Ignoramus et ignorabimus
The new California Academy of Sciences is headed toward completion, and the process of preparing the new facility, readying the exhibits, and moving the more than 20 million specimens in our natural history collections is keeping many of us very busy. You can find out more about the happenings here, and view a very nice video here.
Nevertheless, science goes on. While discussing our planned exhibit on climate change with some external designers a couple of weeks ago, one of them commented on the topic of "uncertainty." She said that we should avoid the word at all costs because the general public already does not trust scientists, and that everytime they hear that particular word, it reinforces the notion that we scientists don't know what we're talking about ("You can't even predict the weather 12 days from now!"). Is this true? Please send comments if you have any! Anyway, nothing could be farther from the truth. Let me tell you, Uncertainty is part of the beauty of the Universe.
When we (scientists) use the term Uncertainty, we mean either unknown, not understood, or unknowable. Let me attempt to explain using climate change science as an example. There is uncertainty in our predictions of the future's climate because there are unknown quantities in our reasoning. Some of these quantities include important feedbacks in climate change processes that we simply have not recognized. For example, who would have thought ten years ago that as ice sheets melt, that they would lubricate and accelerate their own slide towards the sea? Other important unknowns include all the human ones. How quickly will the developing world increase its carbon emissions over the next 100 years? How much international economic cooperation can we all count on? Then there is the "not understood." There are processes and phenomena whose science still escape us. E.g. we know that clouds play a role in climate, but will it be an important role as the planet continues to heat up? Will it be a cooling role? I don't know, though there are some very clever people out there trying to figure it out.
And then there is the unknowable. The notion that once we've understood the mechanisms at work in the world, and have measured the right things, that we will be able to predict the future the way that we predict the ticking of a clock, is a deep-rooted consequence of the Newtonian and Cartesian revolutions. It is a dangerous hubris. The Universe does not work that way. The revolution of quantum physics told us that the Universe is random at the smallest scales. More recently, areas such as Chaos Theory and Catastrophe Theory have revealed that even the most innocent looking phenomena, such as weather(!), can be full of surprises. Take a look at this little equation.
X(t+1) = rX(t)(1-X(t))
It simply tells us that the size of an animal's population, X, at time t+1 is the product of the population's size at time t, multiplied by the typical birthrate of the species (r). If r is 3 (members of the population have 3 offspring per breeding season in excess of deaths), then we see that one can predict population size well into the future; it's a simple cycle (upper graph). Sir Isaac is happy. Now, however, let's say that r is 3.6 (I know, you can't have three and a bit kids, but just indulge me). At this value, and for most values beyond, population size is effectively unpredictable! There's no randomness here folks. This is a deterministic but inherently unknowable system! Welcome to Chaos Theory. And welcome to weather prediction. In this case, Uncertainty is not the result of ignorance, it is part of the inherently unknowable Universe. The system cannot tell us where it's headed if the system itself doesn't know. Beautiful.
Btw, if any of you yougsters out there think that you can predict where the second population is headed, then you deserve a Fields Medal (let me know; I'll nominate you). In the next posting we'll get back to our modeling, touch on Catastrophe Theory, and chat about tipping points.
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