The Mathematics of Beauty
The Mathematics of Beauty
Golden ratios & sacred geometry
The secret weapon of any good cathedral architect is mathematics. Math is what guides the shape and placement of walls, columns, and buttresses, and what allows stone walls to leap to new heights.
But even more importantly, math imbues the sacred place with a sense of awe and wonder that transcends stone and wood. Mathematical harmony touches us with a sense of otherworldly calm, creating a connection between architectural design and divine inspiration.
Medieval stonemasons, fueled by passion and creativity, used sacred geometry passed down from the classical world and took it further than ever before.
Here’s how cathedrals incarnate this ancient tradition of spiritual architecture, and how it continues to define beautiful spaces today…
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A Coherent Cosmos
The geometry of cathedrals begins in an unexpected place: nature. From galaxies to spiral shells, the natural world teems with intricate, yet orderly, shapes.
One reason that nature has such a calming effect on the human mind is its mathematical order, which creates a sense of predictability, proportionality, and hierarchy even in the diversity of zoological and geological wonders of the world.
For example, the Fibonacci sequence — a set of numbers created by adding the previous two numbers in the sequence together — can be represented as the Fibonacci spiral. This spiral famously describes innumerable shapes in the natural world, including the swirl of galaxies and storm clouds, the spiral of a seashell, and the curve of breaking waves. The mathematical harmony hidden in these natural wonders gives them the wordless aesthetic appeal that we associate with the beauty of nature.
Closely related to the Fibonacci sequence is the Golden Ratio. Known as the “most irrational number,” defying all attempts to represent it in terms of whole numbers, the Golden Ratio is usually abbreviated to 1.618 (or represented as φ, the Greek letter phi). The Golden Ratio also abounds in nature, from pinecones to DNA sequences, but is especially relevant to geometry, building, and art.
Medieval masons saw these patterns as evidence of the order that God ordained as He created the world. Sacred icons from this time depict God Himself using mathematical tools to design the cosmos, demonstrating the divinely-ordained logic of the universe.
When it came to building their own monuments to the faith, cathedral architects reflected this belief by designing buildings based on the same mathematically coherent principles. In the words of historian Georges Duby, they turned their architecture into “applied theology”, making the unseen world visible in blocks of stone.
From Temples to Twitter
But medieval architects were far from the first to notice the patterns of the natural world and incorporate them into sacred architecture.
The quasi-mythical polymath Pythagoras is the first known mathematician to connect numerical patterns to the natural world. He and his followers set out to describe reality in terms of intelligible, rational numerical relationships, and an apocryphal legend holds that when they realized the Golden Ratio was irrational, they threw the ratio’s discoverer into the sea.
Pythagoras also connected numbers to the divine. He assigned spiritual significance to many numbers, making math and architecture a metaphysical endeavor, which medieval Europeans would later build upon. For Pythagoras, the Golden Ratio was the perfect combination of mathematics and nature, order and chaos, beauty and rationality.
It’s unsurprising then that the Golden Ratio then came to define ancient Greece’s greatest temple, the Parthenon. The size of its columns, the locations of its statues, and even its overall dimensions are based on the Golden Ratio, creating a structure that embodies both harmony and strength.
Almost a millennium later, this early example of sacred geometry profoundly influenced the Western world. At the same time Medieval architects began to turn their attention to the question of how to build spectacular cathedrals, the channels of cultural communication between the East and West re-opened. Crusaders journeying to Constantinople and Jerusalem brought back the forgotten knowledge of Greek thinkers. Once again, Western architects built their structures upon the Golden Ratio and other mathematical patterns, to great effect.
These numerological harmonies would go on to create the magnetic harmony in virtually all Renaissance paintings, sculptures, and architecture — but they also persist into the modern world, where the Golden Ratio defines even the iconic chirping bird of the Twitter logo.
Most noticeably, however, all of these ratios undergird the West’s most dramatic works of art: cathedrals…