Articles for ACCEL Temperature Project
Math & Science Career Connections
Paul Zandt, Meteorologist
Next time you're out for a walk in the park on a fine autumn day, you may not have mathematics on your mind. But believe it or not, the weather that surrounds you is mathematics in motion. That's right. Every type of weather -- a passing cloud, a sudden summer thunderstorm, or a wicked winter storm -- can be summed up by a series of mathematical equations.
Many, but not all, of the weather forecasters you see on TV are meteorologists. Some colleges offer degrees in meteorology. To become a meteorologist, a student must take courses in advanced mathematics. We study math to better understand how the atmosphere behaves. Different mathematical equations help explain which way the wind will blow and whether the temperature will rise or fall. These equations are programmed into giant computers, which then try to predict the weather for the next day, the next week, even the next month. Meteorologists rely on these computer predictions when they make the forecasts you hear on the radio or TV.
Unfortunately, the weather is often too complicated to be predicted accurately all the time. Even the most powerful computers can't keep track of all the subtle weather changes. Weather predictions are sometimes wrong, and forecasters can look a little foolish.
Not all meteorologists are weather forecasters. Some study climate changes. They also rely on computer models. Other meteorologists keep track of weather conditions around the world and use math to compile weather records.
Meteorologists could not do their jobs without a good understanding of mathematics. So if you think you might want to be a meteorologist some day, you'll certainly want to pay attention in math class!
History of Temperature
In the 1700s, G. Daniel Fahrenheit developed a scale used by meteorologists for measuring surface temperature. The scale was named for the developer, and the unit of measure has become known as degree Fahrenheit (F°). Also in the eighteenth century, a second scale was developed for measuring surface temperature; it became known as the Celsius scale. The unit of measure in the Celsius scale is the degree Celsius (C°). A third scale later developed for use by scientists became known as the Kelvin scale. This scale begins at absolute zero and is sometimes more convenient to use because it does not involve negative temperatures. (The word degree is not used in Kevin measure.) Citizens of the United States primarily use the Fahrenheit scale; the rest of the world uses the Celsius scale, and scientist use either the Celsius or Kelvin scale. Since we can use three different scales used to measure temperature, it seems reasonable to have formulas for changing or converting from scale to the another. Here are some useful conversion formulas.
Laura Huenneke, Ecosystem Ecologist
I am a plant ecologist involved in the study natural ecosystems. I currently work out of New Mexico State University and the Jornada Long Term Ecological Research project. In addition to the Jornada desert, I worked mostly with forested systems and mountain systems. This meant spending time in the mountains of the southwestern United States as well as in the rain forests of Hawaii.
Our work deals quite a bit with population growth and attempting to make predictions about changes in the numbers of an organism. I study rare plants and also their converse or opposites: plants that have become so weedy or aggressively invasive as to become problems by killing out other vegetation. We ask the question, "Is an organism getting rarer or a lot more abundant?" Mathematics gives us the ability to model and project the outcome given the current trends in the ecosystem.
There are still a lot of rare plants left in the mountain systems. The Chihuahuan desert of southern New Mexico doesn't have so many rare or endemic species. That focuses my attention more on the common native desert organisms and the roles they play in the ecosystem, rather than on the conservation-related organisms.
My work on the desert ecosystems in New Mexico has to do in part with changes in the diversity and structure of desert communities. Around the world, humans have had a huge impact on semi-arid ecosystems through their grazing animals, their impact on local water sources, and all kinds of human activities. We are interested in the consequences of these actions on the diversity of plants and animals in desert ecosystems. We are also interested in the impact of changed diversity on the stability and function of desert systems.
Along with modeling and predicting consequences, mathematics is an important tool when describing a desert. Deserts, by their nature, are kind of barren, so the organisms are few and far between, making it impossible to actually count them. This means you have to consider a range of sampling questions. What size area do you have to sample to feel confident that you have observed the diversity of organisms that are in a desert? And how long and how frequently do you have to sample? In the desert something different happens every year because of different rain fall and temperature patterns. These cause the desert to naturally look a little different from year to year. It,s my job to figure out the patterns of change in the desert over time. These might involve local scale changes, such as the cumulative impact of poor grazing practices on the desert. Or it might be more global scale changes, such as changes in climate or changes resulting from increased nitrogen deposits from the atmosphere. Mathematics is really important in all aspects of conservation biology and the study of ecosystems.
When I was in school, I never thought I would be a plant ecologist and conservation biologist. I would encourage all students and teachers to explore and to take as many challenging courses and experiences as they can. Mathematics and science are all about exploration. Even if you don't feel that you are gifted or talented in a particular area, you can still benefit from the exposure and the training. These experiences can help you find what excites you. Even if you think that you're not talented or gifted in math or science, being exposed to it stretches your mind and opens you up to many more possibilities. And watch for local research centers and scientific institutions. There you can often find mathematics, science, and technology in action and might even be able to take part in some educational or hands-on experiences. There is a lot out there!
Ecology as a science is all about synthesis and integration. It puts together biological science, physical science, human impacts, mathematics, and technology. These all come together to address issues that can't really be studied bit by bit. You can bring so many different perspectives to bear so productively on problems that are really important. That's what makes it really exciting!
Keep Exploring! Keep Pushing
Computer Graphic Artist Kevin Baille
As a computer graphics artist, I spend my days creating computer animations and other visual effects for films. If you've seen Star Wars Episode I: The Phantom Menace, one of the films I've worked on, then you probably understand how rich and lifelike visual effects can be. What you may not realize is how many people it takes to create such effects (a lot), or how much artists like me depend on math to create the lifelike creatures and effects you seen on the big screen.
Before explaining how math relates to my work, you'll need to understand a bit about the process we followed on SWI. I worked as a member of animatics team, which was responsible for creating moving blueprints for scenes in the movie. George Lucas and the film's editors would tell us, for example, "we want Anakin Skywalker to fly from this end of the destroyer to the other end in ten shots." Our team would use 3-D modeling and animation programs to create a video game quality "rough draft" of the scene. During this process, a sequence was refined until all were happy with the motion, timing, and overall feel of what they were seeing. Once George had approved a shot (the final animatic) we would send it to a team of artists at Industrial Light & Magic who would then use it as the basis for the much more detailed final shot or scene you see in the movie.
This kind of work requires a whole range of mathematical skills and concepts, from basic measurements, to an understanding of sines and cosines. For example, when we created rough models of the pods for the pod racing scene, we worked from a physical model that had been built by the model shop. We had to take measurements of the physical model in order to recreate it in virtual space. We also had to understand how angles affect what might be going on the other side of a moving object. Without this knowledge, animators would not be able to create objects that look realistic as they move through virtual space.
An understanding of motion, in fact, is central to what we do. I draw on the key concepts I learned in my high school calculus class all the time. In particular, I often need to know about the relationships between positional, velocity, and acceleration curves to animate objects in a realistic way. Knowledge of functions and how mathematical equations work is also essential. The flicker of energy that appears to flow from the light sabre was created using a mathematical function which defined the timing and intensity of the flicker.
Films using lots of 3D visual effects often use simulations to ensure that a complex visual effect is precise and accurate. In one scene from SW I, a rack deploys droids from a large troop carrier. The rack comes out and stops abruptly, jostling the droids. In order to make this scene look real, ILM used a physics simulation. A number of variables were plugged into the simulation, including wind, mass, and velocity. In order to know what to tell the computer to calculate, you have to understand physics, as well as math.
Although I've listed only a few examples here of how math impacts my work, I can think of dozens more. The fact is, I would not be a computer graphics artist at all without a solid grasp of all kinds of math. My advice to students would be, find ways to make math relevant to your life. Encourage your teachers to help you identify the math behind everyday activities. When you see its relevance outside of a textbook, you'll be able to understand and apply it in surprising ways.
Biographical Note:Kevin Baillie, a 1997 graduate of Shorecrest High School in Shoreline, WA, is a computer graphics artist now living in Northern California. Kevin appeared in a documentary called Learn & Live, produced by The George Lucas Educational Foundation. The documentary has been airing on PBS stations nationwide. For more information visithttp://www.glef.org.
John P. Marchant
Retired mathematics teacher and statistician for the Green Bay Packers
I am a retired mathematics teacher and statistician for the Green Bay Packers, a National Football League team. I taught mathematics at De Pere High School in De Pere, Wisconsin for 37 years. I served as a part-time lecturer in the mathematics education department at St. Norberts College, in De Pere, Wisconsin, for 22 years. In addition, I have been one of the statisticians for the Green Bay Packers football team for 33 years.
The primary responsibilities of the statistician for an NFL football team are dictated by theGuide For Statisticiansprovided by the NFL. The statistics recorded are the yards gained or lost and the individual’s cumulative yards immediately after each play, as well as each team’s cumulative yards as the game progresses. The statistics we record cover both the home and visiting teams.
Before I began my tenure with the Green Bay Packers, there were only two people involved in collecting and providing the required statistics. As the demand for more record keeping increased, I was hired, bringing the number of team statisticians to three. Currently, seven people make up what is known as the stats team: two computer operators, two spotters, one and with paper and pencil, kept the statistics manually, and recorded the information using manual typewriters. Today, the job is much easier. We still have to determine the yards gained or lost, but we then enter the yardage for each play into a computer that updates individual and team statistics immediately and simultaneously provides the information to the press and scoreboard. If a play is too complex to record while the play on the field continues, the operator transfers it to a second computer to finish while the first computer keeps current with the on-field plays. At the end of each quarter, we fax the statistics to the Elias Sports Bureau in New York. Elias Sports compiles all of the statistics for the NFL and sends copies to all of the teams after the Monday night game.
Here is an example of a play and the statistics kept by the statistician.
Start of play: Team A has possession, 2nd and 10 at midfield.
The Play: Jones rushes for 10 yards and fumbles. Smith of Team B recovers, advances one yard, and fumbles. Black of team A subsequently gains possession of the ball at the exact spot where Jones originally fumbled.
The statistical record: Jones gets credited with a rush of 10 yards and a fumble. Smith gets credited with an opponent’s fumble recovery and a fumble. Black gets credited with an opponent’s fumble recovery. No fumble yards are credited and no first down is recorded because of the losses of possession.
John P. Marchant is 70 years old, married, and the father of 8 children. He lives in De Pere, Wisconsin and continues to work for the Green Bay Packers at this time.