In this lesson we will learn about Galileo and the way in which his ideas about the physical universe changed as he employed, for the first time, the methods of modern scientist. We will see why and how he transformed from medieval man to modern man and how he crystallized the new paradigm and earned the title of The First Scientist.
Galileo's contributions have earned him the title of "The First Scientist". Sometimes he is called "Father of Science".
Well schooled in classical Greek and Latin, Galileo was trained in the Priesthood and was familiar with the Scholastic Philosophy. In his early years he was very much the medieval man. Against his father's wishes he studied mathematics and eventually earned a professorship. He wrote and delivered lectures and scholarly papers on such Scholastic topics as the size and shape of Dante's Inferno, and gained a reputation all over Europe for his persuasive speaking and intelligent scholarship.
Around the age of thirty, he underwent an amazing transformation. He became a modern man. During a short period he became a convert to the Copernican system and began systematic studies of motion in an attempt to prove Aristotle's views incorrect. He designed controlled experiments and collected data on motion. He compared the data to predictions made by logical discourse using his definitions of motion as first principles. He used Platonic dialogues to argue in favor of his intuitions, just as Aristotle had done, but much more cleverly, and more correctly.
Galileo was an intelligent, well educated, and rebellious man who believed that people have a right to knowledge which is accessible to their own observations. He did not like the idea of an authoritarian cosmology which did not correspond to observations, and he did not like that it was the Church who dispensed knowledge in just the right doses to keep political control.
He thought it more appropriate to redefine the cosmology to fit the observations rather than ignore observations in order to support the cosmology.
His use of the telescope to view the moons of Jupiter, the phases of Venus, the flattening of Saturn, and the mountains and craters of our own moon, marked the first serious observational challenge to the paradigm of geocentric heavenly perfection.
With the publication of a booklet, The Starry Messenger, Galileo drew attention to his Copernican views and set the stage for further events which would forever change the way we study our world
In 1617 Galileo was warned by the Church to stop teaching the Copernican theory at the University of Padua where he was now a professor of mathematics.
In 1632, having secured permission from the Pope to publish scholarly critique of the two systems, he published Dialogues Concerning the Two Chief World Systems. In this book he used a Platonic dialogue to discuss the merits of the two systems. The dialogues were cleverly written in such a way that each debate was conceded by the moderator to have been won by the Ptolemaic advocate, while it was clear to the reader that the Copernican viewpoint was by far a more logical and probable system.
The dialogues fooled the Church censors until Galileo's detractors, who read much more critically than the censors, discovered the obvious intent. Galileo was summoned by the Pope and forced to recant, and as an alternative to even worse punishment was kept confined under house arrest until his death.
While confined he completed the manuscript of Two New Sciences, which was published in Holland in 1638. In this book he detailed his studies on motion which included the law of freefall, discovery of inertia and the explanation for projectile motion.
Is a cone a circle or a triangle?
The resume of Galileo below is intended as a guide to his character, the change of character, and the strength of his convictions to publish his work in spite of its disfavor in support of the Copernican cosmology. It is presented here in outline form. The video program will emphasize the significant events as they relate to his role in our scientific heritage.
Try to put yourself in Galileo's place. Imagine that you are in Padua in Italy. It is just three years from the beginning of a new century. You have been well schooled in the classics, in medicine, and have become a scholar in the field of Scholastic cosmology, traveling around giving lectures. Following your heart, and against your parent's wishes you decide to give up the clergy and become a mathematician (sort of like dropping out of the Harvard Business School and becoming a rock musician in the sixties).
Now imagine your reaction upon looking through the telescope at the heavens and seeing the truth, and realizing that it was Copernican, beyond any doubt. You have just seen the first definitive proof that all of the speculation of two and a half thousand years has only served to justify that which is obviously false. Talk about having a revelation.
This would be a fun one to act out with a friend. For example, for this program response, you might write a short skit wherein Galileo tells a Scholastically skeptical friend what he had seen and what it means.
If you do want to act it out, send us a videotape as your program response for this lesson.
In this section we have used leaders instead of legal numbering because the dates are confusing when preceeded by number .
twenty one years after the death of Copernicus
1556: Latin scholar at monastery, fair command of Greek
1581: Medical studies at University of Pisa
1587 88: Delivered Papers on Site and Dimensions of Dante's Inferno
studied motion of falling bodies
lectures angered Aristotelian colleagues
staged burlesque which ridiculed university regulations
established European reputation as scientist and inventor
lectures attended by persons of highest distinction
military architecture, gnomonics, the sphere,
accelerated motion, special problems in mechanics
machine for raising water, geometrical compass, air thermometer
his student's (Torricelli) barometer measured air pressure changes using Galileo's theories
did many experiments and made observations
speed of light
of falling objects
with telescopes of his design
continued to teach Ptolemaic system at Padua
moons of Jupiter and phases of Venus convinced him of mission
"all my life and being henceforth depends" on the acceptance of Copernican theory
began development of new principles in opposition to Aristotle
saw that he could discredit Ptolemaic theory by proving Aristotle wrong on other counts, specifically motion
Copernican system was already in use by the Church
Church wanted to retain authority and political control
Too much knowledge might cause social breakdown
dedicated book to Pope Urban VIII
". . . a third theory is needed since one is condemned by the Church, the other by reason."
led to audiences with Pope Urban, a former friend of Galileo's
writing encouraged by Pope's reception
got Pope's permission to publish
directed at lay public
written in Italian rather than scholarly Latin
advocate of Aristotle portrayed as simpleton(Simplicio)
advocate of Copernican system (Salviatti)
neutral moderator (Sagredo) who conceded validity of old system
Copernican system was obviously favored
approved by Church censors
true intent and implications noted by opponents
asserted intent to ridicule Church
book banned, copies destroyed
Galileo called to trial, forced to abdicate
given the choice of renunciation or execution
forced to sign an elaborate formal renunciation of Copernican theory
held a prisoner of the inquisition in his home near Florence
Materials and Motion
written in exile
discussed earlier experiments, deductions on kinematics
stated Newton's laws of motion although not concisely
published in Holland
In this part of the lesson we will examine the work of Galileo which has rightfully earned him the title of "The First Scientist". We will see how he used the right tools but used them for a job unintended by their forgers, namely the Scholastics, following the tradition of St. Thomas. It had been three hundred years since Aquinas sealed the Scholastic Philosophy with the Summa Theologica. It is not surprising that the Scholastic philosophy had been slowly adapted to the changing political needs of the Church, as any doctrine will alter over time as it is molded to the desires of those who wield power.
Galileo's work as a scientist is remembered because of the way he combined inductive and deductive logic in the form of observations, mathematical reasoning, the collection and analysis of data, and controlled experiments
The justification and precedent for Galileo's scholarly pursuits lay within the writings of St. Thomas himself. It was Aquinas, as you will recall, who encouraged scholars to seek new knowledge so as to make the scriptures more in accord with nature. having broken Augustine's tradition of disinterest in exterior, physical reality. Aquinas and his contemporary, Roger Bacon had suggested the oneness of God and nature, and the importance of studying many things, including to help understand God. These ideal had largely been buried and ignored by Galileo's time. The Church had recovered its somewhat following it's reform after the Council of Trent. This council was formed in response to the weakening influence of the Church which included the formation of competing Protestant churches. Among other things, the Council incorporated the Copernican system, using it to correct the calendar and bring it back into synch with the seasons. This Gregorian calendar is basically the one we use today.
The Reformation of the Church ushered in the baroque period of art, architecture, and music. In an attempt to get people to attend masses, the Church added theater to its services. Churches were redesigned with lavish artwork and stained glass windows. Music was added to the liturgy in an attempt to increase interest in Church attendance and to draw members away from the competing churches.
The political power of the Church was nowhere stronger than in the States of Italy, where Galileo was born one year after the Council of Trent ended. Had he been born a generation earlier, had he been a young man who could contribute to the reform, it might have been a very different story.
As it was, he emerged into adulthood just as the Church was reestablishing its power following the Reformation, and they were not about to tolerate anyone messing with it. At least not one arrogant and bullheaded as Galileo Galilei.
Galileo was described as being "bullheaded and arrogant". He was selfconfident, rebellious. Unlike Copernicus, whose name the revolution bears, Galileo was the revolutionary.
This is similar to the discovery of America. Columbus "found" the New World, but thought he was somewhere else. The country is named after Amerigo Vespuci (we might have been know as Vespucia!), who knew where he was. Copernicus found a heliocentric solar system but didn't know what he had.
Galileo realized that the world of Copernicus was consistent with his observations with the telescope, but also with his logical arguments and experiments, about which he would not publish his most radical until thirty years had passed.
In the Scholastic philosophy, seeking new knowledge was encouraged, unlike Augustine warning to seek only internal knowledge. The Scholastics not only sought new spiritual knowledge through the Scriptures, but also from the ancient philosophers. They applied the methods of inquiry of the ancients to study all aspects of the spiritual and physical world, with little distinction between the two.
Following the ideas of Roger Bacon, Aquinas himself had stated that nature and God could not be separated. He conjectured the since everything in nature comes from God, then studying nature is a way of studying God.
In the true spirit of a paradigm, the types of questions which were appropriate were determined by the paradigm.
Although Galileo was schooled in the classical and the Scholastic methods, and used them to guide his questioning, he asked the wrong kinds of questions. The change in the style of questioning was the beginning of the modern era in science. It is a classic case of a paradigm shift, suddenly seeing the world in a different way. Once the system was understood in a different way, then it was possible to ask different questions as well as different kinds of questions. Of the two, the kind of questions is probably more important than the questions themselves. For one thing, Galileo asked questions for which a definitive answer could be found, not just a speculative one.
These specific questions, such as how far will a ball roll in a certain amount of time on a slope of a particular angle, were viewed as meaningless and general by his Scholastic contemporaries.
Interesting, isn't it that his specific questions were considered too general, while we consider their specific question too vague. Like night and day, the two ways are vastly different, and not just in terms of simple things like geocentrism and circles.
Galileo's contemporaries thought his approach was "fantastic, his conclusions "preposterous,haughty, and often impious."
You might say it is like looking at the face instead of the vase, if you know what I mean.
22.214.171.124. Right methods, wrong questions
126.96.36.199. Differed from Scholastics in orientation
188.8.131.52.2. what type of questions which are important
184.108.40.206. his specific problems were too general for Scholastic contemporaries
220.127.116.11. he excluded the orthodox philosophical problems
18.104.22.168. his approach "fantastic, his conclusions preposterous, haughty and often impious"
We are about to encounter our first example of what we call the Certs or Miller Lite type of Controversy. The name of this type comes from two TV ads. In one case the question is whether it is a candy mint or a breath mint and in the other whether it tastes great or is less filling. In these ads we see arguments among friends, people taking sides and chanting, and other typically human behaviors.
The eventual message is that Certs is both a candy mint and a breath mint, and that Miller Lite is both great tasting and less filling.
The allegory is clear. In the history of science, as in other endeavors, Certs/Miller Lite controversies take place daily. Is personality nature or nurture? Is light a wave or a particle? Does heat flow like a fluid or is it a form of energy? Is economics driven by supply or demand?
In most cases, the approach which has first been taken was to argue about which it is? Eventually great strides are made when the realization comes that it is both, unimaginable as it may be. Then the question becomes, How can it be both? What properties would allow it to display features of both?
It kind of reminds you of the face and the vase, or the young lady and the hag. You remember, from lesson 3?
We have seen how the use of formalized logic has been used since the times of the ancient Greeks. We have briefly discussed some aspects of that logic, and we have seen it in operation on several occasions. We have mentioned inductive and deductive logic on several occasions. Now it is time to take a closer look at the two forms. Although they are not the only forms of logic, they are important, among other reasons, because it was Galileo's use of deduction and induction as complementary and reinforcing methods which characterized the transition into the scientific age.
Induction is the process of discovering underlying law, rules, and principles from observation. This would be like writing a rule book from watching the game. It is the process used in understanding the rules of grammar of a spoken or a written language, or in deciphering a hieroglyphic.
Francis Bacon was an advocate of the inductive method. He argued that knowledge could be attained and organized most effectively using induction to ascertain the rules by which the universe operates. This is also what Aristotle did in formulating his explanations for motion and change in the universe.
One of the most famous inductions in the history of science is Kepler's Laws. Can you explain why we say these are inductive laws?
Like Aristotle, Bacon failed to characterize knowledge and learning by induction alone.
22.214.171.124. Laws and principles follow from observation
126.96.36.199. Francis Bacon (1521 1626)
188.8.131.52.1. "Laws will be obvious if all facts are known."
184.108.40.206.2. Failed to reorganize knowledge by induction alone
Deduction is the process of predicting outcomes based on knowledge of first principles such as laws or rules. This would be like predicting the orbit of a planet by knowing the principles that govern its motion. It is the process used when making astronomical charts based on Newton's laws.
This is similar to what Plato did in formulating the spherical paradigm with what we called Plato's question in lesson 6. Starting from the first principles of circular perfection and mathematics, how is the universe structured?
220.127.116.11. Results follow from basic principle
18.104.22.168. Descartes (1596 1650)
A strong proponent of the deductive method was Descartes. He believed, like Plato, that observations are not trustworthy. Descartes sought to start from first principles and argue logically to derive results.
Like Bacon, Descartes also failed to adequately describe reality. We will return to Descartes and his mathematics later in this lesson.
22.214.171.124.1. "Observations are not trustworthy."
126.96.36.199.1.1. start from a few principles and argue logically to derive results
Descartes argued that the spiritual and physical universes were of a different nature and could only be properly understood by appropriately different methods.
188.8.131.52.2.1. mind vs. body
He argued that the physical and spiritual worlds coexist in the minds of humans only, and that only humans have souls and feel pain.
184.108.40.206.2.2. man vs. nature
The separation of the mind and the body allows us to study nature as something separate from ourselves. It also allows us to come to justify the rape of the planet and its resources as we arrogantly assume that the planet, and perhaps the entire universe is made for our use. It is also very Christian, the separation of the soul from the physical body.
220.127.116.11.2.3. separate self from the physical universe
18.104.22.168.2.4. understand each separately
22.214.171.124.3. "Cogito ergo est."
Descartes' famous statement, "I think, therefore I am," might be viewed as a confirmation of the existence of the individual as something which must be explained and rationalized.
Come to think of it, it is amazing that we exist and can contemplate the universe which created us, whatever its cause and whatever its reason.
It's a good first principle. I might paraphrase him as "I exist, now what!"
What do you think it means?
126.96.36.199.3.1. all things follow from first principles (deductive)
188.8.131.52.3.2. this is as good a first principle as any
5.3.3. Combination proved most fruitful
It was the combination of the two method which lead to great success, first for Galileo, and later for Newton and science in general. The interaction of induction and deduction reinforce one another, like the graphite and resin in a high tech composite material. When combined with experimental observation and measurements, the three form a triangle of strength. Not coincidentally this same sort of strength is the foundation of our democracy, with the legislative, judicial, and executive branches exerting checks and balances on one another. We shall see that Thomas Jefferson was a great fan of Isaac Newton, but we are getting ahead of the story.
Study the diagram below as you watch the video. You may want to make a note of this figure and refer to it in later lessons as we watch the scientific method unfold the mysteries of the physical world.
184.108.40.206. Induction: Behavior leads to theory
220.127.116.11. Deduction: Theory leads to prediction
18.104.22.168. Experiment: Prediction compared with observation
5.3.4. Important part of scientific method
This three way interaction is an important part of the scientific method even today. Generally speaking there are two types of scientists. A physical scientist is usually either an experimentalist or a theoretician. It is the interaction between the theoretical or deductive and the observational or inductive which drives modern science.
Both types of endeavors attempt to test and modify the paradigm to fit reality, and the interaction between the two keeps either from straying too far one way or the other.
22.214.171.124. interaction between theoretical (deductive) and experimental (inductive)
126.96.36.199. both provide methods to test and modify the paradigm
188.8.131.52.1. new theories generate experiments to test
184.108.40.206.2. new facts generate theories to explain
Now we are ready to specify the tools that Galileo used in his work. We do this as a way of introducing the student to the structure of this "scientific method." We have deliberately chosen to present this material in a nonlinear way. We do this so that the student is not mislead into memorizing formulas, an act which would be comparable to running headon into a tree while searching for the forest.
We will list and delineate these tools now. In the next lesson we will be specific when we look at the development of Galileo's ideas in the context of these four tools, or methods, whichever you prefer to call them. We are interested in the way in which all of these things that Galileo did affected him, and specifically how he was convinced of the truth of the Copernican system with such fervor that he was willing to risk the wrath of the Inquisition to publicize them.
We will see in later lessons that modern science really is the implementation of the tools to various degrees, and sometimes with more success than others. After all having the tools doesn't necessarily mean that you can fix your car.
Galileo used both inductive and deductive logic in the interactive sense we described in the focus earlier in this lesson. When we study his methods and ideas in the next lesson, look for this interaction. Similarly, when we study Newton's development of the law of gravity, we will see a true master of this technique.
In his writings, Galileo employed the age old Platonic dialogue, but with a new twist. Instead of two characters engaging in dialogue, Galileo used three. He had one character arguing each opposing point of view and one moderator, to keep the discussion focused. Here we see the triangle of interaction in a different sense than we examined it in the focus.
220.127.116.11. used both deductive and inductive reasoning
18.104.22.168. used Platonic dialogues
Galileo made many different types of observations, but they seem to fall into three general types. These included observing objects in freefall, data collected during controlled experiments, and observations through the telescope which he also significantly improved over a period of ten years.
22.214.171.124. falling objects
Galileo is alleged to have staged a public demonstration, dropping lead balls of different size and weight off the tower of Pisa, to prove to all that they fell at the same speed, contrary to Aristotle. This is a nice story, but it was probably someone else who did it, at least at Pisa. There is no documentation to support it. Galileo was not the only one dropping things, nor was he the only one to question this aspect of Aristotle's natural motion.
At least he didn't do it at Pisa. He is known to have staged such shows for visitors to his home, as an after dinner act, followed by a persuasive speech about the errors of Aristotle's theories on motion. But most of them shrugged it off as a parlor trick and were neither convinced nor converted.
Galileo did extensive experiments over a period of many years. Most notable were his experiments with the inclined plane, rolling balls of different sizes, different materials, and different surfaces while he collected data on the distance and time. It is these experiments that we will undertake to understand in the next lesson.
It is not just the experiments that interest us. It is also the design of the experiments, the way he collected and analyzed data, the conclusions that he drew, the inferences he made, and the accidental discoveries which might have escaped a less adept experimenter.
You will note that we include experiments here as a type of observation, but also as a separate category, because the experiment is a special kind of controlled observation, usually in the form of some simplified model of a more complex system.
We have already noted Galileo's observations through the telescope in program 10. You may wish to go back and review these briefly to refresh your memory on the observations themselves and their significance in the geocentric/heliocentric controversy. Here is a listing of those observations.
126.96.36.199.2. moon craters and mountains
188.8.131.52.3. crescent of Venus
184.108.40.206.4. moons of Jupiter
220.127.116.11.5. flattening of Saturn
18.104.22.168.6. pinpoint stars of Milky Way
Before Galileo mathematics was for doing calculations, things like predicting planetary motion and keeping track of inventories, shipments and other practical things.. Kepler induced some general laws from Brahe's data using mathematics, but it was still basically doing calculations. It was Galileo who really began to use mathematics for defining, deriving, and understanding relationships. The key word here is relationships.
For whatever reason, Pythagorean or otherwise, these relationships exist. Galileo was one of the first to recognize that it is not necessary to understand why the relationships exist in order to know what they are. Concentrating on the relationships instead of their meaning was one of the ways in which Galileo departed from the Scholasticism of his contemporaries, and for which they found his methods unorthodox.
In lesson twelve we saw how analytical geometry can be used in the graphical analysis of motion, and how the graphs generated by these relationships are related to the geometric shapes. But the shapes and properties of the graphs are not related to numbers so much as they are related to the relationships between numbers. For example the fact that direct proportions exist in nature is a powerful prediction tool once we can show that a linear relationship exists. In the laboratory exercises you will have the opportunity to explore linear relationships of various types.
22.214.171.124. Don't Put Descartes Before the Horse.
Before we give too much credit to Galileo for his mathematics, we must return to Descartes. In Holland, around the same time that Galileo was writing his final work, Rene Descartes, exiled from his homeland in France for his radical ideas, was dreaming up the mathematics now known as analytic geometry. Combined with his reliance on deductive logic, as we noted earlier, and a preference for studying the spiritual world separately from the physical world, Descartes provided the perfect complement to Galileo's studies, and set the stage for Newton in the next generation.
In lesson twelve we combined Galileo's algebra with Cartesian analytic geometry to see motion from a modern perspective. We want to remember that Galileo did all of this without the benefit of this powerful visualization tool. This serves as another tribute to this great intellect. In Galileo's writings we see hints of Cartesian analytic geometry and Newton's laws. Imagine what he might have done with those tools!
Galileo's new use of mathematics generally falls into three types.
126.96.36.199.1. Analytic Geometry
Analytic Geometry is the name given to a branch of mathematics which deals with the nature of equations, types of relationships, and shapes and properties of the graphs generated.
The coordinate system we use to draw graphs is a clever way of showing relationships in pictorial form. From the geometric properties of the figures which are generated we can learn information about the relationships themselves.
This is an important contribution, and one that Galileo himself used but did not formalize the way Descartes did.
188.8.131.52.1.1. Cartesian coordinates show relationships between scalable number lines
184.108.40.206.1.2. relationship of numbers, shapes, equations
220.127.116.11.1.3. important contribution allowed Newton to expand on Galileo's and others' ideas
18.104.22.168. comparing data with predictions
It is not entirely clear how one would know whether a certain behavior has taken place, even after the measurements have been made. Without some way of analyzing the data, it is useless. This is especially true in Galileo's case where he was trying to determine whether or not objects underwent uniform acceleration, without being able to measure acceleration directly. He had to make measurements of distance and time and somehow use them to determine acceleration.
22.214.171.124. finding and verifying relationships between parameters
Verifying relationships is easier for us today with our techniques of graphical analysis and statistical regressions. In Galileo's time none of these techniques existed yet. As we will discover in our own laboratory experiences, because of errors in measuring, it is not always possible to distinguish clearly what kind of relationship exists between two parameters.
126.96.36.199. deriving new relationships
Using algebraic logic, Galileo derived a relationship between distance and time which would allow him to determine whether gravitational acceleration was uniform and the same for all objects. We saw this relationship in program twelve, but we repeat it here. You will see this again in lesson fourteen.
This mathematical wizardry predicts that in uniformly accelerated motion there should be a direct proportion between distance and the second power of time.
Don't panic if this doesn't register just yet. Just let it bounce around in your mind, and we will come back to it several times.
The idea of the experiment was not new with Galileo. Francis Bacon, who espoused an inductive approach was also a contemporary of Galileo, and the idea of testing reality had been published by Roger Bacon back in the time of St. Thomas Aquinas.
Galileo's experiments were well designed, they used well defined and easily measurable variables or parameters, and they allowed him to control the experiment by holding all but one variable constant while changing others.
The process of collecting and analyzing data is often overlooked as an important contribution of Galileo to the scientific method. Although we know that this is done, most of us don't do it. It is not as easy as it looks to keep a record of the variables and the conditions which lends itself to interpretation at a later time or date. You will no doubt experience some of these difficulties in your own efforts in the lab exercises.
188.8.131.52. well defined variables
184.108.40.206. data collection
220.127.116.11. data analysis
In this lesson we have explored the motivation for calling Galileo the First Scientist and the Father of Science. Along the way we encountered such bizarre things as the Certs/Miller Lite Controversy and the relationship between inductive and deductive logic. Weird or not, these things are elements of the development of science and we must touch on them, if for no other reason than to provide color in what might be viewed as a bleak landscape of names and dates. That is not our only reason. They are aspects of human nature which both drive and impede the process of science and our general understanding of ourselves, our universe, and the relationship between them.
We reviewed Galileo's resume, searching for those events which helped to shape him into one of the most influential scientists ever, exerting influence which will have an impact as great or not greater than that of Pythagoras, Socrates, Plato, Aristotle, Hipparchus and Ptolemy (if those names don't sound familiar, you better put down the Discman, turn off the TV and go back to those early lessons.)
In the final section we examined the tools that Galileo used for the first time, noting not just the tools but the methods which have become standard operating procedure for science of all kinds, physical and otherwise.
In the next lesson we will focus on the specifics of Galileo's methods, the discoveries he made and the brilliant conclusions he was able to draw from them.