 This structure built some 12,000 years ago – that's 6,000 years before Stonehenge, 5,000 years before the first pyramid – highlights that for millennia, humans have used the engineering method to solve problems long before the rise of science. In this video, I define and illustrate the essence of the engineering method. This is called Bekle Tepa, an ancient ruin in southeastern Turkey. Stone structures cover 9 hectares, about 18-foot ball fields. Filled with circular rooms, its purpose remains a mystery. Embedded in the stone walls of the rooms are decorative T-shaped pillars. Carved into the pillars are lions, bears, wild boars, lizards, spiders, and surprisingly, ducks. Not only are the stones beautifully carved, they are placed with precision. To see the degree of precision, look at the circular room I showed you initially. At the center are the remains of two T-pillars the tops fell off long ago. If we look at this room from above – keep your eye on the two central pillars highlighted in red – you see two circular rooms nearby, which each have the same arrangement of pillars at their center. The pillars in the two rooms at the bottom sit on a line, with little deviation. If we locate the exact centers between the pillars and the two lower circles, and connect them to the center of pillars in the circle above, we inscribe an equilateral tricle. Its sides deviate less than 1.5% from perfection. This is unlikely to be coincidental, nor the result of some self-organization. My point is that these stones are erected in a purposefully designed layout, not haphazard, that responds to societal needs, which means that Gobekli Tepa is an engineered object. The people of Gobekli Tepa created all this by applying the engineering method. The method we still use today, yet this powerful method, the engineering method, is an all-but-hidden process that few of us have heard of but alone understand, even though it influences every aspect of our lives. In this video series, I explore the essence of that engineering method. The age of Gobekli Tepa highlights that the engineering method long predates science, which conflicts with a commonplace notion that engineering somehow arises from the scientific method. So I start by asking, do engineers need science? And here's the answer. This is a model of Saint-Chapelle, a stunning 13th-century building built nearly 12,000 years after Gobekli Tepa. Saint-Chapelle was designed and constructed by a team who had never learned basic arithmetic or the geometry taught today in third grade that alone anything we'd call science. In fact, they had no standardized length because a foot varied from region to region. The medieval engineers aspired to create a building that celebrated a spiritual world by streaming light through the structure's walls. Sunlight was transformed by the stained glass windows into a diffuse red, blue, and gold that glimmers on the chapel sculptures and gilded arches. To create these stunning displays of light, to house these giant stained glass windows, they built vast walls by constructing spectacularly high ceilings. How did these engineers, called masons, know how to carve a cathedral's thousands of building blocks to create when assembled not only beauty, but also stability? Like all great engineers, they drew on past knowledge. They used an architectural element that originated in present-day Pakistan. Notice that Saint-Chapelle has, as do all cathedrals, pointed arches, some six on the front, at least ten on each side, and on the back six more. And of course, many pointed arches support the ceiling. They chose this pointed arch over the arch used in the Roman's extraordinary pantheon, built about 1,400 years before Saint-Chapelle. The pantheon, typical of all imperial Roman architecture, features a semi-circular arch. It is exactly half of a circle. If a medieval engineer used a semi-circular Roman arch to construct a soaring cathedral, it would cover entire city blocks and use so much stone that the cost would skyrocket. The savings from using a pointed arch instead of a semi-circular arch can be seen clearly by comparing Saint-Chapelle with the pantheon. Note how Saint-Chapelle is nearly the same height as the pantheon, yet just a little over a third is wide. This Roman semi-circular arch was rejected by medieval engineers because its width has to grow proportionally to its height. To see the problem, consider a semi-circular arch that is ten meters in width. It is five meters in height because it's half of a circle. So its height is half of the diameter. Now, if I double the span covered from ten meters to twenty meters, you see that the height is now ten meters. It has doubled. Contrast this to the pointed arch. As the arch increases in height, the span covered can stay the same because the shape of the arch can change as its height increases. Although medieval engineers didn't adopt the Roman semi-circular arch, from the Romans they inherited the key idea that enabled them to build their stunning cathedrals that have stood for centuries. We can see it in this arch from Saint-Chapelle. To support this arch, the medieval engineers had to correctly size the thickness of this wall. If this wall were too thin, the weight of the arch would buckle the wall, the structure would collapse. If too thick, stone would be wasted at a huge cost and the desired open space inside the cathedral diminished. To size the wall, the medieval builder used a rule that created the stable semi-circular arches of the pantheon. A stable arch results when the supporting wall's thickness is between a fourth or a fifth of the arch's span. If an arch's span were this long, then you divide it into about four equal parts and use one of these to size the wall's thickness. But there's a problem with applying this proportional rule. The Mason's knew no mathematics, nor, as I've said, they even have a ruler. So this rule was not a calculation, but was instead an action. The Mason would have a life-size chalk drawing of the interior of this arch on the floor of the drawing room. No. Instead, I've drawn the interior of a pointed arch on a large sheet of paper. In addition to this arch drawing or template, he needed a piece of string the Mason would have used to rope. I need to drape it over the arch, so I'll insert map pins along the arch to support the string. The Mason would have done this on the floor, so he would simply lay the rope on top of his drawing. Now, drape the rope over the arch, mark the string at the base of the arch, then cut the string so it's only as long as the arch. Next, lay the string on the ground and fold it into thirds. I've marked the thirds with pink tape here the Mason would have used colored chalk. That thirds isn't obvious, but it will get us to a wall thickness of about a fourth or a fifth. With the rope now marked into three sections of equal length, return it to its original place along the arch template. We see that this divides the arch into three equal sections. Let's mark one of them. Then pin one end of a new string to that marked spot. Draw a taut and pin it to the base of the arch. We need to attach to the base a length of string exactly equal to the distance from the spot a third of the way along the arch to the base, so I just fold the rope and mark it. And then draw that taut and in a straight line with the pin section. Then pin it to the base. The distance from that pin to the inner line is the width of the wall, which will be between a fourth and a fifth of the arch's span. Let's compare it to the arch section from Saint-Chapelle. If I superimpose it on the string construction, you can see that it matches. It's puzzling that we divided the arch into three sections, which yield a width between a fourth and a fifth, but that's just how the geometry works out. That's part of the rule. I've never worked out why geometrically that works because it doesn't matter. The Mason would never have worked it out analytically. What matters, and that's the point here, is that it works. And to belabor the point a bit, it's the same rule the Romans used to size their supporting walls. Divide the interior of a Roman semi-circular arch into three equal size sections, draw a line from one of these third markings to the base of the arch, then double it, and you see the wall size of a bit less than a fourth of the interior arch's span. With that rule, we've arrived at the core of the engineering method. The proportional rule doesn't come from some scientific analysis of stone and its properties. It comes from centuries of experience, from trial and error. It's called a rule of thumb, more formally a heuristic. An imprecise method used as a shortcut to find the solution to a problem, often by narrowing the range of possible solutions. Here, a Mason sized the walls width in a matter of minutes without understanding the fundamental material properties of stone and without understanding the mathematics needed to apply the rule. That's a paradigm for the engineering method. 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 offer a high probability of success but no guarantee. 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 900 years is proof of that. Instead of being disproved, this rule of thumb for stone became outdated, not wrong, as iron and steel I-beams replace stone. Yet no doubt there's a question in your mind. I've talked about buildings constructed to eight or so centuries ago. So surely you might wonder, is engineering based on rules of thumb antiquated in our scientific age? That line of thought misunderstands the purpose of the engineering method, which is to solve practical problems before we have full scientific knowledge. In the next video, I'll explore how engineers work their way around that lack of scientific understanding, how they overcome uncertainty. I'm Bill Hammack, The Engineer Guy.