Tuesday, August 4, 2009

Thinking Like a (Pagan) Scientist, Part Un

More than 20 centuries ago it was well known that the earth is a sphere. In fact, Cicero, in his famous Dream of Scipio, written in 51 BC, describes the polar, equatorial and temperate climate bands that circle the earth. Figure 1 to the right is an illustration from Macrobius' sixth century AD Commentary on the Dream of Scipio.

Isaac Asimov's classic essay How Did We Find Out Earth Is Round? gives an excellent overview of how ancient people were able to arrive at the conclusion that the earth is a sphere (click here to download a pdf of the essay).

In addition to knowing that the earth is a sphere, it was also known, in theory, how to calculate the size of the earth, in particular its circumference. Scientists even knew (again, at least in theory) how to also calculate the size of the moon, the distance between the earth and the moon and the distance between the earth and the sun.

There was a very basic problem, though, facing ancient scientists. In fact the same problem is ever present in any scientific investigation: all measurements involve some non-zero amount of error. The amount of error, or uncertainty, in the raw data is then "propagated" as that data is used as the basis for calculations. Eratosthenes (see below) is often credited as the first person to calcluate the earth's circumference, but he did not directly measure how big around the earth is using some gigantic tape measure - obviously. Rather he took three measurements (see Figure 2 to the right and below), and used these to do his calculation.

In fact, the results that ancient scientists arrived at were often not that bad. For example, Eratosthenes of Alexandria (c. 276 - c. 195 BC) calculated the circumference of the earth to be about 25,000 miles, which is extremely accurate. But over 100 years later, Posidonius of Rhodes (c. 135 BC - 51 BC) concluded from his measurements and calculations that the earth's circumference is actually about 18,000 miles, and then about 200 years after the famed scientist Ptolemy (90 – 168 AD) (another Alexandrian) concurred with Posidonius.

Erroneous estimates of the earth's circumference (based in large part on those of Posidonius and Ptolemy) that significantly underestimated the size of the earth were what led Christopher Columbus to believe he could sail to the "Indies"!

It is essential to appreciate that ancient scientists were absolutely correct in their fundamentals: they understood the shape of the earth, and they understood in theory how to calculate it's size. In other words they knew how to (1) take observations of the natural world, (2) draw conclusions from those observation in the form of mathematical relationships, and (3) conduct experiments based on those mathematical relationships. Let's look at each of those one at a time in a little more detail.

(1) Reproducible observations. The spherical shape of the earth is readily observable to those who spend time on the open seas. Objects "disappear over the edge" of the sea as they move away from an observer. The higher up the observer is, the further away the "edge" appears to be. But in addition to this observable property of the earth, Eratosthenes, Posidonius and Ptolemy also relied on observations of the relative position of the sun in the sky and how it varies with latitude, as well as on observations of the positions of fixed stars in the sky at different locations at different time. These other observations (of the sun and stars) also played a key role in their experiments.

(2) Mathematical relationships. If the earth is a sphere then all of the known geometrical properties of a sphere hold for the earth. That is, an abstract sphere provides a "mathematical model" for (the shape of) the earth. Also, the earth and the sun, or the earth and one or more fixed stars, can be represented as so many spheres and points suspended in space, and the geometrical relationships between those abstract spheres and points will be the same as those between the actual earth, sun and stars.

(3) Conducting experiments. Based on the abstract geometrical relationships above, practical experiments can be conducted such as the famous one done by Eratosthenes, who simply measured the length of the shadow cast by an obelisk at noon on the day of the summer solstice. With the length of the shadow and the height of the obelisk in hand all he needed was the distance between the obelisk and the earth's equator, which had already been measured. Although he did not use trigonometry, he had methods of doing the same kind of calculations as those implied in Figure 2 above.

Ptolemy, by the way, was also one of the most important Astrologers of the ancient world. In his Tetrabiblos he strove to present Astrology in a way that was "philosophically fitting". Like most philosophically minded Astrologers, Ptolemy was an adherent of the Stoic school, which not only provided the philosophy of choice for Astrologers but also simultaneously "invented astrophysics, for they believed, as we do, that the same physical laws applied throughout the universe." [A History of Western Astrology, S. Jim Tester, pp. 68-9]

Posidonius, for his part, was one of the greatest polymaths of all times, with published works on Astronomy, Geology, Philosophy, Mathematics, History, Meteorology, and Miltary Science. He is often credited as the originator of the Stoic theory of sumpatheia (see especially Karl Reinhardt's Posidonius: Kosmos und Sympathie). Posidonius was a pivotal figure in the history of ancient philosophy. He lived during a time when there was ever increasing "eclecticism", and he himself especially blurred the distinctions between Pythagoreanism, Platonism and Stoicism in a way that was very similar to, and possibly directly influenced, the late antique school of Plotinus and his famous intellectual descendants (especially Porphyry, Iamblichus, Julian and Proclus).

Eratosthenes' was the third person appointed as head of the Library of Alexandria which was simultaneously a center of scientific research and also a religious institution, as part of the larger Musaeum ("Temple of the Muses"), which was run by a head priest appointed by the king, Ptolemy III Euergetes, who also appointed Eratosthenes to his position. Eratosthenes studied philosophy with the famous Ariston of Chios, and may have also studied with Zeno of Citium, the founder of the Stoic school.

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