Squaring the Circle: Humans and Technology


Last weekend, I attended an herbalism lecture where the excellent Sam Perry spoke about Chinese medicine.

Sam focused on the relationship between culture and medicine. Medicine is a product of culture, like clothing, vases, and frescos.

He spoke about Chinese symbols, yin and yang, the tai chi symbol, the sinusoidal shape of the yellow river in china, and the color yellow, and then he offhandedly mentioned the circle in the square.

Squaring the Circle is an ancient paradox and hermetic symbol.

The problem is this:

Can we create a circle and a square with the SAME AREA with only a straight edge and a compass and use a limited number of steps?

The answer is NO. This was finally proved mathematically in 1882, so the mystery existed for a long time.

This problem had mystical dimensions. The circle in the square was used as a symbol for alchemy: transforming lead into gold. The circle in the square was also used to describe the relationship between spirit and matter.

Discrete Steps and Devices

The structure of this problem reminds me of computation. A universal turning machine, a type of computer, reads and writes symbols on a tape.

The theory of computation asks what we can solve and in what period with what physical limitations.

I wonder what is different between the computational engine of a hammer and nail and what is the computational engine of a straight edge and compass.

The Solution!

As it turns out, you can create a circle and a square with the same area, but just not with these tools and a discrete number of steps.

We can use new tools like the Quadratrix of Hippas (which I do not entirely understand), infinite steps, or non-euclidian geometry.

Can a circle turn into a square? What is the relationship between the shape of a thing and what the form contains?


How does the circle shape become the square without losing anything?

This is the mystery of transformation. Ancient myths like Ovid’s Metamorphoses tell how gods turn into trees and humans turn into animals. In China, the 64 hexagrams of the I-Ching describe different types of transformation. Alchemy is about transformation, lead into gold, the individuation of a person from a Jungian perspective.

Squaring the Circle is about tools and processes, about creating a machine for transformation. But there is a limit to the transformative power of a machine. What is this limit? The natural world, life, quantum physics, chance, or just more transformation?

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