Sunday, February 07, 2010

Characterizing the incalculable

It would be nice to be certain about the future. But, absent time travel, no one can be certain about anything that hasn't happened yet. So, as a substitute many specialists build models in disciplines as disparate as finance and physics to guess what the future might look like given certain assumptions.

In physics the models we have for describing the universe and its properties can be remarkably predictive if they only require input based on the laws of physics. But we have considerably more trouble describing the social world of humans and the interactions of human society with nature. This is because we don't have laws of human behavior that can be nailed down in the same precise, repeatable way that laws of physics can.

The upshot is that we can calculate the probability of a comet hitting a planet with some precision. But we cannot calculate the probability of the stock market going up or down in the next five years. Nor can we calculate the probability of any particular outcome of climate change because what we humans do in the future is such an important factor in determining that outcome. The modeling of climate is also problematic because the climate system itself--even absent any human interference--is so complex that we do not fully understand it.

A rule of thumb then might be that the more complex the system, the less likely it is we will be able to model its actions with precision. And, the greater the number of humans involved in affecting that system and the deeper that involvement, the more difficult it becomes to design precise models of the system. In general, the reliability of a model decreases as the complexity of the system it is modeling increases.

What are we left with then? Shall we simply give up and say that much of what we would like to model cannot be modeled? I would counsel against this view. The reason many people tell us not to trust models is that they are mistaken about the purpose of modeling. It is not, as many believe, done in order to predict the future. Rather, most modeling is done in the spirit of scenario planning. What if global temperatures rise by 4 degrees C by 2100? What might that imply for other Earth systems and for the human-built environment? What if temperatures rise by only 1.5 degrees C? What level of preparedness might that imply? What if temperatures plunge in the Northern Hemisphere as a result of the breakdown of the thermohaline current? (For a look at a sampling of temperature scenarios based on various climate models, click here. Note especially the large error bars beside the graphs implying large uncertainties.)

But what likelihood might we assign to any of these scenarios? It is simply impossible to assign a clear, calculable probability to any of them. The best we can do is to characterize the incalculable. We cannot know the precise odds of any climate scenario. But, by knowing the range of presumed outcomes, we can start to characterize the effects and therefore gauge the probable severity of any particular outcome.

Let's review for a moment the three conditions under which we actually make decisions in our daily life. First, we can say with certainty who the current president of the United States is. We might misspeak or simply get the answer wrong, but the data is available and incontrovertible. We are thus making a decision under certainty. The answer is certain whether we know the correct answer or not.

Second, if I flip a coin, there is a 50 percent chance that it will come up heads. I can calculate this because I know in advance that there are only two possible outcomes to this action. I cannot know for certain what the outcome of any one coin toss will be. But I can know with certainty what the possible outcomes are. In this situation, I am making a decision under risk. And, I can calculate precisely what the risks are.

Third, we can describe such decisions as investing in a particular stock, taking a particular job, and marrying a person whom we are dating as decisions made under uncertainty. We cannot possibly discover all the information needed to know the trajectory of our stock pick, the degree of success or failure we might meet in our job, or the state of our possible marriage to a current love interest 10 years hence. And, it turns out that policies in response to climate change also fall under this third category. For decisions made under this category we simply cannot gather all the necessary evidence to calculate even the probability of a particular outcome as we could with the coin toss. This is partly because many of the variables would have to come from the future and partly because these situations are so complex that many of the existing variables are hidden from us. (The foregoing discussion on types of decision making is based on a paper by Nassim Nicholas Taleb and Avital Pilpel entitled "On the Unfortunate Problem of the Nonobservability of the Probability Distribution.")

Future oil supplies also fall under this third category of decision making. The Oil Drum provides periodic updates on various scenarios for future oil output including an analysis of which liquid fuels are included in which forecasts. The variables are much like those involving climate modeling. Some of the current data is unknown. Future human actions with regard to oil consumption, oil exploration and oil production cannot be known with certainty. Oil is found underground and therefore must be measured indirectly. Again, we are faced with making decisions under uncertainty with respect to oil supply.

So, given the wide range of oil production forecasts, which are we to believe? Some forecasts posit a business-as-usual scenario through the next couple of decades. Others assume a rather rapid drop-off of available petroleum in the near future. We can assign neither scenario a calculable probability. But we can once again characterize the possible outcomes. The business-as-usual scenario requires little in the way of changes in public policy or personal behavior. The rapid drop-off scenario suggests an emergency that will require heroic measures to navigate.

Now, which of these characterizations for future oil supplies or climate change should we act upon? First, we need to understand that for all scenarios generated under category number three, the further we go into the future, the more important the range of results becomes rather than the actual forecast. In other words, what are the extremes that we believe are possible? To provide some perspective on how we might proceed, ask yourself this question. If you were told that the trans-Atlantic flight you were about to board only crashes 5 percent of the time, would you still board that plane? My guess is that you would change your reservations. Even with a 95 percent chance of surviving the flight, you would find the risk of death too high.

Now if you were to assume that the worst case scenarios for climate change or future oil production have only a 5 percent chance of occurring, would that suggest to you that we need to make some vigorous preparations in order to mitigate or avoid altogether those scenarios? Keeping in mind that we can't actually calculate such a probability, this illustration shows how sensitive humans are even to low probability events if the outcomes are severe enough.

My own answer to the question, as you might expect, is a resounding "yes." But then I believe that the chances of the worst happening might actually be a significant multiple of 5 percent in both cases.

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