The first traces of something resembling the scientific method appeared to arise in ancient Greece during the sixth and fifth centuries B.C from the city of Miletus near the coast of modern-day Turkey (go here for further details). Thales (624 to 547 BC) appears to be the first important Greek philosopher, mathematician, and scientist. Unfortunately, none of his original writings have been found, and it is left to other sources, and from the writings of his students/followers, to ascertain his influence on the "beginnings of science".

Thales founded the Milesian school of thought. He is given credit for the "discovery of nature", the process where natural phenomenon are explainable in terms of matter interacting by natural laws, and not due to the whims of unseen gods. For example, in ancient Greece, earthquakes were believed to be caused by the anger of the god Poseidon, the God of the Seas. Thales suggested that the (flat) Earth was actually floating on a vast ocean, and that disturbances in this ocean caused the Earth to shake and crack-just like any other floating vessel. The Milesians, including Thales' student Anaximander (610 to 546 BC) and his follower Anaximenes (? to 528 BC), believed that natural phenomena were governed by a set of laws, whether they were understood or not, and not by a collection of gods that occasionally tortured, toyed-with, or even seduced human beings.

The key contribution of the Milesians was that they engaged in critical debate about each other's ideas. They assumed that all theories or explanations were equally competitive, and open to scrutiny. These ideas could then be debated and judged on their effectiveness. If flaws were found, they could be modified, leading to a refined view of that particular phenomenon. This is how modern science works. But during the time of the Milesians, this was not the way things were done. Doctrine about the nature of the universe, that is the multi-theistic religion of the times, was not open to question or discussion. A demonstration of how seriously this technique was used in the Milesian school is demonstrated by the fact that Anaximander rejected many of the ideas of his mentor Thales, and that Anaximenes rejected many of the ideas of his teacher Anaximander! Obviously, Thales imparted a skepticism in his teachings to reexamine all hypotheses, no matter their source.

Thales has been credited with bringing the mathematics of geometry to Greece (from Egypt) that eventually culminated in Euclid's Elements, a textbook containing all known geometrical theorems of the time. From Miletus also sprang the "Atomists", a group that believed that all things were made up atoms, and that there were only a few types of atoms. It was the combination of the various kinds of atoms that gave each substance its unique properties-how insightful was this? (We will return to the Atomists later this semester.) Very close to our modern view. Near Miletus, the first great doctor of ancient times arose, Hippocrates (470 to 410 BC). Hippocrates and his followers believed that diseases were not to due to the wrath of a god, but from some natural cause that might be treatable.

Around 570 BC, the Greek mathematician Pythagoras was born on the island of Samos, about 100 miles from Miletus. Being an contemporary of Anaximenes, he was, undoubtedly, aware of the new study of geometry. To escape the tyrant Polycartes, he moved to Croton, a Greek town in southern Italy at about 530 BC. In Croton, Pythagoras founded a religious cult with strict rules about behavior, diet, immortality and reincarnation-in contrast to the ideas of the Milesians. The Pythagoreans believe that numbers were pure, and represented an eternal truth, and were not subject to the vagaries of human perception. They began a movement based on numbers. Included in this view of nature was the concept that the Earth was not at the center of the Universe, it revolved around a central fire. In their view the Earth was also round--it was round and was not at rest! This idea would not be seriously considered for 2000 years. But the key to the fame of the Pythagoreans is, of course, the theorem of Pythagoras: that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse.

Now the interesting thing about this theorem is that its investigation eventually lead to a contradiction with the Pythagorean notion of the universe! The Pythagoreans believed that the integers (1, 2, 3 , etc.) were the key to understanding the universe. Music, the motion of heavenly bodies, was all about whole numbers. They did not have a problem with fractions, fractions were simply ratios of whole numbers. But irrational numbers, that is numbers that cannot be represented by some fraction of whole numbers, could not exist, for they were impure. But the theorem of Pythagoras was shown to violate this. For example, if you take a right triangle with two sides of length one, the theorem states:

1² + 1² = 2 = (hypotenuse)²

but in this case, the hypotenuse is the square root of two, The square root of two is an irrational number! (It takes a long, involved proof to show this. Go here to see it.) Thus, the Pythagorean's notion of perfect numbers, and a universe based on whole numbers, was incorrect-even though they did not believe this could happen! The significance of the above proof is that it establishes a new idea in mathematics, one that couldn't have been guessed at before the Pythagoreans developed their number-based religion. On top of this, it was something the followers of this faith didn't want to be true! Here is an example of the scientific method overturning a hypothesis based on dogma.

The next great advances in western scientific thought were due to Socrates, Plato and Aristotle. Aristotle was a student of Plato, and Plato was a student of the great philosopher Socrates. What we know about Socrates (470 to 399 BC) comes from Plato's Dialogues, as Socrates apparently did not write down any of his ideas. And thus, it is hard to disentangle the ideas of Socrates from those of Plato. While Socrates seemed more concerned with political ideals, than with understanding nature, Plato (427 to 347 BC) was concerned with both. He established a school at Athens, the center of Greek learning at that time, where he established his own view of the universe. Unfortunately, Plato was not interested in observation-he (or perhaps Socrates) thought everything could be deduced from thought experiments alone. Such a conviction stifled creative scientific investigation. But the Socratic method closely resembles our modern day scientific method:

1) Ask a question.

2) Suggest a plausible answer to this question, a hypothesis, from which some testable propositions can be deduced.

3) Test the hypothesis by performing a thought experiment by imagining cases that support your hypothesis, or any that do not. If you find examples that do not support your hypothesis (counter examples) return to step 2.

4) Accept your hypothesis as provisionally true. Return to step 3 if you, or someone else, can come up with any other example that shows your hypothesis to be incorrect.

5) Act accordingly.

Aristotle (384 to 322 BC), after a life filled with teaching and traveling, came to Athens and formed his own school, the Lyceum, in 335 BC. Aristotle's school had a broader base of study then Plato's academy, including logic, physics, astronomy, meteorology, zoology, metaphysics, theology, psychology, politics, economics, ethics, rhetoric, poetic. The amazing thing is that many of these subjects did not exist before Aristotle developed them. Aristotle developed the system of logic, which he thought must be applied to every discipline of study.

An example of one of his devices, the syllogistic, starts with two premises to reach a conclusion:

1) All humans are mortal.

2) All Greeks are humans.

3) All Greeks are mortal.

Unfortunately, in Aristotle's view, all objects had a purpose, and were made of a substance that could not be easily understood. For example, objects fall because they have a tendency to fall. Aristotle felt that all objects embodied God. Not only did an object fall because it had a tendency to fall, it fell because it was God's will that it did so. As we discussed during our first lecture, this type of reasoning is not open to scientific investigation-it imparts unknowable, or supernatural properties to objects and processes.

Interestingly, much of the ethics and theology of Aristotle was incorporated into early Christian doctrine. This was partly due to the fact that much of the religious writings of the time were done by Greeks, for Greeks, and thus those capable of writing were usually educated in the great traditions of Greek philosophers, and thus were certainly aware of the ideas of Plato and Aristotle.

After Aristotle, Greek advances in science were carried on by such names as Strato, Aristarchus, Euclid, and Archimedes. At this time, the center of Greek thought shifted to Alexandria, Egypt. This is where and how the great Arabic scientists and philosophers come into the picture. But before we leave the Greeks, we must mention Cladius Ptolemy (85 to 165 AD). Ptolemy lived and worked in Alexandria, and used extensive astronomical observations to develop a geocentric view of the universe, that could explain the apparent motions the planets. We will discuss this system, and more about Ptolemy, next week.

As Roman culture succeeded Greek culture, few advances were made in the scientific method, but observations of nature continued. The study of the work followed the format of Aristotle, and it is difficult to find any particularly new revolutionary ideas. With the fall of the Roman empire (at the beginning of the 5^th century) Europe plunged into the "dark ages", and western thought was really only being advanced by the Islamic culture. The Islamic empire was vast, and had contact with cultures from the Mediterranean all the way to India and China. Thus, much cross-fertilization of ideas came about. Significant progress was especially made in mathematics, as the Arabic word Algebra demonstrates. Arabic mathematics benefited by adoption of the Indian numerals (which we call Arabic!). In the Arab world astronomy, trigonometry, chemistry and medicine all make great strides.

It is not until the 13^th century before European intellectualism began to make a come back. This is partly brought about by the translation of the Arabic texts of Greek philosophy and learning into Latin, and other languages of the time. Unfortunately, in the 1340's the black plague kills-off some 50% of the population of Europe. This causes major changes in society, and halts progress on many fronts.

During the 15^th and 16^th centuries the Catholic church, the bastion of the Christian religion, adopts an Aristotelian view on the universe. These ideas had worked their way into Catholicism with the publications of William of Auvergne in the early 13^th century which were based on his studies of Aristotle and the Greek philosophy. (The Aristotelian view of religion essential replaced the Augustinian view that had been in vogue up to that time.)

The sixteenth century sees an explosion of knowledge, the Renaissance. But also considerable controversy. Scientific thought and investigation was making great strides, but it ran into a philosophical brick wall: the Catholic church. We will discuss this encounter when we begin to talk about the Copernican revolution in next week's class: the trial of Galileo. When we meet Galileo, we will also discuss someone who dramatically advanced the techniques of scientific inquiry through experimentation.

As we cover each major subject, we will have to retrace some of the developments which we have just discussed. In those efforts, however, we will talk about those specific developments as they affected the subject under study.