Comments by "EebstertheGreat" (@EebstertheGreat) on "The Coin Hexagon - Numberphile" video.

The verse is actually about the vanity of human ingenuity.
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The author of Ecclesiastes lived in a time when they did not know that things had not always been that way. However, as he was familiar with the Torah and seemed to mostly believe it, I don't think he literally meant that everything had been happening for eternity. He did talk about a beginning and an end. This verse is just part of a much longer dialogue about futility and mortality. The book moves from despair to a conclusion that resembles absurdism in some ways, accepting the finality of death and lack of clear meaning in life with a degree of grace. It's an interesting book, albeit pretty tedious, but it's rather out of place as a book of scripture.
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A mathematically rigorous equivalent to the puzzle would be something like: "Given six unit circles in the coordinate plane in the given arrangement, transform them into the target arrangement [these arrangement could be specified by the coordinates of the circles' centers relative to an arbitrary origin] by translating three circles with the following restrictions: 1. the centers of the translated circle in the preimage and image of each translation are connected by a curve in the plane no point of which is a distance of less than 2 from the center of any other circle. 2. The translated circle is tangent to two other given circles.
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I'm not sure the Teacher believed "learning from the past" was really possible. He denounced the wisdom of reading too many books and indicated that there was not much humans could do to deter them from their cyclic path.He thought that attempting to do so was the "vanity of vanities."
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"Turn! Turn! Turn!" was written by Pete Seeger, not The Byrds (though they have the most famous cover). And it's a decent anti-war song, although I'm not sure its interpretation of the lyrics would make a lot of sense in the context of the original book.
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