Rationalism:

Readings: Roger Bacon Geocentric Model

Science, it is widely agreed, originated from two main sources. One was the need to develop practical knowledge and to pass it from generation to generation. The other was a more spiritual concern with the nature and origin of the world. Common to both of these well-springs of science was an appreciation of the regularity of Nature. One of the first scientists to make frequent use of the concept of a law of Nature, in the sense that we now use that term, was the Franciscan friar and scholar Roger Bacon (c. 1214-1292).

He helped to prepare the way for those who, irrespective of their own religious beliefs, insisted that the scientific investigation of Nature should be rooted in experiment and conducted on a purely rational basis, without reference to dogmatic authority. Laws of Nature are now a central part of science. Carefully defined concepts, often expressed in mathematical terms, are related by natural laws which are themselves often expressed in a mathematical form.

The earliest beginnings of science was to note that there exist patterns of cause and effect that are manifestations of the Universe's rational order. We mostly develop this idea as small children (touch hot stove = burn/pain). But the extrapolation of a rational order to cosmology requires a leap of faith in the beginning years of science, later supported by observation and experimentation.

Thus, the main purpose of science is to trace, within the chaos and flux of phenomena, a consistent structure with order and meaning. This is called the philosophy of rationalism. The purpose of scientific understanding is to coordinate our experiences and bring them into a logical system.

Thoughout history, intellectual efforts are directed towards the discovery of pattern, system and structure, with a special emphasis on order. Why? control of the unpredictable, fear of the unknown, and a person who seeks to understand and discover is called a scientist.

Science is founded on the hope that the world is rational in all its observable aspects. Its possible that there may be some facets of reality which lie beyond the power of human reasoning, that there may be things with explanations that we could never grasp, or no explanation at all, but the fact that the world is rational is connected with the fact that it is ordered.


Eratosthenes:

Perhaps one of the first great discoveries under Greek rationalism was the true shape and size of the Earth. The early Greeks knew the Earth was a sphere due to the shape of the Earth's shadow on the Moon during a lunar eclipse. They also knew the size of the Earth due to the efforts of Eratosthenes (220 B.C.). Eratosthenes succeeded in measuring circumference of Earth in the following manner; he knew that on a certain date that a stick placed in the ground at Syene cast no shadow. Whereas, a stick at Alexandria has a small shadow. Using simple ratios he showed the following:


Geometric Cosmology:

There were only seven objects visible to the ancients, the Sun and the Moon, plus the five planets, Mercury, Venus, Mars, Jupiter and Saturn. It was obvious that the planets were not on the celestial sphere since the Moon clearly passes in front of the Sun and planets, plus Mercury and Venus can be seen to transit the Sun. Plato first proposed that the planets followed perfect circular orbits around the Earth. Later, Heraclides (330 B.C.) developed the first Solar System model, placing the planets in order from the Earth it was is now called the geocentric solar system model.

Note that orbits are perfect circles (for philosophical reasons = all things in the Heavens are "perfect"). Heraclides model became our first cosmology of things outside the Earth's atmosphere.

Slightly later, Aristarchus (270 B.C.) proposed an alternative model of the Solar System placing the Sun at the center with the Earth and the planets in circular orbit around it. The Moon orbits around the Earth. This model became known as the heliocentric theory


Problems for Heliocentric Theory:

While today we know that the Sun is at the center of the solar system, this was not obvious for the technology of the times per-1500's. In particular, Aristarchus' model was ruled out by the philosophers at the time for three reasons:

  1. Earth in orbit around Sun means that the Earth is in motion. Before the discovery of Newton's law of motion, it was impossible to imagine motion without being able to `feel' it. Clearly, no motion is detected (although trade winds are due to the Earth's rotation).
  2. If the Earth undergoes a circular orbit, then nearby stars would have a parallax. A parallax is an apparent shift in the position of nearby stars relative to distant stars.

    Of course, if all the stars are implanted on the crystal celestial sphere, then there is no parallax.

  3. Lastly, geocentric ideas seem more `natural' to a philosopher. Earth at the center of the Universe is a very ego-centric idea, and has an aesthetic appeal.


Ptolemy:

Ptolemy (200 A.D.) was an ancient astronomer, geographer, and mathematician who took the geocentric theory of the solar system and gave it a mathematical foundation (called the "Ptolemaic system").

Ptolemy wrote a great treatise on the celestial sphere and the motion of the planets call the Almagest. The Almagest is divided into 13 books, each of which deals with certain astronomical concepts pertaining to stars and to objects in the solar system. It was, no doubt, the encyclopedic nature of the work that made the Almagest so useful to later astronomers and that gave the views contained in it so profound an influence. In essence, it is a synthesis of the results obtained by Greek astronomy; it is also the major source of knowledge about the work of Hipparchus.

The Christian Aristotelian cosmos, engraving from Peter Apian's Cosmographia, 1524

In the first book of the Almagest, Ptolemy describes his geocentric system and gives various arguments to prove that, in its position at the center of the universe, the Earth must be immovable. Not least, he showed that if the Earth moved, as some earlier philosophers had suggested, then certain phenomena should in consequence be observed. In particular, Ptolemy argued that since all bodies fall to the center of the universe, the Earth must be fixed there at the center, otherwise falling objects would not be seen to drop toward the center of the Earth. Again, if the Earth rotated once every 24 hours, a body thrown vertically upward should not fall back to the same place, as it was seen to do. Ptolemy was able to demonstrate, however, that no contrary observations had ever been obtained.

Ptolemy accepted the following order for celestial objects in the solar system: Earth (center), Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn. However, when the detailed observations of the planets in the skies is examined, the planets undergo motion which is impossible to explain in the geocentric model, a backward track for the outer planets. This behavior is called retrograde motion.

He realized, as had Hipparchus, that the inequalities in the motions of these heavenly bodies necessitated either a system of deferents and epicycles or one of movable eccentrics (both systems devised by Apollonius of Perga, the Greek geometer of the 3rd century BC) in order to account for their movements in terms of uniform circular motion.

In the Ptolemaic system, deferents were large circles centered on the Earth, and epicycles were small circles whose centers moved around the circumferences of the deferents. The Sun, Moon, and planets moved around the circumference of their own epicycles. In the movable eccentric, there was one circle; this was centered on a point displaced from the Earth, with the planet moving around the circumference. These were mathematically equivalent schemes.

Even with these, all observed planetary phenomena still could not be fully taken into account. Ptolemy therefore exhibited brilliant ingenuity by introducing still another concept. He supposed that the Earth was located a short distance from the center of the deferent for each planet and that the center of the planet's deferent and the epicycle described uniform circular motion around what he called the equant, which was an imaginary point that he placed on the diameter of the deferent but at a position opposite to that of the Earth from the center of the deferent (i.e., the center of the deferent was between the Earth and the equant). He further supposed that the distance from the Earth to the center of the deferent was equal to the distance from the center of the deferent to the equant. With this hypothesis, Ptolemy could better account for many observed planetary phenomena.

Although Ptolemy realized that the planets were much closer to the Earth than the "fixed" stars, he seems to have believed in the physical existence of crystalline spheres, to which the heavenly bodies were said to be attached. Outside the sphere of the fixed stars, Ptolemy proposed other spheres, ending with the primum mobile ("prime mover"), which provided the motive power for the remaining spheres that constituted his conception of the universe. His resulting solar system model looked like the following, although the planets had as many as 28 epicycles to account for all the details of their motion.

This model, while complicated, was a complete description of the Solar System that explained, and predicted, the apparent motions of all the planets. The Ptolemic system began the 1st mathematical paradigm or framework for our understanding of Nature.


Copernicus:

As we know from history, the great library at Alexandria burns in 272 AD, destroying a great deal of the astronomical data for the time. Roman culture collapses and we enter the Dark Ages. But, the Roman Catholic Church absorbs Aristotle's scientific methods and Ptolemy's model into its own doctrine. Thus, preserving the scientific method and Ptolemy's Solar System. Unfortunately, the geocentric model was accepted as doctrine and, therefore, was not subjected to the scientific method for hundreds of years.

Copernicus (1500's) reinvented the heliocentric theory and challenged Church doctrine. The heliocentric model had a greater impact than simply an improvement to solve retrograde motion. By placing the Sun at the center of the Solar System, Copernicus forced a change in our worldview = paradigm shift or science revolution.

However, Copernicus, like Ptolemy, also used circular orbits and had to resort to epicycles and deferents to explain retrograde motions. In fact, Copernicus was forced to use more epicycles than Ptolemy, i.e. a more complicated system of circles on circles. Thus, Copernicus' model would have failed our modern criteria that a scientific model be as simple as possible (Occam's Razor).


Planetary Configurations:

The planets outside of the Earth's orbit (Mars, Jupiter, Saturn, Uranus, Neptune, Pluto) are called superior planets

Likewise, the planets inside of the Earth's orbit (Mercury, Venus) are called inferior planets.

Other configurations are:


Aristotelian Universe:

With the discoveries of Galileo, and the mathematical formulation of orbits by Kepler, a complete kinematic description of the solar system was accomplished. While this provided a very accurate predictor of the motions of the planets, and the size of the Solar System, it gave us no understanding of why the Universe is this way or what causes the planets to move (Newton will answer with gravity). Also, a solar system model does not address the question of the stars or what is beyond the stars.

The cosmological model adopted by the Middle Ages was the Platonic model by way of Aristotle. In this scenario, the Universe is composed of a central spherical Earth surrounded by a series of nested spheres. The sphere being the perfect mathematical figure makes the ideal cosmological object. For Aristotle, all motion required continual application of force (see below), therefore a void or vacuum between the spheres was a logical impossibility since isolated bodies would be motionless.

Another key aspect of the Aristotelian Universe is that it was finite in size. The reasoning here is that the outer boundary of stars rotates around the Earth. If the heavens were infinite, and revolve in a circular path, then they would traverse an infinite distance in a finite time. By the same reasoning, straight lines must be an illusion since they can not be of infinite length or they would extend beyond the Universe. All lines are incomplete and imperfect, only circles are complete and therefore perfect.

In addition, an Aristotelian Universe is steady state, meaning that it has existed unchanging through eternity and its perfect motions had no beginning or end. This will be modified by the Church to allow for Creation and God as the First Cause.

The problem of a void or vacuum appears often in early Greek philosophy, often called the problem of the One and the Many. Parmenides was a leading voice during this era emphasizing the unity of the One, a changeless, undifferentiated continuum. The philosophers opposed to the One, led by Anaxagoras, argued for the Many, that the Universe is composed of a void in which moved numberless discrete entities. The Universe of Anaxagoras is infinite in extent and composed of an infinite number of seeds (atoms). They also proposed that the Universe is not ruled by gods, but by a universal rational Mind.

The Stoics, in the early 200's B.C., introduced that idea that the Mind was manifest through the gods and mortals as divine spirit. In addition, all was predestinate and the Universe is a living organic whole (much like New Age philosophy in the 20th century). Finding Aristotle's finite Universe inadequate, the Stoics proposed that the starry cosmos was finite, but beyond the stars stretched an infinite void. This view lasted in scientific circles until the late 19th century.


Middle Ages

The distinction between what makes up matter (the primary elements) and its form became a medieval Christian preoccupation, with the sinfulness of the material world opposed to the holiness of the heavenly realm (which is interesting since modern cosmology is heavily consumed with the issue of dark matter). The medieval Christian cosmology placed the heavens in a realm of perfection, derived from Plato's Theory of Forms

While adopting most of Aristotle's worldview into Christian thought, his finite Universe was at odds with the Church's idea of God of infinite power. If God is without limit then he can not be bounded in one place. Thus, the Church proposed an unlimited Universe rather than an infinite Universe, a subtle difference.

A heliocentric Universe was impossible for the Church to adopt. In the end, medieval cosmology centers on the balance of angelic sphere and the earthy realm. One such cosmology is found in Dante's `The Divine Comedy'.

The political and intellectual authority of the medieval church declined with time, leading to the creative anarchy of the Renaissance. This produced a scientific and philosophical revolution including the birth of modern physics. Foremost to this new style of thinking was a strong connection between ideas and facts (the scientific method).

Since cosmology involves observations of objects very far away (therefore, very faint) advancement in our understanding of the cosmos has been very slow due to limits in our technology. This has changed dramatically in the last few years with the construction of large telescopes and the launch of space-based observatories.