The Unity of Mathematics, Philosophy, Art, Science & Religion

Mathematics has always been something I’ve found fascinating. Even more so when I think about all the theories and ideas that were formulated centuries ago, and how most can be applied to any matter in our observable universe. I wanted to talk about one of those in this blog post.

The Vitruvian Man

Before I started this blog, I had very little knowledge of the Vitruvian Man. What I knew about it was limited to two things: it is one of Da Vinci’s most famous works, and it played a significant role in Dan Brown’s bestseller, The Da Vinci Code (which happens to be one of my favourite books). However, it is an intriguing idea and piece of work, especially because it isn’t just ink on paper, or just art, as I came to understand.

I did some reading to find out more about why this is such a significant piece of work, and it did not fail to leave me in awe.

Da Vinci’s Vitruvian Man is based around an existing mathematical problem: squaring a circle. The methods of finding the area of a circle and of a square are known, but how would you use the area of the circle to create a square with an equal area? This isn’t mathematically possibly yet Da Vinci was able to metaphorically solve this problem using the works of Marcus Vitruvius, a Roman architect.

Vitruvius stated in his work that the naval is the center of the human body, and a compass centered at the naval will allow you to draw a perfect circle around the body. The fingers and toes at the end of the outstretched limbs will touch the circumference of this circle. He also claimed that “just as the human body yields a circular outline, so too a square figure may be found from it” as the span of the outstretched arms was always as wide as the body was tall.  This is the mathematical approach of this famous piece, which Da Vinci was able to fabricate into a drawing. By using the human body as the area, instead of the area of the circle and square, he was able to metaphorically solve the problem of squaring a circle. But the creative genius doesn’t stop there.

Instead he searched for connections between this idealised representation of the human body and nature, and found the Mathematical proportions calculated using
the Vitruvian Man to be present in the universe around us. Da Vinci’s idea was carried forward by neoplatonic-chain-of-beingGiovanni Picco Dela Mirandola, who claimed that, contrary to prior Neoplatonic ideologies of humans being perfectly in the center in a hierarchical system of the universe (due to having a mortal body and immortal soul), “humans have the unique ability to take any position they want”. The Vitruvian man and the idea behind this, he states, is a visual representation of how humans are neither god-like nor animalistic, but can be whatever form we opt to take, placing us at the center of the universe. I think this is supported by the fact that despite only being two bodies, the limbs in the drawing can be arranged into 16 different positions.

‘Mankind can fill whatever shape he pleases geometrically and philosophically.’

I think that is what makes this piece of work so valuable and unique. One ideology is able to bridge multiple perspectives of the universe – artistic, religious, mathematical, scientific, philosophical. The way it is interpreted depends on the person analysing it, but it has all been combined into one work of art. In a world where there are so many disagreements between the different beliefs and prospects, the idea behind this simple sketch is one that can be agreed upon.

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