the irony of a man who turned gods into stones being persecuted by people who turned stones into gods.
Figure 3 Having estimated the size of the Moon, it is relatively easy to work out the distance to the Moon. First, you will notice that you can just block out the Moon with a fingertip at arms length. Therefore, it becomes clear that the ratio of a fingernail’s height to an arm’s length is roughly the same as the ratio of the Moon’s diameter to its distance from the Earth. An arm’s length is roughly a hundred times longer than a fingernail, so the distance to the Moon is roughly a hundred times its diameter.
In the third century BC, Aristarchus built on Anaxagoras’ idea. If moonshine was reflected sunshine, he argued, then the half Moon must occur when the Sun, Moon and Earth formed a right-angled triangle, as shown in Figure 4. Aristarchus measured the angle between the lines connecting the Earth to the Sun and Moon, and then used trigonometry to work out the ratio between the Earth—Moon and Earth—Sun distances. He measured the angle to be 87°, which meant that the Sun was roughly 20 times farther away than the Moon, and our previous calculation has already given us the distance to the Moon. In fact, the correct angle is 89.85°, and the Sun is 400 times further away than the Moon, so Aristarchus had clearly struggled to measure this angle accurately. Once again, accuracy is not the point: the Greeks had come up with a valid method, which was the key breakthrough, and better measuring tools would take future scientists closer to the true answer.
Figure 4 Aristarchus argued that it was possible to estimate the distance to the Sun using the fact that the Earth, Moon and Sun form a right-angled triangle when the Moon is at its half phase. At half Moon he measured the angle shown in the diagram. Simple trigonometry and the known Earth-Moon distance can then be used to determine the Earth-Sun distance.
Finally, deducing the size of the Sun is obvious, because it is a well-established fact that the Moon fits almost perfectly over the Sun during a solar eclipse. Therefore, the ratio of the Sun’s diameter to the Sun’s distance from the Earth must be the same as the ratio of the Moon’s diameter to the Moon’s distance from the Earth, as shown in Figure 5. We already know the Moon’s diameter and its distance from the Earth, and we also know the Sun’s distance from the Earth, so the Sun’s diameter is easy to calculate. This method is identical to the one illustrated in Figure 3, whereby the distance to and height of our fingernail was used to measure the distance to the Moon, except that now the Moon has taken the place of our fingernail as an object of known size and distance.
The amazing achievements of Eratosthenes, Aristarchus and Anaxagoras illustrate the advances in scientific thinking that were taking place in ancient Greece, because their measurements of the universe relied on logic, mathematics, observation and measurement. But do the Greeks really deserve all the credit for laying the foundations of science? After all, what about the Babylonians, who were great practical astronomers, making thousands of detailed observations? It is generally agreed by philosophers and historians of science that the Babylonians were not true scientists, because they were still content with a universe guided by gods and explained with myths. In any case, collecting hundreds of measurements and listing endless stellar and planetary positions was trivial compared with genuine science, which has the glorious ambition of trying to explain such observations by understanding the underlying nature of the universe. As the French mathematician and philosopher of science Henri Poincaré rightly declared: ‘Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.’
Figure 5 It is possible to estimate the size of the Sun, once we know its distance. One approach is to use a total solar eclipse and our knowledge of the Moon’s distance and diameter. A total solar eclipse is visible only from a small patch on the Earth’s surface at any given time, because the Sun and the Moon appear almost the same size when viewed from the Earth. This diagram (not to scale) shows how an eclipse observer on the Earth is at the apex of two similar triangles. The first triangle stretches to the Moon, and the second triangle to the Sun. Knowing the distances to the Moon and to the Sun and knowing the diameter of the Moon is enough to deduce the diameter of the Sun.
If the Babylonians were not the first proto-scientists, then what about the Egyptians? The Great Pyramid of Cheops predates the Parthenon by two thousand years, and the Egyptians were certainly far in advance of the Greeks in terms of their development of weighing scales, cosmetics, inks, wooden locks, candles and many other inventions. These, however, are examples of technology, not science. Technology is a practical activity, as demonstrated by the Egyptian examples already given, which helped to facilitate death rituals, trading, beautification, writing, protection and illumination. In short, technology is all about making life (and death) more comfortable, while science is simply an effort to understand the world. Scientists are driven by curiosity, rather than comfort or utility.
Although scientists and technologists have very different goals, science and technology are frequently confused as being one and the same, probably because scientific discoveries often lead to technological breakthroughs. For example, scientists spent decades making discoveries about electricity, which technologists then used to invent light bulbs and many other devices. In ancient times, however, technology grew without the benefit of science, so the Egyptians could be successful technologists without having any grasp of science. When they brewed beer, they were interested in the technological methods and the results, but not why or how one material was being transformed into another. They had no inkling of the underlying chemical or biochemical mechanisms at work.
So, the Egyptians were technologists, not scientists, whereas Eratosthenes and his colleagues were scientists, not technologists. The intentions of the Greek scientists were identical to those described two thousand years later by Henri Poincaré:
The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Of course I do not here speak of that beauty that strikes the senses, the beauty of qualities and appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmonious order of the parts, and which a pure intelligence can grasp.
In summary, the Greeks had shown how knowing the diameter of the Sun depends on knowing the distance to the Sun, which depends on knowing the distance to the Moon, which depends on knowing the diameter of the Moon, which depends on knowing the diameter of the Earth, and that was Eratosthenes’ great breakthrough. These distance and diameter stepping stones were made possible by exploiting a deep vertical well on the Tropic of Cancer, the Earth’s shadow cast upon the Moon, the fact that the Sun, Earth and Moon form a right angle at half Moon, and the observation that the Moon fits perfectly over the Sun during a solar eclipse. Throw in some assumptions, such as moonlight being nothing more than reflected sunlight, and a framework of scientific logic takes shape. This architecture of scientific logic has an inherent beauty which emerges from how various arguments fit together, how several measurements interlock with one another, and how different theories are suddenly introduced to add strength to the edifice.
Having completed their initial phase of measurement, the astronomers of ancient Greece were now ready to examine the motions of the Sun, Moon and planets. They were about to create a dynamic model of the universe in an attempt to discern the interplay between the various celestial bodies. It would be the next step on the road to a deeper understanding of the universe.
Circles within Circles
Our most distant ancestors studied the sky in detail, whether it was to predict changes in the weather, keep track of time or measure direction. Every day they watched the Sun cross the sky, and every night they watched the procession of stars that followed in its wake.