Author Archives: jeanrochmarion

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.

dondis astrarium

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.

summeryPtolemaicAstron3

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.

Jean-Roch’s rendition of Alberti’s Delineation of the City of Rome

In the text called Delineation of the City of Rome, Alberti describes a tool and its instructions to follow in order to replicate a precise map of Rome. Using a circle divided into 48 degrees and 192 minutes called the “horizon” and a “spoke” the length of the radius of that circle divided into 50 degrees and 200 minutes, he explains how to plot a series of points within the horizon, similarly to a cartesian grid. He then lists multiple tables of points corresponding to various monuments, roads, river, walls and buildings according to their position in the city Rome, either as “corners” or “apexes”, meaning the meeting of two lines or two curves. Once all the corners and apexes are connected together, the result should be an accurate map of Rome proportionally sized to the dimension of the circle originally drawn.

In order to gather those tables of points that represent the positions of different elements of Rome, Alberti created a tool with which he could determine the position of a monument in degrees on the horizon. Standing still at a single point (which corresponds to the center of the circle on the map), Alberti looked through an instrument that allowed him to tell where on the circumference of the circle the various elements were positioned. Assuming that he was standing next to a tall monument with a determined height (in this case, the Capitol), Alberti could determine the distance of those elements from his viewpoint with a simple astrolabe instrument.

Jean-Roch’s astrolabe

This particular astrolabe is a modern rendition of the historical tool used by philosophers, astronomers, mathematicians and builders alike for hundreds of years and still functions in the same way. In short, it is a projection of the sky on a two dimensional surface specific to the viewers geographical coordinates, that can be used to compute various information. Since the location of the different constellations is in constant movement in the sky as the Earth rotates around the sun and on itself, the astrolabe can easily compute the location of various celestial bodies at a precise date and time. Furthermore, since the projection of the sky varies greatly in regards to the user’s latitude and longitude, different sky maps called Plates are placed on the astrolabe, which makes it a site specific tool.
On the Plate of the astrolabe are the projections of different astronomical concepts which are fixed: the Tropic of Capricorn is represented by the outer ring, the Tropic of Cancer by the inner ring and the Equator by the middle ring (the Tropics would be reversed if the astrolabe was to be used in the southern hemisphere). The Almucantar and Azimuth lines are drawn in concordance to the latitude of the user: they represent a grid that is used to locate objects in relation to the horizon, the zenith (at the centre of the Almucantar rings), east and west as well as north and south. On the circumference of the Plate are the 24 hours of the day numbered in clockwise direction.
On top of the Plate is the Rete, which represents a projection of the celestial sphere that can be rotated on the fixed Plate. It consists of the Ecliptic of the sun’s path represented by an offset circle and the most important stars and constellations represented by arrows or dots. Over the Rete is the Rule, which is used to relate the hours of the day to the location of the sun in the sky.
In order to correctly read the astrolabe, you have to position the top of the Plate called the Throne due south, and look at it as you would at a map. In order to know the location of celestial objects at a specific date and time, turn the Rule the the corresponding Zodiac Scale of today’s date (usually found on the backside of the astrolabe) along the sun’s Ecliptic. Turn both Rule and Rete so that the Rule points at the correct time of the day. The end result is a map of the current sky, where the position of objects is read by their degree above the horizon, and degree north or south of east or west. For example, on October 4th (Libra 11) at 4pm, Altair is located at 35 degrees above the horizon, 30 degrees south of east.