Stories tagged Math

Nov
15
2006

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.
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)
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.

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.

Mar
27
2006


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."

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!

Jul
03
2005

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.

Pi diagram

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.

Apr
25
2005

The US Postal Service will release 4 new stamps this month to commemorate important American scientists of the last century.

4 American Scientist StampsOne of my favorite science thinkers, Richard Feynman, will be featured on one of the stamps. Feynman was famous for his discoveries about Quantum Electro Dynamics, which allowed us to understand more about the very strange properties of light. While Feynman was a ground breaking scientist he also excelled as a remarkable teacher. To get a sense for his teaching abilities and to learn more about light, you should watch one of his lectures on Quantum Electro Dynamics

The stamps will also feature:

  • Geneticist Barbara McClintock - McClintock's work on genes in maize (corn) earned her the Nobel Prize in 1983. She was the first person to discover that genes are genes are transposable--they can move between chromosomes.
  • Mathematician John von Neumann - von Neumann's mathematical discoveries helped establish the field of cellular automata and many of the principles that drive modern computers today. He even extended his thories to the field of mining, proposing futuristic ways of mining the moon.
  • Thermodynamicist Josiah Willard Gibbs - Gibbs, who lived from 1839-1903, studied the physics and mathematics involved in how complex fluids move around in space. His work provided a foundation for future discoveries such as vector analysis (a type of math), quantum mechanics, and even the behavior of comets.

Do you think you will buy stamps because they have scientists on them? I will, but I'm kind of a nerd.

Feb
25
2005

If the Venus fly trap doesn't have any muscles, how can it snap closed on its prey in less than 1/10 of a second? Harvard mathematician Lakshminarayanan Mahadevan might have the answer. He discovered that a Venus fly trap uses water pressure to keep its leaves on the brink of slamming shut. When a fly or something else lands inside the plant, tiny hairs trigger an electrochemical reaction. This moves water between the cells of the Venus fly trap's leaves. In the blink of an eye, the plant's bent leaves become unstable and slam shut.

Mahadevan compared this to a bent contact lens or a halved tennis ball. The slightest tap will cause the lens or tennis ball to quickly snap back into shape. Researchers still don't fully understand how the plant triggers the water pressure change.

You're wondering why a mathematician was studying a plant? A student gave Mahadevan a Venus fly trap as a gift. Curious about how the plant's behavior, he used a high-speed camera to watch it eating its prey. From these videos, he developed a mathematical model of the plant's movements. (A mathematical model is a very realistic simulation of the real world using measurements and many mathematical calculations.) His model unraveled the mystery of this carnivorous plant.