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The Divine Cube


Juan de Herrera was one the main collaborators of king Philip II, architect of the Escorial, and long life student of the Art of Ramon Llull. One of his few writings is a manuscript treatise known as Discurso de la figura cubica in which he attempts to adapt the Euclidean definition of the cube to the Art. According to him, the cube is a tridimensional projection of the correlatives that constitute its main axes of action. The cube is a universal form performs Philip II in a epistemological, political, and religious fashion; a form that, at the same time, generates any possible being of nature and can encompass all of it.

Speculative geometry developed as the most theoretical part of the study of the size and shape of figure. For many authors it constituted the opportunity of proving theological or moral arguments based on something other than doctrine. Ramon Llull wrote his New Geometry (Paris, 1299) when he had the opportunity to read Euclid’s Elements of Geometry in the version prepared by Abelard of Bath and revised by Campanus of Novara (1254), popular in academic circles at the time. He thought that his Art would produce a better understanding of geometry than Euclid, hence the adjective of new in the title. Its speculative nature comes from the fact that for Ramon Llull the figures correspond to values already established in the Art: the sides of the triangle was a diagram for the Augustinian theory of the three potencies (understanding, memory, and will) and the sides of the square were the four elements of nature (earth, fire, wind, and water). The master figure of his geometry is the one in which three superposed squares of increasing measure and a circle inside them –one in which a circle is inscribed, one that inscribes the same circle, and a third one in-between– are theorized as solving the problem of squaring the circle. Differently from what this meant to alchemists, the problem of squaring the circle was for Ramon Llull not the solution of an impossible puzzle that would open the door to secret knowledge. Rather than that, Ramon Llull followed in his geometrical treatise his common modus operandi of translate the principles of his own Art to an already established body of knowledge. However, the nature of this endeavor was somewhat paradoxical as the Art is composed itself of geometrical figures. Consequently, the New Geometry would serve as further prove that the figures of the Art possessed an aesthetic quality that translated perfectly from its values to its operative figures.

Llull’s geometry is a purely abstract discipline. Instead, Herrera writes his treatise [Declaración de] las figuras que es neçesario penetrar y entender para introduçión del cubo in order to inscribe again the geometry of the Art in space, to make it applicable to actual problems he was dealing with as the architect of the Escorial. That is certainly the reason why the treatise is preserved in 40 folia of a parchment manuscript with other writings about mathematics and geometry. In a sense, Herrera’s escurialense intervention on the Art is not different from what I explored in the first chapter, in the context of Nicolau de Pacs’s collaboration with Cisneros. Both through printed books and manuscripts put the Art in conversation with other disciplines, make it reflect on current political projects, and defend its legitimacy: “[…] entiendo haber hecho particulares servicios en haber desengañado de muchas máquinas, que algunas personas no fundadas en ellas han traido á estos reinos y á S.M., ofresciendo con ellas cosas imposibles y no concedidas de la natura.” [I claim to have rendered particular service debunking many machines that people not based in sciences have brought to our kingdoms and to his majesty, offering with such machine impossible things and not conceded to nature.] By denying the legitimacy of alchemy and the use of impossible ingenios, Herrera stated the legitimacy of the Art. Juan de Herrera probably knew, as he was the one who had studied the Art for a longer period in the circle of Philip II, that the alchemical works of Ramon Llull were apocryphal. Furthermore, he felt like a part of his scientific expertise had to be devoted to promote good technological options instead of bad and unproductive ones. Inside this role, there is an underlying question of what it means to study nature, what are its boundaries, and why the Art captures its ruling principle. The battle that he seems to have conducted most of his life is one for education and technical knowledge. That seems to point to two different things: he does not come from an understanding of the Art as an instrument of conversion anymore, but from a mainly technical understanding of the Art. In other words, Juan de Herrera represents the historical and epistemological point where the fracture between the Cisnerian complutenses and the Philippine escurialenses occurs.

With writing of the Discurso de la figura cubica, Juan de Herrera attempts to solve the logical puzzle of finding a geometrical development for the Art of Ramon Llull. In order to perform this adaptation does not only Herrera need to know both the Art and Euclidean geometry, but also he needs to be able to tear them inside out and to find out which pieces forming the mechanic of the Ramon Llull’s logic machine can become a way of explaining geometry. Herrera chooses the tridimensional figure of the cube because of its perfection and because it describes a perfectly self-contained portion of space defined by a square angle formed by three equally measuring lines. The three defining lines of the cube coincide with the three possible vectors that decline every subject present in reality according to Ramon Llull; these three vectors have a grammatical nature since the Art is meant to create discourse parsing everyone of its subjects. Herrera reduces the correlatives to a number of three: –tivum [noun], –bile [adjective], and –are [verb]. The cube articulates geometrically a way of understanding reality the same way the Art articulates it in a discursive fashion:

[…] i entonçes ay en el cubo relaçion ternal que es el tivum. bile y Are de Raymundo los cuales son de la essiençia. y natura del mismo cubo, en el qual ay plenitud y cumplimiento total de diferençias plenitudinales, sin falta ni sobra y totalidad de mixtiones i de perfiçiones. (87-8)

[And thus, there is a threefold relationship in the cube that is the –tivum, –bile, and –are from Raymundus, which are the essence and nature of the same cube. There is wholeness, accomplishing of all the plenitudinary differences, without lack or excess, and totality of mixes and perfections.]

In other words, if according to Llull there are nine subjects, according to Herrera the cube contains them all as it develops in three axes that coincide with the three possible states of being. Therefore, by showing that the Art of Ramon Llull and the Euclidean cube are compatible, Herrera states that they share a common principle. A principle that both reveal but that at the same is exterior to both.

Fittingly, the Art of Ramon Llull had proved since its inception to adapt better to informal environments of learning than to academic ones. Even though the Escorial is an institution created partially to pursue academic endeavors, its structure is very different from that of a university inasmuch as it was not built based on a stable curriculum, but on a conversation that had Philip II as a center. Two are arguably the reasons why Philip II decide to build the Escorial as a place of intellectual conversation instead of a university, like Cisneros had done with the Colegio de San Ildefonso. The first is that the Escorial allowed Philip II to not be bound to a place where the business of the state happen, separately from the intellectual discussions he wanted to promote. If the Escorial was an extension of Philip II, then it had to encompass all the facets of his personality without contradiction; at the same time, all the discussions happening inside the Escorial –including the ones about the Art of Ramon Llull– constitute its personality. The second is that university is an institution where the major intellectual agency is outside the king’s influence. In terms of intellectual discussion, building the Escorial might have been the most enduringly forward-thinking move Philip II ever made. Instead of fighting against the universities controlled by the religious establishment, he creates a different place allowing a different conversation to happen. The Univeristy of Paris banned teaching for more than a century, the constitutions of the University of Sevilla banned teaching the Art from its inception, but the Escorial was actually not a place for teaching the Art.

In some forms of private circulation and practice of the Art, a cosmological interpretation is happening. Such interpretation extricates its figures and extrapolates to a new understanding of the world. This understanding comes from the expansion of the horizons of the world, according to the classic thesis of Alexandre Koyré, and characterizes the traditional narrative explaining early modern intellectual history. However, the transition towards this newly acquired consciousness of a vast universe is not without consequence as it entails a dramatic lost of epistemological perspective. If humans are expelled to the edge of their own universe from the center, then trying to read the space and inscribe it inside the logic of the Art of Ramon Llull makes sense as an attempt to find orientation in space. Orientation is a product of the perception of asymmetry, yet the Art is a machine of transforming any possible asymmetry in the world into a product of its own functioning logic. Evidence of this cosmological interpretation infiltrating the portability appears in a printed apocryphal treatise entitled De audito cabbalistico (1516) about the combination of Lullism and Christian Kabbalah written by Piero Mainardi, who taught surgery at the University of Padova. The treatise includes a detailed explanation of the Art according to its simplified version of the Ars brevis combining it with magic symbols and proving its character of universal key to knowledge. It serves as evidence of the porosity of the portability including approaches to the Art that are eccentric in relation to its tradition and, at the same time, of the indistinguishable way it includes original and apocryphal works.

Among the treatises that repurpose the figures of the Art is Pietro Mainardi’s De audito kabbalistico (1508). Its first image represents the three main geometrical components used in Llull’s: circle, square, and triangle. The circle is divided in three equal sections in which it is written: “Figura totum./ Reprehesentans/creatum.” [This figure represents all the creation.] Between the circle above and the square and the triangle below there is a line of text: “Totum creatum est corpus sphaericum extra quod nihil est.” [All the creation is a spherical body outside of which there is nothing.] The geometrical interpretation of the Art of Ramon Llull did not start with Juan de Herrera, but was developed in Lullist apocryphal writings already at least as soon as the beginning of the sixteenth-century. Such interpretation contains a curious paradox. Geometrical figures are the stuff the Art is made off, yet extricating the figures out of the terms of the combinatory was not what Ramon Llull intended to become its intellectual practice. Nonetheless, this literal application of the combinatory mechanisms of the Art to the world seems only a logic consequence of one of the most common criticism the works of Ramon Llull faced throughout the centuries: its impenetrable nature. Superposing the two-dimensional figures of the Art of Ramon Llull upon the world meant also making them three-dimensional, so the defining combinatory circle of the fourth figure becomes spherical as a way of adapting to the consciousness of a vast universe.

If the Escorial is at the same time a monastery, a library, and a palace, the reason is that all those things are integrated in the king’s personality. The place of the cult and the place of the politics and the place of science are one of the same, the Escorial only makes sense is the king is in it, so the Escorial is the place is a metonymy for the king. It points to the paradise and contains the globe metaphorically. So, the Escorial is not only Ramon Llull. The Art of Ramon Llull is responsible for the form of the Escorial, but the Escorial is included in a discourse about the theological sense of history and points to its wholeness, to its ending. The Escorial establishes a paradox of embodying as a form the place where the body of the king can rest and at the same time be inside the theater of power, religion, and knowledge. Behind the Escorial is the idea that the Spanish Empire is a transhistorical subject subject that God chooses and to honor said choice. The Escorial is at the same time an arrow pointing to the mystical destiny of Spain and its receptacle: a window that is open to the edge of the world where salvation resides and to the center where the specifics of the expansion of the Empire is planned. Its position as incarnation of the particularities of history and its transcendence is the foundational paradox of the building.

Last Updated 11 months ago


  • Badia, Lola. ”Ramón Llull y la cuadratura del círculo.” Concentus Libri 12 (2000): 300-305. Print.
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  • Herrera, Juan de. [Declaración de] las figuras que es neçesario penetrar y entender para introduçión del cubo. San Lorenzo del Escorial: Biblioteca del Real Monasterio, [2nd half of Sixteenth-century]. MS. d.III.25. Manuscript.
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  • Wilkinson-Zerner, Catherine. Juan de Herrera: Architect to Philip II of Spain. New Haven & London: Yale UP, 1993. Print.



Noel Blanco Mourelle, « The Divine Cube », Blogs, Columbia University | LAIC, Department of Latin American and Iberian Cultures (online), published on April 20, 2016. Full URL for this article

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