A Brief History of the Universe Page 4
The heavens are eternal and unchanging, whereas the Earth is subject to decay and change.
Most students today can easily recognize the flaws in Aristotle’s ‘science’ and it might seem strange that these ideas found acceptance amongst both his contemporaries and the many later generations who read and accepted his works as absolute wisdom. To understand this it is important to remember that Aristotle’s concepts of astronomy and physics were intertwined with his ideas on philosophy and logic as well as his concepts of social and political order. The important concept of geocentrism, the Earth at the centre of all things, therefore slipped into Aristotle’s cosmology without much alarm. If to Plato it seemed self-evident that heavenly bodies move uniformly in perfect circles, to Aristotle and his contemporaries, it was self-evident that the Earth was stationary at the centre of these circles.
Because Aristotle’s cosmology has had a long lasting – albeit regressive – effect on the progress towards our modern view of astronomy, it is helpful to review its details. A great philosopher he may have been, but as a physicist or cosmologist he relied too much on an a priori approach to the natural world, relying on intuition rather than insisting on testing nature with observations and experiments. Some historians of science would say that although Aristotle may have been wrong, he was not ‘unscientific’ and should still be credited with the birth of science. This view may have some validity if one considers Aristotle’s starting point. However, his view is ultimately flawed given that the observational verification of theory is so fundamental to what we call ‘science’ today. Given that the history of science demonstrates many examples of phenomena in the physical world contradicting intuitive learning or ‘common sense’, the necessity for experimentation is now generally accepted.
From its inception around 350 BC, Aristotle’s cosmological work On The Heavens was the most influential treatise of its kind, accepted as truth for more than eighteen centuries. In this work, Aristotle discussed the general nature of the cosmos and the physical properties of individual bodies, essentially defining the field of ‘science’ for the first time.
Since Aristotle had postulated that all bodies are made up of four elements: earth, water, air and fire; he further theorized that composite objects have the features of the dominant of these elements in its composition. Most things are of this mixed variety since few objects on Earth are totally pure substances. From this, Aristotle concluded that things on the Earth are imperfect.
The natural tendency of objects was all-important to Aristotle and his idea that all bodies, by their very nature, have a natural way of moving is central to Aristotelian cosmology. Movement is not, he states, the result of the influence of one body on another (as we understand it today from Galileo and Newton) but the result of the simple premise that bodies have natural movement: some naturally move in straight lines, some naturally move in circles and others naturally stay put. We know today that the natural state of a body’s motion is at uniform speed in a straight line unless acted upon by an external force. This is called the principle of inertia, which was not discovered until the careful experiments of Galileo twenty centuries after Aristotle.
The most important of the natural movements that Aristotle identified is the circular motion. Since he assumed that for each natural motion there must be a particular corresponding body, Aristotle presumed that heavenly bodies move naturally in perfect circles, as Plato had taught. He accordingly then postulated that heavenly bodies are made of a more perfect substance than earthly objects. Finally, as a last a priori conclusion about heavenly bodies, Aristotle stated that since the stars and planets are so special and move in circles, it is also natural for these objects to be perfectly spherical in shape.
Another of the fundamental propositions of Aristotelian philosophy is that there is no effect without a cause. Applied to moving bodies, this proposition means that there is no motion without a force. Speed, then, is proportional to force and inversely proportional to resistance. This notion is not at all unreasonable if one takes an ox pulling a cart as the defining case of motion: the cart only moves if the ox pulls, and when the ox stops pulling, the cart stops.
When Aristotle applied his rule to falling bodies, he found that the force was equal to the weight pulling a body down and the resistance is that of the medium (air or water, for example) through which the body falls. When a falling object gains speed, Aristotle attributed this to a gain in weight. So, if weight determines the speed of fall, then when two different weights are dropped from a high place, the heavier will fall faster than the lighter, in proportion to the two weights. A 10-pound weight would reach the Earth by the time a 1-pound weight had fallen one-tenth as far. This concept was yet to be refuted when, according to the well-known but probably apocryphal story, Galileo dropped different weights from the Tower of Pisa in the sixteenth century.
If we were to accept Aristotle’s theory we must consider the cosmos to be made up of a central Earth (accepted as spherical) surrounded by a Sun, Moon and stars all moving uniformly in circles around it – a conglomerate he called ‘the world’. Note the strange idea that all celestial bodies are perfect, yet they circle the imperfect earth. Going further, Aristotle hypothesizes that the initial motion of these spheres was caused by the action of a ‘prime mover’ who acts on the outermost sphere of the fixed stars, with the motion then trickling down to the other spheres. Though one might argue that the great man’s logic was sound, Aristotle was wrong in many of his initial assumptions. Particularly misleading is the thesis that different objects have different natural motions.
In his description of the heavens, Aristotle created a complex system containing 55 spheres – an elaboration on the original sphere of an earlier astronomer Eudoxus of Cnidus. This system had the virtue of explaining and predicting most of the observed motions of the stars and planets and all of the characteristics of a scientific theory. He painstakingly modified the model, matching it to the observations available, until all these could be accurately explained.
Yet he did not consider the model a work-in-progress subject to continuous testing and experimentation, as is the norm today. He simply wished to use the model to make predictions, such as the position of a planet a year into the future, satisfying the Greeks’ compelling goal to ‘save the appearances’. In spite of these imperfections, this was the start of the development of the celestial sphere model later developed by Ptolemy, which came to be accepted and utilized by generations of astronomers and astrologers after Aristotle.
Alexander the Great
Aristotle inspired an avid hunger for knowledge among the Greeks. Against this background his pupil Alexander the Great launched his global enterprise of conquest in 334 BC. This was accomplished with meteoric speed until Alexander’s untimely death about a decade later in 323 BC at the age of thirty-three. This was a year before Aristotle, who had lived twice as long.
Alexander’s aim was not restricted to conquests, but also included explorations. He dispatched close companions – generals as well as scholars – to report to him in detail on regions previously unmapped and uncharted. His campaigns therefore resulted in a considerable expansion of empirical knowledge of geography. The reports he acquired stimulated and motivated an unprecedented interest in scientific research and the study of the natural qualities and inhabitants of the Earth. His Age was charged with a new spirit of enquiring.
Scholars have long seen Alexander’s conquest of the Persian Empire as opening the floodgates for the spread of Greek culture in and around the Mediterranean. He attempted to create a unified ruling class of Persians and Greeks, bound by marriage ties, and used both in positions of power. He tried to mix the two cultures, encouraging intermarriage, adopting elements of the Persian court and also attempting to insist on certain Persian practices. Alexander also unified the army, placing Persian soldiers into the Greek ranks.
After Alexander’s death, the Empire was split into separate states under his generals and although
the kings who succeeded him rejected most of Alexander’s cultural changes, other less definite policies were continued. The founding of cities was a major part of the struggle for control of any particular region, and the independence of Greek cities was a political right that his successors sought. They used the existing systems of government within their individual states, but often placed Greeks in the top levels of power. Not surprisingly, the spread of the Greek language also increased, and was often used in tandem with the native language for administrative purposes.
Four main kingdoms maintained Macedonian and Greek rule over native populations, and while they allowed the flourishing of native culture and religion, this was ultimately mixed with their own Greek culture.
The Library of Alexandria
On a visit to Egypt in 330 BC Alexander founded Alexandria, one of the many cities that were to bear his name. Leaving his administrator Cleomenes to build the new city as he made further conquests, Alexandria was destined to become the most important city in his new realm. However soon after Alexander’s death, his empire was subjected to the greedy land-grabbing ambitions of his many generals.
Ptolemy I (305–282 BC), also called Soter, took Egypt and after disposing of Cleomenes, made Alexandria his capital. He and his descendants ruled from Alexandria for three centuries and made little effort to integrate the rest of Egypt into their Greek culture. The Ptolemys formed their coastal capital into the great intellectual and cultural centre of its age, immortalized by the magnificent library founded by Ptolemy I at the beginning of the third century BC. Its collection of papyrus scrolls – said to have numbered nearly half a million – attracted intellectuals from all over the Greek-speaking Mediterranean.
According to the earliest source of information – a second century BC letter of Aristeas paraphrased by the Hebrew historian Josephus – the Library was initially organized by Demetrius of Phaleron, a student of Aristotle, and was modelled after the arrangement of Aristotle’s school in Athens. The library was closely linked to a museum built by the Ptolemys that seems to have focused primarily on editing texts. Initially, libraries were important for textual research in the ancient world, since the same text often existed in several different versions of varying quality and veracity. Later, the library took on a more important function as a repository for all the great books of the day.
When the founder Ptolemy I asked, ‘How many scrolls do we have?’ Demetrius was on hand to answer with the latest count. After all, it was Demetrius who suggested setting up a universal library to hold copies of all the books in the world. Ptolemy I and his successors wanted to understand the people under their rule and store Latin, Persian, Hebrew and Egyptian books, all of which were translated into Greek. The library’s lofty goal was to collect half a million scrolls and the Ptolemys took serious steps to accomplish this ambitious feat. Ptolemy I, for example, composed a letter to all the sovereigns and governors he knew, imploring them ‘not to hesitate to send him’ works by authors of every kind.
The problem of growing the collection was solved through an innovative piece of legislation by Ptolemy III (246–222 BC), the third ruler of the Ptolemaic dynasty. He decreed that all visitors to the city were required to surrender all books and scrolls as well as any form of written media in any language in their possession. Official scribes then swiftly copied these writings and the reproduction was so precise that the originals were often put into the library and the copies were delivered to their unsuspecting owners. This process helped to create a substantial reservoir of books in the relatively new city.
The Ptolemys engaged in further acquisitions, some in an orthodox way, like purchasing writings from throughout the Mediterranean area; and some unorthodox, like confiscating any book not already in the library from passengers arriving in Alexandria. They were obsessed with becoming the most important library in the Hellenistic world and carried out some shocking tactics to achieve this goal. Ptolemy III, for example, deceived Athenian authorities when they let him borrow original manuscripts of Aeschylus, Sophocles and Euripides using silver as collateral. He kept the originals and sent the copies back, letting the authorities keep the silver.
Physically the books were not what we think of today, but rather scrolls, mostly made of papyrus, but sometimes of leather. They were kept in pigeonholes with titles written on wooden tags hung from their outer ends. Older copies were favoured – the older the better – since these would be considered more trustworthy. At its height, the library held nearly 750,000 scrolls, with works by Euclid, Aristarchus, Eratosthenes and Hipparchus. Amongst the most important documents in this vast collection were the writings of Aristotle, which contained his model of the heavens.
Euclid was a Greek mathematician of the Hellenistic period who thrived in Alexandria, almost certainly during the reign of Ptolemy I. His Elements is the most successful textbook in the history of mathematics. In it, the principles of Euclidean geometry are deduced from a small set of axioms. Euclid’s method of proving mathematical theorems by logical deduction from accepted principles remains the backbone of all mathematics. He also wrote works on perspective, conic sections, spherical geometry and quadric surfaces.
Although many of the results in Elements originated with earlier mathematicians, one of Euclid’s accomplishments was to present them in a single, logically coherent framework, making them easy to use and easy to reference. This includes the system of rigorous mathematical proofs that remains the basis of mathematics some twenty-three centuries later. Although best known for its geometric results the Elements also includes number theory and considers the connection between perfect numbers and primes – the infinitude of prime numbers – Euclid’s dilemma on factorization and the Euclidean algorithm for finding the greatest common divisor of two numbers.
The geometrical system described in the Elements was long known simply as ‘geometry’, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the nineteenth century. These include Riemann geometry, which was employed by Einstein in determining his general theory of relativity in the early part of the twentieth century.
An Early Heliocentric System
Aristarchus is an important figure in the history of astronomy even though his advanced ideas on the movement of the Earth were not incorporated into the development of the classic Greek model published by Ptolemy in the second century. He was certainly both a mathematician and astronomer and is celebrated as the first to propose a Sun-centred universe. He also is known for his pioneering attempt to determine the sizes of the Sun and Moon and their distances from the Earth. This idea survives in part because of the work of Archimedes and Plutarch, which further expands on Aristarchus’ only extant work, a short treatise called ‘On the Sizes and Distances of the Sun and Moon’.
In this notable work, Aristarchus provides the details of his remarkable geometric argument. Based on observation, he determined that the Sun was about 20 times as distant from the Earth as the Moon, and 20 times the Moon’s size. Both these estimates were an order of magnitude too small, but the fault was in Aristarchus’ lack of accurate instrumentation rather than in his method of reasoning.
It is due to the prestige of the great Archimedes that we are certain of Aristarchus’ advanced hypothesis on heliocentrism, in which the Sun and not the Earth is at the centre of all things. In his well-known book, The Sand Reckoner, which he addressed to his patron King Gelon in ancient Syracuse, Archimedes describes how to count the number of grains of sand in the universe. In passing, he mentions the latest ideas about the universe from the mainland, reporting on the innovative hypotheses of Aristarchus:
. . . His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same
centre as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.
Aristarchus’ heliocentric system was indeed revolutionary. It was the Earth that rotates, he said, once daily on an axis of its own which causes the apparent daily motion of the stars. He believed that this assumption could explain all the daily motions observed in the sky. The observed angle of the paths of the Sun, Moon and the planets with the celestial equator results from the tilt of the Earth’s own axis. Annual changes in the sky, including retrograde motion of planets, were then explained by assuming that the Earth and the planets revolve around the Sun.
In this model the previously assigned motion of the Sun around the Earth was now subverted so that the Earth moved around the Sun. The Earth essentially became just one among several planets. These bodies were then not made of ‘heavenly material’ to house the gods but were considered to be composed of material rather like that which we think composes the Earth today. There is much debate by historians about why the Greeks rejected the elegant and innovative idea of a Sun-centred universe.
The diagram shows how much Aristarchus’ heliocentric system could explain retrograde motion, that is reversing the orbital motion of Mars, Jupiter and Saturn, the planets outside the orbit of the Earth. The outer planets, assumed to be moving around the Sun in circular orbits, move more slowly than the Earth and when the Earth passes directly between the Sun and the planet, an illusion is observed. To viewers on Earth, the outer planet appears for a time to move backwards in retrograde motion against the fixed background of the stars. The heliocentric hypothesis has one further advantage. It explained the observation that the planets were brighter during retrograde motion as the outer planets were nearer to the Earth during the passing phase.