So he challenged them; people tried, and they couldn’t do it. And they said, “All right, Brunelleschi, how do you make an egg stand on its end?” And he said, “like this”—he cracked the bottom of the egg, so it was flat, and then set the egg there. And as the story goes, “Well, if we knew that, we all could have done it!”
And he said, “Exactly! But you didn’t know that.” He said, “I know how to build this Dome. You wouldn’t understand it. I’m your man. Hire me.”
Well, the decision wasn’t reached until 1420, but he was hired—along with Ghiberti, which was sort of awkward, but Brunelleschi was in charge of the construction, and so in 1420 he was able to start the building of it.

FIGURE 7

The façade of the Ospedale degli Innocenti, Florence.
Now, while the committee was still deciding who would build the Dome, how it would be done, Brunelleschi got a few other commissions, so I want to show some pictures of some of his other work: This is the Ospedale degli Innocenti, which was an orphanage. (Figure 7) And in the likeness of the great palaces of the rich families, Brunelleschi built what’s called a loggia, this patio or this porch on the front of it. This is something he had designed; he really changed the way the columns were used, and this was part of an overall humanist orientation of concern for human beings: a large, beautiful building, built at the expense of one of the guilds, to take care of the orphan children of the city.

FIGURE 8

Brunelleschi’s Pazzi Chapel, completed in 1443.  creative commons/Gryffindor
This is another work of his, and—out of order,—this is the Pazzi Chapel, the “singing chapel,” which actually came much more towards the end of his life. (Figure 8)
Now, back to the Dome: Just to give a sense of how high this thing is, the Cathedral reaches up to a height of 140 feet,—that’s the height of the whole length of the nave; then you see the Dome. Before it starts, there’s another section, which has those large circular windows—it’s called the “tambour,”—that’s another 30 feet. So, the Dome begins at 170 feet! That’s already more than double the height at which the Pantheon’s dome began in Rome. It then extends up to a height of over 300 feet, more than double, again, the height of the Pantheon.
Now, in terms of why centering couldn’t be done, you couldn’t get enough wood to build this. It would have taken between 500 and 1,000 trees; there were no trees that were even tall enough. In later centuries, the only place the British Navy could get timber for their masts of over 100 feet for its largest ships, was in the New World. There simply weren’t enough tall trees anywhere in Europe that they could find. And the same was true at the time this was built. It would just be impossible.
The other thing is that because of the time it took the masonry to set,—because it ended up taking sixteen years to build this Dome,—if a wood frame had been built, it would have lost its shape over sixteen years, and it wouldn’t have worked anyway! So, even if you had had all the wood, you couldn’t have done this with a center.

Inventions

But Brunelleschi had a totally different approach to space and to the physical nature of construction. Instead of looking at a shape very geometrically, as was done with the earlier arches and domes we saw, where you design a geometric shape that you’d like,—It’s not inherently stable during its construction, so you have to support it,—get the shape, and then you’re fine,—Brunelleschi has built a structure—obviously, he succeeded—where along the way, it’s stable. So the stability is built into every part of the Dome, not into the Dome as a whole. As an early Italian historian had said, “It was as if every part of the Dome was the keystone” that gave the stability: It was everywhere stable.

FIGURE 9

Brunelleschi’s winch, featuring forward and reverse gears.
Now, let’s talk about actually building the Dome and the techniques that Brunelleschi used. One of them was that there’s a lot of material that you’ve got to bring up there. If you were going to have workmen carry four million bricks up those steps, it’s going to take you forever, and it just wouldn’t work. So what Brunelleschi had done: he designed a new kind of winch. (Figure 9) Before Brunelleschi, everybody used treadmills for building these cathedrals,—like the hamster wheel you see at the pet store, but a large one, with people in it. And people would run in these treadmills, and it would twist and wind a rope, which would lift up along a pulley, it would lift a load up to the top, where you would have your materials delivered.
Well, instead of having people do this job, Brunelleschi’s design used oxen—this illustration uses a horse instead,—that instead of walking in a treadmill, they walked in a circle. And he also developed for the first time, a gear system. So just like in your car, you can switch your car into reverse,—the same thing with this. You could see the axle that’s being twisted by the animals, this vertical axle. There’s two different ways it can engage with the horizontal winch system. And by raising or lowering the axle that the animals are turning, you can put it in either forward or reverse, because every time you bring a bucket of materials up, you obviously have to bring it back down again.
Apparently oxen are very stubborn, and they will happily walk forward as long as you ask them to, but they won’t walk backwards. So to avoid having to get them out of their harnesses, and turn them around, Brunelleschi developed this transmission system so they could always be oxen, and walk forward, and everybody was happy.

FIGURE 10

Leonardo da Vinci’s depiction of Brunelleschi’s crane.  Code Ambrosiano
Another thing that he had to do, was once you got the material up the top of the Dome, you had to then put it in the right place. Some of these things that he used, weighed thousands of tons. We’re going to get to what some of these large components were. So he also designed a crane, which is perhaps somewhat hard to see, but a crane, called a “castello.” (Figure 10) This is a drawing by da Vinci—da Vinci was actually involved later with the work on the Cathedral. Da Vinci sketched a number of the things that Brunelleschi had done, and so some people thought that he had invented them. but he was just drawing what Brunelleschi had made: a crane complete with counterweight, so you could position and get all of your larger objects exactly where they needed to be in the Cathedral—another major innovation.

FIGURE 11

Drawings adapted from Bartoli’s Requiem per una cupola, Florence, 1988.
Now, on the shape of it: This is a diagram of the shape of the Dome. (Figure 11) It’s not a spherical dome. It goes up to a higher level, so it’s called a “pointed fifth,” where you take two portions of a circle, and then they would meet at a point, except there’s a hole left at the center of the Dome, and this is part of what made it so tall and magnificent compared with the frankly ugly Pantheon. It also reduces the amount of horizontal stress at the base by designing it this way.

Figure 12

View full sizeLando BartoliDrawings adapted from Bartoli’s Requiem per una cupola, Florence, 1988.
So, when Brunelleschi did his construction—this shows you—the Dome is actually two domes: there an inner dome, and then there is an outer dome which is the one we see from the outside. (Figure 12) The inner dome, at its base—remember the Pantheon in Rome, twenty-three feet thick; Brunelleschi’s inner dome is only seven feet thick at the base and only five feet thick at the apex. The outer dome is only two feet thick at the base, and one foot thick at the top. Imagine, something of this size, that outer dome, only one foot thick: The outer dome is supported by the inner dome.

FIGURE 13

One of the four sandstone chains still visible in the Dome.
So in doing this, he had to use this catenary again, and he actually built catenas, he built chains inside the Dome, like the hoops in a barrel that hold the staves together. So this is a picture of one of them. (Figure 13) There are four sandstone chains, where large blocks of sandstone had been quarried: These are some of the things you needed the crane for, because people couldn’t have carried these and put them into place. They’re just too heavy. The crane would be used.

Enemies Attack Him

So these sandstone chains were built, in not exactly circles, because the thing’s octagonal, but there are four of these chains that help hold the stress in, that pull the Cathedral inward so it doesn’t explode outwards. The records also indicate that there are four iron chains as well, although they can’t be seen. If they’re there, they’re inside the masonry; and also a wooden chain, which is still there—a wooden chain to help hold the stress, which is astonishing.
Another aspect of the construction—well, let’s go ahead and do this: Some of the bricks that were laid in the Dome, which was made out of brick rather than stone—brick is lighter than stone, because it has so many air pockets in it. He had the workmen lay the bricks in a very unusual pattern, and it also required unusually shaped bricks, custom-made, custom-shaped bricks: four million bricks.
To get a sense of the work involved, these bricks, after they were formed and put in their molds—it might take two years of preparation before they would be fired,—seasoning time—and the unique pattern that Brunelleschi used, this herringbone or fishbone pattern, meant that you didn’t have just pure shelves of bricks all the same, that could then shear apart. (Figure 14) It also meant that, because of the orientation, it helped the lower levels support the ones above it. So every aspect of this is unique in terms of the engineering, the industrial engineering to produce everything, in terms of the actual construction techniques.

FIGURE 14

The herringbone brickwork in the space between the inner and outer domes.
Okay, a couple more things about the construction: Brunelleschi also received the world’s first patent. It didn’t work out so well, but he built a ship to bring the marble from the quarries to Florence. As you see, the ribs on the Dome are a nice white color; that’s from marble which had then been placed around the brick. And Brunelleschi said, “I’ll make a ship that’ll do this,” and some people think it was to have been powered by either treadmills or oxen that would actually have paddlewheels. Unfortunately the ship sank, the marble was lost; some of it was recovered in an amazing salvage operation. But this just shows you how many different things Brunelleschi’s working on: perspective, construction, engineering.
One other thing about the construction is that, according to the official records, only one workman died in building this Dome, which is phenomenal, considering the height. Brunelleschi had safety rules, safety harnesses, safety platforms. The people working at the very highest levels weren’t allowed to drink wine, pure wine—they had to dilute their wine with one-third water, so they wouldn’t be quite so drunk while working at those heights. And there were strict rules that no one was allowed to sit in the baskets when they were going up and down; you had to use the steps.
As he was building this Dome, at a certain point, Brunelleschi was thrown in jail for not paying his dues to the guild, which was a very small amount of money, and was obviously a political attack against him. And he was attacked explicitly by some of his detractors. People were more cultured at this time, and when they insulted each other, on occasion, they wrote sonnets. So, I’d like to read you these shared insult sonnets. This is from an acquaintance of Ghiberti who attacked Brunelleschi, and he wrote this sonnet to him!

O you deep fountain, pit of ignorance,
You miserable beast and imbecile,
Who thinks uncertain things can be made visible:
There is no substance to your alchemy.
The fickle mob, eternally deceived
In all its hope, may still believe you,
But never will you, worthless nobody,
Make that come true which is impossible.
So if the “Badalon,” your water bird,
Were ever finished—which can never be—
I would no longer read on Dante at school
But finish my existence with my hand.
Because I am certain that you are mad, as you hardly know
Your own profession. Leave us, please, alone.

So this guy didn’t have to commit suicide, as he had offered, because Brunelleschi’s ship, the “Badalon,” didn’t work. But here’s Brunelleschi’s response.

When hope is given to us by Heaven,
O you ridiculous-looking beast,
We rise above corruptible matter
And gain the strength of clearest sight.
A fool will lose what hope he has,
For all experience disappoints him.
For wise men nothing that exists
Remains unseen; they do not share
The idle dreams of would-be scholars.
Only the artist, not the fool
Discovers that which nature hides.
Therefore untangle the web of  your verses,
Lest they strike sour notes in the dance
When your “impossible” comes to pass.

Columbus and Kepler

So, it’s very blatant: What you’re doing is impossible, and you’re an ignorant beast, so give up, it’ll never happen, “experience teaches us it’s impossible. . .” And look at what Brunelleschi said, “Untangle the web of your verses, lest they strike sour notes in the dance, when your ‘impossible’ comes to pass.”
So, a few more things about the Dome: The cupola was completed in 1436, which was a momentous year. Pope Eugene IV came to consecrate the Cathedral. The bishop laid the last brick in the cupola later that year. And then, from 1439 for several years, the Council of Florence—which would have been the Council of Ferrara except that the plague had them move to Florence, courtesy of some financial help from the Medicis—the Council of Florence, organized by Cusa, was held in this amazing Cathedral, the cupola of which had just been completed. And there’s no doubt that the experience of such an awesome work helped the conference, gave a new impetus and concept to the Council. I’m not going to say too much more about that: We need to have a whole discussion about Cusa, but that’s not happening right now.
So, the last few parts: In 1446, Brunelleschi passes away, after having seen the cupola finished. And then, as I said, some other people are involved, as I said. Da Vinci as one of the workmen in Verrocchio’s workshop helped cast the large bronze ball that you see at the top; and then in 1474, or ’75, Toscanelli added a plate into the lantern with a hole in it, so that the Sun would make a nice spot down below. (Figure 15) He used this to correct the Alfonsine astronomical tables, to have the most accurate observations of the Sun that had ever yet been made. Due to the incredible height of the Dome and its stability, it was now possible to have greater precision than ever before by watching—basically, it’s a sundial—the spot move along floor. That marbled circle that you see there is the summer solstice.

FIGURE 15

The Renaissance astonomical instrument called the gnomon in the Cathedral of Santa Maria del Fiore, invented in 1475 by Paolo Toscanelli, and restored by Father Leonardo Ximenes in 1754.
So, Toscanelli was able to redesign these tables which were used by navigators to get around the seas. He works on a world map; Toscanelli had written to the Portuguese royal court to propose sailing west to get to China. He didn’t hear back from them, but later Christopher Columbus found Toscanelli’s letter, and wrote back to him, very excited. So Toscanelli and Columbus, in 1481, entered into a correspondence about this; in 1486, Columbus petitioned to have an audience with the court of Spain, Ferdinand and Isabella. And as we know, in 1492, armed with the knowledge of astronomy from Toscanelli, and a map provided him by Toscanelli, he set sail west to reach the Orient.
So the Dome, in a very real way, helped in the creation of the New World. I know that’s a lot already, but I do want to say a little bit about Kepler, too.
Just very briefly, on this triad—and Cusa, we’re going to have to come back to—but what Brunelleschi had done with understanding that in the small, space isn’t geometric, it’s physical,—this is what Kepler used to solve a problem that had been puzzling him since he was a young man in college. It was in astronomy: Why do the planets move the way that they do,—not just individually, but all of them? Why does the Solar System move as it does, and he did think it was a Solar System.
In his first major book, from 1596, the Mysterium Cosmographicum, Kepler published this model (Figure 16) for the distances between the various planets in the Solar System; Kepler said that they wouldn’t just have arbitrary distances, there must be some reason to it. So what he did was that he looked at something that was characteristic of space itself, which was these five Platonic solids, as they’re known. They get small toward the center, but you can see that we have spheres, separated by a cube; inside it we see the triangle-based tetrahedron; inside it a dodecahedron; and then an icosahedron, and an octahedron.
Those five shapes are the only ways that you can divide up a sphere evenly, with regular shapes. In other words, it’s the only five ways that you could, for example, take an orange, and cut up the peel into tiles, such that all the tiles look exactly the same and were regular shapes—only five of them.

From Brunelleschi to Kepler

Why are there only five? Space seems to be empty: It doesn’t seem to have any characteristics about it, but if you look at doing things in space, you find that some actions are possible, and some aren’t. So Kepler believed that given that these were something inherent in how space works, that it would then be found in the spatial organization of planets.
To determine whether he was right or not, he had to get a more accurate idea about how the planets moved, so in his second very major work, The New Astronomy he completely revolutionized the process of astronomy: very briefly, he took this Brunelleschi approach, that in the small, there is no linearity; there is only physical action. And he implemented his idea that he had had since his college days,—that the Sun was making the planets move,—and developed the idea that at each moment, the distance from the Sun was determining how much the Sun was moving the planet and would determine its speed. He then had to figure out a way to use that motion at each moment, and turn it into an orbit as a whole.
He also had to come back to the distances of the planets, because these solids indicate overall one distance for each planet, but every planet has two characteristic distances—its closest distance from the Sun and its farthest distance. To figure this out, Kepler then moved to another domain—it seems like another; it seems like another sensory domain,—even though he goes beyond the senses,—namely sound.
So just as these solids divide the spatial space, Kepler also looked at dividing aural, “heard” space, the space of hearing, of sound, of music. And by looking at the harmonic intervals, not by building up music from the half-step, from the smallest musical interval—he did not do that! Instead, he looked at the larger ones that were most stable: the octave, the fifth, for example. He built up an idea of how to create the scale, and then looked at how the planets could achieve a musical completeness: How could the planets move, such that they created both the major and the minor scales? (Figure 17)

Figure 17

View full size One of Kepler’s depictions in the Harmonia Mundi.
So Kepler puts himself in God’s shoes; he designs the Solar System himself; he explains why he would have first used the solids as his main grounding, and then he would have incorporated the necessities of music to develop an entirety of the system where nothing was left to chance in the planets, at least not in those two extreme distances. And just to show you,—you don’t have to look at the numbers,—but either the closest or farthest motions of the planets had speeds which, if the speed of motion were heard by the Sun,—which doesn’t have much of a sense of hearing,—as sounds, then these visual speeds as sounds would be harmonic. What a confluence of different senses that seem to be different! They weren’t: It was all one type of harmonics for Kepler.
So putting the whole thing together, Kepler created the Solar System, as a system. He implemented in the small, as Brunelleschi had done, how everything is physical in the small, and he developed the concept of an “all” and why the “all” should be as it is.
We’ll talk more later in other shows about Cusa, who obviously we just mentioned here, as well as the other triad: about Planck in the small, Einstein in the large, the paradoxes between them, and how to resolve that. But hopefully, we provided some good insight into why—how it is that these three, Brunelleschi, Cusa, and Kepler, helped define modern science, and why we have to know what they did.
Lyndon LaRouche: Well, first of all, one thing which is left out here, is the question of the catenary. Because you have two concepts which are at the center of Brunelleschi’s work: one is the infinitesimal, and it was always,—this was the understanding of light. The attempt to understand a system of light, which was one of his earlier works. The second was the hanging chain principle.
Now, the hanging chain principle is something which destroys entirely the concept of linear space and time. His whole design, his construction, was based on the hanging chain principle, which existed widely in Italy. You had these deep clefts and so forth, and you would have bridges from one side of cleft to the other side, and you would walk across these bridges, the bridges would dance, [laughter] themselves. And this is the famous song. . . .
Ross: Oh, “Funiculi, funicula.”

The Struggle against Zeus

LaRouche: Yes, that was the song which was on this theme of the hanging chain. So what happened, is now suddenly you are out of the area of space as such, entirely; it does not exist. What exists is action in space, and you have to define the action in space by its own characteristic. And the hanging chain principle is a demonstration of that characteristic.
So this is the relationship—you know, from that point on, everything that was the so-called “Classical Greek,” heretofore Classical Greek, fell apart. Because there was no way you could have a linear construction of the universe. And through the whole process, that’s what you’re getting at: there’s no linear construction order of the universe. It is not based on a mathematical system.
So mathematics is the deadening of the soul, and we see the mathematicians, we see they have Dead Souls. It’s like the accountants: The accountants have the characteristics of having Dead Souls. They die in the middle of their work, but they weren’t going anyplace anyway.
So this is what the crucial issue is. So the idea, the notion that there is an infinitesimal, comes not from the small. It comes from the large, because we experience the relatively large. And we find that the principle of action does not correspond to a linear extrapolation. And then, you get everything which then comes from Kepler’s work, is actually a finished work! Which is why I’ve defined this thing as a finished work. That Kepler made a phased completion of a concept, of the idea of physical space, action in physical space, as opposed to linear space. So the point is, it was everything against Euclid, and everything that Euclid represented was recognized as being evil. And the necessity was to find a principle which corresponded to that which is not evil.
And evil was equated with slavery: raw human behavior, as a slavery, or a system which reduced itself to slavery. It comes up in the case of the Great Pyramids, where the lie was the attempt to interpret the Great Pyramids as being a linear construction, made by slaves and so forth—nonsense! It couldn’t have been done that way. They were floating these things down the Nile, and that’s why it was there,—they were floating these things. They were using sand as a fluid, and they were using the sand as a fluid form, as a means of construction.
And at the base of these Great Pyramids, what you had there were not slave quarters,—these were engineering quarters! So the Great Pyramid project was an engineering project which used the Nile and used the sands of the desert—it was not as much desert then, but the sands of the desert were used as a device, an engineering device. By moving sand and moving water and displacing one thing and another, you came up with an engineering scheme. And what they called the “slave quarters” in the standard interpretation were actually the engineering headquarters, in which the families lived in these quarters, next to these pyramidal constructions. They lived there, and they did the work.

The pyramids at Giza, Egypt: great projects which were completed in 2540 B.C.
But they did the work based on use of sand and water as media of action. It’s a completely different conception!
So the struggle has always been the anti-Zeusian struggle. Zeusians always insisted that you could do things only one way, by massive use of slaves: the human being as a slave, with no constructive, no dynamic conception whatsoever. And so what the history was, was based on this fraud, this assumption that you have to start from slaves, from primitive human work, done primitively.
The idea of the intellect, the development of the intellect, was completely opposed. And so what you get in this when you get to the hanging chain principle,—you see a very simple demonstration by these hanging chain bridges particularly characteristic of Italy—“Funiculi, Funicula”—that this kind of process was a characteristic, a physical characteristic of physical space-time. It wasn’t the whole characteristic, but it was a reflection of the characteristic.
So, he didn’t go to zero, the concept of a mathematical zero point. There was never a zero point in his work! The point was, the universe was defined by an action process, a process of action, which is only cognizable by the noëtic powers of humanity; that is, the use of the hanging chain as a bridge across a chasm, was typical of this kind of demonstration.
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