filippo brunelleschi's mind and the catenary principle - Pierre ...

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The two greatest domes of former times, the Pantheon in Rome and Hagia Sophia in Istanbul, didnot require the discovery of any new physical principle for their erection, because those two churches hadbrought to the limit of feasibility the erection of great spherical domes, by means of the method ofconstruction from the bottom up; that is, with the use of central wooden platforms and multiplescaffoldings that took care of the two problems that every dome builder encounters, compression andtension, or more commonly known as push and pull, in order to prevent excessive outward horizontalthrust that architects call “hoop stress.” which causes domes to stretch at the circumference of their base.Note the (1) first stone chain at the base of the Brunelleschi cupola (Figure 3.)Figure 3 “STRUCTURAL DESIGN AND CONSTRUCTION OF BRUNELLESCHI’S DUOMO DISANTA MARIA DEL FIORE,” by T. Russell Gentry and Anatoliusz “Tolek” Lesniewski.4
However, for Brunelleschi, what was essential was the discovery of a method of erecting thegreat cupola of Florence from the heavens; that is, from the top down. The task required a state of mindthat was completely different from everyone else’s. The task was fundamentally galactic in character. Thequestion was: how do you replicate the principle underlying the dome of the heavens and apply it to the140 year old octagonal drum of the church of Santa Maria del Fiore?Part of the answer to this question is found in Cusa’s isoperimetric principle of least action. But,the principle of Cusa was not sufficient. Brunelleschi had to devise, first in his own mind, the completedform of a self-erecting cupola that would be completely self-sustaining in each of its parts as well as in itstotality. His problem was to discover what sort of new universal physical principle could resonate inaccordance with the isoperimetric principle of Cusa and be applied to a new form of paradoxical cupolathat never existed before, that is, a Gothic Dome. The fundamental requirement was to establish adynamic vault structure which would be self-reliant and would be erected without any external support.This intention required the discovery of a new physical principle of least action above and beyond whatCusa had already discovered, and above and beyond already existing architectonic principles. Theproblem required going beyond the limits of simple circular and spherical action, and Brunelleschi wasstanding alone in front of the future asking: “How do you go beyond the limits of an axiomatic change?”Specifically, what Brunelleschi had to do was to discover how to go beyond the limits of positivecurvature exemplified by Romanesque domes and arches of the past. He had to break completely withtradition and with every architectural idea that existed up to that time. He had to discover how theprinciple of positive curvature and the principle of negative curvature came together harmonically. Thatwas the only way to solve the limitations posed by the Florentine cupola.By investigating the new domain of negative curvature with Cusa, Brunelleschi was alreadypreparing the terrain for Leonardo da Vinci, Leibniz, Gauss, and Riemann’s transcendental functions ofelliptic and hyperbolic constructive geometry, and he was expanding human knowledge in the direction ofa new form of galactic thinking that required the investigation of singularities of magnetohydrodynamicnature, such as shock waves in the domain of universal cosmic radiation. It is by studying the limitconditions of such an axiomatic system like the system of positive and negative curvatures of a cupola,and by introducing new hypotheses for experimenting with the tensile capacity of change in curvatureunder great pressure that new discoveries of principle are made. Those are the non-linear conditions thatBrunelleschi required to apply to his cupola that Cusa helped to bring about.What Cusa introduced in his 1440 publication of Docta Ignorantia was the sort of meditation thatSaint Augustine had already identified as the extra measure of help that God brings to man when herecognizes his weaknesses at the limits of his creative thinking process. As Augustine put it: “Therefore,as I say, there is in us a certain learned ignorance, but learned from the Spirit of God, who helps us inour weakness.” «Est ergo in nobis quaedam, ut dicam, docta ignorantia, sed docta spiritu dei, quiadiuvat infirmitatem nostram » (Epist. ad Probam 130, c. 15, § 28) That is to say, at the limit, there is aknowledge of principles that is beyond sense-perception and beyond human understanding, but which islocated in the axiomatic changes that Brunelleschi and Cusa identified as the boundary conditionsbetween scientific knowledge, artistic composition, and the infinite. Cusa provided Brunelleschi with theknowledge that would lead him to discover the solution to the identification of opposites in his own5
Page 1: 1 of 26From the desk of Pierre Beau
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Page 25 and 26: While some of Toscanelli’s discov

filippo brunelleschi's mind and the catenary principle - Pierre ...

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