyzed the structure of the songs.
Suzuki says,
"Information theory was the right choice because it allows one to study the structure of humpback songs without knowing what they mean."
Sight and smell are limited in marine environments, so sea mammals often use sound to communicate. During the humpback whale breeding season, all the males in a population sing the same song. And the song evolves over time.
Suzuki says,
"Humpback songs are not like human language, but elements of language are seen in their songs."
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!
Remember this number, 3.14159? It's Pi, the natural number that describes the mathematical properties of a circle. Well, the digits for Pi go on and on and on (for infinity actually) and that makes for some fun competitions and great feats of memory. As a matter of fact a 59-year-old Japanese psychiatric counselor, Akira Haraguchi, has recently broken the world record for reciting the digits of Pi from memory. From the time he started at 3.14 to the time he ended 13 hours later he recited 42,195 digits of Pi.
Can you imagine memorizing that many numbers? Check out the first 10,000 digits of Pi to see how hard it is to remember that many numbers. And if that doesn't wear you out, try for the record by checking out the first 100,000 digits of Pi.
To learn more about the fun aspects of Pi, check out the Exploratorium's Ridiculously Enhanced Pi Page. Every March 14th, international Pi day, in San Francisco the Exploratorium hosts a Pi festival with lots of fun activities, including real pie.
