Author Archives: wdcarey

“A Dialogue Concerning the Two Chief World Systems” by Galileo Galilei

by wdcarey
The Dedication of the Dialogue

The Dedication of the Dialogue

I repost this wonderful offering from my friend and colleague Bill Carey . . .

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A Gallup poll of 6 July 1999 of more than a thousand adults determined that only about four out of five Americans believe that the Earth orbits the Sun. Fully one in five believes that the Sun orbits the Earth. [1] It’s interesting that four in five Americans believe something that seems obviously and demonstrably false. The Earth doesn’t feel like its moving underfoot, and every day we see the Sun rise and set. We believe the moon orbits the Earth, and it sure looks like the behavior of the Sun and moon is pretty similar. Why do four out of five Americans believe that, contrary to our intuition, the Earth orbits the Sun?

I’ve been taking an informal survey of my friends, with just two questions. The first is whether the Earth or the Sun is the center of the solar system. [2] After I assure them it’s not a trick question, everyone answers the Sun. We’re beating Gallup’s averages. The second question confuses people: “How do you know?” The most common answer I’ve gotten is, “Duh, everyone knows that”. Some people know that Copernicus and Galileo got in trouble with the Church for saying the Sun was the center of the solar system. Others vaguely remember a science or history teacher telling them about “heliocentrism”. Fair enough.

When I rephrased the question to ask how human beings originally figured that the Earth orbits the Sun, my friends gave me a quizzical look. I was no better off than them; I knew that Galileo and Copernicus had gotten everyone to switch from the geocentric view to the heliocentric. I didn’t know how or why. How did those astronomers convince everyone to abandon more than a thousand years of careful science and replace it with a new framework? What arguments and data struck the telling blows for heliocentrism?

The Retrogradation of Mars

The Retrogradation of Mars

The work that I turned to to understand the arguments for heliocentrism is Galileo’s delightful Dialogue Concerning the Two Chief World Systems. It is a surprising book. The first surprise it delivers is its style and structure. Galileo imitates a Socratic dialogue. Like all good literature, conflict drives the plot of the Dialogue. In particular, the conflict between Ptolemy and Aristotle on the one hand, and Copernicus on the other, motivates Galileo. His protagonist, Salviati, argues for the Copernican world system. The canny, initially neutral Sagredo drives the conversation forward. The wryly named Simplicio attempts to prop up the Ptolemaic system. Simplicio’s bumbling affords Galileo an opportunity to clearly articulate his ideas about physics and the motion of the stars. Of Aristotle, Salviati says that “[w]e need guides in forests and in unknown lands, but on plains and in open places only the blind need guides. It is better for such people to stay at home, but anyone with eyes in his head and his wits about him could serve as a guide for them. In saying this I do not mean that a person should not listen to Aristotle; indeed, I applaud the reading and careful study of his works, and I reproach only those who give themselves up as slaves to him in such a way as to subscribe blindly to everything he says and take it as inviolable.” [3] The arguments about the motion of the heavens make the work science; the metaphors, plot, dialogue, and humor make it literature.

The second surprise in the Dialogue is Galileo’s outstanding ear for argument. He refutes Aristotle’s arguments bluntly and often amusingly. Aristotle claims that a ball of iron will fall one hundred cubits in the time a block of wood falls ten cubit. This is preposterously false, and Sagredo doubts whether Aristotle ever actually tried it out: “I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall, at the same instant, from a height of, say, 100 cubits, would so differ in speed that when the heavier had reached the ground, the other would not have fallen more than 10 cubits.” Simplicio leaps to the defense of his preposterously wrong philosopher by pointing out that “[Aristotle’s] language would seem to indicate that he had tried the experiment, because he says: ‘we see the heavier’; now the word ‘see’ shows he had made the experiment.” Galileo’s characters are forthright in dismissing this tomfoolery. They describe experimental procedures that we can repeat today that confirm Galileo’s ideas and to refute Aristotle’s.

Epicycles and Deferents

Epicycles and Deferents

Claudius Ptolemy offers Galileo a foil with more scientific substance. [3] Ptolemy’s exposition of the geocentric world system in the unreadably complex Almagest is a surprisingly empirical and scientific work. Ptolemy’s system of deferents and epicycles is a compelling, mathematically precise, vision of the world. To refute it, Galileo works through a detailed analysis of the parallax of various celestial bodies and their distances from the Earth. The argument is technical and subtle. Writing before the great tectonic shift from Euclid to Descartes, Galileo’s mathematical reasoning tends towards geometry as well. Here he argues with Ptolemy on the latter’s home turf. A good edition that reproduces the figures is essential, as the characters lean on them as much as the reader. When a character references a table of astronomical data, Galileo’s language leads one to vividly imagine the characters sitting around a table passing papers to one another as they eat and drink.

The third surprise nestled in the Dialogue is that it’s deeply unsatisfying. It’d be tempting to say that, having read Galileo’s dialogue, I can answer the question about how we know the Earth goes around the Sun. The truth, though, is that I’ve just replaced one authority with another. I haven’t observed the phases of Venus, and I haven’t observed the parallax of the fixed stars (much less of the planets) that would let me work out the celestial mechanics on my own. Even so, reading Galileo’s argument is valuable. When I trust his authority, it’s an authority that I understand a little better than before. It’s an authority that’s grounded in reason and argument that I can wrestle with and assess critically. But if I want to add to the conversation myself, take a stand along with Ptolemy and Galileo, I need to telescope-up and start looking at the stars.

Too often we treat science as an Athena, sprung full grown and clothed from the head of Zeus. We trust our predecessors when they say that the Earth orbits the Sun without understanding how they came to believe that. We belittle people who disagree without understanding the arguments that make us correct. It turns out that the story of scientific discovery is always messy, usually fascinating, often wildly contingent, and occasionally well told. Whenever we can grapple with not only the results of scientific inquiry, but also the story behind it, we should. In his preface to the Dialogue, Einstein writes that, “[t]he leitmotif which I recognize in Galileo’s work is the passionate fight against any kind of dogma based on authority.” Galileo would rue his fate; like Aristotle before him, he’s become an authority, chalky and dead. We can rescue him from that cruel fate by listening carefully to the scientific conversation and the adding our voices to the tumultous banter.

[1] See http://www.gallup.com/poll/3742/new-poll-gauges-americans-general-knowledge-levels.aspx

[2] An astute reader pointed out to me that I beg the question here, so ingrained is the heliocentric system in my mental picture of the universe.

[3] Galileo, The Dialogue, p. 131

[4] Ptolemy will be the subject of another post, I hope. He deserves far more credit as a scientist than we’re inclined to give him.

Law and Gospel

by wdcarey

“Da quod iubes, et iube quod vis.” – Augustine

Martin Luther distinguishes two genera in scripture: Law and Gospel. When God speaks command, threat, accusation, and judgement, there we hear Law. When God speaks gracious promise, there we hear Gospel. Luther understood the primary purpose of the Law not to be condemnation, but evangelization: the Law drives us to the Gospel, where we find God’s gracious promises. The law kills us spiritually–we cannot obey God’s commands and so suffer under his judgement–so that we hear and believe God’s gracious promise of new life in Christ.

Law is about what we do (or don’t do). Gospel is about what is done for us and to us. Rather than thinking about our students working on assignments we could think about assignments working on our students.

The language of grading is assuredly that of Law. Grading begins with commands, which we call “assignments”. Work out problems 25-45, odds only. Write a short essay discussing Christian iconography in Melville’s Billy Budd. Be ready for a quiz on the Krebs cycle tomorrow. Threats accompany the commands: 10% will be deducted for each day the paper is late. No one may graduate without completing the Senior Thesis. No makeup examinations will be given. Blood red accusations spatter the work: -0.5; not in the simplest form. You need to better support your argument here. France is not located in the center of Africa! Judgement concludes the business of the assignment: A-; good arguments, but your introduction was rushed. F; so sloppy as to be unreadable. 82%; somewhat improved.

The parallels between the language of Law and the way we communicate to our students when we grade are striking. What effect does this sort of language and communication have on students? Here too, Luther’s ideas about Law are instructive.

Luther describes the civil use of the Law: Law restrains sinners from (some of) their wicked behavior. The Law tells us that if we murder, we are God’s enemies and he will condemn us. Fear of that retribution might motivate one not to murder, which is assuredly a good thing. Fear, though, is powerless to form souls to desire and love truth. Indeed, because we cannot uphold the law, it spiritually kills us. The righteousness that fear of the Law compels is not the righteousness of Christ. Refraining from murder out of fear (even though we still want to murder!) does not create in us a heart that loves God. By analogy, some students have no desire for truth, for learning. Grading-as-Law serves to restrain their wickedness through fear in a way similar to God’s Law.

Grading-as-Law, though, kills the desire to learn. On the one hand, a student who repeatedly fails and is subject to the judgement of bad grades may be so dispirited that he abandons the hope and pursuit of knowledge as unattainable. The lament that “school is stupid” is a symptom of this sort of intellectual death. Even more spiritually dangerous, the student who says, “tell me what I have to do to get an A” has also suffered a kind of intellectual death. Like the Pharisees (or the elder son in Luke 15), he has abandoned the pursuit of living knowledge for a sterile and ultimately fruitless obedience.

What would it look like if we preached not only Law, but also Gospel to our students? To do that some of our assignments would have to be designed and communicated in such a way that they do work on the students, not the other way around.

First, we must believe that what we teach, while not perhaps the summum bonum, is nevertheless a bonum, valuable in its own right. What that means is that if students neglect an assignment, they deprive themselves of the good that assignment would do to them. If they undertake an assignment, it should do work on them such that they’re a subtly changed person for having completed the assignment.

We need to be able to articulate (to ourselves and to students) what work we expect an assignment to do. Our assignments are doing work on our students, but I often think we don’t have a sense of what work they’re doing. If we have our students do needless busy work, that’s forming their minds and souls. But in a way we want? No.

I suspect this can lead us to talk about assignments differently (exercise might be a good metaphor; physical exercise does work on our bodies the way academic exercises should do work on our minds) and to offer different exercises than we do now. And to communicate about them differently too.

Maybe the best way to talk about Gospel in the sense that I mean it here is to offer up an example. I suspect I have one from my physics class, but I’m hesitant to share it. The exercise requires enormous secrecy to work correctly. It’s risky, but I think it can be formative.

When my physics students, a mix of eleventh and twelfth graders, walked into class on the first day, they found index cards spread out on the tables with names. The students sat and I took back up the cards. These were the assigned seats. The class went about its business. The next day, the students found that the cards as before, but each student had a new seat. They sat, I collected, class proceeded. This went on for a week. Different seats every day. Some students asked about it. I just shrugged and kept teaching. They furrowed their brows.

After a week, the cards stopped appearing. Instead, the students would sit and I’d move some of them to other seats. This repeated itself daily. They started to get frustrated. They asked what was up. I got questions from parents. I got questions from colleagues. I kept shrugging.

After a month, one fine young gentleman came to class and said, “I think there’s structure. There’s a pattern!” I shrugged, ignored him, and taught class. And every day students had to move.

That young man and a few young ladies got a notebook. Every day they wrote down who sat where. When they were going to miss class, they made sure someone else took notes. I ignored them and looked puzzled when people asked about it.

A few more weeks passed. One day I walked into class and didn’t have to move any students. I raised an eyebrow, said nothing, and went to the grocery store after class to buy cake and donuts. I wasn’t sure, but I was hopeful.

The next day, everyone sat in the right seats again. I stopped class, and asked what was going on. They’d been testing different patterns for a couple of weeks at that point, and finally hit on the one I was using. They were coordinating with everyone, who sat where before class to see who I’d move. Finally they had it. We had a party in class. From then on they could sit where they liked. (For us math nerds: the algorithm to figure out who sat where was a modular addition scheme by numbered seat such that the pattern repeated about every 17 days. This was really hard to suss out. They originally thought it was a day of the week thing, and seeing that it wasn’t took a decent sized chunk of data.)

So, what was I doing, besides convincing the students, their parents, and my colleagues that I’d gone off my rocker a bit? I wanted them to experience what it meant to be a scientist: having faith that what seems chaotic is ordered, believing that we can fathom that order, collecting data, wrestling with doubts, formulating theories, testing them, and finally enjoying the fruits of their labor.

When they finally understood the seemingly arbitrary pattern, we had a long talk about what it meant to be a scientist. If they got nothing else out of the class, they got to be scientists and see actually science at work. It was visceral.

It could have gone wrong in a hundred ways. It was an exercise whose effect depended on the students not knowing it even existed. I could have lost my poker face and hinted that there was structure. I could have told a colleague who blabbed. They could have given up in disgust and suffered the bizarre seating for the year. A few could have figured out what was happening and not shared it with their friends. They could have randomly sat in the right seats without understanding why. I could have messed up their data by mis-seating someone (this scared me; it’s hard to follow a pattern precisely while seeming to behave arbitrarily). The exercise could have failed in a million ways, none of which would reflect any fault in the students.

Wrestling with their seating chart did formative work on the students. Just a little bit, it changed the way they saw science and the world around them. It was the best teaching I ever did. And there’s absolutely no way to grade it.