Early Cosmology:

Cosmology is the study of the Universe and its components, how it formed, how its has evolved and what is its future. Modern cosmology grew from ideas before recorded history. Ancient man asked questions such as "What's going on around me?" which then developed into "How does the Universe work?", the key question that cosmology asks.

Many of the earliest recorded scientific observations were about cosmology, and pursue of understanding has continued for over 5000 years. Cosmology has exploded in the last 10 years with radically new information about the structure, origin and evolution of the Universe obtained through recent technological advances in telescopes and space observatories and basically has become a search for the understanding of not only what makes up the Universe (the objects within it) but also its overall architecture.

Modern cosmology is on the borderland between science and philosophy, close to philosophy because it asks fundamental questions about the Universe, close to science since it looks for answers in the form of empirical understanding by observation and rational explanation. Thus, theories about cosmology operate with a tension between a philosophical urge for simplicity and a wish to include all the Universe's features versus the total complexity of it all.

Very early cosmology, from Neolithic times of 20,000 to 100,000 years ago, was extremely local. The Universe was what you immediately interacted with. Cosmological things were weather, earthquakes, sharp changes in your environment, etc. Things outside your daily experience appeared supernatural, and so we call this the time of Magic Cosmology.

Later in history, 5,000 to 20,000 years ago, humankind begins to organize themselves and develop what we now call culture. A greater sense of permanence in your daily existences leads to the development of myths, particularly creation myths to explain the origin of the Universe. Many of the myths still maintained supernatural themes, but there was an internal logical consistence to many of the stories. The myths often attempt a rational explaination of the everyday world. Even if we consider some of the stories to be silly, they were, in some sense, our first scientific theories. We call this the time of Mythical Cosmology.

The third stage, what makes up the core of modern cosmology, grew out of ancient Greek, later adopted by the Church. The underlying theme in Greek science is the use of observation and experimentation to search for simple, universal laws. We call this the time of Geometric Cosmology.


Rationalism:

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.

Science is also a dialogue between humankind and Nature. Science is far from a perfect instrument of knowledge, but it provides something that other philosophies fail to, concrete results. Science is a ``candle in the dark'' to illuminate irrational beliefs or superstitions. Science does not, by itself, advocate courses of human action, but it can certainly illuminate the possible consequences of alternative courses. In this regard, science is both imaginative and disciplined, which is central to its power of prediction.

To support these methods, a scientist also uses a large amount of skepticism to search for any fallacies in hypothesis or scientific arguments. In order to draw conclusions, a scientist uses the scientific method, a rigorous standard of procedure and discussion that sets reason over irrational belief. Central to the scientific method is a system of logic.

Note that there is an emphasis on falsification, not verification. If a theory passes any test then our confidence in the theory is reinforced, but it is never proven correct in a mathematically sense. Thus, a powerful hypothesis is one that is highly vulnerable to falsification and that can be tested in many ways. Science can be separated from pseudo-science by the Principle of Falsification, the concept that ideas must be capable of being proven false in order to be scientifically valid.


Cause+Effect:

The foundation for rationalism rests squarely on the principle of locality, the idea that correlated events are related by a chain of causation.

There are three components to cause and effect:

The necessary connection in cause and effect events is the exchange of energy, which is the foundation of information theory => knowledge is power (energy).

Also key to cause and effect is the concept that an object's existence and properties are independent of the observation or experiment and rooted in reality.

Causal links build an existence of patterns that are a manifestation of the Universe's rational order. Does the chain of cause and effect ever end? Is there an `Initial Cause'?


Mathematics and Science:

The belief that the underlying order of the Universe can be expressed in mathematical form lies at the heart of science and is rarely questioned. But is mathematics a human invention or does it have an independent existence?

Idealization of physical phenomenon led Plato to hypothesize that there were two Universes, the physical world and an immaterial world of `forms', perfect aspects of everyday things such as a table, bird, and ideas/emotions, joy, action, etc. The objects and ideas in our material world are `shadows' of the forms (see Plato's Allegory of the Cave). This solves the problem of how objects in the material world are all distinct (no two tables are exactly the same) yet they all have `tableness' in common. There are different objects reflecting the `tableness' from the Universe of Forms.

Thus, there came into existence two schools of thought. One is attributed to Plato, and finds that Nature is a structure that is precisely governed by timeless mathematical laws. According to Platonists we do not invent mathematical truths, we discover them. The Platonic world exists and physical world is a shadow of the truths in the Platonic world. This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math.

The other school is that mathematical concepts are mere idealizations of our physical world. The world of absolutes, what is called the Platonic world, has existence only through the physical world. In this case, the mathematical world is the same as the Platonic world and would be though of as emerging from the world of physical objects.

Mathematics transcends the physical reality that confronts our senses. The fact that mathematical theorems are discovered by several investigators indicates some objective element to mathematical systems. However, since our brains have evolved to reflect the properties of the physical world, it is of no surprise that we discover mathematical relationships in Nature.

The laws of Nature are mathematical mostly because we define a relationship to be fundamental if it can be expressed mathematically.


Aristotle:

In the center of the `School of Athens' by Raphael are Aristotle and Plato, Aristotle's hand level to the Earth symbolizing his realism view of Nature; Plato's hand pointed towards the heaven symbolizing the mystical nature to his view of the Universe. This image symbols the sharp change in the meaning of how `natural philosophy' or physics will be done for the 2,200 years.

Aristotle stands in the Greek philosophical tradition which asserts that nature is understandable. This tradition, opposed to the idea that nature is under the control of capricious deities which are to be appeased rather than understood, is one of the roots of science.

Aristotle constructed his view of the Universe based on a intuitive feeling of holistic harmony. Central to this philosophy was the concept of teleology or final causation. He supposed that individual objects (e.g. a falling rock) and systems (e.g. the motion of the planets) subordinate their behavior to an overall plan or destiny. This was especially apparent in living systems where the component parts function in a cooperative way to achieve a final purpose or end product.

Aristotle also provides a good example of the way in which what one knows or believes influences the way one understands new information. His theory of motion flows from his understanding of matter as constituted of four elements: air, earth, fire, and water. Objects, being solid like earth, would tend to clump together with other solids (earth), so objects tend to fall to earth, their natural place. Thus, falling is a natural motion.

The way Aristotle believed
objects to fall on the Earth
The way objects actually
fall to Earth

The difficulty comes in thinking about horizontal motion. Making an object move usually has a pretty obvious cause. What's difficult is explaining why something continues in motion.

The way Aristotle thought
projectiles moved
The way projectiles
"really" move

Think of a spear being thrown. At first, it is not in motion, but then the thrower's arm provides an impetus which accelerates it (our vocabulary, not Aristotle's). But then, what keeps it going after it leaves the thrower's hand? It should fall to earth immediately since there's nothing obvious pushing it!

Aristotle's answer was that as the spear flies through the air, it leaves a vacuum behind it. Air rushing in pushes the spear forward until its natural motion (falling) eventually brings it to earth.

Aristotle also thought about the causes which start things moving. In the spear scenario, it's easy to say that the thrower's arm moves the spear, but what moves the thrower's arm? Aristotle said that another motion moved the arm (muscle contraction?) but he also realized that some earlier motion must cause the muscle to contract and that earlier motion must also have its own initiator.

To avoid the idea that there is an infinite chain of causes, Aristotle argued that there must be an "unmoved mover," something which can initiate motion without itself being set in motion. This view was preserved by medieval Church during the Dark Ages and became the ruling paradigm.


Shape 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:


Greek Cosmology

Both Plato and Pythagoras influenced the first logically consistent cosmological worldview, developed by the Greeks in the 4th century B.C. This early cosmology was an extrapolation of the Greek theory of matter proposed by Empedocles. This theory states that all matter in the Universe is composed of some combination of four elements: Earth, Water, Fire, Air. These four elements arise from the working of the two properties of hotness (and its contrary coldness) and dryness (and its contrary wetness) upon an original unqualified or primitive matter. The possible combinations of these two properties of primitive matter give rise to the four elements or elemental forms.

Perhaps only a culture whose leaders were involved with logic and geometry would put the concepts of chemistry in such a logical and geometric form. Fire and Water are obvious opposites, and so are Earth and Air. These opposites share no common properties. There are four properties, each shared by two non-opposite elements: fire and air share the property of hotness, water and air the property of wetness, and so on. Since the four elements are two pairs of opposite elements, so also are the four properties - hotness being the opposite of coldness and wetness the opposite of dryness.

Each of the four elements was held to exist in an ideal pure form, which could not actually be found on earth. The real things around us were considered impure, or mixed, forms of these four ideal elements. Thus the different airs, or gases, were the form of air mixed with different proportions of the forms of fire or water; smoke was a mixture of the forms of air and earth with some of the form of fire added. But there was an ideal or pure form of earth, air, fire, and water, and the real ones which we see and use were not ideal but of lesser purity. In other words, the real or observed different kinds of the same element are due to different degrees of the same properties. The elements could be changed into one another by removal of one property and addition of another.

In a seemingly unrelated discovery, Euclid, a Greek mathematician, proved that there are only five solid shapes that can be made from simple polygons (the triangle, square and hexagon). Plato, strongly influenced by this pure mathematical discovery, revised the four element theory with the proposition that there were five elements to the Universe (earth, water, air, fire and quintessence) in correspondence with the five regular solids.

Elements had a natural tendency to separate in space; fire moved outwards, away from the earth, and earth moved inwards, with air and water being intermediate. Thus, each of these five elements occupied a unique place in the heavens (earth elements were heavy and, therefore, low; fire elements were light and located up high). Thus, Plato's system also became one of the first cosmological models and looked something like the following diagram:

Like any good scientific model, this one offers explanations and various predictions. For example, hot air rises to reach the sphere of Fire, so heated balloons go up. Note that this model also predicts some incorrect things, such as all the planets revolve around the Earth, called the geocentric theory.


Aristarchus:

Aristarchus (270 B.C.) developed the heliocentric theory, placing the Sun at the center of the Universe (Solar System).

This is, of course, the correct model for the Solar System, yet was not adopted by Greek philosophers. Why?

Problems for heliocentric theory:


Ptolemy:

Ptolemy (200 A.D.) was the Librarian of Alexandria who resurrected Heraclides geocentric theory and combined with centuries of data on planetary motions -> formulated complete description of the Solar System that explained/predicted the apparent motions. The Ptolemic system began the 1st paradigm or framework for our understanding of Nature

Unfortunately, the Ptolemy framework was extremely complicated in order to explain retrograde motion.

The solution to retrograde motion was to use a system of circles on circles to explain the orbits of the planets called epicycles and deferents. The main orbit is the deferent, the smaller orbit is the epicycle. Although only one epicycle is shown in the figure below, over 28 were required to explain the actual orbits of the planets.

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.

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.