My tutor said that prior to the understanding of these curves as models for arches, domes etc.. architects and engineers were pretty much just guessing and using the trial and error of previous completed works that were still standing. Which makes all the ancient architecture even more impressive.
I remember that trial and error was taught in mathematics. Before we’d get into the elegant calculations, we’d have to guess with trial and error, inelegant, calculations. 😍
Yeah. Even with the ancient pyramids there were a lot of failed pyramids before they got good at making pyramids. Some of them still survive today with the awkward stopgap measures they installed
What I though this was about: Flipping the model upside down, to give a better perspective on details you'd miss by seeing it right-side up. What I got: An important engineering lesson.
@@confuseatronica my good friend used to teach upside down drawing and painting. It was always cool to see the students faces when they flip their own drawing over and realize how good it is
That's interesting. It's exactly what I've been doing to design space ships in games The perspective shift made them end up feeling much more like space- rather than sea ships, a mistake I loved making before
I remember first hearing about this, if in a lot less detail, when I visited the museum of the cathedral in Aachen, Germany. They had a model like this for it, made by students of the university (the cathedral being much too old for this technique to be used in the original construction). The amazing thing, to me, is that while the students tried to model the existing cathedral, they couldn't get it to work. What they saw could not be described by a model - so they added some weights in specific places to make the rest of the model conform, and then hypothesized from the placement of the added weights that there must be a ring of iron buried in the construction at the base of one dome. Subsequently someone got permission to carefully drill into the building, and indeed found precisely that iron ring. I loved that approach: you know that you *can* model a building like this, so when modeling an existing building appears impossible, you must conclude that there are forces you are not seeing that make it work.
I saw something very similar in the oil and gas industry once. Mooring an oil rig offshore can require dozens of anchor lines and risers (the pipes that bring the oil and gas up from the well), and ensuring those catenaries don't clash with each other is hard to visualize even on a computer screen. It gets even more complicated during installation, as lines are being laid down and picked up by boats on the surface. So this one older engineer's solution was to take a big room in his office building and make a model of the anchor layout with string. The boat models were placed on model railways mounted upside down on the ceiling and had remote-controlled winches. In this way, he designed every phase of installation and the final design intuitively. For fun he had a model-scale Eifel tower on the floor/seabed: it was 10 inches high, whereas the anchor lines went about 15ft to the ceiling.
@@spamcan9208 Probably similar to the way closet doors hang from a track mounted at the top of the door opening. The wheels are mounted on the doors, the doors are lifted slightly above the track, then the wheels are set down onto the track.
Thing is, the top of a stone arch and the bottom of a hanging catenary chain are under a lot less compression/tension than the arch's base or the chain's anchor points. So if an architect wants to make the top of the arch lighter, as it should be, he has to model it with a chain that's proportionally lighter in the middle. So this design technique is far more complicated than people realize.
That's actually extra concerning because the models will have greater compressive/tensile forces, right? The models provide an ideal case, never what you want to work from...
I'm not following you, to simulate an arch with the peak being lighter you would have the chain be lighter at the lowest point. As I was typing this I think I realized what you were saying, when you said the chain in the middle has to be lighter you meant at the lowest point of the chain, aka the middle if measuring from anchor point to anchor point. At first for some reason I was thinking you were talking about some midpoint of height between the anchor points and the lowest hanging point. 😂 Went ahead and still posted this just in case anyone else reads your comment and doesn't quite follow it at first.
As much as I appreciate us “having the math” I still appreciate even more the fact that hook designed something he knew he couldn’t build and then solved the problem by not only using chains but building it upside down. What a madman
Right, and what I got from this video was that he was 10 years into it and still wasn’t 100% sure what he was going to do. That is amazing to me, such confidence.
It's not often that I watch a video that really teaches me something I didn't know before, and does it with visual aids that make me feel that I really understood it. Thank you for teaching me something new and fundamental.
my old drafting book (1912) talks about making the curve using a fine chain on your drafting board, slant steeply so it would hang, and you pricked pointed through the chain links. I didn't realize it was a full on thing for builders back then. cool!!
I've heard similar things from early house rafters were based on upside down boat hulls. Woodworkers were really good at building boats and were able to do both in a similar way.
@@kateapple1 well anyway, the central part of a church is called a nave, and that is because the roof looks like an upturned boat hull. Nave meaning boat in Latin, from which we get words like Navy, navigate etc. So I think that is where Tony got his story a little bit muddled ... though you still get shelters and the odd house on a beach made from an upturned rowing boat sometimes.
This might be the best explanation about how a structural architect thinks compared with a traditional architect. As architects, we still have to know what structural architects and engineers do, but not to the detail or complexity they should.
The new Stuttgart train station follows a similar principle. Here, the architect looked for the smallest possible surface area with a film of soap water that forms on a wire frame. This in turn was used for supports and light eyes in the underground station.
Yes, very awesome. An underground train station that needs pumps running constantly in order to not drown. Or rails where trains break and stop on a decline. Smart through and through (...)
@@maxworx1411 Ever heard of subway railroads? Building underground stations is not exactly a new trend. And the water only had to be pumped during construction, so what! The Feuersse S-Bahn station, also in Stuttgart, has a steeper gradient. And Stuttgart 21 is not a station where trains are parked or assembled, but the trains only stop briefly to board and alight - just like an S-Bahn.
@@hape3862 yup, subway tunnels exist. Feuersee and Schwabstrasse have permanent problems with water ingression due to the surrounding geology. S21 is on the bottom of the same valley and facing the same problems. Edit: ICE or regional trains are different calibers compared to a local city train
@@maxworx1411 Whatever. I'm fed up with all the bad moods and doom and gloom here in Germany. Sometimes one could think we were living in the last shithole country. Nothing is good enough, but everything is too expensive. Stuttgart 21 is almost finished, we'll see how it goes. Get over it and live your life.
I used to work with a friend that designed rock crawler roll cages upside-down. It was eye opening. Calculating the triangulation for areas of high stress was much more obvious.
Siza's pavillion for the 1998 World Exhibition is kind of an extension of Gaudí's work; he made a seemingly impossible arch by suspending a sheet of concrete over a large plaza. Upside-down engineering that remained upside-down. A very different end result, but a very similar design process. (Just with a lot of much more advanced engineering; it takes a LOT to make such a thin sheet of concrete!)
I had to google it after reading your comment. Never heard of it before, but wow, it's quite impressive. The concrete sheet itself looks so bouncy and soft, it kinda reminds me of that split second when a bedsheet hovers above the bed before falling.
Thanks, I did not know this building. It is way more impressive than that : since it is kept upsidedown, it means it works in tension. But it is made of concrete, which works only in compression. So that means they found a way to build a lot of tension in a preconstrained structure while keeping it such a thin veil. It would have been easier to use it as a dome (well, let's say 'less difficult'). The result is stunning. Great piece of design and engineering.
@@paulgrassart8935 Literally pretensioned concrete. You called it. It's used a lot in modern construction of commercial office buildings. It's put under tension at a factory and with tension cable installed inside to keep the tension. Just don't drill into one thinking it's rebar. It tends to compromise the sheet. It's manufactured in large sheets and used as flooring. It allows you to save height since typical concrete pouring requires additional height to support the extra tensioning on load.
Great video, Stewart! Just a quick correction: at 5:20, you mention the model being made by Antoni Gaudí. However, the model you're referring to was actually done by Frei Otto, the German architect and structural engineer. Gaudí’s original model was unfortunately destroyed. Frei Otto's work in lightweight structures and tensile architecture was definitely inspired by Gaudí, though! Keep up the fantastic content!
Thank you for this explanation! I've been to see the Sagrada Familia and even saw the model in the basement being told that it was how he designed the structure. Until now, I didn't really have a conception for how or why his model worked.
Nice video. One thing you didn't explain was the little weighted bags hanging from the strings in Gaudí's models. Those are there to represent the additional forces that would need to be supported at those points. In compression (right-side-up) that would be extra weight, such as a tower supported by the top of an arch. But in tension (upside-down), the analogue is to hang weights from the strings, proportional to the weight of what would need to be supported by the finished structure.
The fact that Sir Cristopher Wren was too radical for his time sort of blows my mind. Also, a very nice fact to have to serve those who oppose anything that’s “new”. As Peter Gabriel puts it, all these old things “were once just a thought/in somebody’s mind.” Perhaps for something to become a “classic”, it has to started out as revolutionary. There’s no shortage of examples to support this hypothesis!
I was coming to make a similar point. So what I'll add is this: To think now St Paul's is at the centre of 8 of Londons 13 protected sight-lines. In a number of cases it has literally defined the architecture of other buildings, by necessity that they do not block views of St Paul's.
Not every great thing ever was new. Language was never new, it evolved, and same with classical architecture like st Paul's which was very similar to st peters basilica, which itself was the pantheon over basilica of maxentius. Many great things are only changed 1 percent many many times, and never were new because they were never at one point invented, but rather evolved.
In art, turning either the canvas or the scene upside down allows the artist to pay more attention to the individual forms and their relation together, resulting in a better artwork.
Fascinating! This reminds me of the work of the late Robert Mark, a professor of civil engineering and architecture at Princeton. He used photoelastic modeling to analyse the structure of ancient buildings, like Gothic cathedrals and Renaissance domes, including St Paul's. He would make structural models in plastic, hang them upside down, add weights at critical junctures, and then heat the models up enough so that they would deform slightly. Using holographic interferometry, he would pinpoint areas of stress or structural failure. This process illustrated in detail why some of these buildings still stood, while others failed, or at least were problematic. I was also reminded of several other Renaissance-period domes, which ended up taking on a distinctly pointed or ogival profile for structural reasons. Brunelleschi's dome on the Duomo in Florence is the earliest example I can think of. Michaelangelo's original design for the dome of St Peter's in Rome had a semi-circular profile, but when the dome was completed after Michaelangelo's death by Giacomo della Porta and Domenico Fontana, they altered the dome's semi-circular profile, so it now has the profile of a catenary arch, much like the arches of Gaudi's Sagrada Familia. Even Wren's dome at St Paul's has a catenary arch hidden in its section -- a brick cone in the form of a catenary arch that is hidden by a low interior semi-circular dome and an exterior dome of timber and lead. I don't know if any of these architects hung structural models upside down like Gaudi, but it wouldn't surprise me if they did.
It’s amazing that somebody is finally completing Gaudi’s cathedral. Perhaps some of the lessons learned during the construction can be disseminated into the rest of the architectural profession so that the architects who were only taught by members of the Cold War-era Modernist orthodoxy can learn how to build buildings in the style of the more artsy, aesthetically-driven styles that came from the generations before that. Perhaps the entire profession could manage to recover a lot of the knowledge that was lost in that era.
No knowledge has been lost. Costs, and a constant striving for something new-and-different, have driven architecture down a route in which aesthetics have diverged from public tastes.
I have worked for over 35 years as a mechanical design engineer and manufacturing consultant. I design and build all sorts of machines, products, tools, etc. I don't work in architecture, civil engineering, or building construction. However, I am surprised, at 60 years old, that this is the first time I have heard of this technique of designing something upside down. It makes perfect sense to do this, but I just never thought of it that way. I have always been impressed by the complexity of architectural designs, especially for structures that were designed hundreds of years ago before any sort of modern computers were available. This designing upside down method could also be accurately described as a sophisticated mechanical analog (not digital) computer. Such a concept of an analog computer is why a mechanical system can be accurately represented by an equivalent hydraulic system, pneumatic system, or electronic system. The problem solution in any one of these analogs will have an equivalent solution in any of the other three analogs. Basically, the correct solution just naturally flows from all of the inputs to the correctly modeled system. So, if a solution is found for one system, it is found for all systems. Very interesting. Ed Schultheis, PE Mechanical design engineer and manufacturing consultant for 35 years Schultek Engineering & Technology, Inc.
This video gives a whole new perspective on the Sagrada Família. It is well known that cathedrals are designed to reach toward heaven (God). In this case, it is as if Sagrada Família is being pulled by God the Father. It’s a beautiful concept even if one is not religious.
I have heard that the pillars inside the church were also designed to resemble trees in a forest. Note all of the natural-looking branches at the tops of the pillars inside that church.
Fun fact: The CATENARY curve is the optimum for self-supporting structures. At the other end of the spectrum, when the structure is supporting something else that is much heavier (like cables in cable bridges supporting decks), the optimal curve is the PARABOLA. Both curves are actually quite similar and in real life situations the optimum is somewhere in between. (All of this can be proven with a little complicated differential calculus.)
The basic catenary is simply a curve that converts an even linear load into two point loads, and vice versa. The direction doesn't matter due to Newton's third law.
Such an inspiring episode - arohanui! Feel really emotional that a fellow Kiwi from so far geographically and culturally away could contribute to such an outstanding piece of Spanish architecture. I visited last in 2010 and hope to see it again before I die.
I adore catenary curves (and catenoid and also hyperboloid) surfaces in architecture/engineering, there's something deeply elegant about them which speaks to me. Some of my favourite minecraft structures that I've built over the years used catenary (cosh) curves, or catenoid and hyperboloid surfaces (typically not done by hand; with tools like e.g. the worldedit plugin, you can generate shapes based on a mathematical formula you give it), but I had no idea about the real-world architectural history of how these shapes were created!
This was an excellent ad for a better shaving razor. But seriously the upside down design process was interesting to learn about, thank you for sharing!
One of the most remarkable building design I've seen is a Japanese shrine with a reflecting pool, that reflects the stones that surround the pond in a manner to form religious symbols. To use nature itself to show a state of mind is astounding.
Great video! But the picture you showed at 7:17 was not a picture of Gaudi, but a picture of Eusebi Güell. Güell was the one that gave Gaudi several architectural projects such as Finca Güell and Park Güell. During their collaboration they became lifelong friends.
As soon as I saw the building under construction at 10:12 I knew that shell design was based off a tarp hung from somewhere. Even though smooth shell-like structures weren't popular in buildings until the late 19th and early 20th centuries, it's crazy to think how something so intuitive eluded architects, engineers, and mathematicians for so long, even with that style of building becoming more and more popular.
As an non believer and engineer I still must insist that you consider visiting Barcelona and the Sagrada Familia! A Breathtaking & Profound experience. And Gaudi's other work is also fantastic, I'd recommend at least visiting casa Batllo. Just splendid!
It's absolutely an analog computer. An analog is a thing that is comparable to another. That's exactly what's going on with the inverted chain or sheet representing the eventual structure. If it doesn't feel like a computer, consider how one could do what-if experiments with the added weights to try out different loading scenarios.
As a mechanical design engineer, this was exactly my thought as well. As I wrote in another part of this thread... This designing upside down method could also be accurately described as a sophisticated mechanical analog (not digital) computer. Such a concept of an analog computer is why a mechanical system can be accurately represented by an equivalent hydraulic system, pneumatic system, or electronic system. The problem solution in any one of these analogs will have an equivalent solution in any of the other three analogs. Basically, the correct solution just naturally flows from all of the inputs to the correctly modeled system. So, if a solution is found for one system, it is found for all systems.
@@edschultheis9537 Fun fact: This is also the thought behind quantum annealing, a form of quantum computing where the system is designed in a way that it naturally evolves to a global minimum in an energy landscape, with this minimum being the desired solution. The difference to other physical analogs like those hanging models is that quantum tunneling allows the system to escape local minima by itself; as if I would build a model on my table, hang it up without caring whether everything hangs down freely, and all the strings would magically untangle themselves to allow the whole model to reach its optimal state.
Ok but imagine this: you get a good german handmade steel straight razor you can sharpen repeatedly and give to your grandkid. No amount of disposability or repurchasing the tool. No irritation, just one blade. Beautiful wooden handle. Great video, very beautiful, very practical, very efficient. Very engineer.
Leo Chow from SOM spoke to our studio last week and he showed us several slides of them doing structural studies upside down, very cool to see a video explaining it more in depth. Crazy coincidence!
one practical aspect which I did not see is this presentation is the margin required for taking up forces other than gravity (e.g. wind), or for the mock up models the variation of direction gravity is applied when the frozen fabric is being turned upside down...
Love this topic. When combined with 3D printing, these fundamental ways of looking at structural forms will be very interesting in the next generation of design and construction.
Amazing work Stewart. You are a model of great UA-cam architectural content. As an architect who worshipped Gaudi as a student, I was inspired to try and apply his style to my projects. I can attest how difficult it was to draw the forms on paper pre computer.
I'd thought he was going to coat the hanging burlap in plaster or something like that, but the idea of using _ice_ is even more amazing. It's easier (provided you've got the right temperatures around), cheaper, and lighter too! That is the kind of creativity that I love so much. The only question I have is, how did Isler avoid the liquid collecting at the 'top' of the structure as it froze? Gravity would've pulled all the water in a single direction, resulting in a slightly different density and therefore a slightly different shape... was it just a matter of applying a thin enough layer that it didn't significantly change the big picture?
I wonder if you could make a negative model using the hanging model. You wouldn't want to dip it, because that would introduce pressure from buoyancy, but maybe something that could deposit on it slowly. Edit... doh, like freezing it... I guess I should wait until the end of the video to make my comments!
I think the most interesting part about catenary chains and thin shell structures is the idea of suspending a lower-dimensional shape against its inherent dimension(s) and allowing it to naturally form itself to fit into this next dimension (line -> curve, plane -> shell).
There is a method of drawing that has you draw from an upside down image. Just concentrate on the shadows and highlights, line weight and shading for a pretty stunning result. This is because as we draw, we try to imagine what the thing, or face should look like and that image interferes with our eye-hand movements. It's easier to draw something if you don't know what the thing is. It's called Drawing With the Left Brain.
I use to build kilns for 30 years, I would use this technique to build my arch forms with a string on cardboard , let it hang then mark that shape of the string. This was a sprung arch.
I do this for graff. If I ever feel like I’m stuck on a piece or lost. I’ll just flip the paper im working on upside down and see how the letters and weight affect each other in that perspective , I’ll tweak the letters to fit better and sometimes it even helps create new versions of letters. It helps me see where the patterns are or should go. Something that I think is important in graff. Basically You can make your letters match more etc... (in my experience at least) A Very ghetto version but try it next time you feel stuck on some graff .
Long ago, I was in practice as a structural engineer. I had started off with a BA in mathematics and then went on to be an academic bum until accidentally becoming an engineer. While in practice, I would sometimes be asked about the difference between architects and structural engineers. Contemptuously, I would reply that architects are required to take calculus in school but engineers are required to pass it. My contempt was mostly fueled by the many architects I had met who were skilled at drawing pretty pictures but who were not qualified to make a block of concrete sit on the ground without collapsing. The truth is, though, that it was always the architects who had a better grasp of both the artistic elements and, especially, the utilization of space. The first is a skill that I never had and still don't have. The second developed in only the most rudimentary form over years of experience. I still know plenty of architects who I would not trust with a box of Lincoln Logs or Tinker Toys, let alone Legos, unless I had proof of liability and malpractice insurance. But I would trust almost all of them to give me a beautiful and functional design as long as they let me or somebody competent review the "pretty pictures" to make sure they won't fall down and "go boom". This video did a great job of pointing out some of that distinction when it explored the thin shells. It also articulated things much better than I could. Don't worry, though, I have not been in practice for a very long time since I threw it all away and went to seminary.
The picture is from Eusebi Güell, not Antoni Gaudí. La Sagrada Familia it's not, nor would be, a Cathedral. The Cathedral of Barcelona it's the temple of La Santa Creu i Santa Eulalia...
I think you should look at Tulsa’s rose bowl (bowling alley) and chapel on the hill in broken arrow. It is thin shell concrete but weirdly I think my friend could have designed it upside down but he designed it like you normally would. It’s also an architect and engineer duo as well. Beautifully done and beautifully executed.
Note that the catenary curve is thus with respect to a chain, which is 2d. It works when the shape is constant in the 3rd dimension. If you want a dome, or funicular shape instead, I believe that the general shape is less wide, due to the greater mass departing from the center.
I never knew about this upside down thing, thanks for the information! I guess it is similar to how the greats used a pinhole camera to project the image of a landscape to trace onto canvass then paint onto it - initially it is upside down then they add a lens to focus and brighten it and it places it right way up. Regarding your sponsor here, I have the same Gillette handle I bought in 1994. It is not cheap plastic, it is metal...lol It still works perfectly after 30 years of use and has been dropped many a time!! Perhaps modern variants handles are cheap plastic crap, but my old one is not!
Very interesting! Reminds me of a process called topology optimization, where you can simulate these sorts of organic forms that put material only where it's needed with computers. I haven't seen an example where the expected loads come from the structure itself, though…
Visited Barcelona earlier this year and spend some time sussing out the architecture of Gaudi. Gaudi and FLW were born the same year. FLW lived around 20 years longer because Gaudi was killed when struck by a streetcar. The fascinating contrast was that, although each man was interested in the interplay between architecture and nature, Frank Lloyd Wrong's answer was to try to control nature, metering the amount of nature that would enter into the interior of his designed spaces. In contrast, Gaudi tried to emulate nature, thereby integrating interior and exterior. Gaudi of course used the hanging line method to design his arches, which is evident in the Sagrada Familia. In other words, he was concerned about designing structures that function. FLWrong simply ignored the physical properties of his materials and the mathematical improbabilities of his cantilevers, shoving rectangles out into the air without concern about whether they would actually function.
It really makes sense, the tension buildt by the weights results in finding the perfect shape which will make the building stronger in the end. It's kind of philosophical. If there is tension you are guided in a specific form which is best suited. If you apply this to philosophy, external guidance helps an individual to behave in a right way and to think clearly. Too many people go through the world suppressing everything which results in them speaking before thinking and really behaving dumb because they suppressed all their thoughts
My tutor said that prior to the understanding of these curves as models for arches, domes etc.. architects and engineers were pretty much just guessing and using the trial and error of previous completed works that were still standing. Which makes all the ancient architecture even more impressive.
I remember that trial and error was taught in mathematics. Before we’d get into the elegant calculations, we’d have to guess with trial and error, inelegant, calculations. 😍
Yeah. Even with the ancient pyramids there were a lot of failed pyramids before they got good at making pyramids. Some of them still survive today with the awkward stopgap measures they installed
They had a bunch of rules of thumb that worked though, but structures were heavier than they needed to be.
Thousands of years of trial and error can achieve amazing results. That's basically all accumulated human knowledge.
YOURE A BOT 😂TUTOR MY ASS!
What I though this was about:
Flipping the model upside down, to give a better perspective on details you'd miss by seeing it right-side up.
What I got:
An important engineering lesson.
yeah its a good thing to do when drawing/painting. Especially in digital when you can mirror it, and especially when drawing people.
@@confuseatronica my good friend used to teach upside down drawing and painting. It was always cool to see the students faces when they flip their own drawing over and realize how good it is
That's interesting. It's exactly what I've been doing to design space ships in games
The perspective shift made them end up feeling much more like space- rather than sea ships, a mistake I loved making before
same
I remember first hearing about this, if in a lot less detail, when I visited the museum of the cathedral in Aachen, Germany.
They had a model like this for it, made by students of the university (the cathedral being much too old for this technique to be used in the original construction).
The amazing thing, to me, is that while the students tried to model the existing cathedral, they couldn't get it to work. What they saw could not be described by a model - so they added some weights in specific places to make the rest of the model conform, and then hypothesized from the placement of the added weights that there must be a ring of iron buried in the construction at the base of one dome.
Subsequently someone got permission to carefully drill into the building, and indeed found precisely that iron ring.
I loved that approach: you know that you *can* model a building like this, so when modeling an existing building appears impossible, you must conclude that there are forces you are not seeing that make it work.
There's an iron or steel ring, or chain, around almost any dome you can think of.
I saw something very similar in the oil and gas industry once. Mooring an oil rig offshore can require dozens of anchor lines and risers (the pipes that bring the oil and gas up from the well), and ensuring those catenaries don't clash with each other is hard to visualize even on a computer screen. It gets even more complicated during installation, as lines are being laid down and picked up by boats on the surface. So this one older engineer's solution was to take a big room in his office building and make a model of the anchor layout with string. The boat models were placed on model railways mounted upside down on the ceiling and had remote-controlled winches. In this way, he designed every phase of installation and the final design intuitively. For fun he had a model-scale Eifel tower on the floor/seabed: it was 10 inches high, whereas the anchor lines went about 15ft to the ceiling.
I'm having trouble visualizing how he got a model train to work upside down unless I'm fundamentally misreading and/or misunderstanding something.
That's so awesome
@@spamcan9208 Probably similar to the way closet doors hang from a track mounted at the top of the door opening. The wheels are mounted on the doors, the doors are lifted slightly above the track, then the wheels are set down onto the track.
That's a man who knows what he's doing and cares about doing a good job. Don't see many people like that anymore.
@@bluedistortions One can't see something that isn't there.
Thing is, the top of a stone arch and the bottom of a hanging catenary chain are under a lot less compression/tension than the arch's base or the chain's anchor points. So if an architect wants to make the top of the arch lighter, as it should be, he has to model it with a chain that's proportionally lighter in the middle. So this design technique is far more complicated than people realize.
That's actually extra concerning because the models will have greater compressive/tensile forces, right? The models provide an ideal case, never what you want to work from...
That is the reason they added weights to the chain. An advantage of a chain is also that the weights will not slide.
so like a noodle?
No it's not , you simply use another chain inside the arch of the first arch
I'm not following you, to simulate an arch with the peak being lighter you would have the chain be lighter at the lowest point.
As I was typing this I think I realized what you were saying, when you said the chain in the middle has to be lighter you meant at the lowest point of the chain, aka the middle if measuring from anchor point to anchor point. At first for some reason I was thinking you were talking about some midpoint of height between the anchor points and the lowest hanging point. 😂
Went ahead and still posted this just in case anyone else reads your comment and doesn't quite follow it at first.
As much as I appreciate us “having the math” I still appreciate even more the fact that hook designed something he knew he couldn’t build and then solved the problem by not only using chains but building it upside down. What a madman
It was Wren who designed and got approval for a building he knew he couldn't build, but Hooke who used the chains upside down.
Right, and what I got from this video was that he was 10 years into it and still wasn’t 100% sure what he was going to do. That is amazing to me, such confidence.
I read too much Newton history so it's very sobering to learn that Hooke was still a mathematician for a reason.
It's not often that I watch a video that really teaches me something I didn't know before, and does it with visual aids that make me feel that I really understood it. Thank you for teaching me something new and fundamental.
The idea of icing a burlap rag is just ... well, genious!
Genius*
@@Oberon4278 Genouis*
Smrtass
@@Oberon4278Jeenyus*
I had no idea Gaudi's plans for the catherdral got destroyed, so glad that the young arcitect was able to figure out a way to rescue the work.
Imagine what masters like this could do with modern tools like CAD and 3d printers...
a lot of the time they only needed just a base unit of measurment, a string and some sand to draw lines into.
1:54 robert hooke jumpscare. Brilliant man, nightmarish picture
Hahahaha, I spat coffe all over reading this. Brilliant comment!!!
Haha thats cuz newton burned all his other portraits lmfao
my old drafting book (1912) talks about making the curve using a fine chain on your drafting board, slant steeply so it would hang, and you pricked pointed through the chain links. I didn't realize it was a full on thing for builders back then. cool!!
I've heard similar things from early house rafters were based on upside down boat hulls. Woodworkers were really good at building boats and were able to do both in a similar way.
oo well, not sure, do you know what the central axis from east to west is called in a church, the bit with the highest roof?
YOURE A BOT
@@MrVorpalswordyou’re not a bot so you’re ok 👍 😂😂 but you’re talking to one
@@kateapple1 well anyway, the central part of a church is called a nave, and that is because the roof looks like an upturned boat hull. Nave meaning boat in Latin, from which we get words like Navy, navigate etc. So I think that is where Tony got his story a little bit muddled ... though you still get shelters and the odd house on a beach made from an upturned rowing boat sometimes.
@@kateapple1what's the reason you think they are a bot?
This might be the best explanation about how a structural architect thinks compared with a traditional architect. As architects, we still have to know what structural architects and engineers do, but not to the detail or complexity they should.
As someone who grew up with a love of architecture in St. Louis, the catenary curve is close to my heart.
The new Stuttgart train station follows a similar principle. Here, the architect looked for the smallest possible surface area with a film of soap water that forms on a wire frame. This in turn was used for supports and light eyes in the underground station.
Yess, I think it looks awesome! The idea is from Frei Otto, he also designed the Olympiapark in Munich
Yes, very awesome. An underground train station that needs pumps running constantly in order to not drown. Or rails where trains break and stop on a decline. Smart through and through (...)
@@maxworx1411 Ever heard of subway railroads? Building underground stations is not exactly a new trend. And the water only had to be pumped during construction, so what! The Feuersse S-Bahn station, also in Stuttgart, has a steeper gradient. And Stuttgart 21 is not a station where trains are parked or assembled, but the trains only stop briefly to board and alight - just like an S-Bahn.
@@hape3862 yup, subway tunnels exist. Feuersee and Schwabstrasse have permanent problems with water ingression due to the surrounding geology. S21 is on the bottom of the same valley and facing the same problems. Edit: ICE or regional trains are different calibers compared to a local city train
@@maxworx1411 Whatever. I'm fed up with all the bad moods and doom and gloom here in Germany. Sometimes one could think we were living in the last shithole country. Nothing is good enough, but everything is too expensive. Stuttgart 21 is almost finished, we'll see how it goes. Get over it and live your life.
I always love it when people are able to solve problems by taking the idea and flipping it on its head.
This is your best video ever: science, history, esthetics, and human nature all described beautifully and skillfully.
I used to work with a friend that designed rock crawler roll cages upside-down. It was eye opening. Calculating the triangulation for areas of high stress was much more obvious.
Siza's pavillion for the 1998 World Exhibition is kind of an extension of Gaudí's work; he made a seemingly impossible arch by suspending a sheet of concrete over a large plaza. Upside-down engineering that remained upside-down. A very different end result, but a very similar design process. (Just with a lot of much more advanced engineering; it takes a LOT to make such a thin sheet of concrete!)
I had to google it after reading your comment. Never heard of it before, but wow, it's quite impressive. The concrete sheet itself looks so bouncy and soft, it kinda reminds me of that split second when a bedsheet hovers above the bed before falling.
Thanks, I did not know this building. It is way more impressive than that : since it is kept upsidedown, it means it works in tension. But it is made of concrete, which works only in compression. So that means they found a way to build a lot of tension in a preconstrained structure while keeping it such a thin veil.
It would have been easier to use it as a dome (well, let's say 'less difficult'). The result is stunning. Great piece of design and engineering.
Huh
@@paulgrassart8935 Literally pretensioned concrete. You called it. It's used a lot in modern construction of commercial office buildings. It's put under tension at a factory and with tension cable installed inside to keep the tension. Just don't drill into one thinking it's rebar. It tends to compromise the sheet. It's manufactured in large sheets and used as flooring. It allows you to save height since typical concrete pouring requires additional height to support the extra tensioning on load.
Great video, Stewart! Just a quick correction: at 5:20, you mention the model being made by Antoni Gaudí. However, the model you're referring to was actually done by Frei Otto, the German architect and structural engineer. Gaudí’s original model was unfortunately destroyed. Frei Otto's work in lightweight structures and tensile architecture was definitely inspired by Gaudí, though! Keep up the fantastic content!
Not really, that photo is from Sagrada Familia archives. Frei Otto was to be born at that time... Rope and cloth models don't last +100 years.
The original model was purposefully destroyed by anarchists, communists and republicans during the Civil War.
so you're telling me that Robert Hook's favourite thing to do was to hang things from hooks?
Was about to comment this 😂
Is this the same person who coined term CELL?
Yes@@rpaapahihi
And he absolutely hated Isaac Newton his whole life
This is so damn clever. When you see it, it's intuitive -- but it takes a really flexible mind to notice it in the first place.
Thank you for this explanation! I've been to see the Sagrada Familia and even saw the model in the basement being told that it was how he designed the structure. Until now, I didn't really have a conception for how or why his model worked.
Nice video. One thing you didn't explain was the little weighted bags hanging from the strings in Gaudí's models. Those are there to represent the additional forces that would need to be supported at those points. In compression (right-side-up) that would be extra weight, such as a tower supported by the top of an arch. But in tension (upside-down), the analogue is to hang weights from the strings, proportional to the weight of what would need to be supported by the finished structure.
The fact that Sir Cristopher Wren was too radical for his time sort of blows my mind. Also, a very nice fact to have to serve those who oppose anything that’s “new”. As Peter Gabriel puts it, all these old things “were once just a thought/in somebody’s mind.” Perhaps for something to become a “classic”, it has to started out as revolutionary. There’s no shortage of examples to support this hypothesis!
Just here for the Peter Gabriel reference.
Opposing some new things can be good. There’s no shortage of examples to support this hypothesis
I was coming to make a similar point. So what I'll add is this: To think now St Paul's is at the centre of 8 of Londons 13 protected sight-lines. In a number of cases it has literally defined the architecture of other buildings, by necessity that they do not block views of St Paul's.
Obviously, not all new things are great. But all great things have been new.
Not every great thing ever was new. Language was never new, it evolved, and same with classical architecture like st Paul's which was very similar to st peters basilica, which itself was the pantheon over basilica of maxentius. Many great things are only changed 1 percent many many times, and never were new because they were never at one point invented, but rather evolved.
In art, turning either the canvas or the scene upside down allows the artist to pay more attention to the individual forms and their relation together, resulting in a better artwork.
0:29 Wren ran?
Wren ran when, ben?
Fascinating! This reminds me of the work of the late Robert Mark, a professor of civil engineering and architecture at Princeton. He used photoelastic modeling to analyse the structure of ancient buildings, like Gothic cathedrals and Renaissance domes, including St Paul's. He would make structural models in plastic, hang them upside down, add weights at critical junctures, and then heat the models up enough so that they would deform slightly. Using holographic interferometry, he would pinpoint areas of stress or structural failure. This process illustrated in detail why some of these buildings still stood, while others failed, or at least were problematic.
I was also reminded of several other Renaissance-period domes, which ended up taking on a distinctly pointed or ogival profile for structural reasons. Brunelleschi's dome on the Duomo in Florence is the earliest example I can think of. Michaelangelo's original design for the dome of St Peter's in Rome had a semi-circular profile, but when the dome was completed after Michaelangelo's death by Giacomo della Porta and Domenico Fontana, they altered the dome's semi-circular profile, so it now has the profile of a catenary arch, much like the arches of Gaudi's Sagrada Familia. Even Wren's dome at St Paul's has a catenary arch hidden in its section -- a brick cone in the form of a catenary arch that is hidden by a low interior semi-circular dome and an exterior dome of timber and lead. I don't know if any of these architects hung structural models upside down like Gaudi, but it wouldn't surprise me if they did.
It’s amazing that somebody is finally completing Gaudi’s cathedral. Perhaps some of the lessons learned during the construction can be disseminated into the rest of the architectural profession so that the architects who were only taught by members of the Cold War-era Modernist orthodoxy can learn how to build buildings in the style of the more artsy, aesthetically-driven styles that came from the generations before that. Perhaps the entire profession could manage to recover a lot of the knowledge that was lost in that era.
Everyone wants fancy neoclassical ornate maximalism architecture, nobody wants to pay fancy neoclassical ornate maximalism consulting fees
No knowledge has been lost. Costs, and a constant striving for something new-and-different, have driven architecture down a route in which aesthetics have diverged from public tastes.
Thanks older Tyler Oakley for another great architectural eye opener
I have worked for over 35 years as a mechanical design engineer and manufacturing consultant. I design and build all sorts of machines, products, tools, etc. I don't work in architecture, civil engineering, or building construction. However, I am surprised, at 60 years old, that this is the first time I have heard of this technique of designing something upside down. It makes perfect sense to do this, but I just never thought of it that way. I have always been impressed by the complexity of architectural designs, especially for structures that were designed hundreds of years ago before any sort of modern computers were available.
This designing upside down method could also be accurately described as a sophisticated mechanical analog (not digital) computer. Such a concept of an analog computer is why a mechanical system can be accurately represented by an equivalent hydraulic system, pneumatic system, or electronic system. The problem solution in any one of these analogs will have an equivalent solution in any of the other three analogs. Basically, the correct solution just naturally flows from all of the inputs to the correctly modeled system. So, if a solution is found for one system, it is found for all systems.
Very interesting.
Ed Schultheis, PE
Mechanical design engineer and manufacturing consultant for 35 years
Schultek Engineering & Technology, Inc.
0:28 "The architect Tristopher Wren"
"Hi my name's Christopher with a t"
"Trisopher!"
Sounded like "tristopher" to me
“Try, Tie mame is Tristopher!”
11:23 other univorse
11:36 underspand
14:05 business bottle
This video gives a whole new perspective on the Sagrada Família. It is well known that cathedrals are designed to reach toward heaven (God). In this case, it is as if Sagrada Família is being pulled by God the Father. It’s a beautiful concept even if one is not religious.
I have heard that the pillars inside the church were also designed to resemble trees in a forest. Note all of the natural-looking branches at the tops of the pillars inside that church.
It's the only time I've been amazed by a building (not counting the wind atop Empire State). Highly recommended.
"cathedrals are designed to reach toward heaven"
Have they learned nothing of the tower of Babel?!
@@yocats9974 I’m not a religious scholar, but I think the motivation was different.😀
Fun fact: The CATENARY curve is the optimum for self-supporting structures. At the other end of the spectrum, when the structure is supporting something else that is much heavier (like cables in cable bridges supporting decks), the optimal curve is the PARABOLA. Both curves are actually quite similar and in real life situations the optimum is somewhere in between. (All of this can be proven with a little complicated differential calculus.)
The basic catenary is simply a curve that converts an even linear load into two point loads, and vice versa. The direction doesn't matter due to Newton's third law.
Wren could have just used hyperbolic trig functions, but he would have had to wait a century for them to be invented.
Lol.
I hate it when that happens.
Instead he invented an analog computer made of strings.
Such an inspiring episode - arohanui! Feel really emotional that a fellow Kiwi from so far geographically and culturally away could contribute to such an outstanding piece of Spanish architecture. I visited last in 2010 and hope to see it again before I die.
I adore catenary curves (and catenoid and also hyperboloid) surfaces in architecture/engineering, there's something deeply elegant about them which speaks to me. Some of my favourite minecraft structures that I've built over the years used catenary (cosh) curves, or catenoid and hyperboloid surfaces (typically not done by hand; with tools like e.g. the worldedit plugin, you can generate shapes based on a mathematical formula you give it), but I had no idea about the real-world architectural history of how these shapes were created!
Now you're making me want to come back to Minecraft
This was an excellent ad for a better shaving razor. But seriously the upside down design process was interesting to learn about, thank you for sharing!
This was insanely interesting - thanks for sharing this!
That was NOT what i expected and that was amazing!!!
Shame they couldn’t build it upside down too, and flip it over upon completion.
If I was strong enough, I’d gladly flip the current monstrosity end over end (the basilica).
Ha ha lool
Build it in Australia, then ship it to NA or EU and you've successfully built it upside down and flipped it after completion
Or just leave it upside down
When an intro to a video makes me say "why?!", I am instantly hooked. It's like my kryptonite
I am so happy that you brought this subject to light in a video! Extremely well presented, as always.
One of the most remarkable building design I've seen is a Japanese shrine with a reflecting pool, that reflects the stones that surround the pond in a manner to form religious symbols. To use nature itself to show a state of mind is astounding.
Great video! But the picture you showed at 7:17 was not a picture of Gaudi, but a picture of Eusebi Güell. Güell was the one that gave Gaudi several architectural projects such as Finca Güell and Park Güell. During their collaboration they became lifelong friends.
As soon as I saw the building under construction at 10:12 I knew that shell design was based off a tarp hung from somewhere. Even though smooth shell-like structures weren't popular in buildings until the late 19th and early 20th centuries, it's crazy to think how something so intuitive eluded architects, engineers, and mathematicians for so long, even with that style of building becoming more and more popular.
This was incredibly interesting. And I have just added seeing the Sagrada Familia to my bucket list. Thanks!
As an non believer and engineer I still must insist that you consider visiting Barcelona and the Sagrada Familia!
A Breathtaking & Profound experience.
And Gaudi's other work is also fantastic, I'd recommend at least visiting casa Batllo. Just splendid!
It's been a while since I watched a video essay produced and structured this well. Amazing work. Thank you
Loved this video. Being a computer scientist, another perspective is that the upside down approach is kinda sorta like an analog computer.
It's absolutely an analog computer. An analog is a thing that is comparable to another. That's exactly what's going on with the inverted chain or sheet representing the eventual structure. If it doesn't feel like a computer, consider how one could do what-if experiments with the added weights to try out different loading scenarios.
That's exactly what I, also a computer scientist, thought while watching the video.
As a mechanical design engineer, this was exactly my thought as well. As I wrote in another part of this thread...
This designing upside down method could also be accurately described as a sophisticated mechanical analog (not digital) computer. Such a concept of an analog computer is why a mechanical system can be accurately represented by an equivalent hydraulic system, pneumatic system, or electronic system. The problem solution in any one of these analogs will have an equivalent solution in any of the other three analogs. Basically, the correct solution just naturally flows from all of the inputs to the correctly modeled system. So, if a solution is found for one system, it is found for all systems.
@@edschultheis9537 Fun fact: This is also the thought behind quantum annealing, a form of quantum computing where the system is designed in a way that it naturally evolves to a global minimum in an energy landscape, with this minimum being the desired solution. The difference to other physical analogs like those hanging models is that quantum tunneling allows the system to escape local minima by itself; as if I would build a model on my table, hang it up without caring whether everything hangs down freely, and all the strings would magically untangle themselves to allow the whole model to reach its optimal state.
Ok but imagine this: you get a good german handmade steel straight razor you can sharpen repeatedly and give to your grandkid. No amount of disposability or repurchasing the tool. No irritation, just one blade. Beautiful wooden handle.
Great video, very beautiful, very practical, very efficient. Very engineer.
Leo Chow from SOM spoke to our studio last week and he showed us several slides of them doing structural studies upside down, very cool to see a video explaining it more in depth. Crazy coincidence!
one practical aspect which I did not see is this presentation is the margin required for taking up forces other than gravity (e.g. wind), or for the mock up models the variation of direction gravity is applied when the frozen fabric is being turned upside down...
Love this topic. When combined with 3D printing, these fundamental ways of looking at structural forms will be very interesting in the next generation of design and construction.
That was quite a ride. Thoroughly enjoyed that. 💜
GREAT episode.
Subscribed!
Addendum: as an illustrator, occasionaly turning the sketch upside down was a great way to make sure it was drawn properly.
Wow. Feels intuitive in retrospect. Amazing what kind of mind would just conceive of this.
Wow, I am blown away at the inginuity discussed in this video.
Amazing work Stewart. You are a model of great UA-cam architectural content. As an architect who worshipped Gaudi as a student, I was inspired to try and apply his style to my projects. I can attest how difficult it was to draw the forms on paper pre computer.
I'd thought he was going to coat the hanging burlap in plaster or something like that, but the idea of using _ice_ is even more amazing. It's easier (provided you've got the right temperatures around), cheaper, and lighter too! That is the kind of creativity that I love so much. The only question I have is, how did Isler avoid the liquid collecting at the 'top' of the structure as it froze? Gravity would've pulled all the water in a single direction, resulting in a slightly different density and therefore a slightly different shape... was it just a matter of applying a thin enough layer that it didn't significantly change the big picture?
One of the most fascinating and inspiring videos I've ever seen.
This is unbelievably cool, I had never heard of this. Cheers for the great video!
Each day provides its own gifts
The upside down model in the Sagrada Família made a huge impression on me. Worth a visit to Barcelona alone.
I wonder if you could make a negative model using the hanging model. You wouldn't want to dip it, because that would introduce pressure from buoyancy, but maybe something that could deposit on it slowly.
Edit... doh, like freezing it... I guess I should wait until the end of the video to make my comments!
YOu too, huh? ;)
Make it from fabric, spray with glue.
Fascinating content. Thank you Stewart.
Thanks for this awesome video!
I made a sketch of a building that had elements of upside-down looking arches and right-side up arches.. It also included columns and obelisks.
Still remember the first time I realized there was a upside-down castle in Castlevania, one of the best moments in gaming.
I think the most interesting part about catenary chains and thin shell structures is the idea of suspending a lower-dimensional shape against its inherent dimension(s) and allowing it to naturally form itself to fit into this next dimension (line -> curve, plane -> shell).
No idea why this channel popped up, but so glad it did. Got yourself a sub!
Absolutely fascinating!! I had no idea this was a process and so early. Great video! Thank you!
mind blowing concept, you have to be extraordinarily clever to think of something that geels that counter intuitive
There is a method of drawing that has you draw from an upside down image. Just concentrate on the shadows and highlights, line weight and shading for a pretty stunning result. This is because as we draw, we try to imagine what the thing, or face should look like and that image interferes with our eye-hand movements. It's easier to draw something if you don't know what the thing is. It's called Drawing With the Left Brain.
This was fascinating to learn about! Thank you for doing this research & storytelling :D
I learn some time ago.
A chain hangs
Like an arch stands.
Every day may not be good, but there's something good in every day
I use to build kilns for 30 years, I would use this technique to build my arch forms with a string on cardboard , let it hang then mark that shape of the string. This was a sprung arch.
I do this for graff. If I ever feel like I’m stuck on a piece or lost. I’ll just flip the paper im working on upside down and see how the letters and weight affect each other in that perspective , I’ll tweak the letters to fit better and sometimes it even helps create new versions of letters. It helps me see where the patterns are or should go. Something that I think is important in graff. Basically You can make your letters match more etc... (in my experience at least) A Very ghetto version but try it next time you feel stuck on some graff .
That was superinteresting.
Wow, this is really cool, and very well done!
Long ago, I was in practice as a structural engineer. I had started off with a BA in mathematics and then went on to be an academic bum until accidentally becoming an engineer. While in practice, I would sometimes be asked about the difference between architects and structural engineers. Contemptuously, I would reply that architects are required to take calculus in school but engineers are required to pass it. My contempt was mostly fueled by the many architects I had met who were skilled at drawing pretty pictures but who were not qualified to make a block of concrete sit on the ground without collapsing. The truth is, though, that it was always the architects who had a better grasp of both the artistic elements and, especially, the utilization of space. The first is a skill that I never had and still don't have. The second developed in only the most rudimentary form over years of experience. I still know plenty of architects who I would not trust with a box of Lincoln Logs or Tinker Toys, let alone Legos, unless I had proof of liability and malpractice insurance. But I would trust almost all of them to give me a beautiful and functional design as long as they let me or somebody competent review the "pretty pictures" to make sure they won't fall down and "go boom". This video did a great job of pointing out some of that distinction when it explored the thin shells. It also articulated things much better than I could.
Don't worry, though, I have not been in practice for a very long time since I threw it all away and went to seminary.
7:54 Thanks. Not many videos point this. Fun fact, Orwell wished the anarcs didn't stop with the models, he wished the same fate to the Cathedral.
That's basically an analog calculator! So cool! ❤
The picture is from Eusebi Güell, not Antoni Gaudí. La Sagrada Familia it's not, nor would be, a Cathedral. The Cathedral of Barcelona it's the temple of La Santa Creu i Santa Eulalia...
I model in revit upside down all the time. It’s also good to see the underside of buildings.
This fixed my attention span. Thanks
She was amazed by the large chunks of ice washing up on the beach.
I think you should look at Tulsa’s rose bowl (bowling alley) and chapel on the hill in broken arrow.
It is thin shell concrete but weirdly I think my friend could have designed it upside down but he designed it like you normally would.
It’s also an architect and engineer duo as well. Beautifully done and beautifully executed.
Note that the catenary curve is thus with respect to a chain, which is 2d. It works when the shape is constant in the 3rd dimension. If you want a dome, or funicular shape instead, I believe that the general shape is less wide, due to the greater mass departing from the center.
Awesome insight. Thanks Stewart.
I never knew about this upside down thing, thanks for the information! I guess it is similar to how the greats used a pinhole camera to project the image of a landscape to trace onto canvass then paint onto it - initially it is upside down then they add a lens to focus and brighten it and it places it right way up.
Regarding your sponsor here, I have the same Gillette handle I bought in 1994. It is not cheap plastic, it is metal...lol It still works perfectly after 30 years of use and has been dropped many a time!! Perhaps modern variants handles are cheap plastic crap, but my old one is not!
I love the fact my country has such a link to the Sagrada Família 🙂
I drove past the indoor Tennis Center in Allschwill, next to Basel, countless of times. It just makes sense that is was Designed this way.
How fascinating and ingenious!
1:52 did we name hooks after this guy
No, but hooke's law, probably
great observation 😂💯
No, he made compound microscope
Very interesting! Reminds me of a process called topology optimization, where you can simulate these sorts of organic forms that put material only where it's needed with computers. I haven't seen an example where the expected loads come from the structure itself, though…
Visited Barcelona earlier this year and spend some time sussing out the architecture of Gaudi. Gaudi and FLW were born the same year. FLW lived around 20 years longer because Gaudi was killed when struck by a streetcar. The fascinating contrast was that, although each man was interested in the interplay between architecture and nature, Frank Lloyd Wrong's answer was to try to control nature, metering the amount of nature that would enter into the interior of his designed spaces. In contrast, Gaudi tried to emulate nature, thereby integrating interior and exterior.
Gaudi of course used the hanging line method to design his arches, which is evident in the Sagrada Familia. In other words, he was concerned about designing structures that function. FLWrong simply ignored the physical properties of his materials and the mathematical improbabilities of his cantilevers, shoving rectangles out into the air without concern about whether they would actually function.
It really makes sense, the tension buildt by the weights results in finding the perfect shape which will make the building stronger in the end. It's kind of philosophical. If there is tension you are guided in a specific form which is best suited. If you apply this to philosophy, external guidance helps an individual to behave in a right way and to think clearly. Too many people go through the world suppressing everything which results in them speaking before thinking and really behaving dumb because they suppressed all their thoughts