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I love reviewing books - have been doing it at Goodreads, but considering moving here.

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Epistemic Dimensions of Personhood

Pattern Recognition and Machine Learning (Information Science and Statistics)

Relativity, Thermodynamics and Cosmology

The Cambridge Handbook of Second Language Acquisition

As other people here have pointed out, the title is misleading. Sir Thomas Heath, an eminent scholar of classical science, published it in 1913. He says his original goal was to provide an English translation of Aristarchus's Greek text describing his method for measuring the distance to the sun; but the project grew considerably, and in the end Heath wrote a history of all Greek astronomy up to Aristarchus (third century B.C.), with several notes about what happened later on.

When I started the book, I didn't know a great deal about the Greek astronomers. I had read Koestler's thoughts in the first few chapters of*The Sleepwalkers*, Laplace's terse but rather good summary in *Exposition du systÃ¨me du monde* and various bits and pieces in other books. It was interesting to see a proper treatment. From our modern perspective, it is easy to fall into the trap of mocking these early scientists and pointing out all the things that they got wrong. (Koestler, who claims to have read Heath, is a particularly flagrant offender). I thought Heath's exposition was far more balanced, and gave a nice feeling for how people progressed towards addressing more and more difficult questions. At the beginning, the questions are perhaps on the ridiculous side. Where does the sun go after it sets in the West? Does it slide down underneath the world, or go around the side, and come up again in the East next day? Or maybe a new sun is created every morning? This idea was, apparently, suggested in all seriousness.

But astronomers looked carefully at the motions of the heavenly bodies and refined their picture. It was impossible to explain the phases of the Moon, or the facts about lunar and solar eclipses, without coming to the conclusion that the Earth and the Moon, at least, are spherical. The motions of the planets, which at first seemed to be more or less random, were carefully analysed, so that specific issues could be addressed. Why do Mercury and Venus always appear near the sun? Why do planets start moving in one direction, then turn around and move the other way for a bit?

There were two people in particular who impressed me. The first was Eudoxus, a student of Plato and one of the great mathematicians of his time. Koestler is rather dismissive of Eudoxus, as far as I can see just because his theories turned out to be wrong. To me, this seems like a gross misunderstanding of how science works. When Eudoxus came in, the state of the art was Plato's handwavy poeticising. Eudoxus had the brilliant idea of developing a quantitative mathematical model, superimposing multiple rotations and rigorously demonstrating that their composition could indeed produce motions which first went in one direction and then in the opposite one; Heath gives a detailed description of how this theory was reconstructed by Schiaparelli in the late 19th century. Eudoxus's model was incorrect, though it did fit the data for some of the planets quite well; but he had moved the debate to a completely new level.

The other person I admired was Aristarchus, the person the book is nominally about. Even from a twenty-first century point of view, you feel that his method for determining the distance to the sun is very elegant. In fact, there were four unknown quantities he wished to determine: the radius of the moon, the distance to the moon, the radius of the sun and the distance to the sun. (He already knew the radius of the Earth, which had been accurately estimated by Eratosthenes). He considers the geometrical relationships between these various quantities in three situations: a total solar eclipse, a total lunar eclipse, and the "dichotomy", the point in the lunar cycle where the moon is exactly half full, and the sun, earth and moon thus form a right-angled triangle. These give a set of simultaneous equations, which can be solved to give all the figures at once. Today, his whole argument can be condensed to less than a page (there is a nice presentation here). When Aristarchus did it, though, people hadn't even discovered trigonometry: he had to invent the necessary methods as he went along. He was an extraordinarily smart guy.

The book is not always an easy read, especially for people like me who don't know Greek, and some parts are, to be honest, a little dull. But Heath writes well, and his love of the subject is infectious. He makes me want to know more about what science was like two thousand years ago.

When I started the book, I didn't know a great deal about the Greek astronomers. I had read Koestler's thoughts in the first few chapters of

But astronomers looked carefully at the motions of the heavenly bodies and refined their picture. It was impossible to explain the phases of the Moon, or the facts about lunar and solar eclipses, without coming to the conclusion that the Earth and the Moon, at least, are spherical. The motions of the planets, which at first seemed to be more or less random, were carefully analysed, so that specific issues could be addressed. Why do Mercury and Venus always appear near the sun? Why do planets start moving in one direction, then turn around and move the other way for a bit?

There were two people in particular who impressed me. The first was Eudoxus, a student of Plato and one of the great mathematicians of his time. Koestler is rather dismissive of Eudoxus, as far as I can see just because his theories turned out to be wrong. To me, this seems like a gross misunderstanding of how science works. When Eudoxus came in, the state of the art was Plato's handwavy poeticising. Eudoxus had the brilliant idea of developing a quantitative mathematical model, superimposing multiple rotations and rigorously demonstrating that their composition could indeed produce motions which first went in one direction and then in the opposite one; Heath gives a detailed description of how this theory was reconstructed by Schiaparelli in the late 19th century. Eudoxus's model was incorrect, though it did fit the data for some of the planets quite well; but he had moved the debate to a completely new level.

The other person I admired was Aristarchus, the person the book is nominally about. Even from a twenty-first century point of view, you feel that his method for determining the distance to the sun is very elegant. In fact, there were four unknown quantities he wished to determine: the radius of the moon, the distance to the moon, the radius of the sun and the distance to the sun. (He already knew the radius of the Earth, which had been accurately estimated by Eratosthenes). He considers the geometrical relationships between these various quantities in three situations: a total solar eclipse, a total lunar eclipse, and the "dichotomy", the point in the lunar cycle where the moon is exactly half full, and the sun, earth and moon thus form a right-angled triangle. These give a set of simultaneous equations, which can be solved to give all the figures at once. Today, his whole argument can be condensed to less than a page (there is a nice presentation here). When Aristarchus did it, though, people hadn't even discovered trigonometry: he had to invent the necessary methods as he went along. He was an extraordinarily smart guy.

The book is not always an easy read, especially for people like me who don't know Greek, and some parts are, to be honest, a little dull. But Heath writes well, and his love of the subject is infectious. He makes me want to know more about what science was like two thousand years ago.