Post mortem for week 5:

Hey folks. Here are the notes I took from today's class, unedited. I think I will take them and go through all the notes you all have sent to me and see if I can come up with a draft of a "polya list for complex problems".

FOR NEXT WEEK, we will examine this draft list closely, refine it,  and then discuss the papers by Lorenz  and Held (they are on the website).
Then we will chose the first case study.

At the bottom of this email are our ideas for case studies. We talked about the advantages of studying a classical complex problem that was successfully solved, and of taking the opposite strategy of looking at a current problem carefully and seeing if we can't come up with a polya list for how we would really attack the problem if we were serious about solving it.  The latter approach would take several weeks, and so we would likely only have one case study for the class. But I am leaning in that direction right now because it would challenge us to demonstrate that it is possible to  lay out a pathway to solve a complex problem and see (after we do it) we really do feel reasonably confident that we could solve it.

Based on the people who showed up today, it seems that Abrupt Climate Change (in the glacial) is a popular choice. Please, if you didn't attend today, let me (and Gerard) know your favorite topic.

candidate checklists (link)

David's in class notes:

1. Statement of the problem: iterate to you get to a question you think you can answer.
Assess complexity of system. This might create a list of sub-questions, or sub-systems that need to be understood. The process should lead to a clean statement of the problem, and the goals that you have to solve the problem (understanding; realism; reduce uncertainty, etc), and an a priori statement of what it would take for you to be satisfied with the results.
i)    What is the problem? What are your goals? What do you want to learn/predict, etc? Make a plan:
ii)    Understanding the complexity of the system: can a sub-system be defined by medium, temporal scale, spatial scale?
iii)    What are the assumptions? What tools/data do you need to solve the subsubsystem questions? What do you require from each of these subsystems (what results are you aiming for?) to move on to the bigger problem?
iv)    What type of result is required from examining each subsystem, such that it makes sense to go the next step and glue the sub-systems together?

2. If you solve all the sub-system questions, how do you know that in gluing them together you will get something sensible (ie, relevant to the big problem you are trying to solve).
3. Are you looking for a result that narrows down the possibilities, or confirms or falsifies the big question?
4. What tools do you need to solve the problem?
5. How much time are you willing/do you have to solve the problem? Is the end result more a statement of a hypothesis, or is it really new knowledge?
6. Self critique is critical at the end.  Critical evaluation is essential.

The good problem might be one that has one or more of the following outcomes:
i)    the result makes a surprising prediction that is verified;
ii)    the result significantly narrows the possible solutions;
iii)    the result reconciles some apparent discrepancies in data/models/etc.

Science – exploration, hypothesis, evaluation  loop  - > knowledge

Case studies in which we would create a poly checklist to solve the big complex problem (if your name is in parentheses, then you expressed an interest in this problem).

 1. Glacial cycles
 2. Climate Change (“Discovery of Global Warming”)
 3. ENSO future?
 4. Abrupt climate change  (Meredith, Rob N., Roo  ) How do we know it? How do we have theories and how do we test it? visitor Eric S.
5.    Downscaling from large scales to regional scales: worthwhile, how you do it? How do you know if you are making progress (Justin M)
6.     Greenland ice sheet (history and fate)/large scale ice sheet stability (Michele, Hans Christian)
7.    Ocean thermohaline circulation:
8.     Re-look at what is considered to be a great problem solved (Evolution; Kevin
9.     Little Ice Age – is it really a globally coordinated phenomenon? (Kevin W)
10.    How do we know the Eocene climate (Rob N) – warm high latitudes: how do we know it?
11.    Superstring theory: why do these people study the unknowable? (Ken)

Bring in people to have a debate? Read a summary paper (academy report on abrupt climate change) and then bring in someone to critique it.
Pick one problem and do it for three weeks.