Building a Cathedral without Science or Mathematics: The Engineering Method Explained

Bill reveals the long-lost methods used by Medieval engineers to design stone cathedrals. Methods that required no science, mathematics, or literacy, yet which reveal the engineering method.

*Learn More: Companion Book*
Explore the ideas in this video series further with its companion book: _The Things We Make: The Unknown History of Invention from Cathedrals to Soda Cans_ (ISBN 978-1728215754)

*Other Videos in this Series*
_Episode 2:_ Controlling Turbulence and Evolution: How Engineers Overcome Uncertainty
_Episode 3:_ The Steam Turbine: The Surprising Relationship of Engineering & Science
_Episode 4:_ The Microwave Oven Magnetron: What an Engineer Means by “Best”

*Video Summary*
0:00 Titles

0:07 Intro
In this first video of the series Bill notes that the engineering method is among the the oldest of human responses to fulfill human needs.

0:28 Göbekli Tepe
Bill illustrates this with a brief discussion of the ruins of Göbekli Tepe, a stone structure in southeastern Turkey built thousands of years before Stonehenge and the pyramids. A structure whose use and purpose remains mysterious. The age of Göbekli Tepe highlights that engineering existed long before science — at least what we mean by “science” today.

0:56 Precision of Göbekli Tepe
The precision of the placement of the stones in the ruin and their manner of preparation indicate that it is an engineered object.

2:39 Do Engineers Need Science?
This leads to the question “Do engineers need science to create.” To answer that question Bill considers the design of Sainte-Chapelle — a stunning thirteenth century stone building. He notes that it was designed and built — as were all medieval cathedrals — by mason who knew no science, or mathematics and who could not even read, nor did they have a measuring stick.

3:13 Gothic Cathedrals: Light
The medieval engineers strive to build cathedrals that could house large stained glass windows that could let in sunlight.

3:54 Pointed Arches
Medieval masons used pointed arches in their cathedrals to create high ceilings.

4:16 Pointed vs Circular Arches
The pointed arch allowed mason to build higher ceiling using less stone, as clearly seen in comparing Sainte-Chapelle to the Pantheon in Rome.

5:00 Width Circular Arch
The width of the circular arch grows proportional to its height.

5:29 Width Pointed Arch
The width of a pointed arch doesn’t expand because the pointed arch changes shape as it grows taller.

5:39 Proportional Rule
Bill explains that these early engineers used a “rule of thumb” inherited from antiquity — one used to build Roman buildings like the Pantheon — to size the supporting walls underneath the arches. The rule was simple: The width of the supporting wall should be between a fifth and a fourth of the arch’s span.

6:51 How Medieval Engineers Sized Walls
These early engineers could not perform the mathematics needed to implement this rule, so, as Bill demonstrates, they turned this into an action that required no calculation or measurement with a marked rule.

9:06 Why Arch Divided into Three Section
As Bill notes, this is just how the geometry works out. It is the same rule as used to size the supporting wall for a semi-circular arch.

9:52 Rule of Thumb
A rule of thumb is the heart of the engineering method: it allowed the masons to build without understand at a deep level the properties of stone or knowing mathematics.

10:29 The Engineering Method
This is defined as “Solving problems using rules of thumb that cause the best change in a poorly understood situation using available resources.” That’s a sharp contrast with the scientific method, because these rules of thumb are only guides that offers a high probability of success, but no guarantee.

10:40 Rule of Thumb Never Disproved
And, unlike a scientific theory, a rule of thumb is never, in a sense, disproved. That hundreds of cathedrals are still around today, standing for eight or nine hundred years is proof. Instead of being disproved, this rule of thumb for stone became outdated, not wrong, as iron and steel I-beams replaced stone.

11:10 Do Engineers Still Use Rules of Thumb?
Bill considers the question “is engineering based on rules of thumb antiquated in our scientific age?” He notes that that line of thought misunderstands the purpose of the engineering method, which is to solve practical problem before we have full scientific knowledge.

11:33 Next Video
Bill notes that in the next video he’ll explore how engineers work their way around that lack of scientific understanding, how they overcome uncertainty.

11:45 End Titles

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