Andy has done a great job of showing why circumscribing a square around a circle is very easy as long as you have some basic tools and know-how. Hancock is obviously very wrong about the need for special advanced mathematical skills or Atlantean earth-wisdom to construct such a shape; hence, the circle-in-square pattern is seen in earthworks in both the Amazon and Ohio because it is a pretty straightforward construction.
To this, I’d like to add that Hancock’s misunderstanding isn’t just a goof up in terminology. Squaring the circle has had a distinct mystical and hermetic connotation for centuries, and Hancock’s use of the term is meant to tie the Amazonian and Ohio earthworks to the “secret” wisdom tradition of Hermeticism, which in Magicians of the Gods Hancock had traced (falsely) to Atlantis.
Basically, the real squaring of the circle is the futile effort to create a square with the same area as a given circle using a finite number of steps and only a compass and a straight edge. The Greeks and the medieval people wasted a great deal of effort looking for a solution, but in 1882, proof that pi is a transcendental number demonstrated that it was impossible to square the circle, for reasons that are too mathematically complex to summarize in a sentence. Look it up if you’d like, but all we need to know here is that squaring the circle isn’t possible.
At various points in history, squaring the circle had been considered a goal of hermeticism and alchemy, and also an important factor in the calculation of longitude (even though, in reality, it wasn’t). Hermeticism held that the squared circle represented the essential salts that held the wisdom of the soul, and some variants see it also as a map of paradise, for it combined the circular symbol of heaven and the square symbol of Earth. The philosopher’s stone, according to hermetic alchemists, was said to be a circle inscribed in a square inscribed in a triangle inscribed in a larger circle.
Hancock clearly has these sorts of ideas in mind when he speaks in awe of an earthwork with a square surrounding a circle. Since European mysticism holds it to symbolize the union of heaven and earth, the spiritual and the material, he is naturally drawn to it since his current philosophy revolves around shamanic efforts to connect the spiritual and the material. By misrepresenting a geometric construction as a mathematical secret, he hopes to imply the existence of a lost spiritual stream that doesn’t actually exist.
I am an author and researcher focusing on pop culture, science, and history. Bylines: New Republic, Slate, etc. There's more about me in the About Jason tab.
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