The Third Cosmology: A Geometric Universe

The previous cosmologies did not make use of any mathematics since none really existed. The key feature of this next phase of cosmological model making is the incorporation of mathematics, or more precisely, geometry as the central feature of the model. The roots of this started about 4000 years ago with the initial development of geometry by the Babylonians. Much of this early development was later amplified by the Greeks, particularly Pythagoras (circa 550 BC), who basically refined geometry into notions of perfection (spheres, a2 + b2 = c2 , etc). The early Greeks, however, borrowed many of the elements of the previous Mythic Universe. In particular, they defined Four Primal Beings as being dominant in their cosmological model:

As before, there are various combinations of gods and sub-gods which form unions in order to help populate the Earth. In this particular model, however, the explicit element of hierarchy emerges. This is manifest by Gaea who has a union with Uranus - the sky god, which produces the Titans who are the first Rulers of the Earth. This is an important departure from the Cosmic Womb idea in which all things are more or less equal (having come from a common origin). Here we are introduced to the concept that one species can rule over others.

The familiar roles of good and evil are also present. Prometheus who molds humans from clay and then breathes into them the spirit of life, also locks away all the evil secrets of the world. Unfortunately, that pesky Pandora somehow finds the key and opens Pandora's Box thus releasing these secrets. In turn, this causes the world to be doomed, as it has been in previous mythology. In that sense, little has changed as the outcome of this cosmology is the same as before, a doomed world waiting for re-birth.

But these elements of early Greek mythology were in the process of being fine tuned to produce a Cosmological Model that will stand for 2000 years before being overturned. This all started around 600 BC when the Greeks began to dissect the world into its component pieces. At this time, another original idea emerges:

All the world can be understood as an interaction between 4 primal elements: Air, Earth Fire and Water.

Although this is a variation on the earlier mythical themes, we have now, perhaps for the first time, the ideas of Cause and Effect . That is, if the primal elements interact in a specific manner, a result will occur that otherwise would not have if this interaction did not occur. This means the Universe now has a physical nature which removes much of its "magical" qualities. The physical foundation of this Universe is described in terms of the four primal forces. All that is observed or created could then be understood as the interaction between these primal forces. This was a highly deterministic Universe where the role of chance was essentially dismissed as being important.

Since we are moving to a hierarchical world view, there is now a contest among various Greek philosophers to see which of the four elements is the most important (in modern cosmology we call this contest - Grand Unified Theory ). Among the contestants were Thales who believed that Water was the most important and that the world floated in some primordial sea out of which all life sprung. In contrast, Anaximander postulated that the interactions between the four primal elements were basically equal but were driven by opposites (light/dark, fire/water, up/down, etc). Still another theory was advanced by Anaximenes who regarded Air as the ultimate of the primal forces. In his cosmology the stars were simply fires (Fire being a lower element now) that burned in the upper atmosphere of the Earth (apparently the ancient Greeks didn't worry much about the energy source that could sustain these fires).

At this point, however, it is important to emphasize that there was a dissenting view to this deterministic hierarchy that Air, Earth, Fire and Water drove the entire dynamics of the Universe. This dissent was voiced by Democritus (circa 500 BC) who explicitly stated that:

The Universe consists of atoms and the Void; all else is opinion and illusion

This is another original idea because it suggests that collisions between atoms actually formed the Universe and that furthermore, the Universe essentially runs by itself. In some sense, the idea of Quantum Mechanics has now been expressed. That is, the Universe can exist without anyone in it! This idea is not very compatible with human ego. As we will learn later, it may well be a phenomenon known as Quantum Fluctuations which produced the Universe in the first place and it has been evolving, on its own, ever since. Clearly this idea was strongly counter to the evolving view at the time.

The next character in this historical drama is Aristotle (circa 350 BC). Aristotle seized on the ideas of Pythagoras and directly incorporated the concept of perfection and geometry to produce the Crystalline Sphere Universe. Since the historical record is necessarily imperfect there is some dispute about who should get proper credit for this model as there is some evidence that Heraclides (330 B.C.) really developed the first Solar System model thus beginning the geocentric versus heliocentric debate that would continue for the next 2000 years. The geocentric model, championed by Aristotle/Heraclides, put the Earth at the center of the Solar System which thus allows humans to occupy a special place in the Cosmos. The alternative view, that the Sun was the center of the Solar System was advanced by Aristarchus (270 B.C.). This heliocentric model, however, was not accepted at the time.

Around this time, Eratosthenes (220 B.C.) used a clever technique for estimating the size of the Earth. He knew that the Earth must be a sphere because of the shape of the shadow it periodically cast on the moon. Of course, a sphere is a prefect figure which was consistent with the important philosophy of perfection that was rampant at this time. Since there are 360 degrees in a sphere then the circumference of the earth can be estimated by determining how many kilometers are required to produce 1 degree of movement on the surface. Because the earth is tilted on its axis, the angle of the sun's rays with respect to any object depends on the latitude of that object. Similarly, the position of the Sun in the sky at a fixed time depends on the latitude. Eratosthenes determined that the angular difference between Alexandria and Syene was about seven degrees based on the difference in the position of the Sun on the longest day of the year. The linear distance between Alexandria and Syene was approximately 500 miles. Well, if 7 degrees corresponds to 800 kilometers of surface distance, then the circumference of the earth must be (360/7) * 800 kilometers. This value is within 1% of the correct diameter.

The last major character in the formulation of Greek cosmology was Hipparchus (circa 150 BC). Hipparchus perhaps can be considered as the greatest astronomical observer among the ancients. He made very precise naked-eye observations and was the first to produce a catalog of the positions of the brightest stars. In the course of observing, he became convinced that the Aristotelian model, shown below in Figure 1.1, was incorrect and that the planets were not in perfect circular motion about the Earth. To explain their motion, he introduced the concept of epicycles which would later be used by Ptolemy to build elaborate machinery for the full description of a planetary orbit.