Blind Oracles

Humankind has always wanted to predict the future. It seems we are genetically inclined to want to find out what is coming up around the next corner. This is especially true of scientists, many of whom believe that prediction is the real aim, and the best test, of any scientific theory. Just ask the writers of those leaked emails from the University of East Anglia’s Climatic Research Unit.

But the histories of science and prediction have long been closely intertwined. The most successful forecasting operation of all time was the oracle at Delphi, in ancient Greece. It lasted for almost a thousand years, beginning in the 8th century BC. The predictions were made by a woman, known as the Pythia, who was chosen from the local population as a channel for the god Apollo. Her predictions were often vague or even two sided, which perhaps explains how she lasted so long—rather like Alan Greenspan.

Our western tradition of numerical prediction can be said to have begun with Pythagoras, named after the Pythia, who in one of her more famous moments of insight had predicted his birth. (She told a gem engraver, who was actually looking for business advice, that his wife would give birth to a boy “unsurpassed in beauty and wisdom.” This was a surprise, especially because no one—including the wife—knew she was pregnant.) As a young man, Pythagoras travelled the world, learning from sages and mystics, before settling in Crotona, southern Italy, where he set up what amounted to a pseudo-religious cult that worshipped numbers. His followers believed that he was a demi-god descended directly from Apollo, with superhuman powers, such as the ability to dart into the future.

The Pythagoreans are credited with a number of mathematical discoveries, but their major insight was actually about music: they found that harmony was based on simple ratios between whole numbers (the frets on a guitar, for example, follow this pattern). Music was considered the most expressive and mysterious of art forms, so the fact that it was governed by numbers implied that all kinds of other things were too. The Pythagoreans believed that the entire cosmos (a word coined by Pythagoras) produced a kind of tune, the music of the spheres, which could be heard by Pythagoras, but not by ordinary mortals.

If the cosmos was based on number, then it could be predicted using mathematics. The ancient Greeks developed highly complex models that could simulate quite accurately the motion of the stars, moon and planets across the sky. They assumed that the heavenly bodies moved in circles, which were considered to be the most perfect and symmetrical of forms; and also that the circles were centred on the Earth. Making this work required some fancy mathematics—it led to the invention of trigonometry—and a lot of circles. The final model by Ptolemy used epicycles, so that planets would go around a small circle that in turn was circling the earth.

The main users of these models were astrologers, who needed to know the positions of the celestial bodies at different times. The Ptolemaic model was eventually adopted by the church, and remained almost unquestioned until the Renaissance.

Classical astronomy was finally overturned by Isaac Newton’s discovery that the force that made an apple fall to the ground and the force that propelled the moon around the earth were one and the same thing. This was as remarkable as the Pythagorean insight that music is governed by number. Newton’s laws of motion implied that the movement of anything, from a cannonball to a ray of light, could be predicted using mechanics. Scientists from all fields, from electromagnetism to chemistry to geology, immediately adopted the Newtonian approach, to enormously powerful effect.

Today, scientists have mostly taken over the mantle of prediction from astrologers or organized religion. Like the Greeks before them, they have built hugely complicated models of the cosmos, based not on circles but on equations. General circulation models predict tomorrow’s weather or the climate in a hundred years’ time. General equilibrium models predict the flow of the economy. Geological models of the Earth’s crust attempt to predict earthquakes or the eruption of volcanoes. When governments want to know the impact of their policies on future generations, or want to protect against disasters, it is to these models that they turn.

Megadisasters: The Science of Predicting the Next Catastrophe explains for lay readers the predictive science behind such hopes. The author, Florin Diacu, is a mathematician at the University of Victoria who specializes in celestial mechanics and chaos theory—the search for patterns in systems complex enough that similar starting points can nevertheless lead to widely varied results. (Take two rafts, for example, set simultaneously adrift at the same point on the Amazon: subtle differences in the many factors affecting the rafts mean they will most likely float ever further apart over time, despite starting very close together.) The motivation for the book, Diacu explains, is to explore areas where chaos theory can be used to predict or explain natural phenomena.

Our desire to predict the future is certainly an interesting story that has led to some fascinating work, and it is well described here. Diacu takes us for a good tour of the science behind predictions in areas as diverse as mudslides, financial crashes, epidemics and climate change. And there are also exciting stories, like the one about the first people to fly into the eye of a hurricane.

In 1943, two U.S. officers at a Texas airbase, provoked by taunts from British pilots about the base’s frail training planes, wanted to prove that aviation skill mattered more than equipment. They therefore took a two-seat training aircraft into the centre of an approaching tropical storm. This proved their point and also ushered in a new era of hurricane research.

The book’s strongest chapters are the ones on geophysics. Here, Diacu recounts the work of thinkers including 18th-century mathematician Joseph-Louis Lagrange and Manhattan Project physicist Enrico Fermi, both of whom made important contributions to the theory of waves. Its applications are surprisingly wide: Fermi’s early computer models of microscopic crystalline structures, for instance, helped give insight into the behaviour of massive, solitary ocean waves, like those in the 2004 Indian Ocean tsunami. Similarly, Diacu explains how mathematical research has helped model the waves that pass through the planet’s crust during earthquakes and the flows of magma within active volcanoes.

But while he cites plenty of examples where equations are useful tools for describing and understanding extreme events such as earthquakes or tsunamis (a worthy goal in itself), as far as I can see, none of the scientific models can reliably predict them (the subject of the book). Prevention therefore usually comes down to things like building codes and early warning systems.

This points to a basic problem with the Newtonian approach to prediction: despite its eminent logic, it just does not seem to work very well when applied to complex systems of the type we really want to know about, such as weather, the economy or our own health. It is sometimes said that prediction is the world’s second oldest profession; but we do not seem to be getting much better at it.

Weather forecasting, for example, has certainly improved since the 1950s, when we did not have supercomputers or weather satellites. But progress has tapered off, and forecasts of precipitation still lose most of their accuracy after just a few days. Economic forecasting is in even worse shape. At the start of 2008, a poll of forecasters by Bloomberg showed an average expected gain for the S&P 500 index of 11 percent, with no one predicting a decline. By year end the market was down 38 percent. In biology, we still cannot predict the effects of a new drug, or a new virus like swine influenza, despite the success of the Human Genome Project at decoding our DNA. And as geophysicist Susan Hough wrote recently in the New York Times, “scientists have been chasing earthquake prediction—the holy grail of earthquake science—for decades … Yet we have little to no real progress to show for our efforts.”

This does not stop anyone from making predictions, of course. Today, we are bombarded more than ever in the media with forecasts about the weather or the economy or politics, and are frightened by stories of climate change or deadly pandemics. Forecasting has become big business, especially in areas such as business and economics, but the poor track record of the oracles is rarely discussed. Our inclination and curiosity toward the future seem to make us equally incurious about going back to see whether past forecasts were right.

The upshot of all this is that the science of prediction has a considerable amount of baggage attached to it. Scientists are in an awkward position, and more than just grant money is at stake. For two millennia they have striven to predict and control the universe, and have held that up as the ultimate test of success or failure. The fact that the models cannot predict is a great concern—and it leads to some rather dysfunctional responses.

The great strength of science, usually, is the way in which it can update itself when a new theory appears that makes better predictions—just as Einstein’s relativity replaced Newtonian physics. A problem occurs, however, when a new theory does not show up—when the existing one clearly has flaws, but no alternative makes better predictions or can be verified experimentally. Scientists then sometimes seem to go in for denial, often involving untestable explanations like string theory, as Lee Smolin documents in The Trouble with Physics: The Rise of String Theory, the Fall of a Science and What Comes Next.

In economics, the inability to predict the future was explained away in the 1960s by the efficient market hypothesis. It saw the market as a kind of deity whose short-term motions no one can anticipate, but held that the long-term risk could still be modelled by equations. The flaws in this theory became increasingly obvious, as the risk models missed even the chance of the credit crunch, and in fact played a large role in making it happen.

In weather forecasting, lack of prediction was explained by chaos theory and by the “butterfly effect.” According to this theory, the atmosphere is so unstable and chaotic in the short term that a butterfly flapping its wings can later cause a hurricane on the other side of the world; but again, long-term prediction of the climate is assumed to be possible. However, while the atmosphere certainly has some unstable dynamics, experiments show they are hardly its defining feature.

In my opinion, both the efficient market and the butterfly effect are fig leaves that explain away forecast error, while allowing scientists to retain some of their oracular authority for longer-term predictions, which are safe because they are for the distant future. The real reason for our lack of forecast ability in all these areas, I believe, is simply that our traditional modelling approach does not work when applied to complex organic systems. These systems tend to be dominated by emergent properties, which by definition cannot be modelled or predicted from knowledge of the components.

An example of an emergent property is a social networking site like Facebook. When computers were invented, everyone predicted that we would use them to perform menial tasks and so would need to work less hours. Instead we work even longer hours, but divert ourselves by getting in touch with friends. Another example (more to the point) is clouds, whose behaviour cannot be reduced to simple physical properties of air or water. There is a law of gravity, but there is no law for a cloud.

Complex systems are also characterized by an internal tension between positive and negative feedback loops. Apparent stability is just a temporary truce; when change comes, it can come suddenly, as with earthquakes or financial crashes. Models that attempt to capture this internal tension are highly unstable, like a mechanical robot that tends to suddenly reel out of control.

Together, these properties represent a game changer, a kind of uncertainty principle for complex systems, which makes them fundamentally different from mechanical systems like the motion of the planets. The music of the spheres, this is not. Newtonian gravity it is not. Techniques from areas such as complexity theory can help us to understand these systems, and in some cases identify patterns, but accurate prediction is usually elusive.

Which brings us back to Megadisasters. Although the book is to be recommended as a guide to the current state of forecasting science, the author and I take different tacks in the premise that complex systems can be realistically modelled using equations, and in what meaning we are to derive from our lack of forecast skill. The author is aware of the limitations of our current models (although there are some odd statements, like the one that weather predictions have a limit of two weeks—that is the theoretical limit due to chaos, not the real limit). But when he implies, for example, that earthquakes are ultimately governed by “differential equations” that await discovery, to me that is a faith-based assertion—like the Ancient Greeks saying the cosmos is based on circles—and one not supported by complexity theory.

This might seem a purely technical point, but it changes the way we approach practical problems, such as climate change. A question that is typically asked is, if scientists cannot predict next week’s weather using their equations, why should we listen to their predictions of what will happen to the overall climate in 50 years time? It is a sensible point—many people deal with forecasts in their jobs and know they often go wrong. The book gives two responses. The first (discussed above) is that climate prediction is “unlike weather forecasting” because the butterfly effect is not an issue.

The other argument given is “were the models wrong, their predictions would likely disagree with one another.” But a well-known phenomenon, when people try to predict things they cannot understand, is that they tend to indulge in groupthink and cluster their forecasts—like when all of Bloomberg’s forecasters thought 2008 would be a good year. Indeed, it is rather suspicious that climate change predictions (for carbon dioxide doubling) have remained essentially unchanged over the last 30 years despite the explosion in observational data, computing power and number of models.

Skeptics rightly sense that these arguments are dodging the issue—they just do not fly. Rather than cling to the forecasts, or use chaos as an excuse, I think it is preferable to employ a medical analogy. When you go to a doctor, you don’t expect them to pull out a crystal ball, or a mathematical model, and tell you what disease will strike you down in 25 years—you just want sensible and practical advice. We cannot model the climate system accurately, any more than we can the economy or the human body, but there is plenty of evidence that a) carbon dioxide has a warming effect, b) the planet is getting warmer, and c) this is already causing problems in our only available planet. There are also many other reasons for cutting down our carbon footprint, so that is what we should do. Climate science and economics can give us some insight into the best course of action, but trying to make detailed mathematical predictions is just a distraction, another symptom of the hubris that got us into this fix in the first place.

Acknowledging uncertainty in this way (as opposed to just fudging) could turn out to be surprisingly productive and positive, because it would imply a more direct, emotional and immediate engagement with the state of our planet. Predictions of climate megadisasters serve to temporarily frighten us, but perhaps paradoxically, they also lead to a false sense of security and passivity—if scientists can model the future, surely they can control it as well.

Confronting the true nature and causes of uncertainty, though, would require we let go of the two-millennia-old quest to predict and control nature, and just admit that sometimes we are out of our depth. That may be the toughest test yet for science.