April marked the beginning of Math Awareness Month. On Apr. 8, 2009 the mathematics department held a panel discussion titled “Math and Climate Change” that featured not only Cornell professors, but also visiting lecturers from the University of Vermont and Ithaca College.
The panel discussed the role of mathematics in everyday weather predictions and in outlining the possible scenarios for climate change, as well as math’s growing role in the fields of economics, medicine and construction. Scientists around the world looking to predict the outcomes of global climate change have been turning to differential equations to minimize uncertainty.
Prof. Chris Danforth, of the University of Vermont is an atmospheric science professor and a mathematician with the task of predicting future weather patterns. While it is impossible for scientists to predict exactly how the global climate is going to change, math and statistics can be used to track patterns and chart possible scenarios.
“You take the factors you want to measure — temperature, pressure, wind direction, humidity, ozone. You want to know these measurements over several locations over the earth and you want to know just how each factor affects with weather. You multiply those together and you get a billion numbers, which is then assessed by a state of the art computer program,” Danforth said of his work with computer systems.
The problem with accurately predicting weather accuracy lies in the fact that weather and climate are governed by a chaotic system. “Ultimately, you’re assessing 7 factors per location at 1,500,000 locations on the surface of the earth and 100 vertical layers up to the edge of space,” Danforth explained. The chaotic aspect of the atmosphere makes small differences have large impacts of the weather, especially in the long term.
“You write down the set of equations you think govern the system, but no matter how accurate your model is, it could be a perfect representation, you’re going to make some measurement error,” Danforth said.
The probability of a particular weather event is determined by computer systems that use partial differential equations to make weather forecasts. For example, to forecast a 40% chance of rain, the program outlines the effects of several weather factors for a given period of time. The program then runs the predicted scenario several times — if precipitation results in 40% of the trials, then there is a 40% chance of rain.
Cornell students who have taken MATH 2930 are familiar with partial differential equations and their applications to the world, but those who are unfamiliar with them may not comprehend just how often partial differential equations are used. Essentially, a partial differential equation relies on a set of variables that can be manipulated to measure how each variable influences the outcome.
In the case of weather prediction, partial differential equations can be used to formulate problems involving several inputs, such as pressure systems, temperature and moisture.
Partial differential equations are also used in economics, physics, architecture, finance, banking and even medicine and biology. Of the 123 undergraduate students in the math department, the majority are double majoring in either physics, economics or business.
Professor Lars Wahlbin, mathematics, recognized that though it may be hard to identify, math is becoming more prevalent in everyday life as technology becomes more and more advanced and society becomes more dependent on it.
“There has always been some mathematics present, but now they have started to use more sophisticated math, such as partial differential equations.” Wahlbin said of math’s role in society. “Just within economics, the guys who designed the Black-Scholes model won the Nobel prize.”
The Black-Scholes model uses a mathematical model of an economic market based on a partial differential equation that must be satisfied by the price of a derivative.
“Math is hidden,” Walhbin said. “You don’t have to be a mathematician to take a pill or be cut up by a surgeon. The surgeon doesn’t have to know mathematics either, but somewhere along the line there might be hidden mathematics. But it’s not at the surface at all. If you’re a consumer you have to look really hard behind that curtain to see that yes there is sophisticated mathematics behind the scenes.”
The panelists noted the need for a Math Awareness Month in drawing attention to a subject about which many students are not enthusiastic. Prof. Thomas Pfaff of Ithaca College spoke on incorporating ideas of climate change into calculus and algebra classes through the use of real data of current and future scenarios as opposed to the fictitious examples often used in textbooks.
“The challenge is quiet enormous in terms of what we might need to do in order to bring down current carbon emissions and its my feeling that its going to be even harder if the general population of the world isn’t well-informed about the problems,” Pfaff said. “Math teaches a large number of people the concepts of calculus and statistics and if we can incorporate ideas of climate change into those courses, we can have a better educated population and therefore it would be easier to bring down emissions.”
For Math Awareness Month, the Mathematics department’s outreach program holds two annual events. First, it coordinates a t-shirt design contest with Ithaca High School students. High school students design three competing t-shirt designs and Cornell students and faculty vote on them throughout the month. Second, the Math department organizes a panel discussion, open to the public, with the purpose of exploring math’s role in different fields.
Math Awareness Month primarily targets high school students, as interest at a college level is highly limited. “I don’t know if we need math awareness at a college level, but if we can get high school students interested in math, that’s half the battle,” Wahlbin said. “Its kind of too late when you get to college, because people have already decided whether or not they want to pursue math as a career.”