Readings - Wolpert, Chapter 3




In Topic 2, we considered the origin of science in Greece about 600 BC and some of the initial scientific ideas that developed up to the time of Aristotle (~330 BC). Greek scientific thought continued for more than 500 years until after the Fall of Rome when the Greco/Roman World was finally partitioned between Byzantium (Eastern Roman Empire) and the Arab World. In this topic, we will consider the final development of Greek ideas on motion, matter, and astronomy prior to the spread of Islam (~600 AD).

The political setting for this time period was quite different from that of Greece prior to the death of Aristotle (322 BC). By that time, Alexander the Great had conquered all of the Greek and Persian World to form one great empire. Upon his death (323 BC), the empire broke up into several kingdoms under the control of Alexander's generals or relatives. The main Greek City States were all under the power of regional kings, yet they maintained local autonomy so that democratic institutions that fostered an interest in philosophy and education did not die. This Helenistic world with kindred rulers broke down many of the societal and political barriers that were present before. This permitted many of the Greek philosophical ideas to be spread to the Middle East and Egypt.

Alexandria, Egypt under the Ptolemaic Dynasty (and later Roman Empire) became the center of Greek thought between ~100 BC and ~200 AD. The Library of Alexandria and Museum of Alexandria were two separate institutions supported by the local rulers that succeeded the Lyceum of Aristotle. These were places where scholars worked and sometimes lived together (some common meals). But, these were not primarily teaching institutions, but rather the first real research institutions.


The Nature of Matter After Aristotle

The prevailing view of matter at the time of Aristotle was that all matter on Earth and the planets is composed of varying proportions of four elements - fire, water, air, earth. All matter can be transmuted from one form to another. By contrast, Aristotle thought that the heavens (stars) are composed of one element, aether, which is eternal and immutable (unchanging). Aristotle did not believe in a void (space absent of matter), but thought that matter in the universe was continuous. Over the next 500 years, these ideas were considered in detail by many people who added more detailed observation, experimentation, and insight to that original conceptual framework. Some of these ideas were significantly modified or alternative ideas presented and debated.

Strato (290 BC)) used actual experiments to deduce that air has substance (is matter). 'If an empty vessel is inverted and pressed into water, the air (in the vessel) does not allow the water to enter. But, if a hole is bored into the bottom of the vessel and the test repeated, the water will enter as the air escapes through the hole.'

Strato also addressed the issue of whether air is a continuous material or composed of small pieces (atoms?!) with intervening void (vacua). He first stated 'Those who assert generally that there is no vacuum are satisfied with inventing many arguments for this and perhaps seeming plausible with their theory in the absense of sensible proof. If, however, by referring to the appearances and to what is accessible to sensation, it is shown that there is a continuous vacuum, but only one produced contrary to nature; that there is a natural vacuum, but one scattered in tiny quantities; and that bodies fill up these scattered vacua by compression; then those who put forward plausible arguments on these matters will no longer have any loop holes.'

The experiment he actually conducted is as follows: prepare a tightly sealed sphere of metal plate so as not to be easily crushed containing about 8 cotylae (~2 liters). Pierce a hole in it and let in a siphon (tube) that is sealed to the sphere with tin (weld). The first experiment tests whether there are scattered vacua in air. If there were none, then air should be incompressible. But, if one blows air into the sphere through the siphon, one will introduce much breadth (air), in addition, without the air that is contained in the sphere escaping. This shows that air is compressible and must be a combination of air particles and small voids (vacua). The second experiment was to show that air can be evacuated from the globe. If one draws air out of the sphere by sucking on the siphon, a fair quantity will come out although no other substance takes its place in the sphere. So that by this means it is conclusively proved that a considerable accumulation of vacuum occurs in the sphere.

Theophrastus (~300 BC) argued that fire is different from air, water, and earth and should not be considered one of the fundamental constituents of all matter. He stated that fire is different in that it can generate itself (not the others), humans can make it (not the others) , fire requires force to come into being, and fire alone needs some other material as a substrate. 'Everything that burns is always as it were in a process of coming-to be and fire is a kind of movement, and it perishes as it comes to be, and as soon as what is combustible is lacking, it too itself perishes. Accordingly, it seems absurd to call this a primary element and as it were a principle, if it cannot exist without matter."


Final Set of Ideas:
1) Water, earth, fire (despite Theophrastus) , and air are fundamental materials.
2) Materials are composed of pieces (atoms).
3) A void exists.
4) Materials can be 'transmuted' from one material to another.


The Nature of Motion After Aristotle

Aristotelian physics contained a group of theories that had to accord with observable motion. From astronomy came the view that the Earth is fixed in the Universe and all planets, moons, and stars revolve around it. From material properties came the notion that all matter is made up of four elements: fire, water, earth, and air. Natural motion of all matter on Earth is up or down depending on the relative quantities of the four elements. All other motion of inanimate objects is then unnatural and requires a motive force (e.g., push or pull). The stars, planets, Sun, and Moon are special cases made of aether and have 'natural' circular motion.

Aristotle thought that all motion is subject two two factors: motive force (F) and resistance (R). He thought that 'natural' vertical motion was due to a force proportional to weight (F~Weight). Heavy objects had proportionally more earth or water and fell fast. The lightest objects had relatively more air or fire and rose fast. For any motion to occur, F >R (Force is greater than Resistance). Aristotle argued that is one drops an object in air and then in water it will fall faster in air. This must mean that there is more resistance in water. One could also drop the same object in syrup and find that it falls even more slowly. Thus the syrup must have even more resistance. Then Rair<Rwater<Rsyrup. It is not clear that he ever did this experiment in any systematic way, yet common experience would have anyone agree that the 'though experiment' should be true.

Another thought experiment would be to drop two objects of similar shape but one twice the weight of the other. Aristotelian physics argued that the objects will drop a distance D, with velocities (V1, V2) proportional to weight and Times (T1, T2) inversly proportional to weight. Velocity is defined as distance travelled per unit time (V=D/T).(Velocity is normally written today as V=dx/dt; where x is a measure of position and t is a measure of time. Velocity is then the rate of change of position, x, per unit time.)

Aristotle and other Greeks never record actually doing this experiment in air and measuring the relationship. They simply assumed it was correct. The first actual recorded test of this thought experiment which got the right answer (!) was carried out by Joannes Philoponus (Byzantium, ~600 AD). This result was largely forgotten or ignored; the same experiment and result was carried out by Galileo almost 1000 years later, who got credit for it.

Aristotle and other ancient Greeks also thought that violent (or forced) motion had to have a continuing source for the motion. For example, if one throws a rock, the rock keeps going because the air in front of the rock is displaced as the rock travels, and moves to behind the rock where it continues to push the rock along.

Over the next 500 years, these ideas were considered in detail by many people who added more detailed observation, experimentation, and insight to that original conceptual framework. Some of these ideas were significantly modified or alternative ideas presented and debated. Key questions that were asked by the Greeks and later scientists were:
What happens when an object is dropped?
What happens when one drops two objects of similar shape but different weight?
What happens when an arrow (later cannon) is fired straight up?
What happens when one drops an object on a moving ship?

One complication to natural motion noted early on is that downward motion is not a simple uniform process. Rather, objects move faster (acceleration) as they come closer to their natural place (Earth). Strato (~290 BC) was the first to describe clear evidence of this fact. He stated that 'If one observes water pouring down from a roof and falling a considerable distance, the flow at the top is seen to be continuous, but the water at the bottom falls to the ground in discontinuous parts. This would never happen unless the water traversed each successive space more swiftly.'

Strato also stated that ' if one drops a stone or other weight from a height of about a finger's breadth, the impact made on the ground will not be perceptible. But, if one drops the object from a height of one hundred feet or more, the impact on the ground will be a powerful one. Now, there is no other cause for this powerful impact. For the weight of the object does not increase, the object itself has not become greater, nor is it impelled by a greater (external) force, rather it moves more quickly.'

Philoponus (6th Century AD) argued against the notion of air continuing to push an object as it moves through the air by stating the following. 'How is it then that the air, pushed by the arrow, does not move in the direction of the impressed impulse, but instead, turning about, as by some command, retraces its course? Furthermore, how is this air, in so turning about, not scattered into space, but instead impinges precisely on the notched end of the arrow and again pushes the arrow on and adheres to it? Such a view is completely implausible and is more like fiction.'

Philoponous developed an alternative 'impetus' theory ­the act of setting an object in motion impresses on that object a force or impetus that keeps it in motion. (This concept is also WRONG, but it took another 1000 years to figure that out.)

Finally, Philiponous described experimental evidence to contradict Aristotle's view that natural motion is proportional to weight. 'For if you let fall at the same time from the same height two weights that differ greatly, you will see that the ratio of the times of motion does not correspond to the ratio of the weights, but that the difference in the times is a very small one.'


Final Set of Ideas:
1) Motion on Earth is natural, violent(unnatural), or animated.
2) Natural motion is not uniform in speed, but has acceleration toward the Earth.
3) Natural motion not linearly dependent on weight of objects.
4) Unnatural motion is due to transfer of motive force to object in motion.
5) Motion of astronomical objects is circular and constant uniform speed.



Astronomy After Aristotle

By the time of Aristotle (~350 BC), the ancient Greeks 'knew' that the Earth is a sphere and that a series of objects revolve around it in circular paths. Those objects are the Sun, Moon, Five planets, and the stars. Most Greeks believed that the Earth is at rest in the center of the Universe, but Heraclides of Pontus (~330 BC) thought the Earth was in motion rotating on its own axis each day. Eudoxus of Knidus (~365 BC) developed a conceptual theory of an Earth-centered universe with all planets and stars embedded in a series of concentric spheres surrounding the Earth. Each sphere rotated about an axis embedded in a sphere that was farther way from the Earth. Over the next 500 years, these ideas were considered in detail by many people who added more detailed observation, experimentation, and insight to that original conceptual framework. Some of these ideas were significantly modified or alternative ideas presented and debated.

Eratosthenes (~225 BC) actually calculated the size (circumference) of the Earth by comparing the vertical angle to the Sun at zenith (noon) from two locations a known distance apart (Alexandria and Aswan, Egypt). The answer he got (Earth circumference is 252,000 stades; that is ~36,000 km to ~41,000 km depending on which estimate of stade length one uses) was within 10% of our current measurement (40,009 km).

Aristarchus (275 BC) believed the Sun was at the center of the Universe and that the Earth revolved around it in an orbit much smaller than the radius of the sphere holding the stars. He also thought that the Earth rotated on its own axis every day rather than that the sphere with stars rotated. This revolutionary theory was not appreciated by other astronomers for two basic reasons. First, why do we see no evidence of Earth's rotation? The planetary surface must be moving at speeds of more than 1000 km/hr if the planet rotates. Second, why do astronomers see no difference in angles between pairs of stars (parallax) as Earth revolves around Sun (and thus changes position with respect to the star sphere which is centered on the Sun.)

First comprehensive star catalog ­ Hipparchus of Nicea (135 BC)

One astronomical problem was why the Earth's seasons are not equal in length. The seasons are measured between two yearly solstices (times of maximum or minimum height of the Sun at Noon, marking Summer and Winter) and two yearly equinoxes (times of equal day and night, marking Spring and Fall). Starting from the Spring equinox, the seasons are 94, 92, 89, and 90 days in length.

Apollonius (~210 BC) was able to expain this by arguing that Solar motion (and maybe all other astronomical motions) is either eccentric or composed of two different circular motions. (The observational results are the same.) The idea of eccentric motion is that the Sun revolves around some point in space in a circular orbit (or sphere), but the Earth is not exactly at the center. Rather it is 'eccentric' and lies a small distance from the center (but still at rest).

Apollonius stated that an equivalent idea is to say that the Earth is at the center of the Sun's circular orbit (or sphere) which he termed the deferent circle. But that, the Sun also revolves in a second circular orbit (or sphere), which he termed the epicycle circle, around a point on the deferent circle. The advantage of this view is that the Earth stays at the center of the Universe and that all motions are still circular.

Ptolemy (150 AD) agreed that all objects rotated about the Earth, but he preferred to define each object's rotation on the basis of mathematical calculation of circular orbits. To account for observed complexities in movement, he calculated each orbit, using the ideas of Apollonius, as the combination of two circular motions, a deferent (the main orbit) and epicycles (smaller orbits superposed on the deferent. He also made many observations of astronomical motions and compared these with his orbital calculations. This model prevailed up to the beginning of the 16th Century.

The Ptolemaic model was able to explain generally the following observations:
- Planets and Sun move at different speeds at different times
- Seasons are not the same length
- Retrograde motion
- Size of planets (and Sun?) change

The Ptolemaic model worked well at describing planetary motions, but was cumbersome. Alfonso the Wise, King of Leon and Castille (13th Century) remarked that 'If the Lord Almighty had consulted me before embarking on the creation, I should have recommended something simpler'.

Final Set of Ideas:
1) Earth at rest at the center of the Universe.
2) Sun, Moon, five planets, and all stars together revolve around Earth on 8 concentric spheres in uniform circular motion.
3) Each sphere (deferent) rotates on an axis embedded in the next outer sphere.
4) Astronomical objects also revolve around smaller epicycle spheres embedded in the deferent spheres.