Friday, October 16, 2015

Moon: Theaetetus

"Theaetetus crater 4103 h1 4103 h2" by James Stuby based on NASA image
Lunar Orbiter 4 photo via Commons
Theaetetus Crater
Theaetetus is a lunar impact crater that is located to the southeast of the crater Cassini near the eastern edge of Mare Imbrium. It lies just to the west of the Montes Caucasus range, which forms the eastern shore of the mare. To the southwest is the prominent crater Aristillus.
The rim of Theaetetus is distinctly polygonal in shape, with a slight rounding at the vertices. There is a low outer rampart and a slight central rise on the crater floor, which is offset to the northeast of the crater midpoint. The interior is otherwise relatively featureless.

This crater has been noted in the past as a site of possible transient lunar phenomena. In 1902, a white cloud was observed briefly in the vicinity of the crater. Other observers, including Patrick Moore and W. H. Pickering, have also noted unusual appearances in this area.

Theaetetus of Athens
Theaetetus of Athens (Greek: Θεαίτητος; c. 417 – 369 BC), possibly the son of Euphronius of the Athenian deme Sunium, was a Greek mathematician. His principal contributions were on irrational lengths, which was included in Book X of Euclid's Elements, and proving that there are precisely five regular convex polyhedra.  A friend of Socrates and Plato, he is the central character in Plato's eponymous Socratic dialogue.

Theaetetus, like Plato, was a student of the Greek mathematician Theodorus of Cyrene (5th century BC).  Cyrene was a prosperous Greek colony on the coast of North Africa, in what is now Libya, on the eastern end of the Gulf of Sidra. Theodorus had explored the theory of incommensurable quantities, and Theaetetus continued those studies with great enthusiasm; specifically, he classified various forms of irrational numbers according to the way they are expressed as square roots. This theory is presented in great detail in Book X of Euclid's Elements.

Accordingly, the name of this crater is unusual because Theaetetus was a mathematician but - as far as I know - is not related in any way to Astronomy like all the other Greek persons whose name is given to craters on the face of the Old Man Moon. Theaetetus of Athens is today famous mainly because of the dialogue with Socrates that was written by Plato c. 360 BC.
In this dialogue, Socrates and Theaetetus discuss three definitions of knowledge: knowledge as nothing but perception, knowledge as true judgment, and, finally, knowledge as a true judgment with an account. Each of these definitions is shown to be unsatisfactory.

Socrates declares Theaetetus will have benefited from discovering what he does not know, and that he may be better able to approach the topic in the future. The conversation ends with Socrates' announcement that he has to go to court to face a criminal indictment.

Excerpts from Wiki texts have been incorporated into the blog as kinds of abstracts for reader's convenience. By clicking the links much more can be learned about these subjects.

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