Recovered Writing: Undergraduate Age of Scientific Discovery, Copernicus and Galileo Essay, March 19, 2002

This is the twenty-third post in a series that I call, “Recovered Writing.” I am going through my personal archive of undergraduate and graduate school writing, recovering those essays I consider interesting but that I am unlikely to revise for traditional publication, and posting those essays as-is on my blog in the hope of engaging others with these ideas that played a formative role in my development as a scholar and teacher. Because this and the other essays in the Recovered Writing series are posted as-is and edited only for web-readability, I hope that readers will accept them for what they are–undergraduate and graduate school essays conveying varying degrees of argumentation, rigor, idea development, and research. Furthermore, I dislike the idea of these essays languishing in a digital tomb, so I offer them here to excite your curiosity and encourage your conversation.

I wrote this essay for Professor Robert Wood’s LCC 2104 Age of Scientific Discovery class at Georgia Tech. This was shortly after I was readmitted to the program after working in IT for several years. My citations are sloppy and incomplete and the writing is evidence of my writing’s early stages and on-going development. This is the second of three essays from Professor Wood’s class.

Jason W. Ellis

Professor Robert Wood

LCC 2104 Age of Discovery

March 19, 2002

Essay 2

Copernicus and Galileo both had unique scientific methodologies that they applied to their work in astronomy. Copernicus shows a reliance on that of the past and he builds on the work of others. He is not merely making commentary, but transposing his own findings on that which came before. Galileo takes this a step further by understanding what has been said and relying on his observational work to be the interpretation of the heavens. He also extends his work into the world through letters and publishings to open discourse between himself and others. Thus creating a dynamic to possibly find faults in his findings or show fault in the findings of others.

The beginning of the revolution concerning understanding how the planets of our solar system are arranged started with the work of Copernicus with the work De revolutionibus. Copernicus conducts his observations and mathematical deductions on the precept in Hallyn that, “as the beneficiary for whom the world was made, man can attain true knowledge. In place of a universe whose beauty and rationality escape us, and which thereby calls us to humility, Copernicus substitutes a cosmos for which man is the final purpose and whose true plane he can reconstruct.” Additionally, Hallyn writes, “Copernicus was not content to admire an inaccessible wisdom “from afar”; he believed that science must permit man to penetrate the arcana of the divine plan and must be willing to submit to complete reform if necessary to achieve this anagogical goal.” Copernicus elevates the status of man and astronomer to one who is able to spy the truth in nature through observation and deductions based on those observations.

Work done by predecessors and particularly, the ancients, Copernicus valued a great deal. He viewed astronomy as building on itself with the work done by those who came before. In Hallyn, there is this passage and quote of Copernicus regarding acknowledging the prior works of others.

Copernicus takes care, moreover, to emphasize that the very theory he is proposing is based on an ancient hypothesis concerning the nature of the universe:

I undertook the task of rereading the works of all the philosophers which I could obtain to learn whether anyone had every proposed other motions of the universe’s spheres than those expounded by the teachers of astronomy in the schools. And in fact first I found in Cicero that Nicetas supposed the earth to move. Later I also discovered in Plutarch that certain others were of this opinion…Therefore, having obtained the opportunity from these sources, I too bean to consider the mobility of the earth. And even though the idea seemed absurd, nevertheless I knew that others before me had been granted the freedom to imagine any circles whatever for the purpose of explaining the heavenly phenomena. Hence I thought that I too would be readily permitted to ascertain whether explanations sounder than those of my predecessors could be found for the revolution of the celestial spheres on the assumption of some motion of the earth.

Hallyn writes, “the importance of this passage lies not only in the way it recalls certain precursors, but also in the weight it ascribes to a particular form of renovatio based on the liberty to think, which may in turn lead to innovatio.” Copernicus is learning about ideas that surfaced in the past. Some of those ideas might not have been popular or they might not have had the ability to prove them properly at that time. Now he decides to take some of these ideas and try them on his own. He makes them his hypotheses which he will test with observation and he will apply his knowledge of mathematics to what he finds. He understands that the technology and mathematics of his time in regard to astronomy is greater than that which they had in previous times. This affords him a certain ability to learn new truths and a liberty to investigate further than those before him. Thus the “renovatio,” the renovation of ideas leads to “innovatio,” innovation born of those ideas.

His work in De revolutionibus is analogous to his search for truth. It is a transformation of old ideas into the next level. He is not merely commenting on previous work, but he is taking what he has learned from others, particularly, Ptolemy, and from his mathematical treatments on that work to develop the next plateau of understanding. Debus writes, “in short, the Ptolemaic system was recast.” The sun was placed at the mathematical center of the universe. This was surrounded by the planets, each set in their crystalline spheres. Outside this was the sphere of fixed stars. The Copernican system retained a good deal of complexity found in the Ptolemaic system, but he had simplified some things. Copernicus had eliminated equant circles and epicycles that explained retrograde motion were almost completely resolved (if he had accepted elipical orbits this would have been fully resolved). Additionally his system allowed for relative distances of the planets from the sun to be calculated using trigonometry.

It cannot be too lightly stressed that Copernicus has a great respect and reliance on Ptolemy. Copernicus even notes concern regarding his belief in the basis of the Ptolemic system when he says in Hallyn, “not to disorient the diligent reader by straying too far from Ptolemy.” He takes Ptolemy’s work, internalizes it and then rebuilds it with the additional information and knowledge that he has. For Copernicus astronomy is an interpretive and transformative process. It is interpretive because new ways of explaining data may be found. it is transformative because an earlier concept or work is elaborated on and changed into a new system based on the old.

The methodology used by Galileo is slightly different than that used by Copernicus. Galileo relies on a system closer to that which we see today in the sciences. The telescope is better refined and it’s power much better than that used by Copernicus. Thus Galileo uses this for more accurate observations. Also he relies on diligent and regular observational data. One cannot observe occasionally and expect to get data that show trends or behavior over time accurately. Building on this concept he puts forth the idea that if someone follows his procedures for observation, using a similar apparatus, the observation can be reproducible from different locations. This means someone in Rome can make the same observation of sun spots that someone in Florence can make.

Standards in observation were something he adherently held to in order to build data that can be accurately interpreted and used by different persons. In his observations on sunspots Galileo notes how he makes these observations so that they are accurate. On pages 115-116 of Drake, Galileo notes the method he uses that was developed by his pupil Benedetto Castelli. His description is very precise and descriptive. If someone wanted to begin observing sunspots they could easily use this method that Galileo describes to do so.

The structure of the “Letters on Sunspots” in Discoveries and Opinions of Galileo also serve to show the desire Galileo had for discourse in the science of astronomy. He believed that a well reasoned argument with supporting evidence should sway any dissenting voice to the truth of his argument. The “Letters on Sunspots” show him answering, by way of letter, questions and counter-arguments from his dissenters. He is exact in explaining his point of view and he follows up by pointing out how the argument from a dissenter might be mistaken or incorrect. During this time the Aristotelians still were a dominant force in the academia. An important point that Galileo makes is that even Aristotle would arrive at similar conclusions as himself if he had had the apparatus that was available during Galileo’s time.

Galileo differs from Copernicus in that instead of relying and giving a great deal of credit to the work done before him, he relies much more heavily on the accumulation of observational data and of reasoning through that data. Through Galileo’s work he was able to prove that the Copernican system was essentially true.

One of the most important distinctions that Galileo presses is that of naming. Prior to and during Galileo’s time, many astronomers would refer to objects or lights in the heavens as “stars.” Planets, supernovae, comets, and everything else were grouped together in this manner and referred to as “stars.” When you are attempting to explain something and how it is different from something else, nomenclature is very important. In his work, “The Starry Messenger,” Galileo goes to great lengths to describe and illustrate the differences between things in the heavens. This is necessary for him to describe the moons of Jupiter, or as he called them, the Medicean planets. In his illustrations on pages 52-65 of Drake, he not only shows regular depictions of the location of the Medicean planets, but also their relative size or brightness. Through the course of the illustrations one can see the nature of rotation they make around Jupiter.

Galileo and Copernicus each have a particular way about which they discovered truth about the way in which the solar system operates. Copernicus built on the knowledge of others augmenting and modifying that with his own intuition, observation, and mathematical ability. Galileo took this a step farther by incorporating a more detached view of the heavens by relying on observational data to prove his points. The methods of Galileo show a strong resemblance to that of scientific observation today: observation, deduction, reporting, peer review and discussion.

 

 

Works Cited

 

Debus, Allen G. Man and Nature in the Renaissance. New York, New York: Cambridge University Press, 1978.

 

Drake, Stillman, ed. Discoveries and Opinions of Galileo. Trans. Stillman Drake. New York, New York: Anchor Books, 1957.

 

Hallyn, Fernand. The Poetic Structure of the World: Copernicus and Kepler. Trans. Donald M. Leslie. New York, New York: Zone Books, 1987.

 

Recovered Writing: Undergraduate Age of Scientific Discovery, Leonardo da Vinci Essay, Feb 14, 2002

This is the twenty-second post in a series that I call, “Recovered Writing.” I am going through my personal archive of undergraduate and graduate school writing, recovering those essays I consider interesting but that I am unlikely to revise for traditional publication, and posting those essays as-is on my blog in the hope of engaging others with these ideas that played a formative role in my development as a scholar and teacher. Because this and the other essays in the Recovered Writing series are posted as-is and edited only for web-readability, I hope that readers will accept them for what they are–undergraduate and graduate school essays conveying varying degrees of argumentation, rigor, idea development, and research. Furthermore, I dislike the idea of these essays languishing in a digital tomb, so I offer them here to excite your curiosity and encourage your conversation.

I wrote this essay for Professor Robert Wood’s LCC 2104 Age of Scientific Discovery class at Georgia Tech. This was shortly after I was readmitted to the program after working in IT for several years.  My citations are sloppy and incomplete and the writing is evidence of my writing’s early stages and on-going development. This is the first of three essays from Professor Wood’s class.

Jason W. Ellis

Professor Robert Wood

LCC 2104 Age of Discovery

February 14, 2002

Essay 1

Florence has established itself as a focus of a great many good things that have come about in such a short time. What follows is a listing of works which I have seen originating in Florence in this “new age.” My attention will first look at the arts and the innovations that took place in perspective and the use of space, as well as the newer sculptures that capture lifelike qualities so exquisitely. Then I will look at the marvel of architecture that dominates the city of Florence and I suspect will continue to do so for many years to come. Then I will look at machines and engineering feats that came about during this time as well.

Artwork has had a blossoming in recent years. Just prior to my birth artists began to investigate spaces and perspective. This work has led to a greater representation of the actuality of how things appear to the eye. What we see around us can thus be reproduced to great accuracy and it provides a more faithful representation of the world. I once saw a pen drawing of a chalice i perspective by Paolo Uccello. It appeared as a network of lines which comprised it’s inner and outer construction. It is a most unique work that delves deeply into the artistic representation of perspective. Uccello used special techniques in his works to represent how things appear. For example in his work, “The Battle of San Romano,” there is a terrific battle scene with fallen men and horses. Riders are attacking one another with their lances drawn. He skillfully laid broken lances on the ground to indicate the lines of perspective, and the horses are drawn with foreshortening. Uccello reconstructs a bloody scene of battle, but he does it in a representative way of reality as it would appear to the eye. Another wonderful example of perspective is Fra Angelico’s altarpiece at San Marco which he completed in 1440. It is much like you are standing off at a distance from the scene where the lines of perspective created by tile work on the floor and the arrangement of two rows of angels and saints leading up to the central focus of the work, the Madonna and Child seated on a classical throne. A work that is seen by everyone in Florence is the Baptistry doors. These were completed by Lorenzo Ghiberti in 1452. It is known as the “Gates of Paradise.” In these panels there is a clear representation of space, and the people and buildings within that space are proportional to one another. He employed a unique handling of the telling of narrative in the panels. One would assume at first looking at a panel that it was several events all happening at the same time, but in fact those separate events are sequential and they take place one at a time. Thus in a small space he is able to tell a story that might take other artists several panels to compose. Other works of art that are notable are those of sculpture in stone and bronze. The beginning of great artistry in sculpture took place when statues were needed to fill niches around Orsanmichele in Florence. Notable sculptures contributing to this project were Donatello, Nanni Di Banco, and Lorenzo Ghiberti. Ghiberti’s bronze statue of St. John the Baptist is a powerful representation. Donatello’s “St. Mark,” which he carved from marble appears more like a real man than Lorenzo’s “St. John the Baptist.” Donatello reveals St. Mark’s arms and legs beneath the robe by the way in which he stands. The division between flesh and stone seems not too great on St. Mark. It is as if he could walk out of the niche in which he stands. Di Banco represents the “Four Crowned Saints” in a niche, standings in a semicircle with one another. His representation is very true to historical accuracy with the depth of investigation and knowledge he applied to this work. The figures are clad in togas and the heads are said to be based on “several Roman portrait types.” Also it is interesting how at the bottom of this work he did another carving representative of a workshop busily in execution of works such as a putto and a small architectural column. A master sculptor who went beyond the work of the before mentioned sculptors is Michelangelo. Two masterful examples of his work is the “Pieta” which he completed in 1499, and “David” which he completed in 1504. The “Pieta” rests in St. Peter’s Basillica in Rome. It is a representation of Christ being held by his young Mother. I have said that sculpture is not as high an art as that of painting, but in this work Michelangelo has created something as far reaching as a work of painting. His “David” again reflects a mastery of the human form. He must have done extensive study of muscles and the body to build this representation.

The next subject I will turn to is that of architecture. The achievement that stands above all others in Florence is the vaulting of the dome of Santa Maria del Fiore. With a span of 143 feet it is the largest dome in the world. The cathedral which the dome rests on was under construction for more than a century. When the time had come to build the dome a competition was announced for designs to be submitted. Filippo Brunelleschi submitted the most brazen of all the designs. He proposed building the dome without the traditional centering which was believed necessary to build a domed structure. After a great deal of debate Brunelleschi’s design was accepted and building commenced. I witnessed part of the work being done on the dome when I was younger. I was an apprentice of Andrea del Verrocchio. The dome is an octagonal design which employs two shells interlaced within by ribs and what is called the “sandstone chain” to give it the support necessary to allow it to hold itself up. The idea for the dome was a great insight into the nature of materials and their construction together to form the whole that we see. In 1436 the dome was completed. All that remained was the lantern that would sit on top of the dome. From the lantern all of Florence can easily be seen. Also, from that height one can make wonderful observations of the heavens. It is of note that a friend of Brunelleschi, Paolo Toscanelli made a great deal of observations from the dome of Santa Maria del Fiore prior to sending a set of maps to Columbus prior to his sailing and discovery of the new world.

In the building of the dome and lantern new innovations were made in the construction of cranes and hoists. The first such invention was the ox-hoist by Brunelleschi. What sets this hoist apart from any before it was that it had a reverse gear. What this means is that the hoist would be driven by a single ox which would walk round in a circle bound to a drive which fed into the gears of the hoist. This walking of the ox would raise material to the top of the cathedral, and then for lowering material into place, the gearing mechanism would be adjusted onto a different gear which would change the direction of the work done by the ox. Thus the ox could continue to walk in the same direction but the work produced by it could be altered simply by the mechanism which it was attached to. This reverse gearing system saved a good deal of time and work for the construction of the dome. Had Brunelleschi not created this new hoist we might well be waiting for the completion of the dome now as I write this! When I was the apprentice of Andrea del Verrocchio I made sketches of a newer hoist and crane that Brunelleschi built for working on the dome and placing the stones where they would be in the construction. This crane was called the castello and it was very durable for the strain which it was placed under. It was still in employ when my master built the the eight foot high bronze sphere which is on top of the lantern of the dome. The castello was a hoist, but it also had a arm which could swing to allow the exact placement of a stone in the construction of the dome. Again Brunelleschi showed his mechanical expertise in the construction of the of castello.

I have been fortunate to live in a time such as this and in a place with such imaginative and practical works. Florence has many good people employed to build the status of the city and the works which gain renown far and wide. I feel that this is the beginning of a great many things that may have began with Florence but will carry on in cooperation with a great many people in many varied places.

Works Cited

King, Ross. Brunelleschi’s Dome. New York, New York: Penguin Books, 2000.

Richter, Irma A., ed. Notebooks of Leonardo Da Vinci, The. Oxford, Great Britain: Oxford University Press, 1980.

Turner, A. Richard. Renaissance Florence. New York: Harry N. Abrams, Incorporated, 1997.