Debbie Huffman, literature, Antikythera Mechanism, Magna Graecia, Greek literature, wandering stars, Homer, fixed stars, Greek mythology, art materials, Student output, Hipparchus, Houston Teachers Institute, Internet access, Eastern Mediterranean, Houston Teachers Institute Activities Students, movements, narrative report, plane of the ecliptic, ancient Greek, Thales of Miletus, scientific information, The Columbia Encyclopedia, historical development, Western science, curriculum unit, historical figures, Junior Classical League � Latin Club, Roman Empire, Roman science and philosophy, imaging technology, astronomical observations, Activities Students, Carnegie Vanguard High School, science and philosophy, Time Debbie Huffman Bellaire High School, the Antikythera Mechanism, 20th C Science Fiction, major scientific discoveries, Columbia Encyclopedia, technology transfer, Joseph Campbell, Antonios D., Instructor Magazine, Astronomy Magazine, University of Arizona Press, University of Pennsylvania Press, Wikimedia Foundation, Inc., Electronic Literature Foundation, Sacred Texts, The Greek language, celestial equator, research accomplishments, biographical data, Hellenistic world, Greek philosophers, Philosophical Schools, Houston Teachers Institute In Hipparchus, advanced technologies, Marcus Aurelius
Hellenic Cosmogonies Man and the Machinery of Time Debbie Huffman Bellaire High School and Carnegie Vanguard High School INTRODUCTION The "Core" curricula are frequently offered as free-standing fields of study. As such, the histories of the disciplines get short shrift. A historical viewpoint, by contrast, reveals that when Western science began, there was no such thing as science. Instead, there was philosophy, the humanistic love of knowledge for its own sake. When the academic core is grounded in its Classical context, cross-curriculum opportunities arise for the classroom. This unit is offered as "theme" content for shared learning, and portions can be pursued concurrently or sequentially in the science, social studies, math, and English classrooms. My Latin class serves as a context within which these studies are integrated. Language is the vehicle of culture, and we find humans asking these same questions in every culture. The Classical context, with its emphasis on the process of questioning, demonstrates our underlying unity as human beings. Rather than only studying astrophysics and math, the students will investigate the ancestors of astronomy as historical figures. They will engage the deep human quest for meaning via the constellations and discover the many levels of meaning which mythology can convey. OBJECTIVES This unit will satisfy HISD objectives in Language Arts
, Math, Science and Social Studies. The student will: - Respond to mythological and other classical texts via art, drama and writing. - Understand the history of the Eastern Mediterranean
from 2000 BCE to 300 CE. - Identify the contributions of significant figures in science and philosophy. - Explore the Historical development
of mathematical and geometric systems. - Explore the historical development of astronomical observations and cosmogony. - Model orbital mechanics and solve problems in astronomy. - Perform direct observations of solar and lunar data. - Model Earth's rotation, revolution, and tilt and their effects on its environment. - Compare and contrast the various viewpoints competing in the marketplace of religious ideas during the early Roman Empire. - Evaluate the impact of scientific progress on individuals and social institutions. - Explain and apply historical [and archeological] research methods. - Demonstrate an understanding of art and culture as records of human achievement.
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RATIONALE In November 2006 new research on the Antikythera Mechanism was published. This artifact, a sophisticated gear train, was discovered in a shipwreck in 1901 and dated to no later than 100 BCE. It is tentatively linked with the Stoics of Rhodes and Posidonius, a close friend of Cicero. With the help of tomographic imaging technology and massive computing power, the individual gear wheels inside the barnacle-encrusted lumps had been visualized and their teeth counted, and an assembly scheme for the clockwork was proposed in the journal Nature and other publications. Further, the imaging had resolved an inscribed plate, which proved to be instructions for "setting" the clock. That news led me into this curriculum unit, even though I have not directly addressed the Antikythera Mechanism herein. The survival of knowledge is one of the great issues in human history. Print is fragile, artifacts can be ephemeral. A pre-literate culture holds its knowledge in the human mind, and expertise will vanish for lack of students. We may have a popular notion of the past as "primitive," but so much of our human past is simply a blank. It is not only that we need a different lens on mythology; we need a different lens on ourselves. Differences of cultural expression do not equate to mental deficiency, and it may well be that members of pre-literate cultures are "smarter" than us just in their sheer powers of observation and engagement in their world. The daytime world which demands our human powers of observation will vary by geography and cultural expression, but the night sky is our common human heritage. The cycles of moon and tide resonate in our bodies. The earliest traces of human culture the cave paintings hint that we are already observing the sky. When writing emerges in Mesopotamia, we see it devoted to the service of mathematics, both the civil accountancy of trade and the priestly astronomy of the temple. Why record and preserve a table of planetary positions if the information were not meaningful? The Antikythera Mechanism shows the considerable attention given to the sky in the Mediterranean world. Few researchers have yet commented on the technology it implies, beyond science and math. Clearly, this is no unique artifact. We know of at least two others like it in the Roman period
. One was fabricated by Archimedes in Syracuse, the other by Posidonius as Cicero describes. The myths speak of living statues such as Talos, Pindar's Seventh Ode speaks of animated figures, and Hero of Alexandria invented the first vending machine at about 50 CE The Classic Mediterranean was never really "primitive" or a technological backwater. Instead we see a world limited only by the temperature of its forges and its use of naturally-available power sources rather than by any lack of skill or knowledge. Some may question my interest in the sciences within a Latin classroom. The language cannot be sundered from the culture which produced it. The language was and is spoken and written by living people, people almost like us except when they aren't. It is through the medium of the language that we touch their minds and their very real and everyday concerns, be they food/water/shelter or the very nature of existence itself. It would be a dry and barren classroom indeed to focus only on grammar and vocabulary without addressing the minds behind the words. Hence, this unit has "something for everyone": History of Astronomy for the science classroom
, and Astrophysics for it to share with math; The Philosophers and Their World for the social studies classroom
; and the Layered Meanings of the Myths for language arts. The lesson plans
need not be unique to a given subject area. Ideally this unit would be implemented via team teaching or as a thematic focus across the disciplines.
UNIT BACKGROUND Why mythology? I have studied mythology predominantly the Mediterranean stories since I first pursued a reading certificate at age 8. I expect to be questioning the why of mythology for the rest of my life. I chose to take Latin at least in part because it would let me read the stories in [some of] their original versions. Imagine my joy when the Junior Classical League Latin Club, to most folks let me compete and win academic recognition of my passion for mythology. Not surprisingly, there are a lot of us "out there" who are interested in mythology, whatever other awareness we have of the Western Tradition. As a Latin teacher, I get to nay, have to bring the question of mythology into my classroom. Like my high-school self, many of my students come to me with existing knowledge of Graeco-Roman mythology and ready for a different lens to understand the stories. Frankly, we need a different lens. The stories themselves, taken at face value, contain elements which are simply preposterous. For example, there is the Minotaur, whose birth is indelicate at best. "The rules are different for the gods," I intone solemnly, and introduce the concept of animal gods Egypt and Mesopotamia are only the least of the cross-culturalism available. Beyond mythology, Greek and Roman science and philosophy offer opportunities for interdisciplinary work with other classrooms. Greek philosophy grows from the Greeks' examination of their own myths. Pursuit of Scientia how it is that we know what we know drives a burst of intellectual inquiry. It is one thing to tell the story of Clytie to explain the existence of sunflowers, another thing entirely to talk of a category of flowers alleged to have once been nymphs. With so many strands of inquiry possible the Classics classroom is an interdisciplinary "natural." The Classical and Modern Worlds bring each other into mutually sharper perspective. The Ancients really are a lot like us.... Advanced genetics and other challenges aside, a literal reading of Greek mythology reveals that the stories involve a small number of families who flourish for fewer than a dozen generations. The narrative arc of these characters culminates in the events of the Trojan War and ends not long afterward. Take Agamemnon and Menelaus, the sons of Atreus, as an example. The story line ends with Orestes. et al., Agamemnon's children and grandchildren. Atreus' grandfather is the infamous Tantalus, who fed his own son Pelops to the Olympians, and scant genealogy precedes him. Within that context, these stories superimpose conveniently upon our knowledge of the Greek Bronze Age. The Eastern Mediterranean in the Bronze Age Topography is, to a certain extent, destiny. That which we call "civilization" our tendency to live together in ever-larger groups arose in a handful of major riverine environments worldwide. The Yalu, the Ganges, the Indus, the Tigris-Euphrates, the Nile, the Mississippi, the Amazon, et al. yielded up fertile farmland within reach of other resources. We can argue exact timelines, but 10,000 BCE is a reasonable marker for our first dabblings in an agrarian lifestyle leading to the resultant rise of "civilization." The Eastern Mediterranean is an exception. In a world where the land falls steeply into the sea, sailing rather than farming becomes the driver of culture. The Phoenicians are establishing navigational control over the Eastern Mediterranean by about 2100 BCE, as the astronomical Age of Taurus is ending. The growing complexity of their mercantile endeavors fuels an innovation. The need to distribute floodplain farmland and its produce drove the birth of bookkeeping, and both the Mesopotamian cuneiform and the Egyptian hieroglyphs require a career class/caste of highly-trained scribes. Each word in these languages is a separate symbol. Literacy is a full-time job. The Phoenician breakthrough assigns the symbol
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to the sound rather than to the noun. Every occurrence of the sound "bee" will share a single glyph, and the sound and its glyph no longer represent only the animal. The literacy rate soars with this first idea of a syllabary script. More people can now invest the effort necessary to master the magic symbols. Fewer than a hundred symbols are now needed, and the Phoenician "aleph-beth" stabilizes at 22 consonants. The Greek myths
confirm that a lineage of "heroes" originates from Phoenicia. Zeus becomes a bull to court the maiden Europa, and abducts her to the island of Crete. Her children rule over the height of the Minoan civilization, and her brother Cadmus introduces writing to the Greek mainland. Generations previously, Zeus had changed her ancestress Io into bovine form to conceal his amorous intents, and when her kin find her, she scratches her name in the dirt with her hoof. The Phoenician woman knows how to read and write! The stories underplay the Phoenicians' abilities. They are, in fact, sailing rather than merely hopping from harbor to harbor along the coastlines. The sailing or rather, the navigating gives rise to an innovation in thought. Humans have already been mapping the sky for generations, and the sun's movement along the horizon between solstices and equinoxes is well known to the Babylonians and Egyptians. The sailor is bereft of a fixed horizon, and moves to the rhythm of the wheeling stars rather than the measures of sunrise and sunset. Sailors in any era are great storytellers, and it is from the cradle of Phoenician sail and its Minoan flourishing that core strands of Greek mythology arise. The archeological record confirms the richness of this Minoan Civilization's half millennium. The Daedalus stories imply a level of technology which includes wind-up toys and automatic doors. Whether or not we credit the Minoans with such marvels, digs reveal an advanced maritime culture with indoor plumbing, literacy, and sufficient leisure for the arts to flourish. The smiling bull dancers of the wall paintings are visibly healthy professional entertainers. All this changes about 1630 BCE. Just over Knossos' horizon, the island Thera is transformed in an instant of geological time into a steaming caldera, tons of incandescent ejecta and a massive tidal wave which destroys Knossos within the hour. Subsequent aftershocks and climate effects collapse the Minoan Civilization within 50 years. By the end, they have sunk to human sacrifice in an effort to placate their angry gods and this practice also appears in the myths. As Minoa declines, the power of Mycenae rises. These are the Achaeans, the Greeks who fight at Troy, led by the aforementioned Atreides. Their fathers and grandfathers found the major cities of the Greek mainland and travel with Jason and Heracles on the Argo. These Greeks are also masterful sailors, and their storytelling preserves epic voyages of discovery. They have a writing system borrowed from the Minoans. The stories of their deeds and ancestry survive into historic times and have come down to us as immortal literature. But everyone knows mythology is just stories. Or is it? Following Schliemann's destructive dig at Hissarlik (Troy), the academic world accepted the truth of Homer's stories. Subsequent work in archeology and linguistics confirmed that the Greeks as we may think of them do not exist at the time of Troy. Instead the Iliad reveals a loose federation of petty kings, each with sworn warriors and shifting personal allegiances. The war is a series of massed skirmishes where individual combat between lineaged champions figures decisively. Attrition of leadership and simple trickery, rather than the siege itself, are the ultimate deciders of Troy's fall. The stories of mythology come to an end in the wake of Troy because these "Greeks" of the Troy era cease to exist within two centuries of Troy's fall. The IndoEuropean migrations send a fresh wave of travelers across Europe in about 1000 BCE, and the Dorians cover the Greek peninsula (King).
The Transition to the Iron Age In the four centuries after Troy (the first Olympic Games are in 776 BCE) a different Greece emerges from the Dark Ages following the Dorian invasion. Magna Graecia now stretches from Asia Minor to southern Italy. The Greeks are fully engaged in questioning the nature of their world, and the two dialects of Greek which will shape philosophy and science now have a fully formed alphabet for their expression. When the 22 borrowed Phoenician consonants were reassigned to the sounds of Greek, symbols were left over so now vowels are also represented in writing. The Greek language's existing aesthetic of poetic rigor and form erupts into the new medium of writing, and some of our earliest Greek literature is those stories which we call mythology, as attributed to the authors Homer and Hesiod. With a mere 22 symbols from which to form myriad combinations, anyone can easily learn to write or, more importantly for our purposes, to read. Obviously those intervening centuries were not so culturally dark as we imagine they were, rather, merely illiterate. The appearance of text as a medium of literary transmission coincides with a flowering of architecture and art which culminates in the building of Pericles' Acropolis and the emergence of the philosophical schools. The Greeks once again live in a culture sufficiently ordered to permit of leisure and creativity. It is easy to forget that Alexander is tutored by Aristotle the student of Plato, who was the student of Socrates, who was murdered for asking too many "why" questions. Even governance and war are subjects for scientific inquiry which can be learned as practical arts the craft of the politician, the craft of the general. Alexander, schooled to the ideals of the philosopher-king, in turn founds colonies with the intent to spread the concept of "Greekness" as a cultural identity. These far-flung Greeks are united by language, and the Mediterranean world becomes a cradle of Hellenism and inquiry. It is into this world that Rome emerges in her turn. Within this context of Greece's flowering, a shift of metaphors may be in order. We can agree that "Homer" gives us the first Greek literature to be captured in writing from a pre-existing oral tradition
. The person of Homer and his role within his culture remains a vague concept to most people. I find myself constantly emphasizing to my Latin students that the Ancients are extraordinarily much like us except when they aren't. More to the point, it is we mobile denizens of a world of machines who are unlike our ancestors. We have lost a large measure of our ability to imagine their lives and their realities with our disconnect from the dimensions of place and manual labor which had marked human life until little more than a century ago. Hercules' labors are matched by the exploits of John Henry and Paul Bunyan. The academic field of Anthropology arises at about the same time as that disconnect begins. Technocratic Modern Man, self-conscious from his birth, makes the quaint primitives an object of study because we know that we are different except when we discover how much so we are still the same. Culture and Its Transmission One pertinent measure of our same-and-different-ness is in the area of music. Today sheer sound human sound is a constant blur of background. The sheer ubiquity of text and sound render the ineffable Word into undulating Rhythm. For the ancients, the limited availability of surfaces on which to capture text gives greater prominence to the ear and the memory. Our popular imagination has Homer as the last of a line of bards who had transmitted the stories of Troy and Odysseus in faithful word-for-word precision until the medium of print became available to capture the tales for further posterity. A different "take" on Homer's world emerges if we think of the bards as leisured professional artists, the traveling pop stars of their day. Everyone knows these stories; they are the common cultural heritage of Magna Graecia. But this one bard has the best version of the story, the best
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"arrangement" and the most consistent performance style, and he is the one who "gets the recording contract." It is Homer's version of the story which wins the Greek Idol competition and continues to saturate the airwaves to this day. I find myself wondering if Homer, like Dylan, developed new "arrangements" as each new "cover band" emerged to faithfully reproduce his original studio cut? That last may be a bit of a stretch, but I offer the image to emphasize the degree to which the Greek mind is focused on the Word the oral and aural elements of language as communication. I suspect that no student of philosophy or of the history of science can achieve a full understanding of the Greeks' contributions without an understanding of the Greek language. When writing emerges and the Greeks are first available for our scrutiny as creators of literature and art, we find them already engaged in debate about what it is that they know and how it is that they know it. Within the confines of the evidence we have, we see the Greeks as at essence an argumentative and hair-splitting lot and the Greek language permits of multiple ways to split any given hair. Inscriptions on stone form the bulk of contemporaneous written evidence about the ancient world. Emphasis on contemporaneous. Editions of popular books are "published" on either papyrus or parchment. Each has a limited annual raw material supply which requires significant preparation for use. Nonetheless, the Greeks and Romans were avid consumers of print, and books were produced in editions of as many as several hundred copies. Lucky for us, since books are so easily lost or destroyed in historical upheavals. Ironically, it is the monastic scribes of the Christian Middle Ages
who preserve much of the Classic material. Since the writing materials are so durable they erase the "pagan" books and re-use the writing surface and we can now use imaging technology and filtered wavelengths of the light spectrum to read the traces of the original ink. Our knowledge of the past grows apace. The Myths as Literature So back to that 8th-Century moment when Greek literature emerges, and the earliest literature we have is Homer and Hesiod recounting the stories which we know as Greek mythology. For the next millennium we see diversity in the marketplace of Religious affiliation
and expression. Deities have jurisdictions and powers of various magnitudes. Most humans have one or more primary deities but will give appropriate honor to others Greek Olympian, Roman Numina, or otherwise as situations warrant. A rich fabric of gods and demigods and heroes and heroic deeds builds up as each successive generation of pop star poets which the Greek playwrights definitely were offers up its definitive renderings of whatever stories are in current vogue. As the stories become literature, they change to reflect whatever concerns political, ethical and otherwise are driving the songwriter/poet. These pop stars are frequently also political activists. Think Dylan. One issue in my use of these stories in the Latin classroom is that they are quite so unvarnished. The Olympians are not presented in a complimentary light. The goddesses are frequently petty and vengeful; the gods are adulterous and bestial. The half-human heroes are flawed in their various ways. Back to the example of Daedalus, and we can scarcely explain the Minotaur as evidence that the people of Atlantis were experimenting with genetic engineering. The myths might indeed begin as an Oral History
of the period from Thera to Troy, and may later become theater and metaphor for the human condition, but at the time they first crystallize as literature many stories differ little from the later European folklore of the Bros. Grimm. On one level of analysis we see a collection of cautionary bogeytales and negative moral instruction, along with proud civic claims of ancient divine ancestry. Something else must explain the myths' persistence.
In many cases, "proud civic claims" is indeed sufficient reason for a story to survive. One of those many ways in which the ancients are "just like us" provides the link there proves to be a thriving tourism industry in the ancient world. No story, no tourist but discover your place's story and tourists may just come. Ah, but land travel is hard and dangerous, and the Greeks like the Phoenicians before them are great mariners. The myths may sing of voyages of exploration, but freight of goods and said tourists as paying passengers is a sailor's daily bread. On a closer look, no few of these irrational [and raunchy] tales end in one or more characters being placed among the stars. Aha! What if the stories are a key to help sailors read the sky and plan voyages? Two millennia and more later, the stars of the Drinking Gourd will provide a similar landmark to enslaved Africans as they, without a steady horizon, navigate from the American confederacy
to the Free State
s of the Northern Union. [See LESSON PLAN #1 Astronomy Myths.] The Emergence of Greek Science A second category of literature we see emerge from 8th-Century Magna Graecia reveals the first glimmers of Greek science. Make no mistake, this world is richly technological. Pottery, fiber crafts, metallurgy, architecture, agriculture, and bookkeeping all emerge in "prehistoric" times which simply means they predate written accounts of their development. The 6th and 5th centuries BCE see Greek advances in these fields, as well as in medicine, mathematics, and astronomy. Especially in these latter fields, a rich body of empirical, hands-on knowledge accrues, and that body of experimentation is captured in writing. The growth of mere literacy which is fueled by the innovation of the Greek alphabet leads in turn to an expansion of inquiry rather than of mere knowledge. We can argue successfully that the roots of Greek learning are in previous cultures. It is among the Greeks that we see the emergence of inquiry, of speculation and experimentation. We name Thales of Miletus as the first philosopher-scientist, the first to "discover" Nature and seek naturalistic explanations for observed phenomena rather than resorting to an explanation of divine agency or caprice. This is the miracle of Greece in the land of the Olympian gods, suddenly the gods are evicted from the picture and men begin to debate the nature of existence and the problem of how we know what we know. Underlying the process of inquiry and the fields of enquiring, the Greeks tend to polarize into the two camps of Empiricism and Rationalism. Not content with debating the question of how we know what we know, the Greeks question whether anything is knowable at all. The material world presents us with phenomena for observation. We have the evidence of our own senses which are themselves material with which to measure and evaluate these phenomena. But and this is a big "but" the very existence of both phenomena and sensorium itself becomes subject to debate. The Rationalists reject the world and the senses, and contend that pure mind, by force of structured contemplation alone, can achieve a true and sufficient explanation of existence. The Empiricists, obdurately, continue to observe, measure, question, and compare. [See LESSON PLAN #2 The Scientists.] The Rise of the Philosophical Schools In the ferment of inquiry and debate, this scientific process leads to the rise of the philosophical schools. Inquiry alone is not sufficient; the Greeks' inquiries take place within the framework of a collective, "moral" aesthetic. The Eleusinian (and Dionysian) Mysteries may well predate the Minoan-Mycenaean interface Heracles is described as an initiate and continue uninterrupted until their suppression by decree of Theodosius I in 392 CE. The Pythagorean and Orphic Cults date to said beginnings of Greek science. The Stoic, Cynic, Epicurean and other Schools arise in the ferment of Athens' golden age and afterward. The questioning of the nature and purpose of existence leads in turn to discussion of the right way to
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live. Aha, there is an existing body of stories set in the Greek afterlife. The myths are recast as a vehicle of instruction in moral principles. Back to the advanced technologies which are already in place as the Greeks burst forth. Agriculture is a strong driving force for technology. Pottery and the fiber crafts service the need for food storage. Metallurgy services the development of farm tools and weapons for defense. Writing as the means of record-keeping enables governance and its control of food distribution. Mathematics furthers the record-keeping and enables the study of astronomy, which is essential to a stable agricultural practice. It is difficult to convey to urban students the significance of the night sky the significance of the sky, period. The constellation myths are one thing, but long-term [even generational] observation of the sky from a fixed location reveals that the sky changes. Sunrise systematically oscillates to the north and south of "due East" over the course of a year, and the height to which the sun rises at noon also varies. The moon shows its own variations and the planetes (planets) the wandering stars have each their own unique motions. The constellations may be fixed relative to each other, but even the apparent sphere of these fixed stars moves, as different stars "rise" at different times of year. The Egyptians and Babylonians have been mapping and recording these various motions for hundreds if not thousands of years by the time the Greeks enter the picture. The Greek afterlife is an underworld, true, but there are also those humans who were placed among the stars. As we move from the Age of Myth to the Age of Philosophy, the stories are increasingly seen as religious allegory rather than as history or fable. And as the philosophers question the very nature of experience and the human soul, its place comes to be seen as among the stars. The stars are there to teach us lessons, the planetes are identified as gods, and the stars and planets [and the patterns they form] are seen as affecting the fates of men. The Greek philosophers proceed to measure this long-since-mapped night sky. Elaborate cosmogonies are constructed to explain the motions of the sky, the old stories are reintegrated into them and new stories are constructed. Astronomy, Astrometry and Astrology Stories aside, and based upon various philosophical idealisms, several schools of thought come to agree that the universe is spherical in structure, a series of nested spheres in which the planets rule the levels between earth and the stars. Within this spherical ideal, we see both geocentric and heliocentric models competing for acceptance, but this spherical, cosmos informs Western thought even unto Copernicus, Galileo, and Kepler. Alexander is born in 356 BCE, and after his death our Greeks exist within a larger Hellenic / Hellenistic world. The radical expansion in mobility of people yields an equivalent mobility of ideas. The emergence of the Roman state fuels both movements, especially after she conquers Greece in 146 BCE. Prior to Alexander, Athens and the Greek theater had fueled the growth of literature as an art form, and the Romans are the first great mass consumers of literature, art and other culture. Beyond their consumption of tangibles, the Romans also "buy into" the teachings of both the Mystery Religions and the Philosophical Schools. As a side note, the Romans are a fantastically superstitious people. Religion aside, the belief that the stars control human fate drives a lucrative pop culture market in natal astrology and fortune-telling. It is in this cultural context that Hipparchus, a prominent Stoic, "discovers" the precession of the equinoxes at about 115 BCE Several assumptions are necessary at this point. He must have had available Egyptian and/or Babylonian astrometric records. His calculations hinge upon the accuracy of his own observations, made with the naked eye and instrumentation of no more complexity than represented by the Antikythera Mechanism. He has a mathematical process
adequate to the calculations underlying his discovery and in fact he and his philosopher peers are ancestors of the Calculus. Hipparchus' successor as head of the Rhodian school, Posidonius, is said by his good friend Cicero to have "fabricated a mechanism" (Ulansey). ...sphaeram hanc, quam nuper familiaris noster effecit Posidonius, cuius singulae conversiones idem efficiunt in sole et in luna et in quinque stellis errantibus, quod efficitur in caelo singulis diebus et noctibus,.. ...this sphere which our friend Posidonius recently constructed, whose each revolution causes the same [movement] in the sun and moon and five wandering stars as is brought about in the sky by each day and night,... (Cicero, Natura Deorum 2.88). Again, our assumptions must include the pre-existence of complex mathematics and the ability to make accurate observations, along with the precision fabrication processes which any clockwork represents. Once we assume artisans capable of such work, it is difficult to believe that the Antikythera device is a unique piece of antiquity and equally difficult to presume that it the most advanced specimen to have survived. It is in fact an orrery rather than a sextant, and the same skills and tools upon which Hipparchus and Posidonius drew are readily available to us today. [See LESSON PLAN #3 the Cosmic Clock of our local Solar System.] Soteriology in the Religious Marketplace The philosophical schools parallel the tradition of the Mystery Religions, and both share a simple goal: to live the good life by being true to one's own nature, and thereby to transcend the workings of fate by returning to that nature after this body's death. We have come to this material world from elsewhere, and our true nature is to be beacons of light in the sphere of pure Mind. Two millennia and more later, Joni Mitchell refrains this simple truth we are stardust, we are made of the stuff of stars, we are both like and unlike the world in which we live. Again, this is one of the Great Questions which occupies humankind and some will go so far as to say that it is the questioning which makes us human, rather than the answers at which any one person or culture will arrive. The Ancients, like us, are seekers after religious Truth. The debate between the Rationalists and the Empiricists on the reality of one's very senses persists, but the Truth which the Mystery Religions offer up is imparted to the Individual as Experience. The Seeker is taken on a journey an Initiation on which s/he discerns the nature of the self and of incarnation, and is taught how to return to the world of Mind after one's death in the world of Matter. These groups variously place their initiatory journeys within well-mapped landscapes, and the maps are taught by wellrehearsed ritual and dramatizations of mythological stories. The myths give rules for right behavior in this world and the next. The stories serve as a mnemonic of one's experiences in this spherical Cosmos as Mind journeys through its levels into and out of Matter. In particular, in the journey of the Mithras initiate the spheres are those of the seven wandering stars the planetes and the final destination is the sphere of the fixed stars. This cosmogony is shared with the Stoics, Cynics, et al., and the tendency is toward a heliocentric cosmos. A millenium later, Dante in his Divine Comedy espouses the same concept of the Soul's journey through the levels of the cosmos. Back to spheres vs. ellipses the observed movements of the planets are more-so resolved by a solar Center rather than a terrestrial one. The geocentric view enjoys few adherents. The assumptions that Mind is Perfection and circles are perfect continue to complicate the math. Back to Hipparchus and the origins of what we know as Calculus, and he is also linked to the origin of the Mithras cult. The central icon of a Mithraic temple the tauroctony is a depiction of Mithras slaying the cosmic bull to bring the world into being.
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In Hipparchus' day the Vernal Equinox was moving from Aires into Pisces, much as we are currently moving into the Age of Aquarius. The tauroctony can be interpreted as a depiction of the night sky when the Vernal Equinox was in Taurus, a period 2000-4000 years before Hipparchus' time but revealed by his calculations and conceivably still available to him as recorded observations from the Minoan era or earlier. Somehow, the perfect and unchanging stars had been set into motion and were still moving. This could only have been done from outside the Cosmos, witness Archimedes' opinion of the lever. Ergo, the religious Truth which the Ancients were seeking was a cosmic Higher Power, one not bounded by the spheres of the World and with the power to move those spheres. Clearly, such a Power would be able to guide the individual journey toward Mind. More of that Greek hair-splitting to escape the world of Matter is to be "saved," and the verb in turn implies nouns for the one who is saved and for the one who does the saving. One could achieve the journey alone, but one who travels the journey of Initiation while in the world of Matter learns how to call upon the Deity for assistance after death. The title soter Savior is attributed to more than one deity presumed powerful enough to move the Cosmos. Oddly, titles overlap and seekers are not expected to adhere to only one deity or rather to only one cult. Apuleius, in Book 11 of his Metamorphoses, says, "Regina caeli, -- ... quoquo nomine, quoquo ritu, quaqua facie te fas est invocare:" "Queen of heaven, by whatever name, by whatever ritual, by whatever appearance it is allowable to call upon you." As the Roman Empire declines, of all the cults and schools discussed herein, Mithras, Isis, and Kristos command the largest numbers of adherents in the religious marketplace. We can better understand Mithraism in particular and the savior-religions in general by exploring the agreed-upon geometry of the sky and the associated popular beliefs. Remember that the sciences are not compartmentalized in the Roman world, and it was not unusual for a "philosopher" to be a polymath, equally comfortable discussing metallurgy or theology. The term "scientist" applies equally to all focused inquiry. Alas, we can not all be scientists, just as we can not all be heroes. We can see the scientist as an explorer on his own journey into the workings of Mind. To convey his experiences and understandings to others, he may employ storytelling techniques mythmaking in multiple layers of meaning. It is not enough to explore only. The immortality lies in the telling, and the storytelling serves as a unifying force, a transmitter of culture and of acculturation and a source of fellow travelers. [See LESSON PLAN #4 New Mythologies for Psychonauts.] LESSON PLANS Lesson One: Astronomical Myths. (This unit will take about one week. Each lesson is 45-50 minutes in length.) Objectives (A complete list of objectives follows lesson plan 4.) Students [singly or in groups] will research creation myths to collect stories which detail the origins of specific constellations in the night sky. Students will share these stories in class through a combination of narrative and visual media. Student output will reference the History of Astronomy rather than Astronomy as contemporary science. §110.55. Humanities (2) (E), (3) (A). §112.48. Astronomy.(7) (D). §117.52. Art, Level I. (3) (A). Materials Needed Information in this lesson plan, Internet access, Library access, writing and art materials.
Rather than being purely creation stories, the myths are used by sailors as teaching tools. The ability to read the night sky allows one to travel the sea; the stories provide the map by which to read the sky, but pose as mere stories to keep the knowledge limited. Activities Students [singly or in groups] select from a list of constellations to research and report on the astronomical myths which explain the constellation. A variety of concrete realia and narrative performances may be produced for assessment. [At teacher's discretion, stories from cultures other than the Mediterranean ones may be included.] Assessment Teachers may choose to restrict student output to specific formats for ease of assessing the product. When a variety of formats is allowed, the rubric should assess the research process and any cooperative effort in addition to the merits of the individual product. For purposes of interdisciplinary work, multiple rubrics may apply. An art teacher could assess visual output, whereas a speech teacher would assess a dramatic rendering. Suggested Resources [via library access to journal articles / archives] - See mythology.org and perseus.tufts.edu in addition to print resources for Greek Mythology, esp. the original works [in translation] of Homer, Hesiod, Ovid et al. - Astronomy Magazine, http://www.astronomy.com/asy/default.aspx, especially the column of Phil Harrington. - Natural History Magazine, http://www.naturalhistorymag.com/. - Various titles by Isaac Asimov
. Lesson Two: The Scientists. (This unit will take about one week. Each lesson is 45-50 minutes in length.) Objectives Students [singly or in groups] will research the major Greek [and Roman] philosophers and scientists, beginning with Thales of Miletus. Student product will consist of capsule biographies including discussion of major discoveries and viewpoints. Students will collectively assemble these biographies into a timeline sorted by the field of study. §112.48. Astronomy. (3) (A) & (E). §113.33. World History
Studies. (1) (B) & (C), (23) (B) & (E), (25) (A) (D) & (E). Materials Needed Information in this lesson plan, Internet access, Library access, writing and art materials. Key Concepts The originators of scientific inquiry in Greece see themselves foremost as philosophers. Their field of study is "Natural History." It is only as their body of knowledge grows that specialized sciences differentiate. As specific Philosophical Schools arise, individual work is informed by an understanding of one's place as inheritor of a lineage of research. We stand on the shoulders of giants; we build on their work in our turn.
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Activities Students [singly or in groups] select from a list of philosophers and scientists to research biographical data. Student output will include discussion of each figure's major scientific discoveries and individual viewpoint within the various strands of ancient inquiry. These individual figures will be assembled into a timeline of Graeco-Roman thought from Thales of Miletus to approximately the time of the Roman Emperor Marcus Aurelius
. [The timeline may be extended to Kepler, who first abandons the concept of sphericity.] Assessment Student output will consist of two components. A narrative report presented in class will include discussion of the subject's biographical details, cultural context, discoveries and research accomplishments
, and contributions to subsequent study. A graphic capsule representation of a limited size will be produced for inclusion in the classroom timeline. Suggested Resources [via library access to journal articles / archives] Biographies of the ancient Greek and Roman "scientists" from print and online resources, especially PBS.org's The Greeks: Crucible of Civilization. Lesson Three: the Cosmic Clock in our local Solar System (This unit will take about one week. Each lesson is 45-50 minutes in length.) Objectives Students [singly or in groups] will investigate the parameters of the Cosmic Clock the geometric movements of our Solar System as observed from Earth's surface and measured against the landmarks and turning backdrop of the "fixed stars." Student product will be graphical in nature. - Understand the relative annual movement of the celestial equator the plane of the ecliptic, and the moments of sunrise and sunset. - Understand the movements which our fellow planets exhibit against this backdrop. - Compare and contrast the geocentric and heliocentric models of the universe which competed for acceptance among researchers. §111.34. Geometry. (1) (B). §111.36. Mathematical Models
with Applications. (3) (C) & (8) (B). §112.48. Astronomy. (3) (A) & (E), (4) (A), (7) (B) & (C), (9) (A), (10) (B). Materials Needed Information in this lesson plan, Internet access, Library access, writing and art materials. Key Concepts The "sphere of the fixed stars" is measured out by various landmarks. The celestial equator and the plane of the ecliptic interact with the moments of sunrise and sunset to form hands of a cosmic clock. The movements of the planets measure various longer intervals of time. The study of these collective movements originates as the study of Astrology, and the Egyptians and Babylonians preserve extensive records their cosmic observations. The Greeks, inheriting this data, bring greater precision of measurement to these observations. At about 120 BCE, Hipparchus of Rhodes synthesizes this accumulated knowledge to discover the Precession of the Equinoxes. He adds another "hand" to the "clock" one which takes 24,000 years to complete a revolution.
Activities Students [singly or in groups] research the terminology used to describe astronomical coordinates. Student output will be both narrative and graphical. In addition to text, students will produce representations of the night sky and its landmarks. These may include such things as star maps, a labeled celestial sphere, strip maps showing the interplay of celestial equator and plane of the ecliptic, a cardstock sundial, etc. Assessment Student output will consist of two components. Narrative output will explain the various terminology used to map the night sky. Graphic output will represent the terminology as applied to the practice of astronomical observation. This output will emphasize history of astronomy issues, specifically the accommodations which were needed to shoehorn elliptical planetary motion into a model initially spherical, and ultimately geocentric. [The teacher may wish to preference manipulable output on the assessment rubric.] Suggested Resources [via library access to journal articles / archives] - The Columbia Encyclopedia has a series of concise explanations of astronomical terms, and can be accessed through a variety of online portals. - Astronomy Magazine, http://www.astronomy.com/asy/default.aspx. - Natural History Magazine, http://www.naturalhistorymag.com/. - [For a tool, www.thesciencesource.com has a Solar Motion Kit which comes with the instructions to generate a local "Stonehenge-type circle" with sundial gnomon.] Lesson Four: New Mythologies for Psychonauts (This unit will take about one week. Each lesson is 45-50 minutes in length.) Objectives Students [singly or in groups] will generate and select from a list of initiatory myths to research and report. Rather than historical content, students may elect to research [or create] new myths for the Age of Space Exploration. A variety of narratives, concrete realia and performances may be produced for assessment during this segment. §110.55. Humanities. (2) (E), (3) (A). §113.33. World History Studies. (2) (A), (19) (A) & (B), (20) (B), (25) (A) & (D). §113.36. Psychology. (18) (A) & (B). §113.37. Sociology. (13) (A), (17) (A). §117.52. Art, Level I. (3) (A) & (B). Materials Needed Information in this lesson plan, Internet access, Library access, writing and art materials. Key Concepts The Mystery Religions provide the initiate with instructions about the afterlife and the nature of the soul. The heavens are our destination, and we travel in and out of the world of Matter through the spheres of the planets. The map is conveyed to the initiate by way of storytelling and dramatization. The information presented "in code" within the stories, because they are meant to be experienced rather than read casually as literature.
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Activities Students [singly or in groups] select from various Classical Mystery Religions and Philosophical Schools to research and report on their myths and the underlying teachings. A variety of concrete realia and narrative performances may be produced for assessment. [At teacher's discretion, the "inner space" focus of this unit can include or be shifted to 20th C science fiction
and the mythologies of outer space exploration.] Assessment Dramatic rendering and other theatrical/storytelling forms are the preferred format for student product. Teachers may choose to restrict student output to specific formats for ease of assessment. When a variety of formats is allowed, the rubric should assess the research process and any cooperative effort in addition to the merits of the individual product. For interdisciplinary work, multiple rubrics may apply. An art teacher could assess visual output, whereas a speech teacher would assess a dramatic rendering. Suggested Resources [via library access to journal articles / archives] - See mythology.org and perseus.tufts.edu in addition to print resources for Greek Mythology, esp. the original works [in translation] of Homer, Hesiod, Ovid et al. - The works of Joseph Campbell, especially his PBS content (with Bill Moyers). - [Various Science Fiction books in the Star Trek and Star Wars genres.] FULL LIST OF HISD OBJECTIVES §110.55. Humanities (2) Express and support responses to mythological texts. (E) identify and analyze how literature is a reflection of philosophical movements. (3) Use writing as a tool for learning and research. (A) show an in-depth understanding of creativity in literature through writing. §111.34. Geometry (1) Understand the structure of, and relationships within, an axiomatic system. (B) recognize the historical development of geometric systems and know that mathematics is developed for a variety of purposes. §111.36. Mathematical Models with Applications (3) Develop and implement a plan for collecting and analyzing data. (C) determine the appropriateness of a model for making predictions from a set of data. (8) Use algebraic and geometric models to describe situations and solve problems. (B) use trigonometric ratios and functions to model periodic motion. §112.48. Astronomy. (3) Scientific processes. Use critical thinking and scientific problem solving skills. (A) analyze, review, and critique scientific explanations
using evidence and information; (E) research and describe the history of astronomy and contributions of scientists. (4) Science concepts. Know scientific information
about the universe.
(A) observe and record data about lunar phases to model the earth, moon, and sun system (7) Science concepts. Know how mathematical models can be used to study the universe. (B) research and describe the historical development of the laws of planetary motion. (C) analyze models that simulate planetary motion and universal gravitation. (D) identify the historical origins of the perceived patterns of constellations and their role in ancient navigation. (9) Science concepts. Know that planets orbit around the Sun. (A) observe the night-time sky to determine movement of the planets relative to stars. (10) Science concepts. Know how life on Earth is affected by placement and orientation in the solar system. (B) determine the effects of the Earth's rotation, revolution, and tilt on its environment. §113.33. World History Studies [See also §113.36. Psychology and §113.37. Sociology] (1) History. Understand traditional historical points of reference. (B) identify changes that resulted from the Greek scientific revolution. (C) sequence significant individuals, events, and time periods. (2) History. Understand how the present relates to the past. (A) identify elements in a contemporary situation that parallel a historical situation; (19) Culture. Understand history and relevance of religious and philosophical traditions. (A) compare the historical origins, central ideas, and the spread of major religious and philosophical traditions including Christianity and Judaism and their contemporaries. (B) identify examples of religious influence in historic world events. (20) Culture. Understand the relationship between the arts and the times during which they were created. (B) analyze examples of how the arts reflect the cultures in which they are produced (23) Science & technology. Understand how discoveries and innovations affect societies. (B) identify ideas in mathematics, science & technology during the Graeco-Roman period (E) identify the contributions of significant scientists such as Archimedes, Erastosthenes, Thales and Pythagorus. (25) Social studies skills. Apply critical-thinking skills
to organize and use information. (A) identify ways archaeologists and historians analyze limited evidence. (D) explain and apply methods that historians use to interpret the past. (E) use the process of historical inquiry to research. §113.36. Psychology (18) Science and technology. Understand the relationship of changes in technology to personal growth and development. (A) analyze examples of attitudes, beliefs, and behaviors related to changes in technology (B) evaluate the impact of changes in technology on personal growth and development.
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§113.37. Sociology (13) Culture. Understand social institutions develop to meet basic needs
in society. (A) summarize the functions of social institutions such as religion. (17) Science, technology, and society. Understand the impact of scientific discoveries and technological innovations on individuals and societies. (A) analyze how individual and societal behavior changes as a result of scientific discoveries and technological innovations. §117.52. Art, Level I. (3) Historical/cultural heritage. Demonstrate an understanding of art history and culture as records of human achievement. (A) compare and contrast historical styles, identifying general themes and trends; (B) describe general characteristics in artworks from a variety of cultures; ANNOTATED BIBLIOGRAPHY Works Cited Apuleius. Metamorphoses. The Latin Library. Book 11, Paragraph 2. . Cicero. Natura Deorum. The Latin Library. Chapter 2, Paragraph 88. . King, Wellington. "Heinrich Schliemann: Heros and Mythos." . Mitchell, Joni. "Woodstock." Ladies of the Canyon. Reprise Records, 1970. Ulansey, David. The Origins of the Mithraic Mysteries: Cosmology and Salvation in the Ancient World. New York: Oxford University Press, 1989. Supplemental Sources Angus, S. The Mystery-Religions. Mineola, NY: Dover Publications, 1975. Asimov, Isaac. Numerous titles on astronomy, mythology, history and mathematics are found among his life's work of 400 titles. Aveni, Anthony F. Conversing with the Planets: How Science and Myth Invented the Cosmos. New York: Random House, Inc. [Times Books], 1992. Bakich, Michael E. "Astrology: Fact or Fiction?" Astronomy, 32.12 (2004): 50-56. Dowling, Melissa Barden. "A Time to Regender: The Transformation of Roman Time." KronoScope 3:2 (2003): 169183. Franзois Charette, "Archeology: High Tech from Ancient Greece." Nature 444.7119 (2006): 551-2. The Antikythera Mechanism, salvaged 100 years ago from an ancient shipwreck, was long known to be some sort of mechanical calendar. But modern analysis is only now revealing just how sophisticated it was. Freeth, T., et al. "Letters: Decoding the Ancient Greek Astronomical Calculator Known as the Antikythera Mechanism." Nature 444.7119 (2006): 587-91 Guthrie, W.K.C. The Greek Philosophers: from Thales to Aristotle. New York: Harper Torchbooks, 1986. Out of print but several similar titles by the same author are available. Kagan, Janet. Uhura's Song. (Star Trek, No 21). Upper Saddle River, NJ: Gregg Press, 1985. In a genre rife with hero journeys, this novel hinges on a story song which encodes hidden knowledge! Lobell, Jarrett A., "The Antikythera Mechanism." Archaeology, 60.2 (2007): 42-5.
Merchant, Jo, "In Search of Lost Time." Nature 444.7119 (2006): 534-8. The ancient Antikythera Mechanism doesn't just challenge our assumptions about technology transfer over the ages -- it gives us fresh insights into history itself. Meyer, Marvin W. Ancient Mysteries: A Sourcebook of Sacred Texts. Philadelphia: University of Pennsylvania Press, 1999. Oliver, Jack. "An Early History of Difficult Multiplication and Division." Australian Senior Mathematics Journal 19:1 (2005): 57-60. Pinotsis, Antonios D. "A Comparative Study of the Evolution of the Geographical Ideas and Measurements until the Time of Eratosthenes." Astronomical & Astrophysical Transactions 24.2 (2005): 127-138. Multiple other citations by this same author. Worthen, Thomas D. The Myth of Replacement: Stars, Gods, and Order in the Universe. Tucson: University of Arizona Press, 1991. Websites "Antikythera Mechanism." Wikipedia, the free encyclopedia. 2007. Wikimedia Foundation, Inc. 30 May 2007. . The article is presented for its links section with easy access to primary sources. Astronomy.com. 2007. Astronomy Magazine. Kalmbach Publishing Co. 14 April 2007. . Site includes magazine archives, with numerous articles on constellations and mythology. See Phil Harrington's columns. Bartel, Nick. (ed.) The Greeks: Crucible of Civilization. (Education Resources page.) 2007. Public Broadcasting Service (PBS). 30 May 2007. . An exhaustive links page of Biographical and other resources. "Columbia Encyclopedia." Wikipedia, The Free Encyclopedia. 2007. Wikimedia Foundation, Inc. 30 May 2007. . The Columbia Encyclopedia is available online via multiple portals. Wikipedia gives external links to seven sites and rates their advertisement loading. Crane, Gregory R. (ed.). The Perseus Project. 2007. Department of Classics, Tufts U. 30 May 2007. . Out-of-copyright translations of Classical authors. Gifford, Gerry (ed.). MythsDreamsSymbols. 2007. "A free service." 30 May 2007. . A large collection of Joseph Campbell material. Instructor. 2007. Instructor Magazine. Scholastic Inc. 30 May 2007. . At the bottom of the page is a search window lesson plans. The Scholastic main page also has an archive. Mythology.org. 2007. Foundation for Mythological Studies (FMS). 30 May 2007. . The exhaustive Links page has a mix of scholarly and student references. Various translations and renderings of the original Greek and Latin texts of mythology etc. can be accessed through these links. Natural History. 2007. Natural History Magazine. American Museum of Natural History, New York. 14 April 2007. . This site includes magazine archives, with articles on constellations and mythology. Smith, Mahlon H. (ed). Virtual Religion Index. 2007. "A free service." 30 May 2007. . A "links central" page includes the three categories Academic Sites, Graeco-Roman Studies, and Philosophy & Theology. These pages include PBS-related links. Good source for biographies. The Divine Comedy by Dante Alighieri. 2006. The Electronic Literature Foundation 30 May 2007. . The Joseph Campbell Foundation. 2007. A non-profit organization and website. 30 May 2007. . One can register for free as an Associate and gain access to the Mythological Resources page.
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The Science Source. 2007. . 30 May 2007. Tab to "earth & environment" and then to "astronomy" for the Solar Motion kit and other visuals.