But Are They Sciences?
Economics, climate, and experiments
“Economics and climatology aren’t sciences at all – you can’t experiment in either.” You can hear this from a lot of people, most of them well-meaning. But confused. They simply haven’t reflected very deeply on the nature of science, or of experiments for that matter.
The truth is that the scope for experimentation is very limited in all scientific fields. You almost never get to experiment with the system you actually want to know about – call it the objective system – in the conditions that are of real interest. You have to settle for experimenting on a model system, and projecting the results onto the objective system. The real question is how well you can depend on the relationships you use in the process of projecting from model to objective system.
We can see all this with greater clarity if we look back at the history of science, at the development of the first of humankind’s “exact sciences,” positional astronomy, or the study of the apparent movements of celestial bodies
One of the earliest scientific interests of our ancestors was astronomy. When humans began cultivating crops, about ten to twelve millennia ago, they found that they needed some guide to when to plant. In the areas the early agriculturists lived in the growing season was fairly narrow and it was important to plant neither too early or too late. Some ancient geniuses realized that the apparent motions of the Sun, planets, and stars, could be used as the basis for construction of a calendar. Even before written records, our ancestors collected data on astronomical events, and used the data to make strikingly accurate models. We can tell this because they left behind structures that were quite precisely aligned with the positions of the Sun or particular stars at special times in the year, such as the equinoxes or solstices. The early civilizations all had priests who made astronomical observations for both practical and religious purposes, and they developed models to predict events such as eclipses.
We know relatively little about how astronomical models were conceived and developed in most places, but in Babylon arithmetic was used to interpolate and extrapolate from organized lists of data, without any apparent attempt to investigate the mechanisms of celestial motion. Then the Ancient Greeks acquired a good deal of astronomical data from the Babylonians and combined this with their knowledge of geometry to develop their models. There were a number of competing Greek astronomical models, but the most successful one reigned supreme until after 1500 AD.
This is generally called the Ptolemaic Model after Claudius Ptolemćus (c.85 AD – c.165), whose Almagest, transmitted via the Arabs, became the most complete and best-known source of astronomical knowledge in Medieval Europe. It assumes that the celestial bodies all revolve on crystalline spheres arranged about Earth like layers of an onion. That is to say that the model employs uniform-speed circular geocentric orbits. The Greeks understood very well that the motions of the planets did not naturally fit into a picture like this, and went to elaborate lengths to invent clever ways to fit them into the circular scheme, involving circles within circles and circles with offset centers of motion. But they believed strongly that the circle was perfect and that the perfection of the heavens had to be made compatible with that of the circle. In effect, this was a transcendental or religious belief, unconnected to what could be observed or measured about astronomy, or the physical world generally.
As European scientists in the Middle Ages gathered additional data about the celestial bodies beyond what the Greeks had known it became steadily more difficult to reconcile it with the Ptolemaic Model, even with a lot of additional circles thrown in. Finally in the early 1500s Nicolaus Copernicus (1473-1543) decided to try a model involving circular orbits not about Earth but the Sun. It fit the data better and more easily than any of the geocentric models, although by no means perfectly, and not without immense labor that consumed all of the time Copernicus could devote to his astronomical studies, right to the end of his life.
His work immediately influenced astronomers all over Europe, but the major impression it made was in its simplification of calculations. Few were ready to agree with Copernicus that the Earth and planets really did revolve about the Sun. Aside from the authority of Greek theories, there was an even greater obstacle in the Bible, which seemed to say fairly plainly that the universe was centered on our world. Eventually, Copernicus’ views were condemned as heretical by both the Catholic Church and the major figures of the Reformation.
Regardless of theological strictures, Johannes Kepler (1571-1630) was convinced that the Copernican Model described the literal situation: the planets truly did orbit about the Sun. He believed, moreover, that the Sun actually drove the planets in their paths, as part of a process expressing an underlying mystical order of the universe. But the difficulties that Copernicus had encountered in making his scheme work became even sharper as better data were gathered on the apparent motions of the planets. His model could give accurate results only with a good deal of arbitrary and uncertain adjustment. Convinced that there had to be a deeply harmonious solution, Kepler carried out intensely laborious calculations and found that all could be explained if it were assumed that the planets followed elliptical orbits focused on the Sun, faster as they approached the Sun more closely and slower as they looped out away from it, at distances from the Sun which bore an exact relationship to the periods of their orbits.
The Keplerian Model described and predicted planetary motions with what seemed to be exact accuracy, but Kepler’s theories of why the planets moved as they did (which involved rather vague ideas about magnetism) did not hold together. It was his contemporary, Galileo Galilei (1564-1642), who provided much of what would become the basis for understanding the mechanisms of motion. While Kepler had understood much about gravity, it was Galileo who recognized its universal influence, and he also showed that in the absence of some force – such as gravity or friction – the motion of a mass (such as a planet or cannonball) would remain constant.
Isaac Newton (1643-1727), using more advanced mathematical tools he had developed as well as Galileo’s insights, showed that Kepler’s results could be derived by assuming that the Sun and planets exerted a mutual attraction that varied inversely with the square of the distance between them: gravity, identical to the force that causes the apple to fall to earth from the tree. It was a harmony more fundamental and profound than any Kepler had imagined.
In modern terms, Newton had put forth a model with a single degree of freedom, a “one-DOF model,” involving only a single force. Once you knew the strength of gravity you knew everything there was to know about the motions of the celestial bodies. With the electrifying example of Newton’s work before them, others began to produce mathematical models of more complex phenomena, involving two, three, or more degrees of freedom. It became widely recognized that these mathematical constructs could be highly exact models of physical processes that seemed quite different in substance. In one of the crowning achievements of pre-relativistic physics, after James Clerk Maxwell (1831-1879) developed his model of electromagnetic phenomena, it was recognized that it implied the possibility of electromagnetic waves propagating through space. Nothing of this sort had been known before, but armed with Maxwell’s model physicists quickly produced and measured them experimentally, leading to the development of radio and a host of other systems.
The Newtonian Model applied just as well to cannonballs as to planets – but only if the cannon was fired in a vacuum. In Earth’s atmosphere, as was quickly understood, aerodynamic forces as well as the force of gravity affected the trajectory. Newton tried to analyze the aerodynamic force, but with poor results. (Great progress was made in the 19th and particularly 20th century, but we still do not have a model of aerodynamic effects that is fully as satisfactory as the Newtonian Model for gravitational effects.) Of course artillerists had long been able to conduct direct experiments, but their misunderstanding of the actual flight of cannonballs had nevertheless undermined their ability to predict the performance of their guns. Even though it was not completely “correct,” the Newtonian Model had an immediate and profound impact on the analysis of cannon fire as well as the motions of planets. Again, the real question is how well you can depend on the relationships you use in the process of projecting from model to objective system. It is not truly a question of whether the model is “right” in any absolute sense, but whether it is adequate for the purpose at hand, and can be known to be so. Scientists can never be God, with complete knowledge of the universe and its workings, but they can learn enough to enhance our understanding and mastery a great deal.
Twentieth century scientists began to develop models of systems so complex that the number of degrees of freedom could not even be counted, not even closely estimated. To deal with them, they resorted to statistical or probabilistic models. Many scientists scoffed at these “gambler’s models,” but they are unavoidable. In some cases it has been shown that a full deterministic model would give the same results (with a great deal more calculation). In quantum mechanics the fundamental phenomena themselves are probabilistic, so far as anyone has been able to determine.
Uncertainties of different sorts appear to be inherent in other sciences which emerged in the 20th century, including both economics and climatology. Both fields had long histories of studies and observation of particular phenomena, without models that were useful for analyzing or predicting the overall course of events. Models of overall economic growth and contraction emerged only with the severe contraction of the 1930s, while global climate models were the product of concerns about the effects of rapidly rising carbon dioxide levels in the atmosphere.
In a certain sense we can compare the current macroeconomic and global climate models to the Ptolemaic Model of celestial motions. Their accuracy is good enough for many purposes. But there are areas where their results do not fully correlate with observed data, and they leave many important details about connections to other phenomena unclear. They represent a great improvement on Medieval Astronomy, however, in that macroeconomists and global climatologists generally are not constrained by external religious or transcendental ideas about how things should be. That is, their ideas about how things work derive from their models, not the other way around, and they show continuing readiness to radically modify their models when important discrepancies or lacunae are revealed. This of course was the central point of the Scientific Revolution of the 16th and 17th centuries, and together with their models it marks today’s macroeconomists and global climatologists as scientists in the full modern sense.
6 February 2009
Copyright © 2009 by William D. O’Neil