I’m running a graduate math seminar called here at U. C. Riverside, and here are the slides for the first class:
• Mathematics of the Environment, 2 October 2012.
I said a lot of things that aren’t on the slides, so they might be a tad cryptic. I began by showing some graphs everyone should know by heart:
• human population and the history of civilization,
• the history of carbon emissions,
• atmospheric CO2 concentration for the last century or so,
• global average temperatures for the last century or so,
• the melting of the Arctic ice, and
• the longer historical perspective of CO2 concentrations.
You can click on these graphs for more details—there are lots of links in the slides.
Then I posed the question of what mathematicians can do about this. I suggested looking at the birth of written mathematics during the agricultural revolution as a good comparison, since we’re at the start of an equally big revolution now. Have you thought about how Babylonian mathematics was intertwined with the agricultural revolution?
Then, I raised the idea of ‘ecotechnology’ as a goal to strive for, assuming our current civilization doesn’t collapse to the point where it becomes pointless to even try. As an example, I describe the perfect machine for reversing global warming—and show a nice picture of it.
Finally, I began sketching how ecotechnology is related to the mathematics of networks, though this will be a much longer story for later on.
Part of the idea here is that mathematics takes time to have an effect, so mathematicians might as well look ahead a little bit, while politicians, economists, business people and engineers should be doing things that have a big effect soon.
Azimuth 
Finally got the time to skim through your slides, and it’s very useful stuff. One thing that did stand out is the statement at the end where you say “This theory uses computers, because it deals with systems too complex to understand with just pencil and paper”. I’m not sure this is quite the right way to look at it: you can pretty much understand most things, once they’ve already been understood and reduced by someone, with just pencil and paper, but it’s almost impossible to discover those things in the first place without outside input. In some cases, like physics, this has been by general observation, structured observation and actual experiment. In some ways computers represent another way to gain external input, in the form of being able to see what the consequences of a model/theory are by simulation. (There’s also the avenue of trying to program computers in such a way that they develop and validate their own theories/models, but that’s a bit of a more niche research avenue.)
And there’s the converse: because computers are finite machines whilst most models are using something infinite (real numbers, unbounded quantities, limits as time goes to infinity), figuring out efficient and faithful (in the ways that you care about) computer representations often involve analysis, combinatorics, algebraic structure, category theory, etc.
I guess I should have said “simulate” or “model in detail” instead of “understand”.
John,
These slides are nice and I look forward to the rest of the course.
Having been a “modeler” working in oceanography for several years now I have come to the conclusion that models (or simulations) can help us understand what we see in the environment. They can show us the consequences of our current level of understanding and see if those consequences match up with what actually observe. I think this matches with what David saying.
Hi John,
have you considered trying to video the seminars? I know it’s extra work, but I suspect that it might be worthwhile. A lot of people are going to be interested in this stuff, and for some the video is helpful.
Since this is my first time giving a seminar about environmental math, I don’t feel like broadcasting videos to the world. I’m afraid pretty soon I’ll be learning things just 10 minutes before explaining them! Later, when I actually know what I’m doing, I’d like to videotape a course like this.
This first lecture is a lot like a talk I’ll be videotaping next week for a public lecture I’ll be giving—virtually—in South Africa. So, this first one should be available in a while.
[…] Part 1 – The mathematics of planet Earth. […]
Just found the beginning of these series of posts. I should draw everyone’s attention to this text: Martin Walter, Mathematics for the Environment, CRC Press, 2011. This is a rich text, covering many topics, densely. Many exercises. It defines “environment” (very) broadly, including policy, economics, and politics, trying to teach the audience how to look at these quantitatively. It does not, to my knowledge (I’ve read most but not all), explicitly introduce calculus, but it does implicitly introduce differential or, rather, difference equations through a “box model” which is used to describe, e.g., an influenza epidemic.
Walter’s book is rich with documentation, references, and problem sets. In fact, it would be rewarding to teach an undergraduate course from these, but bringing in calculus and ODEs.
I bought this book, but now I’m finding it a bit rambling and overly opinionated. There’s a lot in it, though—that’s for sure! I haven’t read all of it.
Rambling, opinionated. In my experience with it, it could be parsed this way. However, I think Walter’s point is to make mathematics pertinent to the discussion, and, to that degree, I applaud his efforts. I thought using selections from this book in conjunction with Harte’s Consider a Spherical Cow might work. Plus, there are a lot of small things in Walter’s book which just are not widely known, such as the opening example from 1951, United States v. National City Lines which, among other things, shows that corporations can collude when it is their common interest, and provides the actual text for the storyline of the movie Who Framed Roger Rabbit?