There is no Nobel prize in mathematics and the rumor that Nobel didn't create a mathematics prize because his wife/mistress/fiance had an affair with mathematician Gosta Mittag-Leffler is in all probability false. There doesn't seem to be a clear explanation of why the field of mathematics is overlooked as prize category.
Mathematics is closely linked to many branches of science. Although not necessarily highlighted, the use of mathematics is recognized, especially with the physics and economics awards. I listen to NPR's Planet Money podcast which covers all things economics and they recently posted an interview with Elinor Ostrom, one of the winners of the Nobel prize in economics, where she explained some of her research.
Her research is about 'the tragedy of the commons' (highlighted in a 1968 paper by Garrett Hardin) which says that if there is a common resource (e.g. fishing grounds that the public makes their living from by harvesting fish), then if this resource is limited then it will ultimately be overused until it is destroyed even if it is not in the public's interest for this to happen. The only way that this can be prevented is for the government to step in and through enforcement, stop the overuse of this resource. In the example of the fishing grounds, the government must come in and put limits on the amounts of fish that people can catch otherwise the grounds will be over-fished.
The discussion in this podcast with Elinor Ostrom highlights that this is a mathematical model which can be used to predict the behavior of a group's action. As she says in this podcast, this model "can be used mathematically to predict outcomes when the problem is pure private goods and you have a highly competitive market." She then goes on to say that it is a challenge to prevent this tragedy from occurring, but since humans are highly complex, this model does not always apply and that solutions for solving the tragedy of the commons can come from within the group.
Some of the ideas about her research became crystal clear in this interview when she was asked about the communal fridge in the office. The 'tragedy of the common fridge' is that it must eventually degrade into a repository for moldy sandwiches. The research of Elinor Ostrom says that, no, in fact human beings are complex enough that they can develop a solution from within the group.
I'm a fan of the podcast because I would like to be more economics literate. Economics reasoning is complex and this podcast looks at a lot of different aspects of it. If you are interested in hearing another good story about how mathematical models can be used to predict behavior, the podcast a day earlier talked about monkey behavior seems to follow a mathematical model for supply and demand, even though monkeys probably don't understand the meaning of 'one half of.'
Subscribe to:
Post Comments (Atom)
This week on the Planet Money blog the team posted lesson plans for an 8th grade economics class in New York City that uses the podcast as a teaching tool in the classroom.
ReplyDeleteMike,
ReplyDeleteIt's 8th period, not 8th grade!
This is clearly an advanced high school class.
But there is some useful stuff here. My advanced (academic) math classes often lament the fact that they never get the opportunity to learn financial math in any depth. For example, this came up recently in my Advanced Functions class as we were discussing the following problem:
"At one time, Maple Leaf Village (which no longer exists) had North America's largest Ferris wheel. The Ferris wheel had a diameter of 56m and one revolution took 2.5 min to complete. Riders could see Niagara Falls if they were higher than 50m above the ground. Assuming the rider gets on at a height of 0.5m at t=0 min, determine the time intervals when the rider could see Niagara Falls."
The student's question was, "So how come the essential and college math classes get to learn about useful math like mortgages and car loans, and all I'm going to be able to do after high school math is figure out the time intervals for a non-existent Ferris wheel (in a non-exisent town)?"
There seems to be a perception that academic students, strong enough mathematically to handle Ferris wheel type questions, will just magically figure out real-world, financial math on their own as adults. Hmmm ... I think I just realized why my Visa bill is so high.
8th period? oops. I only had 6 periods when I was in high school. This school is getting a couple of extra hours per day of teaching time then it is less of a surprise that they have time to cover economics as a subject. My high school didn't offer an economics course at the time but I just went to its web page and now they have a business department.
ReplyDeleteDoes putting a trig problem into a word problem form suddenly make it relevant? You and I have had this conversation recently about max/min problems. Does it help to make the operation of finding the maximum more relevant if it is about throwing an object off a building or shooting a rocket in the air? My thought is 'no.'
Word problems aren't an application (in general) and it is wrong to think that students are going to 'discover' math because of word problems. The way I see it is that students first learn the math, then they come across a word problem and will hopefully be able to say 'ah-ha, I can put that math into good use and use it say something relevant about a rocket.'
I think that in order to present relevant examples like economics teachers need to know TONS of stuff. Good applications like interest rates and amortizing bank loans come from good teachers having the patience to continue to study and learn about subjects that are outside of the curriculum.