I work with climate models in my research. That means I tell a computer to perform some calculations for me. The computer calculates a set of equations in physics that describe how the gas making up the atmosphere of a planet flows and the values of its physical properties, like pressure, density, and temperature, at a given point in time. The model can tell you something like “at time 3 hours, 30 minutes, at latitude 30°, longitude 90°, and height 5 km, the pressure and temperature are A and B and the northward and eastward wind speeds are X and Y.” The Unified Model, which I use, can also calculate other properties, like the concentrations of atmospheric gases and the amount of cloud that is condensing in a particular spot on the globe.

Some of the equations express fundamental logical relationships, like the conservation of mass. Others, like the model’s calculation of cloud formation, are what we call “parametrizations.” That means we don’t have a basic mathematical theory of how clouds form. Instead, we work backwards and create an equation that fits our observations of cloud formation. A better parametrization predicts how much cloud forms and where more accurately than a bad one, but that doesn’t mean it expresses the “real” relationships underlying cloud formation.

This distinction, though technical, is ancient. Let’s travel back in time a few thousand years to early Greece and Babylon. Both cultural spheres had a tradition of astronomy/astrology (then one and the same science), but they approached the heavens in completely different ways.

Astronomers in the Old Babylonian period, roughly the early 2^{nd} millennium BCE, noticed that the movements of astronomical objects are periodic–not only the Sun and Moon, but the stars and planets as well. They began to make detailed lists of the positions of objects (like the Sun) and events (like conjunctions of planets) on the celestial sphere on different dates. Objects and events in the sky were considered to be omens that predicted events on Earth, such as battles, rain, insurrections, or the health of livestock. An example Babylonian omen: “When the Moon and the Sun are seen with one another on the sixteenth day, king to king will send hostility. The king will be besieged in his palace for the space of a month.” This is information you wanted to know if you were the king! The predictions were not deterministic, but could be fulfilled or avoided by engaging in rituals or taking other countermeasures. The goal of Babylonian astronomy was to predict when omens would occur and what they meant so the state could exploit them.

The Babylonians predicted astronomical events using what we might call a parametrization or a model fit to the data. As an example, let’s look at how they modelled the motion of the Sun across the celestial sphere: their “solar theory.”

If you observe which constellations surround the Sun when it sets in the evening throughout the year, you’ll see that they change with time. Because the Earth revolves around the Sun, the backdrop of stars behind the Sun shifts. If you mapped the location of the Sun on the celestial sphere, you would see that it travels in a circular path, returning to its original location in one year. The Babylonians developed a theory of the Sun now called “System A” by scholars to describe this apparent motion. (They also had a System B, but we’ll just use System A as our example.)

To describe positions in the sky, Babylonian astronomers divided the celestial sphere into 12 regions, each labelled by a zodiacal sign. They invented the zodiac we still use today–four thousand years later! Not only that, they also divided the heavens into 360 degrees, and subdivided those degrees into minutes and seconds, just as we *also* still do today. (To my knowledge, this is the oldest scientific/pseudo-scientific system in continuous use to the present day.)

In System A, the zodiac is divided into two “zones.” The Sun travels at a different but constant speed in each of these zones. The first zone extends from Virgo 13° to Pisces 27°; here, the Sun moves at a speed of 30° per lunar month. The second zone completes the circle of the zodiac, from Pisces 27° back to Virgo 13°. In this section, the Sun travels 28° 7’ 30” per lunar month. We can call the speeds *V* and *v*, respectively. In modern terms, System A is a step function which alternates between *V* and *v*. These two speeds produce other parameters of the system, such as the period, *P*. Since the period is the solar year, System A provides a means for predicting when the Sun will return to a certain place on the celestial sphere.

In the Babylonian model, the Sun moves faster in one half of the sky than the other, and jumps from one constant speed to the other instantly, rather than experiencing smooth acceleration and deceleration. Did astronomers actually believe this happened? Considering how closely the Babylonians monitored the heavens, probably not. System A wasn’t intended to be a cosmological model of the universe, but to predict when events of interest would be observed. It remained agnostic as to the reasons for patterns in the Sun’s motion.

Contrast this approach to the Greek astronomy expressed in Aristotle’s *On the Heavens *(350 BCE). The Greeks conceived of the universe as a series of concentric, internested heavenly spheres with the Earth at the middle of the cosmos. This model has five main principles:

- The Earth is a sphere.
- It lies at the centre of the universe.
- It is of negligible size compared with the universe.
- The universe is finite and spherical.
- The spherical cosmos makes a daily rotation around the Earth with uniform, circular motion.

The Sun actually does move across the sky at varying speeds, which conflicted with the Greek desire to model heavenly motions as constant and heavenly spheres as perfect circles. They developed two further theories to compensate for the dissonance: the eccentric model and the epicyclic model.

The eccentric model discards one of the basic assumptions about the universe: that the Earth is at the centre. Instead, it places the Earth slightly off-centre, while keeping the motions of the heavenly bodies uniform and constant. Since, from the Earth’s point of view, the Sun’s orbit now has an apogee and a perigee, the Sun will appear to move faster near the perigee and slower near the apogee, matching the model to the observations without having to abandon the perfect, uniform motion of the Sun.

The alternative theory, the epicyclic model, adds a smaller sphere or “epicycle” to the large one carrying the Sun. The centre of the small sphere travels along the large sphere, while the astronomical body itself moves around the epicycle. The epicyclic model produces the same motion as the eccentric one; in fact, the two are mathematically equivalent if the radius of the epicycle in the epicyclic model is equal to the eccentricity of the eccentric model. The epicyclic model preserves both the uniform motion and the perfect circles of the universe. That’s probably why it ended up more popular and more long-lasting.

Unlike the Babylonians, the Greeks did intend their models to describe the actual, physical universe. An overriding concern was to model a universe that was harmonious, rational, and “perfect.” Theoretical innovations to the model were driven by this desire. For the Babylonians, meanwhile, a model could be ugly irregular, and ad hoc, as long as the calculations turned out right and the king knew to be prepared for that siege.

That’s not where the tale of two models ends, though.

The Greek astronomer Hipparchus of Nicaea (2^{nd} century BCE) was probably the first to systematically integrate Babylonian observational and mathematical methods into the Greek geometric model of the universe. His work survives only in fragments, but it is believed to have influenced Ptolemy and been substantially incorporated into the *Almagest*. This book describes the cosmos in both geometric and quantitative terms and was the definitive astronomical textbook for over a thousand years: the *ultimate* high-impact publication! Like our climate models today, it used both theoretical and empirical relationships. Ptolemy’s model made surprisingly accurate predictions of celestial motions–a reminder to us today that an accurate model isn’t the same as a *true* one.