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

[Music] this structure built some 12 000 years ago that six thousand 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 Beckley Tepper an ancient ruin in Southeastern turkey stone structures cover nine hectares about 18 football 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 that 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 triangle its sides deviate less than 1.5 percent 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 Hazard that responds to societal needs which means the 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 orbit hidden process that few of us have heard of that 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 San Chapelle a stunning 13th century building built nearly 12 000 years after Gobekli tepa San Chappelle was designed and constructed by a team who had never learned basic arithmetic or the geometry taught today in third grade let 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's 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 do these Engineers called Masons know how to carve a Cathedral of thousands of building blocks to create when assembled not only Beauty but also stability like all great Engineers they draw and past knowledge they used an architectural element that originated in present-day Pakistan notice that San Chapel has as to all cathedrals pointed arches some six on the front at least 10 on each side and on the back six more and of course many pointed archers support the ceiling they chose this pointed Arch over the arch used in the Romans extraordinary Pantheon built about 1400 years before Saint Chapel 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 semicircular 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 sent Chappelle with the pantheon note how Central pill is nearly the same height as the pantheon get 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 10 meters in width it is 5 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 10 meters to 20 meters you see that the height is now 10 meters it is 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 semicircular 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 San Chappelle 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 arches his band 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 new 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 now instead I've drawn the interior of appointed Arch on a large sheet of paper in addition to this Arch drawing or template you need a piece of string the Mason would have used a rope I need to drape it over the arch so I'll insert map pins along the arch to support the string Mason would have done this on the floor so you 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 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 pen 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 arts section from San Chappelle 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 use to size their supporting walls divide the interior of a Roman semicircular 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 arches 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 in its properties it comes from centuries of experience from trial and error it's called the 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 signs 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 nine hundred 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 building this constructed 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 hammock the engineer guy [Music] foreign

Channel: engineerguy

Views: 733,767

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Id: _ivqWN4L3zU

Length: 11min 54sec (714 seconds)

Published: Tue May 09 2023