HISTORICAL REVIEW OF SCIENCE I:
ANCIENT TIMES TO THE RENAISSANCE

I think it essential that any course on physical science should include a brief review of science, because, I believe, as the French philosopher Auguste Comte said,

Of course, it will be strictly a personal view! To be more precise, I will concentrate on physics and hardly refer to mathematics or chemistry. I like to think that the work of Copernicus initiated a 're-birth of science' - a renaissance in science and scientific thought and discovery, if you like - that heralded the era of 'Modern Science'; I define the scientific Renaissance, very loosely, as the period beginning with the publication of Nicholas Copernicus's famous book De Revolutionibus Orbium Coelestium (On the Revolutions of the Heavenly Spheres) in 1543. Therefore in this essay I will concentrate on developments up to that time. Progress has sometimes been slow and hampered by politics, war, expediency and most often, religious dogma, but occasionally there have been times of rapid change. (War has also often precipitated developments; for example, in World War II much scientific effort was expended in perfecting radar, etc.) Only rare geniuses have succeeded in making the huge leaps of understanding that push science dramatically ahead in a single step. I will identify some of those scientists in this review.

Alright, then what is physics? Well, far too many people regard the word 'physics' as synonymous with 'plague' as in "to be avoided like the ..." Of course, this is a misconception! The word 'physics' actually comes from the Greek physika, meaning nature, or more precisely, natural things. When we use it, physics refers to that branch of science dealing with nature at its most fundamental level. Thus, the behavior of atoms, gravity, light, all fall within the domain of physics; the sightings of Elvis Presley on Mars, or anywhere else for that matter, do not! Physics is best thought of as the study of observations - let's call them facts - and the search for the rules that govern them and relate them to each other. These facts have to be organized and this is done by seeking 'Laws', often written in the form of a mathematical expression, that relate the observations, for example, how the pressure of a gas is related to the volume of its container or to the temperature, or how the length of a spring depends on the weight hung on the end. When we have the laws, in these cases Boyle's Law, Charles' Law and Hooke's Law, we can then predict behavior with certainty. Furthermore, as far as we can tell, the Laws of physics apply everywhere in the observable universe; a Law on Earth will be equally true on the Moon, and so on. In order to explain the Laws we introduce 'theories'; often theories are speculative because of a lack of knowledge, but what is surprising is that as our understanding improves theories often become simpler! It is often useful to introduce 'models' as well, i.e., a pictorial representation of what's happening; you may remember that when you studied magnetism in high school, a magnet was thought of as containing a lot of little magnets, drawn as arrows, all pointing in the same direction. Of course, we know that these little arrows do not actually exist, but they can be used to help us understand magnetism. In fact, pictures have a very important place in physics; a good deal of the early physics of the Greeks was deduced from drawings, constructions and geometry, Newton's Principia Mathematica, arguably the finest scientific book ever written, contains many pictures and drawings and more recently, Richard Feynman used exquisite diagrams to explain Quantum-Electrodynamics, see figure 1, a very complex subject for which he won the Nobel Prize in 1965. Tomanaga and Schwinger, with whom he shared the Nobel Prize, used pages and pages of algebra for each one of Feynman's diagrams!

So, physics is based on observation and measurement; that means we need units. During the first class with Science students, I introduce myself by saying I'm "190" and I ask them what that means. Some flatter me by saying that must be my age in months - yes it's true - others venture to suggest it's my weight in pounds! However, it's neither; actually I'm 190 cm tall! I tell them that if they went to the bakery section in the supermarket and asked for "2" the sales assistant behind the counter would say "2 WHAT?" The "WHAT" then is like a unit. So units are an essential part of science because we are dealing with quantities that have size. That means we must have standard units that everyone can understand. Centuries ago, the accepted unit of length was the "foot" or, in France, "le pied du roi", the length of the king's foot. Fine, if you were a merchant selling fabric and the king had a small foot, but disaster if his successor had a foot twice the size! Clearly, internationally agreed standards were required now we define the meter as the distance traveled by light in 1/299,792,458 th's of a second! Similarly, with time; it was measured first in units connected with the rotation of the Earth but now we can measure time so accurately with atomic clocks that we find that the Earth's motion is not constant and corrections have to be made to keep atomic time and 'normal time' in synchronization; in fact, at the end of 1995 a second was added so that 1995 was actually 1 second longer than 1996! Standard units form such a fundamental place in physics that Norman Ramsey shared the Nobel Prize in 1989 for 'advancing the art' of high precision measurement.

From the earliest times we can speculate that once the species homo developed sufficient brain capacity, he became curious about the things around him. Once civilizations formed it seems that the Sun, the Moon and the tiny 'sparkly things' that appeared at night drew most attention; indeed, we know that for 1000's of years science was concerned principally with the heavens. To early observers all objects in the sky were thought of as stars - on a clear night as many as 3,000 stars are visible to the naked eye - some were 'fixed' stars and a few were 'wandering' stars (planets). Of course, there were very important developments in other areas, for example, the significance of pi had been recognized by the Babylonians about 4,000 years ago and they even had a value for it (3-1/8); in mathematics - particularly in geometry - there were important discoveries during the classical Greek period; but chemistry was mostly 'magic' or alchemy until only a couple of hundred years ago. And so, at least initially, I will, of necessity, concentrate on astronomy and the solar system.

In order to survive it was essential that ancient peoples knew when to plant and when to harvest their crops; their only way of forecasting was from observing the positions of the planets [1], Moon and stars (principally the Sun) and forming 'rules'. For example, by 2700 BC the Egyptians had observed that the annual overflow of the Nile, on which the livelihood of many farmers depended, coincided almost exactly with the rising of the brightest star in the sky, Sothis (now known as Sirius, the Dog star), and the Sun. They also noticed that the whole scenario repeated itself about every 365 days. In fact, they found that it took 1461 days for Sothis and the Sun to rise together four times, so the length of the year was actually 1461/4 = 365.25 days; the Egyptians added the extra day every four years [2]. Also, Hesiod (ca. 700 BC) in Works and Days wrote:

Also stones were erected, such as those at Stonehenge (started ca. 2800 BC), see figure 2, that could be used for alignment purposes. Some of the earliest applications of science - what today we call technology - were based an astronomy. I've already referred to the 'agricultural calendar' through the use of the positions of the stars and planets. Similarly, in weather forecasting. Again, Hesiod in Works and Days also wrote:

As soon as it was realized that the North star was stationary, navigators had a fixed reference point. In Homer's epic poem the Odyssey, for example, written around 700 BC, the goddess Calypso gave Odysseus directions as steering aids:

Incidentally, the positions of stars also helped guide the astronauts on the Apollo missions and they serve as reference points for the Hubble telescope, and so nothing is new! Since my own area of specialization in physics can be loosely described as Materials Science I have to make mention of the development of different designs and types of blades and cutting implements about 100,000 years ago during the late Stone Age. Although copper had been discovered and used around 7,000 years ago, it was softer than stone ware. The first real metallurgical development occurred in the Bronze age (around 3000 BC) with the discovery that a small addition of tin to molten copper resulted in an alloy, bronze, much stronger than either copper or tin alone. Bronze was used to make all sorts of implements and jewelry but the greatest impact was on the manufacture of weapons and armor. Armies equipped with weapons other than bronze were no match for armies using the new alloy, as the Egyptians found out when they were defeated by the bronze-wielding Hyksos invaders in 1750 BC. A few hundred years later, iron was extracted from iron ore, thus, heralding the Iron Age. Iron is much superior to bronze in strength and around 1200 BC the Dorians, a crude and brutal Greek tribe overran much of Greece, because of their use of their more effective iron weaponry. (The Dorian onslaught also had a major influence on the disintegration of Mycenaean culture - the decline of writing, record keeping, etc. - that led, inevitably, to the Dark Age of Greece.) Surely, many of these developments must have been based on (a) having and recognizing a problem, (b) trying experiments and (c) observing the results. This seems a pretty good example of what we now call 'the scientific method' to me! Then, of course, there were the developments and inventions associated with glazes (Mesopotamia, ca. 1650 BC), fine glass (Egypt, 1580-1465 BC), paints, dyes, soaps and cosmetics, even beer!

Many weights have been discovered in the forms of ducks and lions. The earliest duck weights are from Mesopotamia (ca. 1040 BC) and the earliest lion weights are from Assyria and date from the 11th century BC. Though weights implies scales or balances, apparently no Mesopotamian scales are known.

Now, the ancients had to be careful; goodness knows how many times they made mistakes. Observation implies truth but often perception gets in the way! For example, and you have all seen this before, the lines drawn in figure 3 are the same length although one 'looks' longer than the other! Hence the need for measurements in standard units. Again, how often have you marveled at the size of the Moon when it's near the horizon, where it seems much bigger than when it's high in the sky, see figure 4, ... but it's an illusion. Also, if you had studied carefully the motion of the planet Mars in 1971, see figure 5, or during 1996-1997, it appeared to do a loop... and that's also an illusion; Mars did not actually do a loop, it's a consequence of the relative motion of the Earth and Mars as they go around the Sun. It will also do a loop in 1997-98 so that's something to look forward to. Now try this one yourself ... hold your hands side-by-side in front of you with your left hand about 1 foot from your face and your right hand about 2 feet from your face. Now, which hand looks bigger? Maybe they look about the same size, maybe the left hand looks a little bigger. Now look at your hands with one eye, and if you line up the tips of the fingers you will see that the left hand is actually twice as big as the right! So we can speculate that the ancients must have had a great deal of trouble in sorting out truth from perception.

Around 2500 BC the Minoans gave names of mythological figures to the groups of brightest stars - the constellations - that were always in the same relative positions each season. The constellations represented animals, mythological figures and other objects; the names generated 'stories' and so astrology and its connection with mythology was born, see figure 6.

Altogether there are 88 constellations [3] and they are used today to identify a region in the sky in which a celestial object can be found - for instance, the first source of radio waves outside our own solar system was discovered in the constellation Cygnus (and called Cygnus A) - so they act as 'markers'. A special band of 12 constellations, called the zodiac, lies in the same plane as the Earth's orbit around the Sun, i.e., they lie on the path through which the Sun appears to be traveling during the year [4]. They have a history of being considered as influential in human affairs, i.e., astrology.

By ca. 2000 BC the Babylonians had perfected a complete sexagesimal numbering system, i.e., they were responsible for the introduction of '60' as a base unit (in contrast to our present day base 10) [5]. Around 2200 BC they, like the early Egyptians, thought there were 360 days in the year and they divided the day (and night, the nychthemeron) into 12 equal hours of 30 gesh (i.e., 4 minutes [6]) each. (Later, around 350-550 BC, the same division into 360 degrees was applied to the zodiac by the Achaimenians (Persians).). Their calendar was based on the Moon and they recognized months of 29 and 30 days in a regular pattern. In order to harmonize the lunar and solar cycles, they divided the year into twelve months but introduced a thirteenth when necessary to synchronize with the yearly solstice and the agricultural seasons. They are credited with inventing the week as they attached special importance to the 7th, 14th, 21st and 28th days of the month as certain things were forbidden by the king on those 'special' days! However, their weeks were not continuous - the first day of each month was the first day of the week - although their hours were [7]. If that had not been the case, astronomical calculations would have been impossible. Thus, our own hours are derived from the Babylonian nychthemeron for their equality and from the Egyptian calendar for their number (24); a form of counting that has survived over 4000 years. The Babylonians made many observations, particularly of Venus and Mercury and they knew that the Moon and planets do not move far away in latitude from the Sun's path. They were arguably the founders of scientific astronomy since they had a profound influence on the results of the later Greek astronomers.

It is tempting to continue with such stories but it is to the Greeks in the so-called Golden Age of Greece that we must now turn our attention. Of course, there are many other cultures whose histories are full of interest, like the Chinese, Indian and Mayan. The Chinese, for example, although not enlightened from the theoretical point of view, were skillful observers. Eclipses tend to recur after an interval of a little over 18 years - 6,585 days 8 hours, to be more precise - a period known as the Saros. So after one Saros the Sun, Moon and Earth return to the same relative positions, almost. The Greeks knew about it, possibly the Babylonians - although if they did it is not clear when - and so did the Chinese. Also, there is evidence of a Hindu lunar calendar developed around 3100 BC, and it seems that decimals were in use about that time. So, let us turn our attention to the Greeks.

Prior to about the 6th century BC it was thought that everything was controlled by Deities; for example, Homer (around 750 BC) populates both the Iliad and the Odyssey with gods, goddesses and nymphs whose meddling was largely responsible for the fiasco's experienced by the heroes. But let us remind ourselves that we are dealing with 'scientific astronomy', by which we mean a system of rational explanations of the movement of celestial objects in contrast to 'astrology'. The former did originate, albeit only through observation, with the Babylonians and Egyptians, but the desire for explanation was characteristically Greek. They were unique in the sense that they not only created a 'religion' that attempted to explain natural phenomena but they also went on to interpret and hypothesize. It was these curious people then, the Ionians, some 25 centuries ago who started the questioning, thinking and probing that produced the evolution of Western thought. It may appear to the casual observer that the Greeks caused a complete change in the way we think in a very short period of time. That is not the case. The first of the real philosopher-scientists was Thales, who was born around 634 BC, and the last was Ptolemy, who died around 180 AD. So the story takes place over a period of more than 800 years; Ptolemy was as distant from Thales as we are from the Crusades! Developments took place at a very slow pace indeed and some of the early Greek philosophers held views that were little more advanced than those of the Egyptians or Babylonians.

In the 6th century BC a group of Greeks in the Ionian City of Miletus (now in Turkey) came on the scene who wanted to know WHY things happened. The first of this group of whom we have any record is Thales of Miletus, figure 7, who lived from ca. 634-546 BC and he is often referred to as the 'father of philosophy'. He was a statesman, engineer, astronomer, mathematician and philosopher; such activity was not at all uncommon among academics in ancient Greece. Among his theorems are: (i) a circle is bisected by its diameter, (ii) the base angles of an isosceles triangle are equal, (iii) opposite angles are equal, and (iv) similar triangles have proportional sides. He is also credited with measuring the height of a pyramid by the use of shadows. He engaged in astronomical observations and according to Heroditus (in Histories) he predicted the eclipse of May 28, 585 BC. When the eclipse occurred the Lydians and Persians had been at war for a long time with no advantage to either side. The two warring kings were so impressed by Thales' prediction that they promptly ceased fighting, concluded a sworn agreement and arranged a marriage! One theory is that Thales was able to do so by researching Babylonian astronomical data that showed that eclipses recur every Saros, see above; indeed he may have even witnessed the Egyptian eclipse of 603 BC, or have been told of it. Plato (in Theaetetus) tells the following story about Thales:

So Thales comes down to us as the first absent minded professor! Be that as it may, Thales thought the Earth was flat and floating on water and he is also remembered for claiming that water is the basic substance of the world.

Anaximander (ca. 610-545 BC), who probably received some guidance and stimulation from Thales, thought of the Earth as a cylinder suspended in space, whose height was about one-third of the diameter. The Earth was surrounded by the ocean and by great anchor rings (solar, lunar, stellar). Using a gnomon, a stick or pole stuck vertically in the ground, he observed that the Sun moved each day in a plane and described a semi-circle from east to west, with the meridian at noon. The inclination of that plane to the horizon varied from day to day, being smallest at the winter solstice, and largest at the summer solstice (when the noon shadow was shortest) reaching its half-way position at the equinoxes.

Anaximines of Miletus (ca. 525 BC) refined the flat-Earth idea by conceiving the Earth and other planets, including the Sun and Moon, as disks supported by the air. However, he was the first among the Greeks to think of the stars as located on a rotating sphere, like nails on the surface of a sphere, thus preserving the eternal rotation of Anaximander. He thought of the planets as freely suspended but he rejected the Egyptian idea that the stars and planets pass under Earth, instead he claimed that they turned around and disappeared from view when they passed behind the mountains at the edge of the world.

Pythagoras of Samos (ca. 582-500 BC), figure 8, reasoned that the Earth was round, but how did he arrive at that conclusion? First, he may have seen that the surface of the ocean is curved and that the top of a ship's mast is seen first and the sail and rest appears gradually. Second, he may have seen the curved shadow of the Earth on the Moon during an eclipse (although it is not certain that an understanding of eclipses was known at the time). It is possible that a 'spherical Earth' was just a wild guess since it could not be flat! Of course, the Sun and Moon appeared spherical and so why not the Earth. He also was the first to remove the Earth from the center of the universe, probably on the basis of moral and religious grounds. You see, humanity and the Earth were imperfect and only by sacrifice and a strict regimen of conduct could one strive to reach the divine. Accordingly, Pythagoras placed the divine, the 'Hearth of the Universe' or 'Throne of Zeus', at the center of a finite spherical universe, as shown in figure 9. The Sun was a glass sphere that caught and reflected the Hearth-light. A counter-Earth was put directly between the Earth and hearth that solved the problem of eclipsing the hearth-fire so that Man could not look God in the face. All celestial bodies were spherical and moved in circle and so the planets were not 'errant' bodies; they must have circular and uniform motion. The Pythagoreans had noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole number; indeed our scales of today are based on that. So the distances between the earth, Moon and planets were set on these musical intervals to ensure 'celestial harmony'. Two other (arbitrary) opinions held by the Pythagoreans represented quite a leap forward, but they dominated the whole of Greek astronomy.

In fact, this dualism influenced scientific thought until, essentially, the time of Galileo. Even then, it was not entirely abandoned, as we shall see.

Empedocles (ca. 492-430 BC) was a member of one of the prominent families in Agrigentum, on the south coast of Sicily. He traveled extensively and many philosophers came to Agrigentum, so it was natural that he participated in the many varied discussions on philosophy, religion and science. He is part of our story because he made some important postulates concerning matter, forces and light and vision, some of which dominated Western thought until as late as the 16th and 17th centuries and the birth of modern chemistry. Some texts associate the claim that there are four fundamental elements or roots (rhizomata) to Aristotle, or that Aristotle plagiarized Empedocles ideas, but that is not the case. For Aristotle (in Metaphysics) writes:

Previously, Anaximander (see above) had claimed that an intangible substance, aperion, was the one, basic element. Later, as we will see, Plato and Aristotle added a fifth. Furthermore, later in Metaphysics, Empedocles is said to have reasoned that everything was a mixture of the four elements in proper proportions:

He also claimed the existence of two moving forces, one centripetal, love (philotes), the other centrifugal, strife (neicos). One observation that he is credited with proved that air had 'body'. He used a clepsydra, a vessel that had a hole at its top and holes at its base; we can reproduce his experiment using a drinking straw. If the upper end is closed with a finger and the lower end is placed in water, the straw does not fill. On the other hand, if the finger is removed then water rushes in. Empedocles also had some ideas about light and vision. He suggested that some emanations (aporroai) are released by luminous bodies that are met by rays from the eye [8]. He also argued that light must have a finite velocity, not that he carried out experiments; he used reasoning. In De sensu et sensibili Aristotle writes:

Although Aristotle accepted the fact that odor and sound have finite velocities, he was less sure about light for he says later:

Clearly then, Empedocles plays an important role in our historical survey of science.

Leucippus (born ca. 500 BC) and Democritus of Abdera in Thrace (ca. 460-370 BC) are credited with postulating the existence of atoms although their views were, for centuries, to be ignored.. Very little is known about Leucippus, not even his birthplace, although Miletus is the most likely. On the other hand, more is known about Democritus; he is associated with a number of 'proverb-like' observations, in addition to his atomic theory, for example:

According to Democritus the world is made of the full (pleres, stereon) and the empty, the vacuum (cenon, manon). The full is divided into into small particles called atoms (atomon), that cannot be cut, or indivisible. The atoms are infinite in number, eternal, absolutely simple, and alike in quality but, according to Aristotle (in Metaphysics):

Each substance was made up of atoms with an infinite number of combinations in an infinity of ways. Objects exist as long as the atoms remain together but if the atoms move away from each other, the objects ceases to exist. So the various changes that occur in nature result from the continuous coming together and breaking apart of atoms; an astonishing idea! Of course, the precise nature of such ideas - how atoms move, how they group, how they separate - could not be explained by Democritus. In fact, such questions were not answered until the 19th and 20th centuries AD! But we have to be careful not to exaggerate the connection between the modern atomic theory introduced by Dalton in the 19th century - based on experiment and observation - and that of Democritus.

Then, depending on your point of view, unfortunately, Plato of Athens (428-347 BC), figure 10, and Aristotle of Stagirus in Macedonia (384-322 BC), figure 11, got in the way of progress. Plato, in 387 BC, established a school of philosophy in Athens, teaching deduction without observation and experimentation. However, he must have sneaked a glimpse at the real world because he said that the motions in the universe were circular and heavenly bodies were spherical. Euduxos of Cnidos (ca. 408-355 BC) was a pupil of Plato in ca. 385 BC for a short time - about two months - but then traveled widely and spent some time in Egypt. His main achievement was the theory of homocentric spheres, which was supposed to give a mathematical account of the positions of celestial objects, a challenge from Plato to his pupils to 'save the phenomena' (sozein ta phainomena), a concept that dominated Greek science from then on. The motions of the stars was easily explained but the retrograde motions of planets - referred to as the hippopede by Euduxos - was a much more difficult kinematical problem. The Sun, the Moon and each of the planets were points on the surface of various interconnected spheres with the Earth at the center. The spheres were aligned along different axes, revolving at constant speeds but at different rates and in different directions; thus satisfying the old Pythagorean concept of circular and uniform motion. The model for the Moon's motion is shown in figure 12. Euduxos introduced 27 spheres [9] in order to explain the motions of all the celestial objects. The theory is a wonderful example of Greek ingenuity and showed a deep understanding of spherical geometry but it did not 'save the phenomena'. The data that Euduxos had to work with were incomplete and imprecise and his ideas of sizes and distances were very crude for, according to Aristarchos (see below) he thought the Sun's diameter was 9 times that of the Moon. Also since in the theory the distances from the Earth to celestial objects were constant, critics, like Polemarchos and Autolycos, wondered how it could account for the change in relative size of the Sun and Moon and the variations in the brightness of planets. According to Aristotle (in Metaphysics),, Callippos of Cyzicos (born ca. 370 BC), in an effort to improve the theory and 'explain the observed facts':

So now we have a total of 34 concentric spheres, 33 of which describe the motions of the planets!

At about the same time Heracleides (ca 388-310 BC) of Pontos (now Eregli, Turkey), who had emigrated to Athens and was a pupil of Plato (until ca. 339 BC when he returned home), considered the universe to be infinite with the Earth at the center of the solar system. The Sun, Moon and the superior planets (Mars, Jupiter and Saturn) revolve around the Earth but the inferior planets (Mercury and Venus) revolve around the Sun. Furthermore, he postulated that the Earth rotates daily on its own axis (replacing the idea that the stars rotate around the Earth). What is remarkable is the similarity with some later ideas, for example, those of Tycho Brähe (of whom, more later) in 1588 and Riccioli in 1651 [10] Looked at from a modern viewpoint his system is a compromise between the Ptolemaic (Earth-centered) and Copernican (Sun-centered) systems. So, Heracleides' picture of the solar system, though imperfect, was astonishingly good for its time but it was not sufficiently supported with observations and so was pretty much ignored.

Aristotle's views on astronomy and physics are presented in Metaphysics, Physics, and De caelo. Although Plato may have taken a peek at the real world Aristotle was not inclined to do so and his explanations were based more on philosophical speculation that empirical observation. He acknowledged the importance of 'scientific astronomy' - involving the study of the positions and motions of celestial objects - but he treated it in the abstract and connecting it with his overall philosophical picture of the world. Aristotle's ideas have had such a profound effect on the development of science that it is appropriate that we spend some time reviewing them.

Aristotle was not satisfied with Callippos's theory of homocentric spheres, even after he added twenty-two more (Metaphysics):

This complication was not an improvement, however.

Briefly, Aristotle identified three types of motion - rectilinear, circular and mixed - and he accepted the idea of four basic elements suggested by Empedocles (above) in the 'sub-lunar' world. Sub-lunar bodies do not move if they are in their natural places; if they are removed from those places they will return along a straight line. So, in explaining natural motion, as distinct from forced motion, he said that position was important. The reason a stone fell to the ground was because it contained a lot of earth and so 'looked' for the Earth as its natural place. Smoke rose in the sky because it contained a lot of air; leaves and feathers fell slowly because they contained both air and earth. Once an object was in its proper place it would only move by 'forced' or 'violent' motion, i.e., pulling, pushing, winds, flowing water, etc. He did not accept the idea of vacuum [11] so motion only took place in a resisting medium. On the basis of crude observations he concluded that the speed of a body is proportional to the pushing or pulling force acting on it and inversely proportional to the resistance of the medium. So any object moving in a resisting medium would come to a stop unless a force continues to push it but in a vacuum its speed would be infinite. He also thought that the speed of a falling object would be proportional to its weight and that it would increase as the body was further removed from its natural place. So the speed would be proportional to the distance fallen. One of the erroneous consequences of his theory of motion, as we shall see, was that heavier objects, i.e., those that contain more earth, fall more quickly than lighter objects. In fairness to Aristotle, erroneous as these ideas are, they were not unreasonable considering his lack of experimental knowledge.

For the celestial world above the Moon, Aristotle added a fifth, incorruptible, unchanging, element, the aether, and conjectured that celestial bodies move eternally, with constant speed in circles. Of course, he knew about comets and the Milky Way but he thought they originated below the Moon, and so were meteorological rather than astronomic in origin, a view that was to prevail until the 1570's when, on November 11, 1572, Tycho Brähe observed a 'new' star in the constellation of Cassiopeia [12]. He also made measurements and observations of the comet of 1577, see figure 13, and proved by parallax that the new object was not sub-lunar as its orbit exceeded that of Venus. This idea, of course, was a direct contravention of the Aristotelian view [13]. But, more of this later.

He thought the universe was spherical, because a sphere is the most perfect shape, and finite, because it has a center, the center of the Earth, and an infinite object cannot have a center. He took the universe to be complete with nothing outside it. He said the Earth must be spherical for reasons of symmetry, since all objects that fall on it fall from every direction the final result must be a sphere. Also, during lunar eclipses the Earth's shadow is circular and on traveling northward (and southward) the layout of stays change and the fact that such a small change in position makes such a difference is proof that the Earth is relatively small, as he described in De caelo:

The mathematicians he referred to are probably Euduxos and Callipos and this estimate of the size of the Earth is the earliest known and was reasonably accurate [14]

It is easy to criticize Aristotle and complain that the Plato/Aristotle doctrine set back the course of science for 2000 years but that's a little unfair. True, many of the ideas were wrong, some even foolish, for example, in De caelo, there are discussions about the shape of the heavens and stars, and the musical harmony generated by their motions. But in Aristotle's defense, one needs to realize that many totally irrelevant and ridiculous questions had to be asked and discussed before the truly appropriate ones emerge. Scientific progress occurs whenever the right question is asked - perhaps it even provides the direction for the solution - but we can hardly expect the right questions to appear when knowledge was so limited. The real culprits were the zealots who not only signed in blood, but chiseled Aristotle's words into stone and refrained from any critical thinking of their own. Although Ramus (1512-1572) proclaimed that everything Aristotle said was wrong, and the foundations of Aristotelian physics were seriously undermined by Galileo and others around 1600, his views were not forgotten nor overlooked. And even as late as the 18th century his ideas were very much alive, though on the defensive. Then again, Aristotelian ideas foreshadowed many principles in mechanics, for example, levers, the parallelogram of forces, the concept of center of gravity and density. Some of these ideas were developed almost straight away by Archimedes, others were developed later, but the seeds had been planted by Aristotle.

Luckily for us, there were some, in the city of Alexandria - which boasted a university, a fine museum and library, built around 270 BC - who continued with independent thought; men like Euclid (ca. 300 BC) and Archimedes of Syracuse (ca. 287-212 BC), see figure 14. The latter, in his book The Sand-Reckoner refers, in the following way, to a remarkable hypothesis of Aristarchus of Samos (ca. 310-230 BC) :

Sadly, Aristarchus' book is lost so it is not known whether he had any observations to back up his hypothesis. Plutarch also made reference to it in his De facie in orbe lunae and to the way it was received:

So, by these very statements, there can be little doubt that it was Aristarchus who 'invented' the Sun-centered solar system and rotating Earth some 1800 years before Nicholas Copernicus [15]. The only surviving work of Aristarchus in his treatise On the Sizes and Distances of the Sun and Moon and it gives details of his geometrical arguments for determining the relative sizes and relative distances of the Sun and Moon. Altogether there are 18 propositions but the three most well-known are:

These values are seriously in error, but that was due to his lack of accurate instruments rather than in his method of reasoning. Indeed, his approach, involving lunar and solar eclipses, represented a breakthrough in determining large distances and, as adapted by Hipparchus (180-125 BC) a little more than a century later, and others, was used well into the 17th century.

Archimedes of Syracuse (ca. 287-212 BC), figure 14, greatest contributions were in geometry; his favorite theorem, that the volume of a sphere is 2/3 the volume of a circumscribed cylinder, which he considered his most significant accomplishment, was inscribed on his tomb at his request. He developed a number of mechanical inventions, including the water-screw as a method of drawing water out of the Nile for irrigation, although it is also suggested that he invented it to drain bilge water from a huge ship built for Hiero, King of Syracuse. However, he is probably most well-known for his writings On floating bodies in which he makes a series of propositions that are very familiar, for example, from Book I:

Apparently, asked by Hiero to discover whether a goldsmith had alloyed his gold crown with silver, Archimedes found the answer after considering the amount of water his body displaced while he was bathing. Legend has it that he ran home, naked, shouting "Eureka!" (I have found it!). Another story that occurs about Archimedes is that around 214 BC saved his home town, Syracuse, by burning the attacking Roman ships using sunlight directed by an arrangement of 'burning glasses' (mirrors?) located on land [16]. His preoccupation with scientific problems is said to have led to his death; in 212 BC after Syracuse was captured by Marcellus, it is reported that Archimedes was so wrapped up in a problem that when he was ordered to visit the victorious general he refused until the problem was solved, and was killed by an enraged Roman soldier.

Archimedes' colleague Eratosthenes (275-195 BC) of Cyrene, who was educated in Athens but spent most of his life as Chief Librarian at Alexandria, made a significant contribution to science by recomputing the circumference of the Earth, see figure 15. Having heard that at noon of the summer-solstice the Sun reached the bottom of water wells in Syene (now Aswan) he concluded the Sun stood vertically overhead (so Syene was on the tropic). He reasoned that since the Sun was so far away the beam of light was parallel and so would reach Alexandria at a slant. Accordingly, although it's not clear exactly how he did it, at the summer-solstice he measured the length of the shadow at Alexandria when it became shortest (indicating local noon). He determined the angle to be 7.2o. Since he knew the distance from Syene to Alexandria was 5,000 stadia he reasoned that since that distance subtends an angle of 7.2o at the center of the Earth, then the polar circumference would be:

5000 x (360/7.2) = 250,000 stadia

Although the length of the stadium is not known precisely, (see above), it's about 0.1 mile, so Eratosthenes estimate of the polar circumference of the Earth is 25,000 miles. Modern satellite technology gives us a value of 24,902 miles, so his determination was astoundingly accurate.

Although Aristotle's cosmological ideas had a very long life, mathematicians who tried to model the actual motions of planets began using different constructions within a 100 years of his death. These constructions violated Aristotle's principles somewhat but they were ultimately successful in accounting for the motions of celestial objects. It is with the work of Ptolemy (ca. 90-170 AD), figure 16, that we see the culmination of this effort. The Aristotelian insistence that the Earth was at the center of the cosmos and only circular orbits were allowed led inevitably to the Ptolemiac system of the universe, completed by Ptolemy in the second century AD. The system, which was an extension of the ideas of Apollonius (ca. 262-190 BC) and Hipparchus, figure 17, depended on three constructions; the eccentric, the epicycle and the equant, as shown in figure 18. He believed the Moon, planets and Sun orbited the Earth in the order, Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn, moving on epicycles in the same direction as the epicycle moves on the deferent. It was cumbersome but, apparently, it could account for the retrograde motion of the planets, see figure 19, such as we have seen for Mars in figure 5, and there were no obvious faults with it (although that is not strictly true [17]). Furthermore, it predicted the positions of planets accurately enough for naked-eye observations although some of the predictions, such as the distance between the Earth and Moon varying by a factor of two over its orbit, were somewhat far-fetched! Since it fitted in with the accepted science as well as with the religion it became the definitive description, see figure 20.

Little is known about Ptolemy except that he studied in Alexandria for most of his life. His system is described in the Almagest , see figure 21, which was believed to have been written in the reign of the Roman Emperor Antoninus Pius (131-161 AD). (This work was originally known as The Mathematical Syntaxis, but after it had become a standard text in astronomy it was called The Great Astronomer to distinguish it from a collection known as The Little Astronomer. The Arabs called it "The Greatest," prefixing the article al to the Greek megiste.) The Almagest comprises 13 books and contains a great deal of information, not only on Ptolemy's basic concepts and constructions but on elements of spherical geometry, the dates of equinoxes, the length of year, etc. and a catalog of the positions of 1028 stars in 48 constellations, using the names we use today. According to Ptolemy, the observations were made between 127 and 138 AD [18]. Near the end of the Almagest Ptolemy admits his system is very complicated and self-contradictory but he says:

He argues that what may appear contradictory in Earthly terms may not be so in the heavens, nor that humans can judge what may be simple in heavenly terms. He also published a book called Geography in which he provides maps of the known world that were based more on scientific measurement rather than guesswork.

With the death of Ptolemy we come to the end of an era. Unfortunately for science, having come close to discovering modern astronomy - and from there, modern physics - the Greeks turned their backs on it. Much had been achieved and some golden opportunities had been missed. The succeeding centuries were barren of ideas and, tragically, many of the books in the great Alexandrian Library - at its height the library may well have held one million scrolls, of information obtained from literally everywhere and copied! - were lost during the 3rd to 5th centuries AD, purportedly mostly at the hands of the Romans and Christian mobs. One story tells us the end came in 646 when the Arabs captured the city and the victorious general asked the Caliph what was to be done with the books. The Caliph decreed that if the books contradicted the Koran they were heretical - and if they agreed with the Koran they were superfluous ... so they were burned! By one piece of good fortune Ptolemy's great book had somehow reached Baghdad by the 8th century and was translated into Arabic with its new title the Almagest. Without that, our knowledge of the astronomy of the classical period would have been very slender indeed.

The study and development of the physical sciences essentially stood still throughout the period of the Roman Empire and the Middle Ages. Christianity became more firmly established during the early centuries AD and in the 5th century the Roman Empire disintegrated. With the Greek and Roman Empire's in tatters, religious leaders took hold and 'steered their flocks' towards the teachings of the Bible. Science was replaced by superstition and mysticism. Rational thought gave way to divine revelation as the test for truth, and the Scriptures dominated all philosophy ... the view was that 'God, not Greek science, would determine the shape of the Earth'. Various Kings and explorers became obsessed with 'finding Paradise'; indeed, even as late as the 1880's a British explorer named Gordon claimed he had found the 'Garden of Eden' and the 'tree of good and evil'. In an effort to reconcile reason with theology a system of thought called Scholasticism appeared in the 12-13th centuries. This was an authoritarian, man-centered philosophy aimed primarily at discovering how to achieve salvation in the hereafter; it consisted of discovering the ends or purposes that things served - that is, their ultimate good. There was little interest in observation and a complete distrust in the senses as guides to the ultimate nature of things.

It was the Arabs who, in some sense, were responsible for the rebirth of astronomy although their original motives were not scientific. During the early centuries the Arabs were astrologically minded and this meant they needed good star catalogs as well as tables that would predict the movements of the planets. It is believed that in the 8th and 9th centuries, because of the growing interest in Greek science in the Islamic world, the Almagest reappeared and was translated into Syrian and later into Arabic. In the 10th century the first medieval star catalog was created by the Arabic astronomer Abd Al-Raham Al-Sufi (903-966) - known in the west as Azophi - in Baghdad and another appeared by Ulugh Beg (1394-1449) in Samarkand, conistsing of 992 stars. By the 12th century it is believed that at least five versions of the translations of the Almagest existed. Actually, the Almagest had become the basic textbook in astronomy for over a thousand years. It influenced greatly late medieval astronomy, both in Islamic and Christian regions, up to the 16th century.

In fact, the Arabs did a great service for science during the 'bleak' period in Europe from around 600-1200. They saved a lot of ancient Greek texts and formed a great civilization that spread westward to Spain and eastward to Iran, India and central Asia. Indeed, Arabic scientists had interests in topics other than astronomy; for example; Abu Ali Hasan Ibn Al-Haitham (ca. 965-1039), see figure 22, known in the west as Alhazen, who studied the principles of the reflection and refraction of light, made lenses and explained their properties and magnifying power. His study of magnification, for example, led him to conclude that magnification was caused by the curvature of the lens. Also, he gave the first correct explanation of vision showing that light is reflected from an object into the eye, not by light emanating from the object as the Pythagoreans and Aristotelians had thought. Because of his extensive studies on optics he has been considered in some circles as the father of modern optics. In addition, his writings - although very few of his books exist - show that he was a methodical worker and, for the first time, he placed the scientific method, that is the relationship between observation, hypothesis and verification, on a firm foundation.

Not everything had come to a standstill in Europe. Roger Bacon (1220-1292), figure 23, a Franciscan monk working in Oxford, England, studied reflection in mirrors and refraction in lenses, and suggested that lenses could be used as magnifiers for close work. He also suggested the use of a single lens for viewing distant objects but, apparently, failed to invent the telescope! He was later imprisoned in his room from 1281-1291 when results of his optical studies were condemned as witchcraft. It appears that an Italian monk, Alexandro della Spina, reported the invention of spectacles sometime between 1285 and 1300. Also, some interesting studies of magnetism were carried out by Peregrenus (Peter de Maricourt) (1240-?), a French engineer, who was interested in the properties of lodestone, a naturally magnetized mineral (iron oxide). He showed that a needle of lodestone has a north and south pole and that like poles repel and unlike poles attract. He showed further that one could not separate a single pole. He believed that the north pole of a magnetized needle was attracted by the north pole of the celestial sphere. The compass, which had been invented by the Chinese and brought to Europe by Arab sailors, was perfected by Peregrenus when he used a pivoted magnetized needle on a graduated scale.

Eventually, interest in astronomy re-appeared in Europe, and the spread of knowledge was made much easier by the invention of printing presses; indeed, by the middle of the 15th century astronomical information was being published regularly. Aristotle's and Ptolemy's writings had been rediscovered, now in Arabic and Latin rather the (original) Greek, see figure 24 and figure 25. Aristotelian philosophy suited the beliefs of the religious leaders and so in Europe in particular, Aristotle's work was taken to be authoritative in all matters by the Church and State and any questioning or opposition to the accepted scientific principles ran the risk of severe penalty, even death. The fiery and outspoken Giordano Bruno, see figure 26, for example, was burned at the stake in Rome in 1600. Among many other indiscretions, he had commented that the preface to the De Revolutionibus Orbium Coelestium by Nicholas Copernicus (1473-1543), figure 27, completed sometime between 1530-1533 and published in 1543, was written by one ignorant ass for the benefit of other ignorant asses! In fact, the preface had been written by Andreas Osiander, a Lutheran clergyman, who had supervised the preparation and publication of the book. With the publication of Nicholas Copernicus's De Revolutionibus, figure 28, we come to the end of our review of Science to the Renaissance; the era of Modern Science has begun!

FOOTNOTES

[1] The ancients recognized early on that almost all the stars were stationary, but they also identified 'errant' objects, apart from the Sun and Moon, that moved around the sky. Such objects were later called planets, from the Greek 'planetes', a wandering, misleading body.

[2] The Egyptians had first tried to take account of the passing of time by means of the Moon but they soon discovered the ambiguities that caused and so they adopted a solar calendar. Their year was divided into twelve months of 30 days each but they soon added a holiday season of 5 extra days. The conflict between the civil year (365 days) and the Sothic year (365.25 days) caused some complications, but was resolved by the introduction of the Sothic (or Julian) year in Rome in 45 BC by Julius Caesar.

[3] Within each constellation the stars are now identified by Greek letters, with alpha representing the brighest star, etc.

[4] Around 200 BC the Greeks changed the names of the constellations to the ones we know now. The 12 zodiac constellations represent mainly animals; hence the name zodiac from the Greek for animal.

[5] In some ways, the Babylonian system is more advanced than our present system because 10 has only two proper divisors, 2 and 5, whereas 60 has ten proper divisors and so many more numbers have a finite form.

[6] It appears that it was Ptolemy (ca. 150 AD) who divided the hour into 60 parts and divided the circle into 360 degrees.

[7] The introduction of a continuous seven-day week and of the names given to each day was not completed until the last few centuries BC. Each day was named after the planet dominating its first hour.

[8] It seems that there had been two schools of thought; the Pythagoreans had particles coming from the object, others had rays coming from the eyes. Therefore, Empedocles offered a 'compromise'.

[9] One for the fixed stars, three spheres each for the Moon and Sun, and four spheres each for the five planets.

[10] Whereas Heracleides had two planets revolving around the Sun, Brähe had all five and Riccioli three (Mercury, Venus and Mars).

[11] The proper laws of motion deduced by Galileo and Newton became possible only when the Aristotelian idea of no vacuum was rejected.

[12] This new star was, in fact, a supernova. Brähe published his observations in 1573 in De Nova et Nullius Aevi Memoria Prius Visa Stella (On the New and Never Previously Seen Star).

[13] Brähe published his observations in 1588 in De Mundi Aetherei Recentioribus Phaenomenis (Concerning the New Phenomena in the Ethereal World). He also concluded the orbit was elliptical, which was the first time any astronomer had claimed that an orbit was not circular.

[14] The exact size of a stadium referred to is not known, for its size varied from place to place and time to time. But a reasonable estimate of about 10 stadia = 1 mile gives a circumference of 40,000 miles somewhat larger than today's value of about 25,000 miles, but remarkable nevertheless!

[15] The only other persons who followed Aristarchus' philosophy were Seleucus (ca. 150 BC) who attributed ocean tides to the stirring of air caused by the rotation of the Earth and an interaction with the rotation of the Moon. Later in the 1st century BC Seneca also mentioned the possibility of a rotating Earth.

[16] Is this fact or fantasy? Well, in his book The Flying Circus of Physics Jearl Walker writes:

[17] The fact that the Earth was displaced slightly from the center of the paths violated the rule that the Earth was the center of the cosmos and all planetary motions. However, the displacement was minimal and was considered only a slight bending of the rules rather than a violation! Also, the introduction of the equant violated the stricture of perfectly circular motion and this bothered philosophers a good deal.

[18] There are suggestions that Ptolemy did not make all of the observations himself in the 2nd century AD. It appears that he may have used the data of Hipparchus of Rhodes (180-125 BC), who published a catalog of about 850 stars in 129 BC, which he 'corrected'.

REFERENCES

I have made use of many texts, certainly too numerous to mention them all here, but the main sources have been (and I have often quoted passages verbatim):

George Sarton, Ancient Science through the Golden Age of Greece (Dover Publications, Inc., New York, 1993). This is a remarkable book, first published by The Harvard University Press in 1952 with the title A History of Science, Volume I: Ancient Science Through the Golden Age of Greece, and I have used a good deal of material from it.

Cesare Emiliani, Planet Earth (Cambridge University Press, 1992).

Patrick Moore, Watchers of the Stars (Michael Joseph Ltd., 1973).

I have also used material from many Web-sites including the following (and they are all worth visiting):

Biographies and historical topics:

The Almagest:

The Galileo Project Homepage and Ptolemaic system:

History of Astronomy:

Perseus Project:

Muslim scientists, mathematicians and astronomers before the Renaissance:

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