The cosmos corner.

Abstract

Secondary and university students are perennially bombarded with confusing historic theories regarding celestial mechanics. Most textbook discussions are guided by either strict historic chronology or conceptual frameworks and are generally devoid of the historic philosophical and theological developments which accompanied the work of the respective scientists. Without an understanding of theological and philosophical debates concurrent with scientific hypotheses and discoveries, the significance of the scientific discussions becomes hollow. In the form of a play, this paper seeks to provide an understanding of the science, philosophies, and theological viewpoints which surrounded scientists in their historic work. This fictitious dialog seeks to open the investigation of the history of celestial mechanics by allowing seminal historic participants to discuss their ideas with others who may have predated or postdated them by a millennium or more.

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Play Development and Purpose

Writing Play Plays have had a fertile heritage within the history of mathematics and science. Arguably, one of history's most influential plays may have been Dialogue Concerning the Two Chief Systems of the World--Ptolemaic and Copernican (1632) by Galileo Galilei (1564-1642). Publications from mathematics and science education reform efforts repeatedly promote the pedagogical and epistemological value of writing for both learning and assessment (NCSE, 1995; NCTM, 2000, 1995, 1991, 1989). The approach to teaching and learning through both role playing and play writing is not novel; both practices have been touted as valuable activities for the learning of mathematics and science ideas (Bonnet, 2000; Duveen & Solomon, 1994; Francis & Byrne, 1999; Harwood, McKinster, Cruz & Gabel; 2002). Play writing and role-play may be particularly valuable in assisting students to learn more esoteric concepts. Recently, both methodologies have been used to make mathematics and science more understandable to students (Bosse & Nandakumar, 1998; Duveen & Solomon, 1994; Francis & Byrne, 1999).

The Experience of This Project The following play was written as a collaboration between five students and the instructor in a college History of Mathematics course. The assignment was initially intended to assist those students master the morass of culture, science, mathematics, religion and philosophy within the development and evolution of theories of celestial mechanics. Group planning and delineation of individualized investigatory tasks led each student to study people, ideas, and events associated with the topic; thus, each student wrote individual reports and became expert in certain aspects of the study. Through frequent group meetings, students hashed out hypothetical dialogs constructed upon their findings. Although the student-authors found this task much more challenging than they had anticipated, they took great pleasure as they saw separate components and ideas become integrated. The participating student-authors reported the process of collecting, analyzing, and synthesizing data into the usable, coherent, and user-friendly form of a play to have been instrumental in assisting them to master the complex material. Prompted by the instructional success of this endeavor, the play was later used to teach the historical development of celestial mechanics in sections of History of Mathematics and Liberal Arts Mathematics in a novel and fresh manner. Herein, the play was used as both a read-only homework assignment and acted out as a play by student actors. The play writing process was found to have two primary uses. First, the development of the play required the synthesis of great volumes of scientific, mathematical, philosophic, theological, and biographical information. This allowed students to construct a thorough understanding of salient factors affecting the historic development of the topic. Second, students in other classes who later read the play were introduced to a novel and interesting rendition of the material. In the format of a play, the material became animated and inspired far more interest than previous encounters of static encyclopedic facts. The Cosmos Corner and other plays can act as models for teacher and students for creating new plays to study other mathematic and scientific concepts. For teachers considering the assignment of play writing in their classes, it should be understood that the task is profoundly more difficult than other forms of instruction and investigation and that this difficulty is only eclipsed by the depth of student understanding that ensues.

The Purpose of The Cosmos Corner Play Theories regarding celestial mechanics have been a significant part of human intellectual and cultural evolution for more than two millennia. Often secondary grade students find the plethora of scientific theories which have been developed by noted philosophers, scientists and mathematicians to be a tangled, nearly undecipherable, knot. Added to the complexity of simple scientific theories are cultural and theological interactions which exponentially complicate the study. Without an understanding of theological and cultural debates concurrent with scientific hypotheses and discoveries, the significance of the scientific discussions becomes hollow. This play seeks to open the investigation of the history of celestial mechanics by allowing seminal historic participants to discuss their ideas with others who may have predated or postdated them by a millennium or more. Through a feat of cosmic intervention, seminal participants are free to debate each other's position in person. These discussions bring light to the historic cultural and theological debates surrounding respective scientific discussions. All too frequently, historic personalities are recognized by modern students as inert rather than animated and conjoined with the Zeitgeist of their day. It is hoped that this play will vivify a historic investigation encountered by many secondary mathematics and science students. The bulk of the dialog within this play is necessarily fictitious. Some lines, however, are adapted from statements directly attributable to the seminal characters. Since some of these quotations are relatively well known, and so as to avoid altering the flow of the play, precise citations and references for these specific quotations are not provided within the play.

References

Bonnet, C. The relevance of role playing in environmental education. Proceedings of The International Union of Biological Sciences Commssion for Biological Education (IUBS-CBE): International Symposium on Biological Education, IUFM Versailles, Centre de Cergy, France, 15-18 May, 2000.

Bosse, Michael J.; Nandakumar, N. R. (1998). Calculus Ideas Generated through Cooperative Learning. Mathematics and Computer Education Vol 32, No. 1, 52-61.

Duveen, J. and Solomon, J. (1994). The great evolution trial: Use of role-play in the classroom. Journal of Research in Science Teaching Vol. 31, No. 5, 575-582.

Francis, P.J. and Byrne, A.P. Use of Role-playing in Teaching Undergraduate Astronomy and Science. Publications of the Astrononomical Society of Australia Vol. 46, No. 2, 203-211.

Harwood, W.S., McKinster, J.G., Cruz, L. and Gabel, D. (2002). Acting out science. Journal of College Science Teaching Vol. 31, No. 7, 442-447.

National Committee on Science Education Standards and Assessment, National Research Council [NCSE] (1995). National Science Education Standards. National Academic Press

National Council of Teachers of Mathematics [NCTM] (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics [NCTM] (1991). Professional standards for teaching mathematics. Reston, VA: The National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics [NCTM] (1995). Assessment standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics.

The Play

Character Notes Characters descriptions offered are intended to provide a glimpse into the personalities, rather than the scientific achievements of these men.

BARTENDER: Artistic license creates a young, hard-working, witty individual who is willing to help even the most peculiar strangers, unfazed by their out-of-era appearance and language.

ARISTOTLE (384 BC--322 B. C.) A kindly, affectionate character. Most accounts diminish the self-importance that some scholars infer from his works. Tradition characterizes him with speaking with a lisp and constantly attentive to fashion. While articulate, lucid in his lectures, and persuasive in conversation, history records his discourses as encapsulated within a mordant wit. His numerous enemies characterized him as arrogant and overbearing.

CLAUDIUS PTOLEMY (100 A. D.--170 A. D.) Ptolemy is oft vilified for inventing a cosmological system so intellectually sound that it was scientifically unassailable for nearly 1500 years! One extremely critical commentary, The Crime of Claudius Ptolemy, went so far as to allege that Ptolemy could only invent such a system using faked data.

NICOLAUS COPERNICUS (1473--1543) Well versed in many fields, including medicine, finance, and optics, Copernicus moved in the highest circles of social, political, and religious standing. However, self-abasing in his private medical practice, he was known to serve the poor gratis. Upon his return to Poland, after studying in Italy, he spent the rest of his life as a physician, lawyer, and church administrator. As a recreational pursuit, he continued his research in astronomy. Initially, his perfectionism hindered his desire to publish his theories.

GALILEO GALILEI (1564--1642) Galileo's abrasive, confrontational, and argumentative personality, exacerbated by an aura of arrogance, created, and gave ammunition to, his enemies who eventually worked to undo him. He eagerly baited scholars and clergy into debates. In Galileo we see a brilliant and original scientist, known to most people for his controversial writings. However, his blunt persona effectively alienated many people.

MARTIN LUTHER (1483--1546) History characterizes Luther as temperamental, peevish, egomaniacal, and argumentative. But his single-mindedness, enormous self-confidence, and strident belief in the rightness of his arguments, allowed him to stand against opposition and harden his position even in the face of death by fire, the usual punishment for heretics.

JOHN CALVIN (1509--1564) A reticent man, he rarely expressed himself in the first person singular. This reserve contributed to his reputation as cold, intellectual, and unapproachable. However, friends simultaneously recognized his talent for friendship and his hot temper. The need for personal and environmental control, often associated with Calvinists, can be understood as a function of Calvin's own anxiety and bouts of doubt.

ROBERT CARDINAL BELLARMINE (1542--1621) Born to a noble family, Bellarmine was well read in both Copernicus and Galileo and understood the mathematical foundations within the writings of each. He deeply believed that the Bible was literal, God-given truth.

POPE URBAN VIII (1568--1644) Born Maffeo Barberini, Pope Urban VIII entered the priesthood through a politically powerful family. An accomplished man of letters, Maffeo Barberini published several volumes of verse and was recognized for his great knowledge and for his love of art and literature. Admiring Galileo's intelligence and sharp wit, a strong friendship developed between the two until 1633.

JOHANNES KEPLER (1571--1630) As a sickly child, Kepler was unable to regularly attend school. An attack of smallpox nearly killed him and left him with crippled hands and impaired vision. He once contemplated entering the Lutheran ministry, but refused due to the Lutheran's strong opposition to Copernicanism.

PIERRE-SIMON LAPLACE (1749--1827) Evolving from relatively humble origins in Normandy, history unkindly recognizes Laplace as a self-serving scientist. Immodest about his abilities and achievements, he wished it to be widely known that he considered himself the best mathematician in France. Unfortunately, he failed to foresee the effects his attitude would have on his colleagues.

ALBERT EINSTEIN (1879--1955) One of the most recognized scientists of the twentieth century, Albert Einstein's theories altered both the scientific and non-scientific views of the world and physical forces. A self-proclaimed agnostic, he constantly searched for perfection in his work, which led to his discovery of general and specific relativity. He openly published his research and readily shared it with others. Known as a humanist, Einstein cared deeply for mankind.

STEPHEN HAWKING (1942--) Stephen Hawking is often recognized as the greatest mind in physics since Albert Einstein. Desiring to discover the deepest workings of the universe, he has an uncanny ability to communicate complex and mysterious matters to the general public. Raised in London, his educational career was extraordinary. Although stricken with Lou Gehrig's disease and confined to wheelchair and voice synthesizer, he remains active.

Scene The action takes place in a dusty, rustic pub in the near future. Three or four round tables each adequate to comfortably seat approximately four to six people are near the front of the stage. A light fixture hangs over each table. A bar sit further back, near an entryway. Four to six stools are placed in front of the bar. Apart from the characters, the bar is empty of patrons. The bar is uncharacteristically quiet with no music or activity. For audience instruction, a projection screen is located over the bar (for projections of drawings); characters in the play will not notice the screen or the projections. Prior to the beginning of the play, all stage lights are dimmed.

Scene I

NARRATION PRIOR TO LIGHTS UP (no person, just voice) Space; the sun; the moon; the night sky. For over two millennia, we have wondered. Who, or what created the universe? Why does it, or we, exist? Since its beginnings, mankind has investigated the cosmos in order to understand our place in the universe. From antiquity, the relationship between science and theology has been turbulent. For nearly an entire millennium, all astronomical research had to agree with the biblical interpretation promulgated by Holy Roman Catholic Church--the earth remained stable and was the center of the universe. To this day, religion and science remain at loggerheads over celestial mechanics regarding the Big Bang versus creation. Utilizing the beliefs and personalities of seminal characters within the development of historic cosmological theories, this play hypothesizes a discussion which could transpire if these people all met at one moment of time.

Lights up to illuminate the stage and activity. The BARTENDER is busy cleaning and stocking his supplies. A man in ancient garb is sitting at the far end of the bar from the entrance. Another man in similar dress wanders into the pub, bewildered and apparently out-of-sorts. Already seated at the bar (or round table) is a similar looking man with his mug half-full.

BARTENDER Welcome. May I help you? (Stranger too confused to respond.) Oh, you must be here for the conference. Do you have an invitation?

STRANGER (handing invitation): Yes, but ... where am I and what's this about?

BARTENDER (ignoring last question, reading the invitation aloud): "Your attendance is required at the opening of the first annual Cosmos Corner ... your host, 'Grand Ole Debate'". You're in the right place. That gentleman at the end of the bar (pointing) is also a guest. Others will be arriving soon. Stranger meanders to where the other man is sitting, and speaks to the man.

STRANGER Good sir, can you explain the meaning of this request and by what means I arrived in this strange place?

MAN AT BAR I cannot. I am as confounded as you. My name is Aristotle; I live in

Athens.

STRANGER I once read of a great philosopher by that same name from that same region.

ARISTOTLE May I be the one of whom you speak?

STRANGER (laughing) Certainly not. The scholar I mentioned died nearly 400 years before my birth. His brilliant notions were the basis for some of my greatest research.

ARISTOTLE (smugly) And what research is that?

STRANGER I published a work called Almagest. Certainly you have heard of it. In it I constructed a mathematical model of planetary motion. In fact, I fused my model with the cosmology and physics of Aristotle, refining some of his original findings about the universe. Namely, I proposed that the planets travel in epicycles, not perfect spheres as he originally maintained.

ARISTOTLE (somewhat impatient) Sir, I am that man of whom you speak. How dare you alter my work, which is of utmost soundness?!

STRANGER (eyes wide and aghast) Sir, I deeply apologize if I have offended you. I am, however, having difficulty digesting the events of this day. If indeed you are the great Aristotle, this day is all the more troubling. My name is Claudius Ptolemy, from Alexandria. I repeat, IF you are whom you say, then I owe you the utmost respect, for it is you after whom I modeled my work.

ARISTOTLE Very well. Now, if you have indeed extensively studied my work, then you know why the universe is spherical and finite. The sphere is the most perfect shape. God would not create anything less than perfect. The Earth is the center of this universe. And as you know, a body with a center cannot be infinite. Here, let me show you. Aristotle begins to draw a diagram on a napkin. Projected upon a wall is a diagram of Aristotle's universe.

PTOLEMY I agree that Earth is the center of the universe. However, sir, your model falls short; it cannot explain the changing speeds and the retrograde motion of the planets surrounding ours. My theory provides an explanation: Earth is slightly off-center, mimicking an ellipse. Also, if we allow the center of the epicycle to move at a constant angular speed around a third point on the opposite side of the deferent, one can predict the positions of the planets much more accurately. Allow me. Ptolemy reaches for a napkin and begins to roughly sketch out his theory. Projected upon a wall is a diagram of Ptolemy's universe. In the background, another man enters (with invitation visible) the bar and is instructed as before by the bartender.

ARISTOTLE What you propose makes perfect mathematical sense. I continue to be troubled, though, by some facets of the hypothesis. Sir--The newcomer apprehensively walks toward the pair.

NEWCOMER Gentleman, if I may ask of your assistance--

PTOLEMY (to the man) One moment, if you please. (Back to Aristotle.) Please understand, Aristotle, that my work does not contradict yours; it simply provides answers to questions which in your day were yet unasked. I agree that Earth is the central body, about which the remainder of the heavenly bodies revolve. However, in your model, the explanation of varying planetary brightness and retrograde motion cannot be accommodated. The newcomer is seen staring at Aristotle and Ptolemy with disbelief, but listening intently.

ARISTOTLE What you propose may help explain some minor details, but it may take some time for your new ideas to supersede mine. My theory is based upon a system of logic and observations. The wanderer takes a seat on a stool next to Aristotle.

PTOLEMY Again, I am not trying to diminish any of your foundational principles. However, much of your work seemed to be based simply on what others had previously said on the matter.

ARISTOTLE How dare you! While I do not deny that any scientist and philosopher must entertain the notions of others, MY ideas are based on my own theories and observations.

NEWCOMER Gentleman, if I may ... I've been listening intently to your discussion. I hope I have not been rude. Your conversation, however, causes me to believe that I know both of you, or the characters whom you are aping. Although your existence at this moment flies against every ounce of sound science or common sense, you (pointing at Aristotle) are the great Greek philosopher and scientist Aristotle. And (leaning forward to see) I believe you are Claudius Ptolemaeus. (Aristotle and Ptolemy nod, impressed by the newcomer's discernment. Newcomer signals to the Bartender.) Drink, please! (bartender sits drink down and man gulps due to his surprise that he is correct) Your astronomical theories and explanations dominated scientific thought until my day.

BARTENDER (interrupting) He is from the 16th Century.

NEWCOMER (to Ptolemy) You'll be happy to know that you are also remembered for your contributions to the fields of mathematics, optics and geography. (Aristotle's attention is focused on Ptolemy's pictures and notes.)

PTOLEMY What is the 16th Century? And who might you be?

NEWCOMER My name is Nicolaus Copernicus, from Poland. My life's work is devoted to the very subject you have been feverishly discussing.

ARISTOTLE I am not aware of this "Poland." I am certain, then, that your research can confirm that the solar system moves as I propose.

COPERNICUS Well, unfortunately, your groundbreaking work is now somewhat dated. I developed a more radical, yet more explicable, conjecture.

ARISTOTLE Nothing could be as radical as the developments this day has wrought.

PTOLEMY Are you saying that you dispute our models of the universe? (Acquiescing, Copernicus nods. Aristotle snobbishly chuckles.)

ARISTOTLE (laughing also) My good man, not only does our system adequately describe celestial motion which is anchored by the earth as its center, but God, the Creator of all, has ordained it. The Creator cannot be removed from the creation.

COPERNICUS Of that I am well aware. In fact, it was the connection of science and religion which set the stage for the struggle which I endured.

ARISTOTLE (sarcastically) This should be interesting. We know that science and religion cannot disagree.

COPERNICUS Your models for celestial mechanics, with Earth as center, have become known as geocentric theories, for obvious reasons. However, since navigation, the calendar, and holy observances, which depended on heavenly positions, were becoming increasingly less accurate, about 1800 years after your (nodding toward Aristotle) model, there was a push to take another look at the cosmos.

PTOLEMY Come, now. You can't throw out good, sound theory because of ineptness in observation.

COPERNICUS Please, sir. Even a peasant, untrained in celestial movement, can observe the movement of the Moon, stars, and planets. What I propose is a much simpler, heliocentric system, with the sun as center. (Aristotle chuckles at the thought.)

PTOLEMY I'm sorry, Nicolaus. Not only is the basis of the geocentric model sound, but it is even consistent with our knowledge of the Divine.

COPERNICUS Yes, I understand that some interpret the Bible and the Book of Joshua to speak of the Sun being halted in motion and standing still.

ARISTOTLE Who is Joshua, and what is the Bible?

COPERNICUS Joshua is one of the characters within a compendium of books considered to be holy writ by a number of religions. Undoubtedly, for its time (motioning towards Ptolemy), your system's accuracy was unrivaled. However, the most accurate and modern tables of King Alfonso X demonstrated error within your model. The mathematics in the Almagest is both complex and exquisite and produces a model which is much simpler.

PTOLEMY (angrily) I wholeheartedly believe in the existence of God and His creative enterprise. I doubt that you'll convince me of a sun-centered universe. I propose that no one can intelligently discus the heavens while disagreeing with Heaven itself.

COPERNICUS Why do you believe that my theory threatens your faith? Believe me gentlemen, I certainly empathize with your dilemma. In fact, my faith is also important; I was a candidate for the priesthood.

BARTENDER (purposely goading the conversation into a frenzy) The Bible states: "In the beginning, God created the heavens and the universe ... and God said 'Let there be light' and there was light." Why would God create such a perfect orb--the Earth, the very dwelling place of man, God's created and adopted children--only to have it merely travel around another in the mediocrity of all the other planets?

COPERNICUS (impatiently) Again, I also believe in God Almighty. I believe the psalmist who wrote, "The heavens declare the glory of God; And the firmament shows His handiwork." I also realize that my model may antagonize the religious beliefs of many. (Aristotle & Ptolemy nod acquiescently) Not only does my model explain a planet's occasional backward motion, but it also explains why the two planets closest to the sun, Mercury and Venus, never seem to stray far from the sun in the sky. In my book On the Revolutions of the Celestial Orbs--most of which was a technical mathematical work in the tradition of your (nodding toward Ptolemy) Almagest--my hypothesis states that the Sun is the center of the universe and that the Earth has a triple motion around this center. I maintain the status of circular motion. My system orders the planets by distance together with period, with the actual distance to each planet linked to the size of the Earth's orbit. Copernicus grabs a napkin, which is quickly becoming rare, and begins to diagram his theory. Projected upon a wall is a diagram of Copernicus' universe.

COPERNICUS In this arrangement, we discover a marvelous symmetry of the universe, and an established harmonious linkage between the motion of the spheres and their size, which can be discovered in no other way. Thus we perceive why the direct and retrograde arcs appear greater in Jupiter and Saturn and smaller than in Mars, and why this reversal in direction appears more frequently in Saturn than in Jupiter, and more rarely in Mars and Venus than in Mercury. Yet, none of these phenomena appear in the fixed stars. This proves their immense height, which makes the annual parallax vanish from before our eyes. All these phenomena proceed from the same cause: the Earth's motion.

PTOLEMY Nicolaus, during my time, people readily accepted dogma and absolute ideas, especially when reinforced by the religious authorities who felt that such ideas were part of their domain. Are you saying that my theory is entirely wrong?

COPERNICUS My new theory was rejected by most of my peers for several years, as "merely hypothetical." By the time I gained the courage to publish my theory, I was nearly dead ... or so I thought. Which brings me to my most recent quandary ... Nothing can explain how the three of us can be having this discussion. Have I died? Are we all dead?

ARISTOTLE I have no idea how this is occurring, nor do I wish to entertain the possibilities. But, if I may, something is troubling me. I am having difficulty keeping track of time.

COPERNICUS My stomach tells me that it is nearly time for dinner.

ARISTOTLE Not the time of day, you sun-centered fool!

COPERNICUS Oh, yes ... of course. Approximately 1000 years after you walked the earth, a venerable thought that the birth of Jesus Christ--a man thought by some to be the Son of God--would be a good benchmark for measuring time. Therefore, by most measures, you were born 384 BC, or 384 years before the birth of Christ. (Aristotle questioningly nods toward Ptolemy) Most accurate accounts place Nicolaus at roughly 100 to 150 years AD, Anno Domini, or, years after the birth of Christ. And I was born in 1473 AD.

ARISTOTLE & PTOLEMY (simultaneously) Drink, please! Lights, end of Scene I.

Scene II

Lights up, two men enter the pub, engaged in a passionate deliberation. Focus goes to their discussion.

MAN 1 (LUTHER) People gave ear to an upstart astrologer who strove to show that the Earth itself revolves rather than the heavens or the firmament, the Sun and the Moon. This fool wished to reverse the entire science of astronomy and contradict the Holy Scripture.

MAN 2 (CALVIN) As stated in Psalms 93: "The world is firmly established; it cannot be moved." Who will venture to place the authority of Copernicus above that of the Holy Spirit?

COPERNICUS (angrily, rising) Excuse me, gentlemen! If you will speak ill of me, please do so out of earshot. (Luther shrugs his shoulders in snobbish disbelief that he is being challenged.) I am Nicolaus Copernicus. Man 1 and Man 2 look at each other quizzically, eyes wide.

MAN 1 (LUTHER) YOU, are Nicolaus Copernicus? The man who chose to ignore that which is right and obvious for some half-baked astrological "theory"?

COPERNICUS I am, and what gives you the right to speak so vainly? I have spent many years studying the heavens. I suggest that unless you have studied mathematics, physics and astronomy, you humble your tone.

MAN 1 (LUTHER) And you should study the Bible. A literal interpretation of the Scripture is quite straightforward. Science must submit to Scripture and not Scripture to science.

MAN 2 (CALVIN) (calmly) Mr. Copernicus, I'd watch your tongue. You are now face to face with Martin Luther, leader of the Protestant Reformation.

COPERNICUS The Bible can be interpreted in many ways. As I've heard, a sect led by John Calvin has le ... the Church because their view of the Bible differed from that of Catholicism. If I'm not mistaken, Mr. Luther, the same holds true with you.

CALVIN I am John Calvin, and while I do not agree with some Roman Catholic theology, I do know the Bible. Your scientific views clearly contradict God's Word.

LUTHER I have also had a falling out with the Roman Church over it's views on the authority, inspiration, and interpretation of the Bible. I have studied the Scriptures and have recognized that there is no need for the Papacy in salvation. Through this same method of literal interpretation, we know the Scriptures state that the Earth is the stationary center of all God's creation. It is inconsistent to simultaneously believe in the movement of the Earth and in the Bible's teachings.

COPERNICUS While clearly you have extensively studied the Bible, I assure you that I have studied the heavens. I have found that my theories show the true courses of planets in the simplest way.

CALVIN You begin with the assumption that the heavens, God's creation, are simple? You speak of science and the heavens. So you believe in God?

COPERNICUS Yes, and in the Bible also. I simply believe it was written by men in a style meant to avoid confusing the common man. So it is written from man's impressions and perspective, even regarding the movement of the planets. (Turning his attention to Ptolemy) It was through your teaching that I learned that scientists should interpret nature in the simplest way using the minimum number of hypotheses. This method led me to my discoveries.

CALVIN Again, I do not agree with the presupposition that all of creation is simply and readily understood by man.

LUTHER No evidence or rhetoric outside of the Bible will convince me that anything but the Earth is the center of God's creation. I will not yield to this blasphemy. I think you wish to appear clever, turning astronomy upside down.

ARISTOTLE (to Luther) While I do not agree with your logic, I agree with your conclusion. My good man, (speaking to Copernicus) you now have four minds, working as one, with whom to contend. You must see that your model is simply untenable to the rational mind.

COPERNICUS I am quite acquainted with encountering resistance to my theory. I admit that my theory is revolutionary. Nevertheless, it adequately answers our questions.

ARISTOTLE As does mine. Although I do not yet know how, when, or where we are, I firmly believe that my cosmological position explains the physical construction of the universe. I do not know of this Bible, but it still seems as though it confirms my position.

PTOLEMY I certainly believe that my model is both mathematically and theologically sound.

CALVIN (sarcastically) And what of your heliocentric model? Tell us how well your model describes the heavens. Although, I wonder how much you really know about Heaven, or, better yet, if you'll even get there. Luther and Calvin laugh uncontrollably, while Aristotle and Ptolemy look away, chuckling.

COPERNICUS I, too, wholeheartedly believe that my model is physically accurate. As the debate between the five men at the table continues, two men in similar dress, engaged in a conversation not audible to the audience, enter the pub. As they make their way to a separate, smaller table (invitations in hand), a third man enters. As he looks around, spotlight fades the larger table to black and focuses on the man, which had just entered, and the two most recently seated men.

MAN JUST ENTERED (nodding toward each) Cardinal. Pope.

CARDINAL BELLARMINE (with a smirk) Galileo. It's been a long time.

POPE URBAN VIII Galileo, my old friend; I hope time has healed your wounds, and that we can still call each other 'friend.'

GALILEO Only God and time can heal the wounds caused by the persecution 1 suffered from your hands. However, I am less bitter about my fate, than I am about you forbidding science to move forward.

BELLARMINE Come now, you knew full well before you published your Dialogue on the Great World Systems, that the Roman Catholic Church would intervene. Pope Urban keeps looking down towards the table, hesitant to look Galileo in the eyes.

GALILEO I hold no grudge toward the Roman Catholic Church. She is also my Church, and I desire no other. (to Urban) What upsets me is having you, a friend, abandon our friendship for political gain and public perception.

URBAN (pleading) What would you have me do? (Pointing at Bellarmine) He is our leading theologian, and the Jesuits are becoming increasingly uneasy. (Seeing Galileo's invitation.) We received the same invitation and were pondering its meaning.

BELLARMINE What is this strange place? Have we already left the living, and if we have not, (to Galileo) aren't you violating the Church sanctioned house arrest?

GALILEO (sarcastically) Your Holiness, even in this confusing moment, you attempt to keep me under your thumb? Have we nothing to discover in this moment? Will religious blindness again bully scientific inquiry?

BELLARMINE Galileo, you are a great scholar, scientist and man. Why could you not leave well enough alone? Why couldn't you just accept the Dane's model?

GALILEO (chuckling) You mean Brahe? Tycho Brahe? That hotheaded, truth-bending, poor excuse for a scientist? He sought the best of both worlds. He claimed the other planets orbited the sun, but the sun and moon still circled a stationary earth. He explained the inconsistencies in planetary movement and size in Copernican terms, but his model remained legal according to Aristotle.

BELLARMINE While Brahe's system was mathematically equivalent to Copernicus' and was quite different from the Aristotelian universe, it was much more acceptable to the Church. Brahe left Earth in the center and his system was consistent with Aristotelian physics and Roman Catholic doctrine.

GALILEO (to Bellarmine, more calmly) Okay, I'll give Brahe some credit; he developed a workable model for his day. However, he stated, "It is impossible to accept the earth's motion as long as nobody can produce new and stronger arguments to show clearly that the violent motion is not prevented." Based on the observations using my improved telescope, my observations do produce new and stronger arguments!

URBAN I warned you. I told you to treat Copernicanism no more than as a hypothetical construct.

GALILEO How could I have been more hypothetical? Upon my request to teach Copernicanism, in 1616 Pope Paul V told me that I could not. He was largely concerned to avoid Protestant criticisms that the Catholic Church was "not Biblical enough." Pope Paul told me to abandon "the holding or defending of that view." So I--

BELLARMINE (interrupting) So you went and wrote the Copernican view anyway. GALILEO (becoming annoyed and angry) So I returned to Florence, where I decided to write the Dialogue, which would offer both sides equal time. Salviati played the Copernican, Sagredo was the interested layman, and Simplicius was the Aristotelian. I didn't take sides.

URBAN (more forcefully) You took sides when you made Salviati so clever and Simplicius out to be a fool. You used Simplicius to quote me and painted me a fool!!

GALILEO But you, Father Riccardi, and others gave me permission to publish my Dialogue.

BELLARMINE Riccardi only allowed it because the license had already been granted! And besides, we all know he wasn't well versed in mathematics, of which the Dialogue had no shortage.

URBAN (slowly and deliberately) The Vatican records show that you were not to discuss the Copernican doctrine at all, and if you did you would be thrown in jail.

GALILEO The Pope never said that!!

URBAN It seemed like you had deliberately broken the law and insulted me. How did you expect the Church to react? The motion of the Earth was not the point. You had cheated, reneged on your own promises, and broken your word!

GALILEO (rising) Why don't you get it?! (Loudly) It is time for science and religion to separate. (Lights come up on entire stage) Reason, experiment, and mathematics are needed for the first, but faith and revelation are required for the second. Each and every one of the earlier guests is now fully focused on the table of three. In the background, another guest enters (Kepler) and sits alone at the bar.

LUTHER (standing) Gentlemen, come join us. I am Martin Luther. It sounds as if we're involved in a similar debate. Although Aristotle, Mr. Ptolemy, Mr. Calvin and myself (motioning towards each as he mentions them) disagree with you, sir (pointing at Galileo), I believe you'll find an ally in Mr. Copernicus. Please, sit. Bellarmine, Urban, and Galileo make their way to the larger table and take their seats.

BELLARMINE Thank you ... this should prove interesting. I am Robert Cardinal Bellarmine. This is Pope Urban VIII, and here I present, Galileo Galilei, the heretic. Galileo lunges at Bellarmine (everyone reacts, a drink or two is spilled) but is restrained by Urban and Copernicus. After order is restored, Kepler approaches the table. As he approaches, the remainder of the introductions are completed.

KEPLER Good evening. I couldn't help but overhear your introductions. If you are discussing celestial mechanics, I believe that I have some insight on the subject. My name is Johannes Kepler, former assistant to Tycho Brahe. In his quest to solve the planetary mysteries, Brahe assigned me to decipher the orbits of Mars. As I later learned, this was a ploy to distract me from making my own advances regarding celestial mechanics. Although I did not necessarily agree with Tycho's system, it was his data, which allowed me to put forth my laws of planetary motion.

GALILEO I'd be very careful if I were you. If you accept anything that contradicts Scripture, you may not be welcomed by some. I regard my research as a loving duty to seek the truth in all things, and they still fail to see the forest for the trees.

LUTHER I turned my back on the Roman Catholic Church ... I'm used to being outnumbered.

KEPLER Ironically, gentlemen, you (pointing at Copernicus) have been called the Luther of astronomy. And you, Luther, have been called the Copernicus of theology. (Luther shows disgust.) I'm no stranger to religious persecution. Mr. Galilei, can we put our differences aside on the issue of tidal movements for the good of our cause this evening?

CALVIN You two know one another?

GALILEO We've communicated on a few occasions. (turning to Kepler) You did some nice work as a Copernican, continue.

KEPLER My first law, which is most relevant here, states that every planet follows an oval-shaped path around the Sun. (Those clinging to the geocentric model grumble and shift in their chairs.) This oval-shape is an ellipse. In my model, the sun is located at one focus of the elliptical orbit. Here, let me show you. Kepler brushes aside pervious diagrams and begins to draw his own. Projected on a wall is a diagram of Kepler's universe.

CALVIN Here we go again! Has everyone taken to a life of heresy? Has the Church so little influence anymore that men can openly refute the Earth as the center of the Universe?

URBAN Do you mean The True Church, or your newly formed religion which mocks our faith? Mind you, Mr. Calvin, that the Roman Church recognizes your theological positions as no less heretical than the theories presented in Galileo's Dialogue. However, for now let us limit our debate to discerning what is right regarding our solar system.

COPERNICUS You don't care what's right! You want us, the scientists, to force our observations into a framework which will also accommodate your religious presuppositions. Instinct and rationale compels us to explain what is happening in the skies above us, not make it conform to a predetermined theological position.

GALILEO Hear, hear! Scripture tell us how to go to heaven, not how the heavens go.

KEPLER If I may continue, I think you'll see that my model offers an equally harmonious view of the perfection which God created. At first, I too was disgusted with my non-circular orbits. The circle is an archetypal symbol of harmony and perfection. Yet my elliptical orbits eventually revealed a scheme of celestial harmony more subtle and profound than any that had been previously developed. I was fundamentally driven by my religious convictions. God is present in the order and harmony of the Universe, and Geometry represent the perfection of God. I am convinced that the five perfect solids of Pythagoras are the framework of the spheres of the planets. Each sphere is circumscribed around one of the perfect solids. The next sphere is inscribed by the faces of the solid. The actual ratios of the spheres for the different solids can be arranged to crudely correspond to the ratios of the planets' orbits. That is why Geometry is God. Out of the offstage darkness, a man walks to the table.

LAPLACE (snidely) You men speak of God?! (tossing his invitation, folded as paper airplane, onto the table) I once told my emperor that I have no need of God in my origin of the universe. Cosmology has nothing to do with God.

URBAN (jumping out of his seat) Blasphemy! Who speaks with such a heretical tongue? Creation without a Creator?!?

LAPLACE I am Pierre-Simon Laplace, of France. I studied many branches of science and mathematics, but most of my original astronomical work took place in the late 1700s.

ARISTOTLE You mean 1700, as in years. 1700 years after Mr. Christ walked the earth?

LAPLACE Well of course, old-timer. And that's Jesus Christ. (to self) The man acts like he's from an entirely different millennium or something. As the conversation continues, a man is attempting to navigate his wheelchair through the doorway (visible to audience). Another man with disheveled hair offers to assist him. Lights dim on table, but not to black, more light to pair in doorway. Now in the pub, he turns his electric wheelchair to face the man and does a 'double-take', but says nothing. Both men recognize that the other also has an invitation in hand. Einstein pushes Hawking to the bar, and they proceed as others have. Focus back on table as Einstein and Hawking approach and listen in. Strange stares come from members already at table at Hawking's contraption.

LAPLACE In the late 1780s, I set myself out to write a work which should offer a complete solution of the great mechanical problem presented by the solar system, and bring theory to coincide so closely with observation that empirical equations should no longer find a place in astronomical tables. (Copernicus gestures in an impatient, get-to-the-point manner) In my Exposition du systeme du monde, my nebular hypothesis is articulated. A nebula is any, of many, vast cloudlike masses of gas or dust among the stars. According to my hypothesis, the solar system has evolved from a globular mass of incandescent gas rotating around an axis through its center of mass. As it cooled, this mass contracted and successive rings broke off from its outer edge. These rings in their turn cooled, and finally condensed into the planets, while the sun represents the central core, which is still left. Laplace's diagram is projected upon a wall.

COPERNICUS (to Laplace) So, you also believe in a heliocentric solar system?

LAPLACE (irritated, but calm) You simpleton ... (snapping) Of course!!

BELLARMINE What, then, is God's role?

LAPLACE (kicking his feet up on the table) After completing my work, I went to convince the Emperor of France, Napoleon Bonaparte, to accept a copy. Napoleon, who was fond of probing others through embarrassing questions, received it with the remark, "Monsieur Laplace, they tell me you have written this large book on the system of the universe, and have never even mentioned it's Creator." Although I was a supple politician myself, I am stiff as a martyr on every point of my philosophy. I drew myself up and answered bluntly, "Sire, I had no need of that hypothesis." Laplace bursts out, arrogantly and uncontrollably in laughter, while the other guests stare at him, and each other, in amazement. End of scene II.

Scene III

HAWKING (through a computer generated voice) Gentlemen ... allow me to interject. As a great mathematician once said, " Science without religion is lame. Religion without science is blind." Einstein perks up at this spoken quote.

BELLARMINE Who dare call the Church blind? Any man who questions the character of the Church is not a man of God. The Lord's book tells us all we need to know about our world and anyone who questions the word of God is a reckless fool.

HAWKING No, Your Holiness ... you misunderstand. This great man was not defaming the Church; he was merely stating that the Church could not turn its back to the astounding discoveries of science. My name is Stephen Hawking. Before we go on, I would just like to say that your conversation is most intriguing, and your costumes are exquisite. You bear a striking resemblance to Nicolaus Copernicus. And you, if I didn't know better, I'd take you for Galileo Galilei. And what do you think of Mr. Einstein, here? (he laughs)

EINSTEIN Sir, I AM Albert Einstein.

LAPLACE (whispering) Someone forgot to brush his powdered wig.

HAWKING (confused) I don't understand ... Have I died? ... Is this heaven?

GALILEO Well, if you ask me, it feels more like Hell.

Urban and Bellarmine turn and give Galileo a look of disgust.

CALVIN None of us can explain it ... yet we are all here together, somehow plucked from our lives.

COPERNICUS We have been discussing cosmology, but cannot seem to agree on the coexistence of science and the Church.

HAWKING Your Holiness, gentlemen ... please take heed in the words which my displaced colleague once spoke. (Signaling toward Einstein) He is considered to be one of the greatest scholars of all time. All the other men start to mumble their disenchantment to each other.

EINSTEIN (embarrassed) Please ... I do not feel myself to be better than the other great minds of history. On the contrary, I have admired and studied your collective works for years. I am deeply indebted to you all. I find this whole experience very exciting. Through additional dimensions, I always believed transcending time was possible.

URBAN Nonsense! God certainly did not mean for us to move freely about time.

HAWKING It is impossible for us to say what plans God has for us or what mysteries He has left for us to discover. Mr. Laplace, you yourself argued that, in theory, if mankind could know the position and speed of all the particles making up the universe, then it would be possible to predict the future. Through this rationale, fully understanding yesterday, today and tomorrow would be rather simplistic. This theory of scientific determinism of this variety held sway during much of the 19th century. Could this help explain how together we all simultaneously arrived here?

URBAN We have God's word. Everything we need to know He has told us in the Scriptures. It is quite clear how the universe came to be.

HAWKING Yes, the biblical story of creation does seem quite literal and comprehendible, but there are still many unanswered questions. The main one being 'Why were we created?' The answer would be the ultimate triumph of human reason. For then we would know the mind of God.

CALVIN (Privately, whispering to Luther.) We know why we were created, to glorify and praise God. Unfortunately, the unregenerate will never be able to understand this.

HAWKING It is my privilege to tell you, Galileo, that in the 21st century, you are regarded as one of the greatest astronomers of all time. We even have space traveling vehicles named after you. In fact, in 1992, Pope John Paul II exonerated you and recognized the scholarship of your work. Bellarmine and Urban cry out in disbelief

LAPLACE How many space objects are named after Pierre-Simon Laplace? Some guests turn and give Laplace a look of contempt.

BELLARMINE This Pope of whom you speak disgraces the Church!

HAWKING Not at all. The Roman Catholic Church is alive and well in the 21st century. But, as I mentioned earlier, it is impossible for the Church to ignore the astounding discoveries of modern science. In my lifetime, men and women regularly fly space shuttles into outer space and have walked on the moon numerous times. Pictures taken from space have shown us the layout of the galaxy. In fact, we have been able to prove that the universe is changing and expanding.

EINSTEIN I don't believed it!

HAWKING It's true. The notion that space is expanding is a logical implication and extension of Einstein's theory of gravity, which describes a simple but universal relationship between space, time, and matter. But it was an implication in which even Einstein did not believe; in fact he tried to modify his theory to avoid this natural extension. (to Einstein) Your theory of gravity enables us to run the "movie" of the universe backwards. We can calculate the density that the universe must have had in the past. The result: any chunk of the universe we can observe--no matter how large--must have expanded from an infinitesimally small, but infinitely dense, volume.

BELLARMINE I've said it once and I'll say it again ... all this talk is heresy. God created this world for man, so that he should have a beautiful place in which to live.

HAWKING Your Holiness ... we still believe that the universe should be logical and beautiful; we have only dropped the word "God."

GALILEO I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use.

EINSTEIN In my opinion, 'God was a mathematician.' 'The great book of nature can be read only by those who know the language in which it was written. And this language is mathematics.' (to Bellarmine) God did create a beautiful world for man. This mystery of man's origin is one of the greatest gifts he has given us. What would human existence be like if we knew all the answers?

HAWKING (motioning to all) We have been simultaneously given the gifts of understanding and of curiosity. It is this curiosity which compels us to attempt to unlock the secrets of the universe. The heliocentric "lobbyists 'pronounce their agreement.

BELLARMINE I refuse to accept anything that opposes the Bible. Furthermore God is immutable ... unchangeable; which is more than we can say for man's observations and rationale. You cannot attempt to alter God and His truths simply so that He and His work may fit into your system. I pray for your godless souls.

EINSTEIN Your Holiness, men like us continually seek to be in constant contact with God. Furthermore, while we are trying to unlock the secrets of the universe are we not also trying to unlock God's intentions for us? As we weave our way through the complexities of nature we are forced to question and also reflect on His creation and its greatness. You will hardly find one among us without a peculiar religious feeling of his own. But it is different from the religion of the naive man; the scientist is possessed by the sense of universal causation. The future, to him is every bit as necessary and determined as the past. There is nothing divine about morality; it is a purely a human affair. His religious feeling takes the form of rapturous amazement in the harmony of natural law. This natural law reveals an intelligence of such superiority that when compared to the systematic thinking and acting of human beings ... we are an utterly insignificant reflection. This feeling is the guiding principle of a scientist's life and work and it is beyond question, closely akin to that which has possessed the religious geniuses of all ages. Suddenly, the lights flicker and the door swings open. Noises come from outside as if a storm is coming. The men look at each other, startled.

GALILEO It seems we are about to have another guest.

LAPLACE Who on earth could it be now?

HAWKING Maybe he (or she) is not from earth.

Lights fade to black ... Just as in the beginning of the play, it is pitch black with a projection of the night sky. Men stare in apprehensive wonderment in the direction of the door.

NARRATION The universe is filled with questions; and as we discover some answers, we continue to uncover more mysteries and puzzles. However, scientific questions are never devoid of implications for other fields such as theology, ethics, philosophy and social science. These questions are not unique to the history of cosmology. Many other modern scientific developments are currently being investigated through natural implications and interconnections with other areas of concern. Thus, the history, present, and future of scientific discovery and development can only be fully understood through investigations into other cultural dimensions surrounding the science. It is hoped that this play has reminded all of the complexities of science and theology, developed an appreciation for the difficulties associated with the historic evolution of scientific thought, and provided fodder for future inquiry into the history of science and mathematics. End of Play

Selected Bibliography for the Play

Anglin, W. S. (1994). Mathematics: A Concise History and Philosophy. New York: Springer-Verlag

Ball, W.W. Rouse (1927). A Short Account of the History of Mathematics. London: MacMillan

Bell, E.T. (1987). Mathematics: Queen and Servant of Science. Washington, DC: Mathematics Association of America

Burton, David (1985). The History of Mathematics, An Introduction. Newton, MA: Allyn And Bacon

Cajori, Florian (1931). A History of Mathematics. London: MacMillan

Calinger, R. (1997). Vita Mathematica: Historical Research and Integration with Teaching. Washington, DC: Mathematical Association of America 

Gouvea, F. & Berlinghoff, W. (2002). Math Through the Ages: A Gentle History for Teachers and Others. Washington, DC: Mathematical Association of America

Hawking, Stephen (1998). A Brief History of Time: The Updated and Expanded Tenth Anniversary Edition. New York: Bantam

Katz, V. (2000). Using History to Teach Mathematics. Washington, DC: Mathematical Association of America

Kirk, H.E. (1932). Stars, Atoms, and God. U.N.C. Press, North Carolina 

Kuhn, T. (1970) The structure of scientific revolutions. Chicago: University of Chicago (Press)

Kuhn, T. (1977). The essential tension: Selected studies in scientific tradition and change. Chicago: University of Chicago Press.

Lancozos, Cornelius (1970). Space Through The Ages: The Evolution of Geometrical Ideas From Pythagoras to Hilbert and Einstein. London: Academic Press

Stabler, Edward Russell (1953). An Introduction To Mathematical Thought. New York: Addison-Wesley

Stillwell, J. (1994). Mathematics and its History. New York: Springer--Verlag

Swetz, F. et al (1995). Learn from the Masters. Washington, DC: Mathematical Association of America

Michael J. Bosse teaches in the Doctoral Program in Mathematics and Science Education at Morgan State University, Baltimore, MD. His areas of research include the learning and teaching of K-12 mathematics, [e-mail] David H. Morrison works in the Smyrna Delaware School District as an administrator. Stephen Williams is completing his BS in Mathematics Education, Delaware State University. Brandi Nowakowski works in the Delaware public school system. Kristin Arrigenna teaches mathematics at Sussex Tech High School Georgetown, DE. Laurie Davis is employed at Delaware State University.