de natura instrumentorum

Welcome to the Fall 2012 project section of ARCH531 (Architectural Intentions from Vitruvius to the Renaissance), a lecture course taught by Prof. Alberto Perez-Gomez at McGill University, School of Architecture, with this project segment conceived and taught by me.

The project theme for this term was de natura instrumentorum, or the nature of instruments, and following books 9 and 10 in Vitruvius’s Ten Books of Architecture, we explored the status of instruments and machines from antiquity through to the Renaissance. In Exercise 1, early forms of computing (e.g. paper machines or volvelles, astrolabes) were investigated, and Exercise 2 involved replicating the map of Rome as well as the ‘horizon’ instrument invented by Leon Battista Alberti (1404-1472). Exercise 3 explored machines, mechanisms, and contrivances from antiquity to the Renaissance, using them as inspiration towards creating original work.

Please click on the links above to see the project and exercise descriptions, and to leave comments.

Yelda Nasifoglu, project instructor for Fall 2012
@YeldaNasif
yelda.nasifoglu[at]mail.mcgill.ca

Exercise 3: Drawing machine – deconstructing a 2-D image

Our initial research focused on several drawing machines from the Renaissance such as Jacopo Barozzi da Vignola’s Bi-Dimensional perspectograph (developed between 1527-1545), Jacques Besson’s Drawing Machine from Theatrum instrumentorum et machinarum (1578), Albrecht Dürer’s perspectograph (Dürer’s Door – 1525) and other machines that have since been reiterated by people such as JH Lambert in 1752 and recently for purposes of abstract art by Eske Rex.

 Inspired in most part by a machine developed by an unknown artist we saw on the internet, we became interested in developing a drawing machine that would generate the cams that could produce a 2-D drawing.

A cam changes the input motion, which is usually rotary, to a reciprocating motion of the follower. Cams can be shaped to change the way the follower moves. The shape of the cam is called the profile. If a cam rotates clockwise, the movement of the follower in 1 would be a gradual rise and fall motion for each rotation; the follower in 2 would rise and fall twice for each rotation; in 3, the follower would be motionless for half the cycle and then rise and fall; and the follower in 4 would rise gradually and then fall suddenly. Note that 1, 2 and 3 would have the same result if the cam was rotating anticlockwise; 3 would jam. These aren’t the only shapes you can use. Anything goes…depending on what sort of motion you want…though there are practical limitations to making these things out of wood.

Our drawing machine, thus, acts to develop a shape (not necessarily circular) that would deconstruct a drawing into horizontal and vertical data. Theoretically, this data could in turn be plugged back into the process to generate the original drawing.

Next we decided to fabricate a machine that would automate step two. For this to occur, a series of gears would navigate two arms vertically and horizontally. These arms are connected to the “master” pen that traces a 2-dimensional drawing. The veritcal and horixzontal arms hold pens to record data on a moving canvas. We decided to deconstruct Henri Matisse’s “Blue Nude” (1952). Matisse’s painting is a rather simple outline of 2-Dimensional figure, one that would be fairly easy to trace with our machine. Furthermore, we were intrigued to see the outcome that would occur by deconstructing an already semi-abstract painting.

Alberti conference

For those of you interested in Alberti: University of Coimbra in Portugal is organizing an international conference “Digital Alberti: Tradition and innovation in the architectural theory and practice.”

Deadline for abstract submissions is February 3rd.

Exercise 3: Jack Bian’s Verge and Foliot Escapement Clock

A verge and foliot is a clock reduced to its simplest elements. A suspended mass M provides a torque that drives the verge and foliot escapement (at top) alternately in one direction and then the other.
The verge and foliot escapement mechanism permits a mathematically simple illustration of a dynamical system exhibiting a limit cycle and stability. Similar to the previous exercise in the construction of the astrolabe and Alberti’s map of Rome, the Verge and Foliot Escapement follows a mathematical logic. One can determine time by the dial’s position or the mass’s location above the ground.

The beauty lies in the physical connection to the surrounding world. The clock is gravity-driven and one could sense this connection as the mass drops. Like how the astrolabe relate to the heavenly bodies, the Verge and Foliot relate to the earthly body.

The suspended weight causes the gear wheel to rotate. This rotation brings a peg into contract with one of the pallets. The rotation brings a peg into contact with one of the pallets, causing the verge and foliot escapement to rotate. By the time that the escapement rotation has reached angle P, the right gear wheel has disengaged the right pallet, and now the left gear wheel engages the left pallet, causing the escapement to rotate in the opposite sense. Because of the inertia provided by the foliot masses, the gear wheels’ rotation is interrupted. The result is a regular oscillation of the escapement and a slow rotation of the gear wheels.

Giovanni Dondi’s Astrarium

by Jean-Roch Marion

When first confronted with the task of making a paper astrolabe as our first assignment, I became interested in the history of different types of medieval astronomical computers (clocks, astrolabes, equatoriums) in order to understand the origins of modern technology and modern thought. Contrary to contemporary electronics, the function of mechanical computers can be perceived by our senses and allow us to understand complicated processes with a simple physical action. Just like clocks and watches, the astrolabes were instruments created in order to compute what was perceived as natural cycles (the moon, the sun and the stars). They simulate the movement of the main celestial objects on a small scale map of the skies engraved on discs that you can manipulate to compute various data. Behind the front plate of the astrolabe, you can also find mathematical instruments that allow you to make complicated operations physically (trigonometry, conversion of units, etc.) Geared versions of astrolabes were also created in order to process more complex data. The earliest mechanical computer to be discovered is a calendar computer mechanism found in a shipwreck off the coast of Antikythera in Greece dating back to 80 B.C. (De Solla Price). In 1000 A.D., Muslim scholar al-Biruni describes a geared calendar that features similar mechanisms to the Antikythera and is found in various astrolabes dating from the Medieval Era. These instruments are at the origin of the common mechanical clock (Boudet) that rapidly become common integrations to towers of cathedrals of the 13th century.

As a first step to this third project of the semester, I wanted to reproduce an early mechanical computer in order to understand and its mechanism. Researching for detailed drawings and photographs of mechanical calendars and astrolabes lead me to discover Giovanni Dondi’s astrarium: a 14th century astronomical clock which displayed the position of the sun, the moon, five planets as well as the date and time on various dials. On display at the Castello Visconteo at Pavia, the astrarium was a complicated simulacrum of the geocentric universe following the Ptolemaic theory of motion of the planets. It was apparently marvelled upon by Leonardo Da Vinci, who sketched dials of the astrarium in his notebooks (Bedini et Maddison). Dondi also produced a manuscript that describes his masterpiece in detail entitled Tractatus astrarii. Since the original machine disappeared 150 years after its creation, this manuscript allowed replicas of the astronomical clock to be made. A model of the astrarium is on display at the Smithsonian Institute.

Using the Tractatus astrarii manuscript as well as various photographs of the existing replica of the astrarium, I reproduced the mechanism of its moon dial using thick chipboard and wooden dials. This mechanism simulates an epicyclical movement of the moon’s orbit: a eccentric elliptical rotation, as well as a circular oscillation. The complexity of the mechanism is hard to understand, as it integrates both sliding rules and rotating gears. Just like Leonardo in his time, I wanted to draw the movement of to the moon dial in order to understand it. Based on Leonardo’s drawings of the transmission rods found in his Codex Madrid I, I installed a drawing arm to the moon dial in order to trace its movement on paper. I discovered that the machine that I fabricated produced an elaborate oscillating shape with 14 indents that harmonizes every 5th rotation of the dial.

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SOURCES

Bedini, Selvio A. and Francis R. Maddison. “Mechanical Universe: The Astrarium of Giovanni De Dondi.” Transactions of the American Philosophical Society (1996): 1-69.

Boudet, Jean-Patrice. “L’apparition des horloges mécaniques en Occident.” Revue Historique (1998): 145-154.

De Solla Price, Derek. “Automata and the Origins of Mechanism and Mechanistic Philosophy.” Source: Technology and Culture (1964): 9-23.

—. “Gears From The Greeks. The Antikythera Mechanism: A Calendar Computer from ca. 80 B.C.” Transactions of the American Philosophical Society 64.7 (1974): 1-70.

Leonardo’s Machines: Secrets and Inventions in the Da Vinci Codices, Firenze: Giunti, 2005

Sawday, Jonathan, Engines of the Imagination: Renaissance Culture and the Rise of the Machine, New York: Routledge, 2007

Lefevre, Wolfgang, ed., Picturing Machines 1400-1700, Cambridge, MA: The MIT Press, 2004.

Abstract Art by a Gearograph by C.Wong

In Leonardo Da Vinci’s machines, gears are often the main mechanism that initiates rotation and movement. To combine my personal interest and part of Leonardo’s invention, I decided to design a drawing machine from scratch, which can be used to create my own abstract art.

 

Gearograph, a combination of gear; operates like a pantograph and a spirograph, but with a sense of freedom and unpredictability. Testing on material was the main part of the research, as well as reading different sources of books for inspiration. Two dimensional images contain a capacity for spatial illusion and I think this perspective of abstract art is related to architectural design.

    

Abstraction comes from the world. The interesting aspect of creating an abstract art is that the author controls the image but not the reaction to it. “Composition, harmony, proportion, light, color, line texture, mass, and motion are all part of the vocabulary of sight, we tap this vocabulary, and the pattern that go with it. When we compose or frame images the commonality that allow us to respond to images, even abstract ones, is rooted in our ability to recognize infinite manifestation of the physical world and the mental constructs to which they correspond.” – Kit White, 101 Things to Learn in Art School

  Red, Grey and Black | pen on 51x 60cm paper

 Sandstorm in Pieces| Pen on 56x76cm paper

 

 

Exercise 3 / project: the contrivances_Omar Alameddine

http://sammlungen.ub.uni-frankfurt.de/msma/content/pageview/3657179

Vitruvius mentions in Book X of The Ten Books On Architecture, that the astronomical bodies are connected by a mechanism of revolution which rests on the circular geometry as its trajectory. So the items that govern our lives on earth are bound by a geometry which could be imitated and used for human convenience. Vitruvius explains the components of such a contraption emphasizing two main elements: the circle and the line. Combined together, these elements form a machine or an engine which facilitates different tasks such as hoisting materials for construction. Other items stem from this technological advance such as military machines: The Ballistae, The Catapult, and other siege weapons.

The interest on the circular form is not unwarranted. A few experiments with different forms as the backdrops of a rotary machine has led to the realization that the circle is probably the ideal form by which one uniform force can be transformed into another uniform force with the same magnitude but a different direction. The illustrations below show three different geometries which were the subject of this experiment. The result for the square background was an interruption of movement focused around the edges of the square. The result for the elliptical background was an interruption of movement focused around the far ends of the ellipse. The circular background returned an uninterrupted motion.

 

 

 

A prominent figure in the history of Renaissance Art, Leonardo Da Vinci, has displayed an interest in the potential of the machine. Several designs of rotary machines figure in his sketches. The book entitled Leonardo’s Machines: Secrets and Inventions in the Da Vinci Codices reveals many of Da Vinci’s sketches which focused on different functional machinery. His sketches would often describe the different elements of the composition along with the means to assemble them.

An interesting aspect of Da Vinci’s design is that he uses the circle oriented in one direction to manipulate another circle in another direction. For this exercise, I will address the different possibilities generated by this change of orientation to produce a machine not as a tool for production rather a product in itself. Buildings are characterized with having a specific program. By using a mechanical process such as those described in both Vitruvius’ writings and Leonardo Da Vinci’s sketches; is there a way to manipulate the program of a building; or at least its envelope?.

The Facade that has been developed using this mechanical system introduces an architecture that actually announces its activity. If the pattern is opened up, that would mean that the space behind it is active; if the pattern is closed off, that would mean that the space is currently inactive. In this modern age, architects have been aspiring to create architecture that would reveal its function. A government building has a typology that is different from that of a residential building. To push the boundaries of that definition to the point where the architecture would reveal if the space is occupied or not is a breakthrough. Also, when the facade is opened up, it allows light to shine through the openings and creates a patterned shadow on the ground which would move as the day passes.

 

A Study of the Human Head

Inspired by Leonardo’s drawing of the Vitruvian man, I became interested in the study of human proportion and its evolution over the Renaissance Era. I focused my research by comparing the work of two Renaissance artists, Piero Della Francesca and Albrecht Durer.

Elevations and Horizontal Outlines of the Human Head | Piero della Francesca

In Piero’s manuscript entitled De Prospectiva Pingendi (On the Perspective for Painting) written between 1474 and 1482, he produces a drawing of the human head entitled Elevations and Horizontal Outlines of the Human Head. Through this drawing he attempted to realize the ideal proportions of the human head through significant geometrical and cosmological numbers. His drawing consists of two groups of four sectional plans; radially divided into sixteen sections and two elevations; horizontally segregated into 8 parts. He intersected these two drawings to plot a series of data points on a polar coordinate grid. Through orthographic projection, used these points to reorient and draw the head at any angle. This surveying technique is very similar to that of Alberti in his map of Rome, which Alberti describes by saying,  “The man who possesses them [the numbers] can so record the outlines and position and arrangement of the parts of any given body in accurate and absolutely reliably written forms that not merely a day later, but even after a whole cycle of the heavens, he can again at will situate and arrange the same body.”(Smedley 2001)

In 2001, artist Geoffrey Smedley showcased his work at an exhibition put on at the Canadian Centre for Architecture entitled Meditations on Piero. His work consisted of a series of drawings and sculptural meditations based on Piero’s drawings of the human head. His study engaged concepts of cosmology, perspective, anatomy and surveying, apparent in Piero’s work. In one of his models entitled The Numbers, Smedley constructed a sculpture that consisted of nine horizontal surfaces, which carefully follows Piero’s mapping of the head. This inspired me to construct a model as a way to materialize my own interpretation of Piero’s drawing.

The Numbers | Geoffrey Smedley

model based on Piero’s drawings

Albrecht Durer’s theory of human proportion derived from the geometrical canon that Leonardo used to construct the Vitruvian man. Durer did not generalize man through idealized proportions, rather recognized the immense diversity of the human form that existed in society. In his book entitled Four Books on Human Proportion he states, “If you wish to make a beautiful figure, it is necessary that you probe the nature and proportions of many people: a head from one; a breast, arm, leg from another.”( Durer 2003) To create the drawings illustrated in this book, he first defines a system of geometrical measure.  He then adjusts this system using relative proportion and fractional relations to conform to different body types. His system divides the profile of the head into eight sections and front of the head into seven.

Human Proportions | Albrecht Durer

Through the imposition of Durer’s system on Piero’s head I found that their divisions were essentially the same, excluding the addition of one division line between the top of the head and the top of the hairline in Piero’s drawing. Durer also applied his method of drawing perspective as a way to reorganize the grid to draw different orientations of the head.

Durer’s proportions overlaid on model of Piero’s head

A modern exploration by Stephan Marquardt featured in a four-part BBC documentary entitled The Human Face, examines beauty in reference to symmetrical proportions. He used to the golden ratio to create a mask known as the Golden Mast, which he claims encapsulates absolute, universal beauty. He explains his view by stating, “the closer the face conforms to this mask, the more beautiful it is.” (Human Head, BBC One 2001)

Golden Mask | Stephan Marquart

References:

“Albrecht Durer: 1471-1528.” The Metropolitan Museum of Art. 2000-2012 <http://www.metmuseum.org/toah/hd/durr/hd_durr.htm&gt;

“Collections: Printed Books & Bindings.” The Morgan Library & Museum. New York. <http://www.themorgan.org/collections/collections.asp?id=577&gt;.

Dodds, George., Tavernor, Robert., Rykwert, Joseph. “Body and Building: Essays on the Changing Relation of Body and Architecture.” Massachusetts: Massachusetts Institute of Technology, 2001.

Durer, Albrecht. “De symmetria partium in rectis formis humanorum corporum : Nuremberg.” 1532 Oakland: Octavo Corp, 2003.

Field, J.“Piero Della Francesca: A Mathematician’s Art.”London, 2005

Franscesca, D. Piero. De Prospectiva Pingendi. Firenze: Casa Editrice Le Lettre, 1984.

Gates, H. William. The Art of Drawing The Human Figure. London: Bailliere, Tindall and Cox.

Neher, Allister. “Albrecht Durrer and Nicholas Suanus: the Real, the Ideal, and the Quantification of the Body.” Luxemburg: Jean-Paul Riopelle, 1992. <http://www.uqtr.uquebec.ca/AE/Vol_11/libre/Neher.htm&gt;

Human Head. Dir. Erskine, James., Stewart, David. BBC One, 2001.

Smedley, Geoffrey. Meditations on Piero: Sculptures by Geoffrey Smedley. Montreal: Centre Canadien d’Architecture/Canadian Centre for Architecture, 2001.

Williams, Kim., Lionel, March., Wassel, Stephen., “The Mathematical Works of Leon Battista Alberti.” Washington: Birkhauser, 2010.

The Modern Theatre of Anatomy – Martina Amato & Noushig Kadian

Understanding the Renaissance Body

When looking at the Renaissance we must keep in mind that the beliefs of the time differ from our understanding of the world today. In the next few paragraphs we will explore the Renaissance body, the pursuit of understanding anatomy and the theater of anatomy.

The Renaissance was a time of enlightenment and pursuit of knowledge. During the Renaissance the pursuit of knowledge of the anatomy gained importance. This pursuit saw no social boundaries; everyone, no matter their social standing, was intrigued and affected by this new exploration of the human body. As explained by Jonathan Sawday in The Body Emblazoned: “It is perhaps the very impossibility of gazing within our own bodies which makes the sight of the interior of other bodies so compelling. Denied direct experience of ourselves, we can only explore others in the hope that this other might also be us.”⁴ Unlike our purely scientific view of the anatomy today, cosmology, theology and theunderstanding of the soul were essential in the pursuit of anatomical research in the Renaissance.

Firstly, we will illustrate Renaissance beliefs of the body through the lens of cosmology. The stars were seen as the only regular and ordered system within nature. The rigor observed in the sky helped decipher the disorder of terrestrial life. Navigation, time, a person’s fate or health, are a few examples of human conditions depicted by the movement of the planets and the formation of the constellations. The stars contained the answers to our mortal questions. Furthermore, the significance of celestial movement extended to the Renaissance views on anatomy. The body was seen as a microcosm of the cosmos, encapsulating the regularity in the sky. For example, a doctor would refer to the zodiac signs to prescribe certain therapies to his patients whose fate and demeanor was predetermined by their constellation.

Secondly, the Renaissance body had a theological importance.  Such a complex and mysterious system, as that of the stars, must have been touched by a divine hand during their creation. The same deduction can be made about human anatomy, seeing as it is a microcosm of God’s work. This point is further illustrated by Sawday: “The human body expressed in miniature the divine workmanship of God, and that its form corresponded to the greater form of the macrocosm.”⁴ Viewing the body as a divine creation makes it a sacred entity. The pursuit of anatomical knowledge, through dissection, then becomes a religious ceremony. A poetic and lyrical ceremony surrounds these dissections with religious implications.

The Theater of Anatomy

An important moment in the Renaissance in terms of anatomical research was the modernity of Vesalius and his theater of anatomy. In the pre-Rennaissance, theories of anatomy were based on Galen, a Roman physician, and his discoveries. These theories were universally accepted and the dissection was meant to prove the written word. “Even when the text diverged from the body before them, that misinformed, though accepted text, was understood to be correct. The seemingly anomalous corpse was the recipient of the authorial word, and was made to exemplify it.”³ On the other hand, Vesalius viewed the body as a container of knowledge. He also believed the written word should not be used as an instruction manual when approaching dissection. In his theater he was both lecturer and dissector. “He read from the text, but more importantly he was able to revise the textual authority as the dissection disagreed with it.”³

Dissections were a means to gain knowledge and make new discoveries. As previously mentioned, the body was a mystical construct that required a sensitivity towards the lyrical arts in trying to understand it. This was a time when cause and effect was not the natural thought process, and could therefore not be used in the anatomical discoveries being made. “The body, despite all attempts at poetic deconstruction, was still secret”.⁴ The body was like a territory waiting to be concurred; a territory whose fruitful, lush ecosystems contained the secrets to cotton, spice, silk…Anatomists became explorers, and organs, their unchartered territory. Once an organ was discovered, the anatomist had the honor of naming his new found land (e.g. Gabriele Falloppio).¹

Previously to Vesalius’ theater, public dissections were loud, carnivalesque gatherings. Vesalius’ modernity narrowed his audience to professors, students and other invited guests from the academic realm.  The audience adopted a code of conduct and decorum within the theater. Poetry and music were seamlessly integrated in the ceremony, creating an impactful instructive ambience. Vesalius’ theater was a tactile learning environment unlike previous anatomy theaters which relied on an auditory experience. Students were encouraged to actively participate by touching organs and feeling their inherent significance.

The Role of the Modern Anatomist

As we began our adventure with this final phase of the project, we decided to take a similar approach to the renaissance anatomist. The body of man for them was an emblem created by the hands of God. The body was a sacred mystery to which they could not comprehend systemically. The choice of dissecting a machine in our case became clear when we realized that although we are creators of machines, their mechanisms still remain mysterious. Exposing the innards of a body conjures up even more questions of its system rather than revealing the answers. Even in the day and age of the machine, their world is not as transparent as we assume.

By taking the machine apart, piece-by-piece, we begin to grasp an idea of the mechanism behind it and how it might function as a whole. One advantage of observing the machine alive was that we could potentially understand its mechanism when taken apart. Our projections demonstrate the machine in its living state until we symbolically “cut the cord.” Each piece was meticulously dismembered for individual observation. The entire process of the dissection took 30 minutes. Our presentation was the projection of films showing the machine functioning when it was alive juxtaposed with a film of its dissection and ultimate death. The internal organs were laid out on the death bed, against the backdrop of the projections.

The “Replication Box”

Le projet de recherche est issu d’une expérimentation à l’aide d’instruments de relevés inventés à la Renaissance. Il s’agit d’une suite logique des exercices sur la mesure et la cartographie effectuées dans le cadre de ce cours.

La plupart des instruments de mesures des arpenteurs de l’époque dépendent d’artifices mathématiques dont certains ont été résumés dans l’œuvre de Leon Battista Alberti, Ludi Mathematica. Dans cet ouvrage, il explique diverses astuces mathématiques relatives à l’art de la mesure. Suite à la reproduction de la carte de Rome d’Alberti en deuxième exercice, nous avons défini deux points d’intérêts pour le projet final : la numérisation des points du relevés d’Alberti est indépendante du support sur lequel le relevé a été fait; il est possible pour n’importe qui de reproduire cette carte peu importe sa taille, pourvu que l’instrument qu’il décrit soit reproduit consciencieusement. L’élément fascinant est que sans le savoir, Alberti utilisait un système d’analyse computationnel peu différent que le langage d’un ordinateur moderne. Deuxièmement, l’instrument utilisé par Alberti pour construire sa carte démontre à notre avis l’introduction d’un système de coordonnées polaires appliquées dans l’art de la mesure. Ce système allait définir le point de départ du projet.

 Le projet est né d’une recherche approfondie sur les divers instruments de mesure inventés par Alberti. Nous avons consulté tout d’abord les Ludi Mathematica afin de comprendre comment Alberti avait transposé les éléments remarquables de Rome en nuage de points mathématiques. Il s’avère qu’Alberti utilisait un instrument circulaire de grande dimension déposé sur le sol permettant d’établir à vue les angles des points d’intérêts par rapport au lieu de mesure. Au cours de nos recherches, nous avons lu attentivement le traité De Statua, où Alberti décrit un deuxième instrument de mesure inspiré du premier permettant de mesurer une statue. Alberti donne un système de proportion à son instrument dans la mesure où la hauteur de la statue est égale à 6 pieds. Il présente ensuite l’instrument de mesure, le finitorium. Il s’agit d’un instrument semblable à celui utilisé pour la carte de Rome, excepté qu’il implique maintenant une composante tridimensionnelle à son fonctionnement en la qualité d’un fil à plomb suspendu à son rayon. Ce dernier est de 3 pieds, chacun divisés en 10 uncia et subdivisées en minuta.

En utilisant l’instrument décrit par Alberti, de manière très imprécise disons-le, on comprend qu’il serait possible de diviser le contour de n’importe quel objet en coordonnées spatiales, qu’il serait ensuite possible de retracer sans la présence de l’objet de référence. Nous avons fait d’autres recherches à comprendre exactement le fonctionnement de cet instrument. Nous avons établi que sa reproduction exacte n’avait à notre connaissance jamais été tentée. Mathématiquement, ce sytème repose sur les coordonnées cylindriques où un point dans l’espace est défini par le rayon, l’angle dans le plan horizontal et z, la distance verticale. D’autre part, il s’avère que le principe d’Alberti a été effectivement utilisé par les sculpteurs afin de reproduire des statues. Le principe est le suivant : le sculpteur positionne deux ou trois points de référence majeurs (le coude, le genou, etc) par rapport au centre de l’axe vertical et sait ainsi la position de chaque point par rapport à l’épaisseur du bloc de matériel à tailler.

Le projet final se veut une hybridation des différents principes de mesure inventés par Alberti. Nous avons voulu modifier l’instrument afin de le rendre capable de mesurer n’importe quel objet. Le résultat final est une « boîte de duplication », où un objet peut être inséré, mesuré, transformé en une série de coordonnées tridimensionnelles, et par la suite reproduit. Plus le nombre de points mesurés au départ a été grand, plus la reproduction de l’objet sera précise.

 Le définisseur mesure 30 cm de diamètre et la hauteur de la boîte mesure 24 cm, soit 80% du rayon de mesure. On pourrait étendre ce système de proportion à volonté, en multipliant ces mesures du facteurs de notre choix, afin de mesurer un objet plus gros.

 La première étape est donc d’insérer un objet dans la boîte et d’utiliser la plaque de mesure afin de noter une série de points judicieux en terme de rayon, d’angle et de distance z. Par la suite, si on imagine ne posséder que cette série de coordonnées, il est possible de reproduire le contour de l’objet à l’aide d’une seconde plaque contenant un tableau de coordonnées polaires. On suspend alors chaque point sur cette plaque à l’aide d’un fil à plomb. Le nuage de points qui en résulte reprend alors le contour de l’objet mesuré au départ.

 Finalement, nous avons souhaité expérimenter avec la notion de projection, de vision et de parallaxe en tentant d’introduire une grille de mesure sur les faces latérales de la boîte. Nous espérions pouvoir obtenir une projection parallèle du contour de l’objet une fois les points suspendus dans l’espace. Cette méthode aurait alors pu fournir l’élévation de des contours de l’objet mesuré.

***

The research project is the result of an experiment using surveying instruments invented in the Renaissance. It is a logical step forward from previous exercises on measuring and mapping.

 Most instruments surveyors used at the time depend on mathematical artifices. Some of them were summarized in the work of Leon Battista Alberti, Ludi Mathematica. In this treatise, he explains various mathematical tricks on the art of measurement. Following the reproduction of the map of Rome as a second exercise for this class, we identified tree points of interest for the final project:

 –        Alberti’s surveys coordinates are independent of the medium on which the map has to be drawn. It is possible for anyone to reproduce this map in any size, assuming Alberti’s instrument is conscientiously reproduced.

–        The other fascinating element is that without knowing it, Alberti used a computational analysis system which is in our opinion not much different than the language of a modern computer.

–        Finally, the instrument used by Alberti to build his map introduces the notion of polar coordinate system applied in the art of measurement. This system defined the starting point of the project.

Alberti’s Finitorium, as pictured in De Statua treatise.

The project originated from extensive research on various measuring instruments invented by Alberti. We first consulted the Ludi Mathematica treatise to understand how Alberti had transposed the remarkable features of his Rome map into a discrete mathematical array of points. It turns out that Alberti used a large circular instrument placed on the ground in order to establish the angles of points of interest in relation to his location on site (For the Map of Rome, the zero coordinate was the summit of Capitola). During our research, we then examined Alberti’s De Statua, where Alberti describes a second measuring instrument used to survey a standing statue. Alberti confers a proportion system into his instrument by defining that the height of the statue to be measured is to be “6 feet” tall. It then presents the measuring instrument itself, which is called the finitorium. It is an instrument similar to the one used for the map of Rome, except that it now involves a component for its operation in a three-dimensional space. The added component is a plumb line suspended from the radius of the instrument. The radius is 3 feet, each divided into 10 uncia and subdivided into minuta. By using this defined proportional system, one’s can enlarge or reduce the instrument according to the height of the statue to be measured.

 By replicating the instrument described by Alberti, we can understand that it would be possible to divide the outline of any object into spatial coordinates. Having these coordinates at hand, it would also be possible to replicate its outline without the presence of the reference object. Some other research was done in order to understand exactly how this instrument could work in a practical way. To our knowledge, an exact replication of the finitorium instrument has never been attempted. Mathematically, this point-by-point survey of a body is based on cylindrical coordinates, where any point in space is defined by it’s radius, it’s angle in the horizontal plane, and z it’s vertical distance from the horizontal plane where the radius sits. On the other hand, it turns out that the measurement principle invented by Alberti was actually picked up by sculptors to reproduce statues. The principle is as follow: the sculptor positioned two or three major reference points (elbow, knee, etc.) from the center of the vertical axis and thus could know the position of each point relative to the thickness of the material to be cut.

The final project is intended to be an hybridization of these different measurement principles invented by Alberti. We wanted to change the above instrument to make it able to measure any object. The end result is a “replication box”, where an object may be inserted, measured, converted into a series of three-dimensional coordinates, and then reproduced. The greater the number of points is measured, the greater the resolution of the reproduced object will be.

 The Finitorium measures 30 cm in diameter and the height of the box is 24 cm, or 80% of the radius span. In order to measure a larger object, this proportion system can be easily extended. One’s only need to multiply these dimensions by a given factor of choice.

 The first step is to insert an object into the box and use the measuring plate to compute a succession of wisely chosen points in terms of radius, angle and z distance. Subsequently, it is possible to reproduce the contour of the object with a second plate containing a polar array. Each point is to be suspended from the plate with a plumb line, with correct z distance. The resulting points cloud will approximate the contour of the object.

 Finally, I wanted to experiment with the concept of projection and vision, by trying to introduce a measurement grid on the sides of the box. That way, I was hoping to catch a parallel projection of the object’s contour points, once being suspended in space. This method could then provide key elevation contour points of the measured object.

Alberti’s Finitorium replicated following his instructions.

Preliminary sketch of the instrument

Preliminary sketch of the instrument

Experimental set of cylindrical coordinates.

Computer generated plot of measured points for validation purposes.

Step 1: Measurement of a point following Alberti’s method.

Step 1: Measurement of a point following Alberti’s method.

Step 1: Measurement of a point following Alberti’s method.

Step 2: reconstruction of the measured coordinates into a model.

Step 2: reconstruction of the measured coordinates into a model.

Step 2: reconstruction of the measured coordinates into a model.

Step 2: reconstruction of the measured coordinates into a model.Measurement of Z coordinates projection using an orthogonal grid.

Step 3: validation of the measured points.

Step 3: validation of the measured points.

Step 3: validation of the measured points.

Bibliography

 Académie d’Art de Meudon et des Hauts De Seine, Histoire d’une commande imago pietatis Les procédés de reproduction, [online], http://www.academieart-meudon.fr/wdp/wp-content/uploads/2011/10/Texte-rencontre-Agn%C3%A8s-Bracquemond1.pdf

 Alberti, Leon Battista. Ex ludis rerum mathematicarum, in Williams, Kim, The Mathematical Works of Leon Battista Alberti, Birkhäuser, Berlin, 2010.

 Alberti, Leon Battista, De La Statue et de La Peinture, traduit du Latin en Français par Claudius Popelin, A. Lévy Éditeur, Paris, 1868.

 Carpo, Mario, The Alphabet And The Algorithm, MIT Press, Cambridge, 2011, 169p.

 Grafton, Anthony, Leon Battista Alberti Master Builder Of The Renaissance, Hill and Wang, New-York, 2000, 417p.

 Miller, Naomi, Mapping the City, Continuum, London, 2003, 270p.

 Scaglia, Gustina, Instruments Perfected for measurements of man and statues illustrated in Leon

Battista Alberti’s De Statua, Nuncius, Volume 8, Number 2, 1993, pp.555-596.

 Williams, Kim, The Mathematical Works of Leon Battista Alberti, Birkhäuser, Berlin, 2010.

Device for evacuating water – Christina

In this third phase of projects, I have decided to explore and research Leonardo da Vinci’s machines and inventions.  His varied personal explorations can be classified under the four elements: air, earth, fire and water.  Water was perhaps the most interesting of the subjects, since Leonardo both admired and feared this element, he called it the “driver of nature”.  If water was humanly controlled, then it became the most valuable natural resource.  However, if left unattended, water could be the most powerful destructive force found in nature.

Da Vinci was interested in exploring the potential water offered in producing power from its movement and interested in the problem of swimmers, but these questions also brought to his attention more sinister thoughts.  As mentionned previously, he knew of water’s destructive capabilities and became obsessed with this fact.  He had actually predicted a sort of “end of the world” in terms of a massive flooding that would destroy the entire world and had drawn some sketches of this prediction.  This idea drove him to find ingenious solutions for aiding cities as well as people in case this actually happened.  Also, Leonardo was developping these ideas during a time of war and had thought of several devices that could be useful to the military.These included the breathing tube, the webbed gloves and the floating device.

He also invented a device for walking on water to allow anyone to escape in case of a flood.  The set of instruments was comprised of two poles that were to be used to propel oneself on the surface of the water as well as two large “shoes” that would allow the person to float.

As DaVinci was often inspired by nature for his designs, he also looked into science for informing his decision.  The device for walking on water needed consider the Archimedes principle called buoyancy to ensure that one could float on water.  He also looked into the Archimedes screw when he was designing machines for moving water to feed aqueducts for example.

Before DaVinci, Vitruvius also studied the Archimedes screw as a machine to move water and he developped his own machines for moving water.  In his tenth book on architecture he explains principles governing machines and devotes more than a chapter to water.  A large part of what he studied and machines he describes are related to the circular movement of parts working together.  He obviously looked to the heavens for inspiration and guidance.  As the movement of the stars was considered to be ruled by the gods, then these rules had to be followed or mimicked for the design of any machine on earth in order for these devices to be of any validity.

Vitruvius describes in detail a water wheel onto which buckets are attached.  The motion of the water running below the wheel activates the machine and as the wheel is turning the buckets fill with water one by one and are carried around the wheel.  When they reach the top, they spill into a container nearby and this allows for water to be raised from a river to a different level, depending on the diameter of the wheel.  In his book, he also clearly describes how to construct an Archimedes screw.

My interest in water devices was also fueled by the fact that I realized that even today, we still do not have adequate buildings or devices to help us when floods afflict certain areas of civilization. After several failed attempts at building my own Archimedes screw for bringing water from one level to another, I designed a different device incorporating many of the concepts elaborated by both Vitruvius and DaVinci. I was inspired by the idea of a conveyor system found in the Archimedes screw where a surface continuously pushes the water upwards and also by the idea of having containers to prevent the loss or leakage of water through the device.  I wanted to develop a machine to evacuate water that could be readily available to anyone, portable and did not need any kind of power in case of flooding and power outage.  My intention was to create a device that could be dismantled and assembled in small simple pieces.  All the necessary pieces would fit into one box, so the machine could be easily stored or even transported.  People could use this device to evacuate water from a flooded basement for example by setting it up to lift water from that lower level, through a window and out to the ground level.

 SOURCES

COOPER, Margaret.  The Inventions of Leonardo da Vinci. New York : The MacMillan Company, 1965.

GIBBS-SMITH, Charles and REES, Gareth.  The Inventions of Leonardo da Vinci. Oxford : Phaidon, 1978.

VITRUVIUS. (Translated by Morris Hickey Morgan) The Ten Books on Architecture. New York : Dover Publications, Inc. ,1960.

Image sources

Figure 1 – COOPER, Margaret.  The Inventions of Leonardo da Vinci. New York : The MacMillan Company, 1965, p.  162.

Figure 2 – GIBBS-SMITH, Charles and REES, Gareth.  The Inventions of Leonardo da Vinci. Oxford : Phaidon, 1978, p. 70.

Figure 3 – www.ecogeek.org/component/content/article/2262

Figure 4 – VITRUVIUS. (Translated by Morris Hickey Morgan) The Ten Books on Architecture. New York : Dover Publications, Inc. ,1960, p.295.

Figure 5 – VITRUVIUS. (Translated by Morris Hickey Morgan) The Ten Books on Architecture. New York : Dover Publications, Inc. ,1960, p.296.

Figure 6 & 7 – http://www.machinerylubrication.com/Read/1294/Noria-history

Deformations / Circulus & Cosmos III

L’objet réalisé s’inspire d’abord des recherches précédentes sur le quadrant, la projection orthographique, ainsi que le torquetum.  Il est également une hybridation entre les projets antérieurs du cours, soit l’astrolabe pour le calcul de la position des astres ainsi que la carte de Rome pour la représentation par coordonnées polaires.

L’instrument consiste à faire un relevé d’un espace, d’un paysage ou d’astres sur 360 degrés en prenant en note des coordonnées de points.  Dans l’exemple suivant, le relevé a été fait dans la salle 102 du bâtiment Macdonald-Harrington.  Le dessin alors obtenu transforme la réalité en la déformant de manière à ce que toute ligne horizontale devienne un arc de cercle et une ligne verticale devienne une ligne axiale.  Une base en bois, horizontale, est divisée en 360 degrés et est alignée de préférence avec les points cardinaux.  Sur cette base, un mat rotatif soutient un quadrant de 90 degrés, avec un pointeur qui peut ainsi déterminer l’angle de vision d’un point déterminé.  Cet angle calculé, on se réfère à une règle graduée sur la base horizontale pour noter le point en question.  Comme cette règle suit exactement la direction du pointeur, elle détermine la coordonnée polaire du point.

Ces deux «coordonnées» peuvent également être notées pour permettre au lecteur de construire/imprimer lui-même sa propre image comme le système utilisé par Alberti pour la carte de Rome.  La hauteur à laquelle l’instrument est placé détermine la hauteur de l’horizon, soit le degré zéro.  Donc, il n’est pas possible de prendre le relevé de ce qu’il y a plus bas que cet horizon sauf en baissant l’instrument.  Autrement, une solution envisageable serait de calculer les angles avec un demi cercle au lieu d’un quadrant, et donc de graduer la règle sur 180 degrés plutôt que 90.  Une des itérations également possible en terme de représentation est d’inverser l’horizon sur le dessin pour la périphérie du cercle plutôt qu’en son centre.

Comme le dessin final obtenu à partir du nouvel instrument est expérimental et inattendu, l’interprétation du dessin l’est également.  L’hypothèse formulée fut de rapprocher ce type de déformation à celles obtenues pour créer des anamorphoses avec des miroirs.  Différentes formes et dimensions de miroirs (cylindriques, coniques et sphériques) ont été reproduits pour “lire” le dessin et mieux comprendre ce type de relevé.  Comme l’instrument est un quart de cercle rotationnant sur 360 degrés, il est logique que le miroir sphérique soit celui qui reflète le dessin en corrigeant sa déformation.

Une attention particulière a également été porté au design et à la conception de l’objet en respectant l’idée d’artisanat et d’utilisation d’outils de mesure plus rudimentaires.  Les proportions ont aussi été calculées, en plus de respecter les formes géométriques pures telles le cercle et le carré.  Le dessin obtenu est inspiré de la technique de cartographie du ciel étoilé, mais pour dessiner l’univers, représenter 360 degrés sur une surface.  La technique systématique et rigoureuse du relevé y confère une certaine subjectivité.  Cependant, il n’y a pas de précision à ce type de dessin, il est difficilement calculable et c’est une vision impossible.  Expérimentale, cette “perspective sphérique” est également une représentation symbolique de l’univers, le cercle étant traditionnellement réservée aux cieux, à la perfection, l’absolu, l’infini, le divin.

* * *

The object made is first based on the previous research on the quadrant, the orthographic projection, and the torquetum. But it is also a hybrid of earlier projects of the course; the astrolabe for the calculation of the position of the stars and the map of Rome for the representation by polar coordinates.

The instrument takes a survey of a space, a landscape or even stars, on 360 degrees by drawing the coordinate points.  The drawing is then transformed by deforming reality so horizontal lines become circular arcs and vertical lines become axial lines.  A horizontal wooden base is divided into 360 degrees and is preferably aligned with the cardinals.  On this basis, a rotary mat supports a 90 degrees quadrant, with a pointer that can determine the angle of view of a given point. This angle calculated, it refers to a ruler on the horizontal base to draw the calculated point.  As this rule follows exactly the direction of the pointer, it determines the polar coordinate of the point.

These two “coordinates” can also be recorded to enable the reader to build / print itself its own image as the system used by Alberti’s map of Rome.  The height at which the instrument is situated determines the height of the horizon, or the zero degree. Therefore, it is not possible to survey below this horizon except by lowering the instrument. Otherwise, a possible solution would be to calculate the angles with a half circle instead of a quadrant, and thus grade the rule with 180 degrees rather than 90.  One of iterations also possible in representation, would be to reverse the horizon of the drawing at the periphery of the circle instead of its center.

Because the final obtained drawing is experimental and unexpected, his interpretation is also unexpected.  The hypothesis was to link this type of deformation to those obtained with mirrored anamorphosis.  Different shapes and sizes of mirrors (cylindrical, conical and spherical) were reproduced to “read” the drawing and understand this type of survey.  Because the instrument is a quarter circle rotating on 360 degrees, it is logical that the spherical mirror is the good reflection which correct the deformation.

A particular care was paid to the design and the realisation of the object, by respecting the idea of ​​craftsmanship and use of more rudimentary measurement tools in order to fully understand it.  The proportions were also calculated, in addition to meet the pure geometric shapes such as the circle and the square.  The drawings obtained were inspired by the cartography technique of the heavens, but in that case to draw from the universe, on 360 degrees, graphically transferred on a surface.  The systematic and rigorous technique confers a subjectivity.  However, there is no precision in that drawing, it is difficult to calculate and it is an impossible vision.  Experimental, this “spherical perspective” is also a symbolic representation of the universe, the circle traditionally reserved for heaven, to perfection, the absolute, the infinite, the divine.

Émélie DT

Early Modern volvelles from the Bodleian (part I)

First page of a 15th-century guidebook on constructing volvelles, and some Early Modern ones, reproduced here with the kind permission of The Bodleian Libraries, The University of Oxford.

You may click on any one of the images to view a slideshow with further information, including the manuscript and folio numbers. As these are simple snapshots I took of the manuscripts, you are encouraged to contact the Imaging Services of the Bodleian Libraries directly to obtain professional reproductions.

According to the Oxford English Dictionary, this is the first use of the word ‘volvelle’ in English (written in red about 2/3 of the page down), ‘ye rewle of the volvelle’ [the rule of the volvelle], 15th century. The Bodleian Libraries, The University of Oxford, MS Ashmole 191, f.199r.

Calendrical volvelle? c1552. The Bodleian Libraries, The University of Oxford, MS Savile 100, f.6r.

Equatorium (instrument for finding planetary positions), c1552. The Bodleian Libraries, The University of Oxford, MS Savile 100, f.8r.

Please note that MS Savile 100, f.8r has also been reproduced on the LUNA site of the Bodleian Libraries. See also the late 15th-century brass equatorium and astrolabe at the Museum of the History of Science at Oxford (inventory #49847).

Yelda Nasifoglu

Early Modern volvelles from the Bodleian (part II)

Illustrations from a late 14th century manuscript by Nicholas of Lynn, reproduced here with the kind permission of The Bodleian Libraries, The University of Oxford.

You may click on any one of the images to view a slideshow with further information, including the manuscript and folio numbers. As these are simple snapshots I took of the manuscripts, you are encouraged to contact the Imaging Services of the Bodleian Libraries directly to obtain professional reproductions. 

Zodiac man with volvelle, Nicholas of Lynn, end of the 14th century (after 1387). The Bodleian Libraries, The University of Oxford, MS Ashmole 789, f.363r. Text on the volvelle reads “Pone volvellem solis super gradum in quo sol fuerit illo die et volvellam lune super etatem lune et ipsa volvella ostendet tibi signum et gradum lune. et foramen quomodo luna secundum cuis etatem nobis apparebit et figura…” [full text to come]

Calendar tables and illustrations of solar eclipses, Nicholas of Lynn, end of the 14th century (after 1387). The Bodleian Libraries, The University of Oxford, MS Ashmole 789, f.363r.

Illustrations of lunar eclipses, Nicholas of Lynn, end of the 14th century (after 1387). The Bodleian Libraries, The University of Oxford, MS Ashmole 789, f.364r.

Urine analysis chart, Nicholas of Lynn, end of the 14th century (after 1387). The Bodleian Libraries, The University of Oxford, MS Ashmole 789, f.364v.

Blood-letting figure, Nicholas of Lynn, end of the 14th century (after 1387). The Bodleian Libraries, The University of Oxford, MS Ashmole 789, f.365r.

Nicholas of Lynn, end of the 14th century (after 1387). The Bodleian Libraries, The University of Oxford, MS Ashmole 789, f.365v

Please note that MS Ashmole 789 f.365r has also been produced on the LUNA site of the Bodleian Libraries.

Select sources on Nicholas of Lynn:

• Eisner, Sigmund, “Lynn, Nicholas (fl. 1386–1411),” Oxford Dictionary of National Biography, Oxford University Press, 2004. [Subscription-based site (ODNB)]
• Jones, Peter Murray, “Medicine and Science,” the Cambridge History of the Book in Britain, Volume III: 1400-1557, eds. Lotte Hellinga and J. B. Trapp, Cambridge University Press, 1999, pp. 433-448. [Subscription-based site (Cambridge Histories Online)]
• Kuczynski, Michael P., “A New Manuscript of Nicholas of Lynn’s ‘Kalendarium’: MS Chapel Hill 522, fols. 159^r–202^r,” Traditio, Vol. 43, 1987, pp. 299-319. [Subscription-based site (JSTOR)]
• O’Boyle, Cornelius, “Astrology and Medicine in Later Medieval England The Calendars of John Somer and Nicholas of Lynn,” Sudhoffs Archiv, Bd. 89, H. 1, 2005, pp. 1-22. [Subscription-based site (JSTOR)]
• Taylor, E. G. R. and Mercator, “A Letter Dated 1577 from Mercator to John Dee,” Imago Mundi, Vol. 13, 1956, pp. 56-68. [Subscription-based site (JSTOR)]
• The Bodleian Library, LUNA online source; other images from manuscripts by Nicholas of Lynn, and other illustrations of the zodiac man in various manuscripts.

Other sources:

• For various illustrations of the zodiac man, see also the Images Collection of the Wellcome Institute.
• You may also find interesting Ulrich Pinder’s Epiphaniae medicorum (1506).

Yelda Nasifoglu

Deformations / Circulus & Cosmos II

[TEXT]

RÉPLIQUE D’UN QUADRANT / QUADRANT REPLICA

MAQUETTE DE L’INSTRUMENT / MODEL OF THE INSTRUMENT

LIBESKIND’S MACHINES

Reblogged from the late Lebbeus Woods’s site.

LEBBEUS WOODS

By the mid-1980s, the reputation of Daniel Libeskind as a leading avant-garde figure in architecture was rapidly rising. This was based on his work as a teacher—he was director and principal teacher at the Cranbrook Academy School of Architecture from 1978 to 1985, establishing it as one of the most creative schools in the world—and on the publication and exhibition of a number of projects that, on their face, seemed to have little to do with architecture. Notable among these were his Memory Machine, Reading Machine, and Writing Machine.

Elaborately constructed and enigmatic in purpose, Libeskind’s machines are striking and sumptuous manifestations of ideas that were, at the time he made them, of obsessive interest to academics, critics and avant-gardists in architecture and out. Principal among these was the idea that architecture must be read, that is, understood, in the same way as a written text.

The chief structural features…

View original post 711 more words

Libeskind’s Ramelli

Daniel Libeskind’s & Agostino Ramelli’s (1531–1600) reading machines:  

For Libeskind’s other machines, please refer to Lebbeus Wood’s post on his blog site.

Besson’s drawing instruments

Drawing instruments from Jacques Besson’s Theatrum instrumentorum et machinarum (1578):

   

and for the aging priest, a pulpit with a magnifier:

Duchamp’s circles and machines

Marcel Duchamp’s Rotoreliefs (1920s):

and of course, the Large Glass (1926):

Last, but not least, the Dimensionist Manifesto (1936) (original text, reproduction, and translation) signed by Duchamp.

Rodchenko’s circles

More Russian constructivism –

here are some ‘circles’ by Alexander Rodchenko (1891-1956):

  

cf. 16th-century volvelles & armillary sphere:

   

Tatlin’s wings

You know of the Russian constructivist Vladimir Tatlin’s Monument to the Third International (1919):

Here is Letatlin (1929-1932), his take on the flying machine:

 

Kyeser and Hejduk

For those of you interested in architectural poetry, here is (what appears to be) a spiked shield from Conrad Kyeser’s Bellifortis (1460):

and the Magistrate from John Hejduk‘s Vladivostok (1989):

and his House of the Suicide (1980-1982):

Holbein’s instruments

Holbein’s Double Portrait of Jean de Dinteville, the Bailly of Troyes and Georges de Selve, Bishop of Lavaur, or ‘the Ambassadors’ (1533), famous for the anamorphic skull at the bottom of the painting,

but some of you might be interested in the instruments depicted:

See also the article by Elly Dekker and Kristen Lippincott, “The Scientific Instruments in Holbein’s Ambassadors: A Re-Examination,” Journal of the Warburg and Courtauld Institutes, Vol. 62, 1999, pp. 93-125. [Subscription-based site (JSTOR); accesible via McGill]

 

Renaissance wireframe

For those of you interested in drawing (and computing), here is a wireframe study of a chalice attributed to Paolo di Dono (aka Paolo Uccello), dating to c.1450-70. (Note that there are competing theories about its creator; some think it may have been Piero della Francesca.)

And a study of a mazzocchio:

with a ‘rendered’ version:

(project idea: geometric head gear?)

Deformations / Circulus & Cosmos I

Le PANTOGRAPHE est un instrument simple qui permet de reproduire un dessin avec la possibilité de réduire ou d’agrandir son échelle.  L’outil transmet mécaniquement le mouvement dont la forme suit un parallélogramme.  La majorité des pantographes comportent un point de fixation ainsi que plusieurs espaceurs aux articulations pour garder l’instrument bien parallèle à la feuille de papier.  Un pointeur reprend le dessin existant tandis que l’autre dessine une deuxième version de la figure.  Certains pantographes sont plus élaborés avec des mécanismes de roulement.  Le tout premier pantographe fut construit en 1603 par l’astronome allemand Christoph Scheiner.

The PANTOGRAPH is a simple tool that allows to reproduce a drawing with the possibility of reducing or enlarging its scale. The tool mechanically transmits the movement in a parallelogram shape.  Pantographs have a point of rotation (like a compass) as well as several joint spacers to keep the instrument parallel to the sheet of paper. A pointer follows the existing lines or the drawing while the other draws a second version of the figure. Some pantographs are more elaborate with running gear.  The first pantograph was made by the german astronomer Christoph Scheiner.

Le QUADRANT est un instrument de 90 degrés qui mesure l’angle d’altitude d’astres ou d’objets.  Plus répandu dans l’histoire arabe, il reprend plus simplement l’idée de l’astrolabe, mais avec un poids au bout d’une corde.  Pour prendre la mesure d’une étoile, l’observeur tient l’objet à la verticale et cadre l’astre ou l’objet dans le viseur.  Cet alignement créé, il place son doigt sur la corde qui est alors perpendiculaire au sol par la gravité et ainsi, la corde indique de nombre de degrés.  Certaines sources en attribuent l’invention au romain Claude Ptolémée (né vers 90) à Alexandrie en Égypte.  Le quadrant mural ci-dessous fut construit par Robert Hook (environ vers 1676).  (Voir aussi le sextant de Tycho Brahe). 

The QUADRANT is a 90 degrees instrument which mesures the angle of the altitude of objects. More prevalent in Arab history, it is used like an astrolabe, but with a weight at the end of a rope. To measure the angle, the observer holds the quadrant vertically and frame the star or object in the viewfinder. This alignment created, he puts a finger on the string which is then perpendicular to the ground by gravity and thus the string indicates the number of degrees.  Some sources attribute the invention of the quadrant to the roman Claudius Ptolemy (born around 90) in Alexandria, in Egypt.  The mural quadrant below was made by Robert Hook (about 1676).  (See also Tycho Brahe’s sextant).

La PROJECTION ORTHOGRAPHIQUE est une technique développée notamment pour cartographier le ciel, mais également la planète, à partir de lignes appelées parallèles et méridiens.  L’instrument de projection orthographique consiste en un pointeur qui prend en mémoire l’emplacement d’un point dans l’espace, puis on rotationne la plaque selon un axe vertical pour inscrire ce point sur la surface.  Cet exercice permet de dessiner un objet selon ses coordonnées en trois dimensions en limitant sa déformation et par conséquent à éliminer toute forme de perspective.

The ORTHOGRAPHIC PROJECTION is a technique used also for mapping the sky, but also the planet, from lines called parallels and meridians. The instrument of orthographic projection consists of a pointer which memorize the location of a point in space, then we rotationne a plate around a vertical axis in order to do a record on the surface. This exercise allows to draw an object according to its three-dimensional coordinates, but also to limiti its deformation and thus eliminate all forms of perspective.

Le principe de l’ANAMORPHOSE CYLINDRIQUE est de déformer une image pour qu’elle apparaisse sous sa forme initiale lorsqu’on l’observe avec un miroir cylindrique.  Cette rationalisation de la vision permet de systématiser les techniques de projection.  Certains l’appellent la perspective secrète, mais elle conduit aussi aux techniques de trompe-l’œil bien présentes en architecture (voir le “dôme” de l’église San Ignazio à Rome).  En effet, un crâne anamorphique, un torquetum et un quadrant sont visibles dans le célèbre tableau d’Holbein.

The CYLINDRICAL ANAMORPHOSIS principle is to distort an image and then to make it appear in its original form when viewed with a cylindrical mirror. This rationalization of vision has allowed systematizing projection techniques. Some call it the secret perspective, but it also leads to “trompe-l’oeil” techniques often present in architecture (see the “dome” of San Ignazio Church, in Rome).  Indeed, an anamorphosis skull, a torquetum and a quadrant are present on Holbein’s famous painting.

Anamorphosis video

Le TORQUETUM est conçu pour prendre la mesure et convertir les informations concernant l’horizon, l’équatorial et l’écliptique.  Le plan horizontal est ajusté selon la latitude locale.  Le disque vertical ressemble beaucoup à un astrolabe.  Il fut inventé autour du 13e siècle par Jabir idn Aflah, un astronome et mathématicien musulman de Séville, en Espagne.  Les exemplaires qui ont survit au temps datent du 16e siècle.

The TORQUETUM is designed to measure and convert the information on the horizon, the equatorial and the ecliptic. The horizontal plane is adjusted according to the local latitude. The vertical disk is based on the same principles of an astrolabe.  It was invented by Jabir idn Aflah, a muslim astronomer and mathematician from Seville, in Spain.  The copies which have survived are from the 16th century.

LE PROJET

La proposition consiste en une forme d’hybridation entre un instrument de relevé et un type de représentation.  Les instruments qui ont retenu mon attention sont le quadrant, le torquetum ainsi que les principes de projection orthographiques appris lors des deux exercices précédents.  J’aimerais utiliser le quadrant à titre d’outil pour prendre un relevé des astres et pouvoir directement inscrire leur position sur un plan horizontal, avec un poids au bout d’une corde.  Le quadrant serait ainsi fixé selon un axe vertical et pourrait rotationner sur 360 degrés.  Le plan horizontal, de bois, pourrait être recouvert d’une feuille de papier et ainsi je pourrais cartographier/relever des astres en temps réel, de manière précise, selon la projection orthographique.  J’aimerais également tenter de prendre un relevé d’une pièce ou d’un paysage selon cette technique, sur 360 degrés.  Je suis curieuse de voir le résultat d’un tel type de représentation.  Je prévois également comparer mes résultats et les interpréter avec un miroir cylindrique ou conique au centre du dessin et faire un rapprochement avec les anamorphoses.

THE PROJECT

The proposal consists of a form of hybridization between a survey instrument and a type of representation.  Instruments that have caught my attention are the quadrant, the torquetum and the principles of orthographic projection learned in the previous two exercices.  I would like to use the quadrant as a tool to mesure the stars and directly register their position on a horizontal plane, with a weight and a graphit at the end of a rope.  The quadrant would be fixed on a vertical axis and could rotate 360 degrees. The horizontal plane of wood could be covered with a sheet of paper so I could map the stars in real time, accurately, according to an orthographic projection. I would also try to make that type of survey in a room or with a landscape using this technique on 360 degrees. I’m curious to see the result of this type of representation. I also plan to compare my results and interpret them with a cylindrical or conical mirror in the center of the drawing and make a comparison with anamorphosis.

Émélie DT

Sources:

The Alphabet and The Algorithm, Mario Carpo, MIT Press, 169 pages.

Vitruvius, The Ten Books On Architecture, Marris H. Morgan, Kessinger Publishing, 331 pages.

Eleven Exercices in the art or architectural drawing : slow food for the architect’s imagination, Marco Frascari, Routledge, 213 pages.

Cosmos: An Illustrated History of Astronomy and Cosmology, James Evans, Oxford University Press, 496 pages.

Cosmographia, Petri Apiani

Research and preliminary proposal

For my project I have narrowed my research to two main fields of interest:

1/ In researching ancient drawing machines, I came across a website that contains replications from an exhibition that belongs to the collection “Theatrum Machinarum” at the University of Modena and Reggio Emilia, Mathematics department. All the models, also the ones reproducing machines that have been largely used in the past (since the 15th century) to carry out a number of different activities (painting, architecture, design, cartography, military art, etc), have been constructed with a “didactical intention, in order to introduce a historical discourse about perspective constructions and the mathematics of central projections”

Link: http://archiviomacmat.unimore.it/PAWeb/Sito/Inglese/Templatei.htm

The perspectograph, in particular, is a famous instrument that allows one to obtain a correct perspective drawing of a threedimensional object. Painters and architects including Leon Battista Alberti in the 16th and 17th centuries used Perspectographs. Some types of perspectographs are very simple (as these reproduced in Dürer’s perspectograph), some types are rather complex.

Jacopo Barozzi da Vignola’s Bi-Dimensional perspectograph (developed between 1527-1545) uses two rulers, one fixed in the vanishing point and the other one in the point at a distance (both on the horizon line), many dead lines (to be deleted after the drawing is finished), which would appear if following the Second Rule, will not be needed. The premise for this device has been reiterated by JH Lambert in 1752 and recently employed for purposes of abstract art rather than perspective by Eske Rex.

2/ Gimbal: I find this device intriguing because it is not clear who invented the object but it has been used countless times in navigational devices, in telescopes, lighting devices, etc.

Drawing of a compass supported by gimbals (1570)

The Gimbal is essentially a pivoted support that allows the rotation of an object about a single axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of the rotation of its support.

The device is beautiful in its construction, as it seems to enact the rotation of the cosmos while allowing itself to be useful in numerous, everyday tasks.

Research and Bibliography

http://www.rarebookroom.org/

http://archiviomacmat.unimore.it/PAWeb/Sito/Inglese/Templatei.htm

Sawday, Jonathan. Engines of the Imagination: renaissance culture and the rise of the machine. New York: Routledge, 2007.