Want to Make Your Reputation in Academia? Here is an Important Class of Problem For Which We Have No Solution Approach
Here is the problem: There exists a highly dynamic, multi- multi- variable system. One input is changed. How much, and in what ways, did that change affect the system?
Here are two examples:
- The government makes a trillion dollars in deficit spending to try to boost the economy. Did it do so? By how much? (This Reason article got me thinking about it)
- Man's actions increase the amount of CO2 in the atmosphere. We are fairly confident that this has some warming effect, but how how much? There are big policy differences between the response to a lot and a little.
The difficulty, of course, is that there is no way to do a controlled study, and while one's studied variable is changing, so are thousands, even millions of others. These two examples have a number of things in common:
- We know feedbacks play a large role in the answer, but the system is so hard to pin down that we are not even sure of the sign, much less the magnitude, of the feedback. Do positive feedbacks such as ice melting and cloud formation multiply CO2 warming many times, or is warming offset by negative feedback from things like cloud formation? Similarly in the economy, does deficit spending get multiplied many times as the money gets respent over and over, or is it offset by declines in other categories of spending like business investment?
- In both examples, we have recent cases where the system has not behaved as expected (at least by some). The economy remained at best flat after the recent stimulus. We have not seen global temperatures increase for 15-20 years despite a lot of CO2 prodcution. Are these evidence that the hypothesized relationship between cause and effect does not exist (or is small), or simply evidence that other effects independently drove the system in the opposite direction such that, for example, the economy would have been even worse without the stimulus or the world would have cooled without CO2 additions.
- In both examples, we use computer models not only to predict the future, but to explain the past. When the government said that the stimulus had worked, they did so based on a computer model whose core assumptions were that stimulus works. In both fields, we get this sort of circular proof, with the output of computer models that assume a causal relationship being used to prove the causal relationship
So, for those of you who may think that we are at the end of math (or science), here is a class of problem that is clearly, just from these two examples, enormously important. And we cannot solve it -- we can't even come close, despite the hubris of Paul Krugman or Michael Mann who may argue differently. We are explaining fire with Phlogiston.
I have no idea where the solution lies. Perhaps all we can hope for is a Goedel to tell us the problem is impossible to solve so stop trying. Perhaps the seeds of a solution exist but they are buried in another discipline (God knows the climate science field often lacks even the most basic connection to math and statistics knowledge).
Maybe I am missing something, but who is even working on this? By "working on it" I do not mean trying to build incrementally "better" economics or climate models. Plenty of folks doing that. But who is working on new approaches to tease out relationships in complex multi-variable systems?