myths inevitably invoke at least one supernatural being to play a crucial role in explaining the creation of the universe. Also, every myth represents the absolute truth within its society. The word ‘myth’ is derived from the Greek word mythos, which can mean ‘story’, but also means ‘word’, in the sense of ‘the final word’. Indeed, anybody who dared to question these explanations would have laid themselves open to accusations of heresy.
Nothing much changed until the sixth century BC, when there was a sudden outbreak of tolerance among the intelligentsia. For the very first time, philosophers were free to abandon accepted mythological explanations of the universe and develop their own theories. For example, Anaximander of Miletus argued that the Sun was a hole in a fire-filled ring that encircled the Earth and revolved around it. Similarly, he believed that the Moon and stars were nothing more than holes in the firmament, revealing otherwise hidden fires. Alternatively, Xenophanes of Colophon believed that the Earth exuded combustible gases that accumulated at night until they reached a critical mass and ignited, thereby creating the Sun. Night fell again when the ball of gas had burned out, leaving behind just the few sparks that we call stars. He explained the Moon in a similar way, with gases developing and burning over a twenty-eight-day cycle.
The fact that Xenophanes and Anaximander were not very close to the truth is unimportant, because the real point is that they were developing theories that explained the natural world without resorting to supernatural devices or deities. Theories that say that the Sun is a celestial fire seen through a hole in the firmament or a ball of burning gas are qualitatively different from the Greek myth that explained the Sun by invoking a fiery chariot driven across the sky by the god Helios. This is not to say that the new wave of philosophers necessarily wanted to deny the existence of the gods, rather that they merely refused to believe that it was divine meddling that was responsible for natural phenomena.
These philosophers were the first cosmologists, inasmuch as they were interested in the scientific study of the physical universe and its origins. The word ‘cosmology’ is derived from the ancient Greek word kosmeo, which means ‘to order’ or ‘to organise’, reflecting the belief that the universe could be understood and is worthy of analytical study. The cosmos had patterns, and it was the ambition of the Greeks to recognise these patterns, to scrutinise them and to understand what was behind them.
It would be a great exaggeration to call Xenophanes and Anaximander scientists in the modern sense of the term, and it would flatter them to consider their ideas as full-blown scientific theories. Nevertheless, they were certainly contributing to the birth of scientific thinking, and their ethos had much in common with modern science. For example, just like ideas in modern science, the ideas of the Greek cosmologists could be criticised and compared, refined or abandoned. The Greeks loved a good argument, so a community of philosophers would examine theories, question the reasoning behind them and ultimately choose which was the most convincing. In contrast, individuals in many other cultures would not dare to question their own mythology. Each mythology was an article of faith within its own society.
Pythagoras of Samos helped to reinforce the foundations of this new rationalist movement from around 540 BC. As part of his philosophy, he developed a passion for mathematics and demonstrated how numbers and equations could be used to help formulate scientific theories. One of his first breakthroughs was to explain the harmony of music via the harmony of numbers. The most important instrument in early Hellenic music was the tetrachord, or four-stringed lyre, but Pythagoras developed his theory by experimenting with the single-stringed monochord. The string was kept under a fixed tension, but the length of the string could be altered. Plucking a particular length of string generated a particular note, and Pythagoras realised that halving the length of the same string created a note that was one octave higher and in harmony with the note from the plucking of the original string. In fact, changing the string’s length by any simple fraction or ratio would create a note harmonious with the first (e.g. a ratio of 3:2, now called a musical fifth), but changing the length by an awkward ratio (e.g. 15:37) would lead to a discord.
Once Pythagoras had shown that mathematics could be used to help explain and describe music, subsequent generations of scientists used numbers to explore everything from the trajectory of a cannonball to chaotic weather patterns. Wilhelm Röntgen, who discovered X-rays in 1895, was a firm believer in the Pythagorean philosophy of mathematical science, and once pointed out: ‘The physicist in preparing for his work needs three things: mathematics, mathematics and mathematics.’
Pythagoras’ own mantra was ‘Everything is number.’ Fuelled by this belief, he tried to find the mathematical rules that governed the heavenly bodies. He argued that the movement of the Sun, Moon and planets across the sky generated particular musical notes, which were determined by the lengths of their orbits. Therefore, Pythagoras concluded, these orbits and notes had to have specific numerical proportions for the universe to be in harmony. This became a popular theory in its time. We can re-examine it from a modern perspective and see how it stands up to the rigours of today’s scientific method. On the positive side, Pythagoras’ claim that the universe is filled with music does not rely on any supernatural force. Also, the theory is rather simple and quite elegant, two qualities that are highly valued in science. In general, a theory founded on a single short, beautiful equation is preferred to a theory that relies on several awkward, ugly equations qualified by lots of complicated and spurious caveats. As the physicist Berndt Matthias put it: ‘If you see a formula in the Physical Review that extends over a quarter of a page, forget it. It’s wrong. Nature isn’t that complicated.’ However, simplicity and elegance are secondary to the most important feature of any scientific theory, which is that it must match reality and it must be open to testing, and this is where the theory of celestial music fails completely. According to Pythagoras, we are constantly bathed in his hypothetical heavenly music, but we cannot perceive it because we have been hearing it since birth and have become habituated to it. Ultimately, any theory that predicts a music that could never be heard, or anything else that could never be detected, is a poor scientific theory.
Every genuine scientific theory must make a prediction about the universe that can be observed or measured. If the results of an experiment or observation match the theoretical prediction, this is a good reason why the theory might become accepted and then incorporated into the grander scientific framework. On the other hand, if the theoretical prediction is inaccurate and conflicts with an experiment or observation, then the theory must be rejected, or at least adapted, regardless of how well the theory does in terms of beauty or simplicity. It is the supreme challenge, and a brutal one, but every scientific theory must be testable and compatible with reality. The nineteenth-century naturalist Thomas Huxley stated it thus: ‘The great tragedy of Science — the slaying of a beautiful hypothesis by an ugly fact.’
Fortunately, Pythagoras’ successors built on his ideas and improved on his methodology. Science gradually became an increasingly sophisticated and powerful discipline, capable of staggering achievements such as measuring the actual diameters of the Sun, Moon and Earth, and the distances between them. These measurements were milestones in the history of astronomy, representing as they do the first tentative steps on the road to understanding the entire universe. As such, these measurements deserve to be described in a little detail.
Before any celestial distances or sizes could be calculated, the ancient Greeks first had to establish that the Earth is a sphere. This view gained acceptance in ancient Greece as philosophers became familiar with the notion that ships gradually disappear over the horizon until only the tip of the mast could be seen. This made sense only if the surface of the sea curves and falls away. If the sea has a curved surface, then presumably so too does the Earth, which means it is probably a sphere. This view was reinforced by observing lunar eclipses, when the Earth casts a disc-shaped shadow upon the Moon, exactly the shape you would expect from a spherical object. Of equal significance was the fact that everyone could see that the Moon itself was round, suggesting that the sphere was the natural state of being, adding even more ammunition to the round Earth hypothesis. Everything began to make sense, including the writings of the Greek historian and traveller Herodotus, who told of people in the far north who slept for half the year. If the Earth was spherical, then different parts of the globe would be illuminated in different ways according to their latitude, which naturally gave rise