Lecture 5a: Byzantium, continued

Unlike Alexandria, a certain amount of Byzantium was saved as they modernized the city into present-day Istanbul. Old Alexandria is completely paved over by new Alexandria. I've never been to Istanbul, but I guess you could actually take a tour of the earliest churches of Christendom. We're going on to Bagdad today, but as I don't feel that I've successfully evoked the spirit of Byzantium yet, I will read you a story that will give you a better feeling for that culture. Byzantium is not well known in our culture, and the study of the art history and political and military history and so on of the Byzantine empire is a new enterprise, therefore there's not a great deal of literature. But here is one of the pioneering historiographers of the Byzantine empresses: French historian Charlotte Diehl has written a book as kind of a hobby about Byzantine empresses. I've chosen a chapter on Theodora, who was the empress at the time. The main focus is Euclid and events around Euclid in Byzantium.

In the early years of the 6th century, the notoriety of the actress and dancer Theodora was widespread throughout Constantinople. Little is known of her origins. Some of the later chroniclers say that she was born in Cypress, the hot passionate land of Aphrodite. Others with greater likelihood bring her from Syria. But whatever her birthplace, she came while still a child to Byzantium with her parents, and it was in the corrupt and turbulent capital that her youth was spent. Her family, equally obscure, is a legend. Out of reverence for the imperial rank which she attained, she is given an illustrious, or at least presentable, ancestry in the person of a steady and respectable father of senatorial rank. As a matter of fact, she seems to have been of humbler origin. Her father, if the secret history may be trusted, was a poor man named Acasius, by profession guardian of the bears in the amphitheatre. Her mother was no better than she should be, like many connected with the stage and the circus.

Into this professional household, two daughters were born, the second a future empress about the year 500. Early in life, Theodora came into contact with the people whom she was later to charm as an actress before governing as empress. Acasius had died, leaving his widow and his two daughters in very straightened circumstances. To retain her late husband's position, the family's only means of support, the mother found no better way than to take up with another man who should obtain the guardianship of the bears, and therefore look after the family and the animals. But the success of her plan depended upon the consent of Astarius, the head of the Greens, and Astarius had accepted money to support a rival candidate. In order to overcome opposition, Theodora's mother thought she might be able to interest the people in her cause, and one day, when the crowd was assembled, she appeared in the arena, thrusting before her her two little daughters.

The crowd threw flowers and she held out their hands in supplication to the spectators. The Greens merely laughed at the touching request. But fortunately, the Blues, who were always delighted to oppose their adversaries, hastened to grant the prayer which the Greens refused, and awarded Acasius' family an employment similar to that which it had lost. Theodora never forgot the scornful indifference with which the Greens had received her and Trudy[?], and from that moment began in the child the tendency toward long cherished rancor and the implacable desire for vengeance, which became so strong in the woman.

Thus Theodora grew up in the casual society of the hippodrome, and in the course of time was ready for her future career. The eldest of her sisters had made a success on the stage and Theodora followed in her footsteps. She went on the (?) with her big sister and played the part of ladies maid. She also accompanied her to entertainments where in the mixed company of the more public apartments she came across much impurity and indiscrete familiarity. Then she in her turn became a full-fledged actress, but she had no desire to be a flute player, a singer or a dancer like some of the others. She preferred to appear in living pictures in which she could display undraped the beauty of which she was so proud and in pantomines where her vivacity and her feeling for comedy could have full scope. She was pretty and rather small but extraordinarily graceful and her charming face with its pale creamy coloring was livened up by large, vivacious, sparkling eyes.

Little of this all-powerful charm is left in her official picture inside the Tower of Rivana. Beneath her imperial mantle she appears stiff and tall, under the diadem that hides her forehead, her delicate small face and the narrow oval shape, and her large, thin, straight nose invests her with a sort of solemn gravity, almost with melancholy. One feature alone remains unaltered in this faded portrait, and that is the beautiful black eyes that Procorpius speaks of under the harried meeting eyebrows which still illumine her face and seem almost to engulf it. But Theodora had something else beside her beauty. She was intelligent, witty and amusing. She had bohemian high spirits which were often exerted at the expense of her fellow actresses, and a pleasing and comic way with her that kept even the most volatile adorers firmly attached. She was not always kindly and did not stop at hard words if they would provoke a laugh, but when she wanted to please, she knew how to put forth irresistible powers of fascination. Bold, enterprising and audacious with all, she was not content to wait for favor to seek her out, but set forth consciously to joyously provoke and encourage it. And having but little moral sense, it was difficult to see where she could have acquired it, as well as a (?) degree, the perfect amorous temperament. She became an immediate success both without and within the theatre. Beyond her profession, of which virtue is not a necessary attribute, she (?), charmed and scandalized Constantinople.

On the stage she indulged in the most audicious exhibitions and the most immodest affects. (?) she soon became celebrated for her wild suppers, her adventuresomeness, and the number of her lovers. Soon she became so compromised that respectable people passing her in the street drew aside lest they should sully themselves by contact with a creature so impure, and the very fact of meeting her was considered an ill omen. At this time she was not yet 20 years of age. Suddenly she disappeared. She had a Syrian lover, Hekabulus by name, who was appointed governor of the African Pentabeles. Theodora decided to accompany him to his distant province. The romance, unfortunately, did not last long. For reasons unknown Hekabulus rudely sent her away penniless and without the necessities of life. The unfortunate Theodora for some time roamed all the East in misery. In Alexandria at last, she settled down for a while and her sojourn there was not without its effect upon her future.

The capital of Egypt was not merely a great commercial center, a rich and splendid city of loose habits, corrupt, the favorite abode of many celebrated courtesans. From the (?), it was also one of the capitals of Christianity. Nowhere else were religious quarrels more bitter nor theological disputes more subtle and heated, nor fanaticism more easily excited. Nowhere else had the memory of the great founders of the solitary life produced a richer flowering of monasteries, of mystics, and of ascetics. The suburbs of Alexandria were studded with religious houses, and the Lybian desert was so full of hermits as to be (?) its name, Desert of the Saints. In her moral distress, Theodora was not insensitive to the influence of the sphere into which circumstances had cast her. She had (pierced?) such holy men as the patriarch Timothy and Thedeus of Antioch, who preached especially to women, and it is not improbable that owing to them the penitent courtesan may, momentarily at least, have entered upon a purer and more Christian mode of life.

By the time of her return to Constantinople, she had become more sensible, more mature, and was weary of her wandering existence and of her wild adventures. Whether sincerely or not, she was careful to lead a more virtuous retired life. According to one tradition she was respectable and proper and lived in an unpretentious little house, staying at home and spinning, like (Matrix?) did in those Roman times. It was under these circumstances that she met Justinian. We cannot tell how much she managed to enslave and hold this man--no longer young, he was nearly 40--this politician in so delicate a situation with a future which must not be compromised. Precorpius talks of magic and philters, but that really complicates matters too much and leaves out of account the consumate intelligence, easy grace, humor and wit with which Theodora had conquered so many hearts. Above all it omits her clear, inflexible courage that was to influence so powerfully her lover's feeble and undecided character.

In all events, we know that the prince was comletely enslaved. They were madly in love. He refused his mistress nothing. She was fond of many, so he mated her with (?). She coveted honor and distinctions, so he persuaded his uncle the emporer to raise her to the high rank of patrician. She was ambitious and keen for power, so he allowed himself to be swayed by her advice and by the (?) instrument of her likes and of her hates. Soon he came to the point of insisting upon marriage. The good emporer Justin was not ruined (?) by her lack of noble birth and did not seem to have grudged his consent to his beloved nephew. The opposition to Justinian's scheme came from an unexpected corner. In her present mind, the (?) common sense of the Empress Eugenia was shocked at the thought of having Theodora as her successor, and in spite of all her affection for her nephew, in spite of her usual compliance with his every wish, on this point she stood firm. Though fortunately she died in 523 in the nick of time. Henceforth (?) just plain (?). Senators and high dignitaries were forbidden by law to marry women of such vile condition, inkeeper's daughters, actresses or courtesans.

To please Justinian, Justin abregated this law. He went even further when in April 527 he associated his nephew, Justinian, with him officially in the imperial power. Theodora shared in her husband's elevation and triumph. With him on Easter Day in St. Sophia, which we have just seen gleaming with candlelight, she was solemnly crowned. Afterward, according to the custom of Byzantine soverence, she went to the Hippodrome and received the acclamations of the people at the place where she had made her first public appearance. Her dream had come true. Such is the story of Theodora's youth. At least, that is how Precorpius tells it. And for some two centuries and a half, since the discovery of the manuscript of the secret history, this scandalous narrative has received almost universal credence. Must it therefore be accepted without reserve? A pamphlet is not history and (?) will inquire into the truth of these amazing adventures. Given the (?) that no one would invent such incredible things and that therefore they must be true. Of late years, on the other hand, intelligent scholars have at various times doubted the authority of Precorpius' unsupported statements and have made serious talk of the Theodora legend. Without wishing to reopen the question, or to belittle the value of some of the comments that have been made, I should hesitate to whitewash too thoroughly her whom the secret history has so outrageously blackened.

It is a pity that John Bishop of Athesis, who had access to Theodora and knew her well should, out of respect for the great ones of the earth, have omitted to give us full particulars concerning the (?) which the pious but (?) outspoken monks more than once, so he tells us, directed against the Empress. It is certain by all events that Precorpius was not alone among her contemporaries in criticizing her and that there were persons attached to the imperial court, such as the secretary Briscus and the prefect John of Capadocia, who knew the chinks in her armor. I do not know whether, as Precorpius states, she really had decided to use these (?), it appears such an unfortunate accident. It is certain at all events that she had a daughter of whom Justinian was not the father. This reminder of her sordid past did not seem, however, if you may judge by its success that this girl's (?) had at court, either to have (?) very much, or to have troubled the emporer. It is certain that Theodora's characteristics fit in fairly well with the stories that are told about her youth: the interest she took in poor girls in the capitol who had been led astray, more often through want than through viciousness, and the steps she took to rescue these unfortunates and to free them, as a contemporary writer puts it, "from the yoke of their shameful slavery," and also the rather contentuous harshness with which she always treated men, and if all this that is undeniable is admitted, it would be impossible to reject the secret history in its entirety.

But I was also obliged to believe that Theodora's adventures had the (?) and the variety that Precorpius invests them with, that she was, as in his account, a courtesan on a heroic scale, an angel of evil whom the devil permitted to go flaunting her life to and fro upon the rest. It must not be forgotten that Precorpius has a habit of investing his characters with an almost epic perversity and that although he tries hard to determine to a hair's breadth the lowest point to which Theodora fell, I for my my part regard her, though her interest may thereby be diminished, as the heroine of a less extraordinary tale. She was a dancer who had led the same life as the majority of her commonal agents, tired suddenly of her precarious amours, and finding a sensible man who could provide her with a home, settled down to married life and conjugal devotion, adventurous perhaps but at the same time astute, quiet and cleverness, she was able to keep up appearances, one who could marry even a future emporer without a (?) scandal. (?), I know, created just such a character and named her (Virginia Caramel), but it was not just Theodora who is of importance to us, for there is another, a less well known and a far more interesting Theodora, a great empress closely associated in all Justinian's works, who often played a decisive part in the government, a woman of high courage, of exceptional intelligence, energetic, despotic, proud, violent, passionate, complex, baffling, but always extraordinarily fascinating.

In the (?) from the Tower at Ravena, (?) the golden mosaics, we may still see Theodora in all the splendor of her majesty. The costume she is wearing is of unparalleled magnificance. Clad in a long purple violet mantle, with a broad border of gold embroidery flowering and glistening (?), she wears on her oiled head a lofty diadem of gold and precious stones. In and out through her hair are wound twisted strands of gems and pearls, while other jewels fall in sparkling sprays upon her shoulders. Thus she appears in this official portrait to the eyes of posterity and thus in her lifetime she desired to appear to her contemporaries. Seldom has upstart accustomed herself more rapidly to the exigencies of her newly acquired majesty. Seldom has (?) and sovereign loved and appreciated more thoroughly the many pleasures, the delights of luxury, and the little gratifications of pride which the exercise of supreme power can bestow. Very (?), always elegant, eager to please, she loved sensuous apartments, magnificant plays, marvelous jewels, and exquisite and delicate (?). She took careful and constant care of her beauty. To keep her face kind and serene, she lengthened her hours of sleep by endless siestas. To preserve the freshness of her complexion, she took frequent baths followed by long hours of rest, so she felt that her charm was the surest guarantee of her influence. Even though tenaciously (?) the circumstances of power, she would have her own court, her own following, her own guides and processions. Like the upstart she was, she loved the complications of (ceremonial?) and added to them. To win her approval, one had to be constantly paying court to her, to prostrate oneself at her feet, to dance the (?) interminably every day for (?) to get her hours of audience. Her theatrical experience had given her a taste for stage effects as well as the knowledge of how to attain them.

But (?) of being very happy, she inflicted jealously upon her rank and it doubtless gave her a secret delight to see so many great nobles who in former days had treated her more familiarity than the (?) over her purple buskins. It would be somewhat ingenuous however, to imagine that all this display, this apparent insistence upon etiquette must necessarily have excluded such adventures as those that Sidu has invented for his Theodora. It is certain that many mysterious things about which Justinian knew nothing could take place in the imperial (?)acium. The story of the patriarch Anfeminus which I had already related is proof of this. Nor would I be so foolish as to insist upon Theodora's post-marital virtue. Although as is well known it is always difficult to be certain on such points, I am not ready to believe that Theodora's life was without reproach. I am fully convinced that during her youth she went to (?) and I do not feel called upon to be scandalized if she picked it up and made her life. Justinian would have been the only person entitled to complain. But facts are facts, and one must take them as one finds them.

Now it is certain that no contemporary writers nor any historians of a later age--and it is these last who have strongly censored Theodora for her turpitude, her despotic and violent temper, her obsessive influence over Justinian, and the scandal to which her hetero(?) gave rise, not one of them recalls anything which cast doubt upon the correctness of her private life after her marriage, even Precorpius, who has so calumniated her, relating so fully the adventures of youth and telling with a notorious wealth of detail of her (?), her cruelties, her infamies, as one woman, even he, (???) when they wish to read the text, did not hint at the shadow of an amorous adventure after her marriage on the part of ths absolutely corrupt woman. I think it would be (?) that if the empress had given the slightest occasion the (?) would not have been backward in describing her (?) in detail. He has told of nothing of the sort because there was really nothing to tell. But this reflects no credit upon Theodora's moral qualities. Aside from the fact that she was no longer young when she ascended the throne--an Eastern woman at 30 is almost on the threshold of old age--she was too intelligent and too ambitious to risk compromising by love intrigues the position she had won for herself. Supreme power was worth taking some pains to preserve and the dignity of her life reflects quite as much upon her common sense as upon her moral qualities. But chiefly this courageous and ambitious woman who so eagerly desires power had other interests than the pursuit of vulgar amours.

She was endowed with several of the personal qualities which justify the striving for supreme power: a proud energy, a stern fixity of purpose, the serene courage that never failed her even in the most difficult circumstances. It was owing to these qualities that during 21 years she shared Justinian's throne she exercised a profound and legitimate influence over her adoring husband. One incident that must never be forgotten when writing about Theodora is the part she played on a tragic 18 January in 532 when the transient rebels stormed at the gates of the imperial palace and the distracted emporer completely lost his head and thought only of flight. Theodora was present at the council. In the midst of the general discouragement, she alone was (?) and self-controlled. At first she said nothing. Suddenly in the silence she arose, disgusted with the universal cowardice, and recalled the (?) emporer and his ministers to their duty. "If they were left me no safety but in flight I would not fly," said she. "(?) who have worn the crown should never survive its loss. Never will I see the day that I am not hailed empress. If you wish to fly, Caesar, more and good. You have money, the ships are ready, the sea is clear. But I shall stay, for I love the old proverb that says 'The purple is the best warming sheet.'" On that day when, to quote a contemporary, the very empire seemed upon the brink of destruction Theodora stayed desperately enthroned and in this supreme struggle when her crown and her life were at stake, ambition inspired her to real heroism. At this decisive moment, Theodora, by her (?) and energy, showed herself a statesman, and as has been well said, she proved herself worthy of a place in the imperial council which until then she had owed to the emporer's weakness. Henceforth, she never lost it, and Justinian did not begrudge it.

To the very last he was passionately devoted to the woman he had adored in his younger days and as he was completely under the influence of her superior ingelligence and of her strong and resolute will, he never refused her anything, either the outward show, or the real exercise of supreme power. Upon the church walls of that time, and over the gates of citadels, Theodora's name may still be read alongside of the emporer's. Inside the Tower at Ravena, her portrait is appendant to that of her imperial husband. And in the mosaics that decorated the apartments of the sacred palace, Justinian had (?) associated (?) with him in connection with his military triumphs and the (?) glories of his reign. The people erected statues to her, and officials did homage to her, as they did to Justinian, for throughout her life she was the equal of the emperor. (?) the most momentous questions, Justinian was pleased to take the advice of the most revered spouse whom God had given unto him, whom he loved to call his "sweetest delight," and her contemporaries are unanimous in declaring that she was unscrupulous in her boundless influence over the sovereign, and that her power was quite as great as his and perhaps greater."

There's more historiography on our agenda, and then we'll go on toward Bagdad. We won't get to Bagdad, but we'll begin to get some background on early Islam. I want to show you this best ever (?) I have ever seen -- the Wall Chart of World History, from earliest times to the present. This is a (facsimile?) edition. It was published in 1988. I don't know the dates of the earlier editions. It's a wall chart, not a book. It's in accordian form. [trying to fit it in room?] It starts down here on the lower level, there's this wavy line, now that's the (?) of time, then they marked each century about two inches, and on it goes, starting with the beginning of the world according to the fundamentalist version in the year 4004 B.C., just out of sight here, where you have these three, they look like snakes, Adam, Abel and Cain. They have Enoch and (?) and so on. ...It's small, just about 4 inches. And then, eventually, turn one page, it gets much bigger. So in each of these lines -- here's the biblical generations up above, and down below our cultures. For example, here are the dynasties of Egypt. Here is Assyria, Libera, Asia Minor...And then over these snakes there are little pictures, so you get a feeling for the place. The roots of the tree trunk indicate more or less the population. I've got a bifurcation on the screen ...This bar here, that's Alexander's conquest. To the left of it is the Persian Empire, about 2 inches wide from here, you can just see the edge of it at the bottom. And then there's Sparta, Athens, little line out of your sight for all these separate city states, polities of Ancient Greece. And this long bar where they're all unified. So this is kind of like a meltdown. To the left the caterpillar and to the right the butterfly, and then this very short-lived bar united all, which is Alexander's conquest. Then out of it we have, here's Egypt over the Tolomes, and Syria under the Salucids, and Asia Minor and so on. Then in this line in Egypt, each successor ruler, Tolome, is given a different color, so you see the length of their reign very graphically. Here is Tolome I Satir, Tolome II Philadelphus, and so on. This is an inspiring example and everything I talked about is somehow represented. I'm going to set this out here so you can have a look after the lecture.

Just a little more about historiogrpahy. I want to show you this new official definition of mathematics according to the American Mathematical Society. Here is a little article I did called "The New Mathematics." It starts with a quote by Alfred North Whitehead. He says, "Understanding is the aperception of pattern as such." And Gregory Bateson, who I mentioned last time, says, "What is the pattern which connects all the living creatures? The pattern which connects is a metapattern. It is a pattern of patterns. It is that metapattern which defines the vast generalization that indeed it is patterns which connect." He said that in 1979 while he was still professor at Santa Cruz, the year before he died. And here is the new definition that appeared in the American Mathematical Society monthly notices in 1988: "Mathematics is often defined as the science of space and number. It was not until the recent resonance of computers and mathematics that a new apt definition became fully evident: mathematics is the science of patterns."

I mentioned different names and never made a list, a chronology or a chronograph, but as this list will soon come to an end, let me do it now. Burkhardt, Inervesse tried to come up with a definition of crisis in 304 named steps that seeded such major transformations as the Renaissance or Alexander's Conquest. I mentioned Sir Flinders Petrie, who dug up Ancient Egypt, and his work is called The Crises of History. Sir Flinders Petrie published a book in 1911 called Revolutions of Civilization in which he proposed another step-by-step dynamical model for a major social transformation. In 1917, Louis Frye Richardson, a successful physicist and meterologist was called to service in World War I as a Quaker. He became a conscientious objector, went to France as an ambulance driver in World War I, and became convinced that war could be avoided by coming to understand it. He proposed mathematical models for the arms race, founding a whole field called Political Metrics, which was used by Gregory Bateson in 1935 in his idea of Schizmogenesis, coming from a perspective of a cultural anthropologist. I haven't mentioned Ludwig Fleck yet, I'll speak about him right now. Hopefully I'll end soon with a discussion of Rosenstat Kissi, I think maybe I mentioned him last time. His book is called Out of Revolution.

We're almost done with historiography here, just want to give an idea of this person who was succeeded by Thomas Kuhn. More people probably have heard about Thomas Kuhn. Kuhn popularized the notion of paradigm shift, particularly in the context of history of science, and therefore one could think seriously of applying the notion to history of mathematics too. Kuhn emphasized paradigm shift as a sociological phenomenon occurring within a community of scholars. People who get the new idea too early are expelled. Eventually there's sort of a quickening, an increase in the population of the subgroup interested in the new idea which, in the context of the history of science, is stimulated by, is demanded by data coming from the laboratory that doesn't fit the current paradigm. Many people would like to stick to the consensus, they can't stand the essential tension between the current paradigm and the new incoming data. One of Kuhn's books is called The Essential Tension.

Fleck was a medical scientist in Nazi Germany. In spite of being a Jew he survived the entire Nazi period because of his scientific skills. He was sent to Auschwitz, among other death camps, and there he was employed as a medical scientist, slave labor essentially, doing pretty much what he usually did anyway. His life was there. He saw his family go one by one to the showers, a one-way trip to the showers in Auschwitz. And then, when the camp was liberated by the allies, he went right back to work in the University of Levoff, his hometown. His book is called Genesis and Development of a Scientific Fact. It's his theory, it's a sociological idea about how a society changes its mind. It is related in the context of a particular example of a scientific paradigm shift that has to do with syphilis and the Wasserman test, a certain theoretical diagnostic for syphilis. He was involved in that kind of work in connection with Typhoid and other diseases. The syphilis example preceded [?] him a few years. I'll just give you an idea of the quality of his thinking and how this could possibly be used in understanding Euclid's voyage and the transformations that occur in a society when the foreign (toxic?) information from Ancient Greece arrived in a book. This is just about a page worth:

"This example exhibits three stages: (1) vague visual perception and inadequate initial observation; (2) an irrational, concept- forming and style-converting state of experience; (3) developed reproducable and stylized visual perception of form." He's talking about scientific research in a laboratory, so when the results come in, he's inspired by the hermeneutic concept that the experiment itself is formed in the concept of a theory. The results of the experiment can only be perceived in the context of the theory, and when there might be a mismatch that creates that essential tension, there might be a slight drift in the theory, then a slight drift in the design of the experiment, then a slight drift in the data that's obtained, then a slight drift in the perception of the data that's obtained, and all of this perception he is thinking of as a thought process and uses the metaphor of visual perception.

"This description demonstrates how a finding originates. Many research scientists will certainly recognize an analogy with their own method of research. The first, chaotically-styled observation resembles a chaos of feelings, amazement, a searching for similarities, trial by experiment, the attraction, as well as hope and disappointment. Feeling, will and intellect all come together as an individual unit. The research worker gropes, but everything recedes. Nowhere is there a firm support. Everything seems to be an artificial effect, inspired by his own personal will. Every formulation melts away at the next test. He looks for that resistance and seeks constraint in the face of which he could feel passive. Aids appear in the form of memory and education. At the moment of scientific genesis, the research worker personifies the totality of his physical and intellectual ancestors and of all his friends and enemies that both promote and inhibit his search. The worker, the research scientist knows that in the context of confusion and chaos which he faces, he must distinguish that which obeys his will from that which arises spontaneously and opposes it. This is the firm ground that he, as representative of the thought collective, continuously seeks. These are the passive connections, as we have called them. The general aim of intellectual work is therefore maximum thought constraint with minimum thought caprice. This is how a fact arises. At first, there's a (?) of resistance in the chaotic initial thinking, then a definite thought constraint, and finally, a form to be directly perceived. The fact always occurs in the context of the history of thought and is always the result of a definite thought style."

Well, there's a whole book to read and study here. Thomas Kuhn seems more readable, but still, in these works, it's very difficult to get the idea. What he's confronting is something like the Abidema. Abida was a meditation teacher who taught meditation based on meditation experience. In the meditation experience he figured out a lot about the thought process by simply paying attention, and the Abidema describes how an idea comes into your head. If you practice meditation and pay attention, you'll find that you are constantly being distracted from your meditation by an unwanted thought coming into your head. Abida dissected that process of a thought coming into your head by watching, and then watching some more, and then watching some more, and he wrote all of this down in the Abidema and the other text of the Polycannon. So here we have sort of the Polycannon of the research scientist. This man never came out of the lab. Hitler came and went. His family was dragged off to the oven, and he kept working in the lab. What he was doing was writing an inside report of the exact process of scientific facts coming into your head. It's a kind of psychology which can't be found anywhere else, where the visualization of all the ancestors is sort of the thought constraint within which you must find your way. Deviation from it is the cause of this very painful essential tension.

The mathematicians on our list in the History of Mathematics, Archimedes and so on, were all caught in this essential tension, in the struggle between the confinement and the thought process in the past, and opening the way for a new idea in the future. We can think of this as the psychological process of a bifurcation of this sort: a pitchfork bifurcation, or an explosive bifurcation, or a subtle bifurcation. If such a thing is happening in the history of consciousness, and you are a person lurking in that (review?) at the moment of the crisis in history or the revolution of thought or the paradigm shift or the bifurcation and so on, you have an experience that is relatively unique in history, due to the fact that these bifurcation points are sort of a discrete point set of measure 0 or practically 0 within the infinitude or continuity of all possible time. Nevertheless, within all of the rare moments that ever occured in the history of the thought process in that particular milieu, there are all these large numbers of previous instants in which people have felt the exceptional, and the exceptional was, as a matter of fact, the same. The dynamical systems theory in its program to give a detailed list and explicit mathematical model for all these bifurcations is, as it were, codifying, explaining, analyzing, modeling, presenting, groking the bifurcation process as it occurs in the consciousness of an individual person like you and me and everyone else.

And now...on to Bagdad. Today I want to blow up this part of the map from roughly 500 A.D. We have these main sections which, excluding Babylonian Egypt, the ancient prehistory, we started with Athens. Athens' mathematical and philosophical history ended in 529 when the Academies were closed by Justinian. In defense of Theodora -- they were married in 530 when she was 30 years old (she was born in 500) -- the closing of the academies probably wouldn't have happened when she took hold of the reins, because she was much more open-minded than Justinian or his father Justin. She came on the scene in 530, but in 529 the Academies were closed and that was the end of the Academy in Athens. The Academy in Alexandria somehow survived by converting to a Christian academy, and thanks to it, we have the famous case of Hypatia.

Maybe I didn't give Hypatia the attention she deserves in lectures on Euclid's voyage, because as you see in the first volume of Heath, an extensive history of all the (rescensions) of Euclid's Elements came to us, such as the Holy Eight Rescensions that we see. The most important and influential, especially during Medieval times, was that of Theon. Theon was Hypatia's father. He not only edited and probably improved them, he also wrote commentaries on Euclid, nourished them and saw to their survival. It's very likely that the editing on Euclid's Elements and other works, like Ptolome's Almagest, was actually done by Hypatia. It's a pattern in mathematics and in science that if a woman ever should find her way into an important position, her work would be abregated by men. Theodora's work in ruling the Byzantine Empire was claimed, or at least assigned by historians to have been done by her husband Justinian. She was torn apart by a Christian mob at the instigation of Bishop Fleural. She was the last of the pagan philosophers, and that was pretty much the end of the neoplatonic tradition in Alexandria, although there are some important figures in the history of mathematics afterwards who were associated with Alexandria, particularly Micomasa of Jurasa and Theon of Smyrna, another Theon. MAP BEING SHOWN HERE

It all comes to an end in 610 or 11 or whenever it was. In 620, 622, 623, the Muslim army arrives, invades the town and destroys the library, while Byzantium, just recently started, goes on forever. It exists to this day. The revival of the university in the time of Justinian held out until 1453, when the Ottoman Turks arrived and destroyed what had long been a kind of plug protecting Europe from Islam. That's the fragment of the main map, the map of the main stations we have looked at so far, and we're going to add Bagdad, which starts around 800. It has a prehistory in, we'll call it early Islam. Where do Euclid's Elements go? In 300, they go to Alexandria, and in 400 or 500, to Byzantium, and in 800, to Bagdad. There's the history of Euclid's Elements in Alexandria and then this history of Byzantium, and in order to understand the lifetime of Euclid's Elements in Islam, we need to have a little bit of a basic sketch of Islam before the foundation of Bagdad. I'll end with just this outline here. This is the part, early Islam, that I'm going to call (it all?) Bagdad, all between the beginning of Islam around 600 and the arrival of the book in 800.

We have four periods, I'll call them M, R, U, and A. The first chapter on the throne of Islam is the lifetime of Muhammed, and then the first four (Ahelid?), the early (Calif), and then the (Umayed), and the Otassid Dynasties. Under the Otassid Dynasty the foundation of the University of Bagdad is laid. It is modeled on the Alexandrian museum, the attraction of Euclid's Elements carried by hand by Louis the Mathematician and so on, that's the story that we will come to here. For these three periods we need just a brief sketch to understand the flavor of the thing. I recommend that you read about Islam somewhere, but let me warn you about one thing. There are many, many books on Islam, they can be sorted into two categories: those written by Muslims, and all the others. If you want to understand anything about Islam, you have to read those histories written by Muslims, because all the others share the same disgusting feature -- a very negative view of Islam. Everything is interpreted and twisted in a manner that makes the sense of Islam and the history of such a large part of the world completely incomprehensible. We're talking about a billion people here, occupying and controlling a large part of the inhabitable planet.

Here's the story of Muhammed. The idea is that the Jewish, Christian, and Islam religions are very similar, based on the same literature and basic story as seen from the perspective of Islam. The Judeo-Christian traditions begin with something correct, which then gradually deviates from truth and essentially disintegrates through a natural process. In order to maintain the connection between the human species and the divine, it is necessary for God to constantly be sending prophets to renew the message. Without actually criticizing the early Hebrews or the early Christians, Mohammed could claim that the religions of this tradition needed renewal. After his death the Moslems compiled an official list of 28 prophets, including all the ones mentioned in the Old Testament, and Jesus is on the list. His divinity is denied. This could be put in the context of a spectrum of opinions about Christology, between the Orthodox Church, the Monocruxites, the Monotelemites. What all these deviant Christian sects disagreed about is the exact degree of the divinity of Christ, or the exact degree of the divinity of Mary, or the exact degree of the divinity of the Holy Spirit and so on. Islam affirms the divinity of God and denies the divinity of Christ, but puts all these prophets who had a historical mission in coming to a certain culture at a certain time on a high level. Muhammed was one of these, according to the story, and he has the peculiar distinction, as the 28th, to be the last.

I don't really understand -- why is he the last? There are let's say 500 years between Christ and Muhammed, and 500 years after Mohammed we're still on our last prophet. They said that there would not be any more prophets, and there hasn't been one as far as I know. Anyway, Mohammed was born in 570 in Mukah of the Payosh, the tribe of Mukah. He married a wealthy woman, relieving him of some of life's stresses, had a family and so on. In 610 he had a vision in a cave outside Mukah, which was later called a vision of the Angel Gabriel. In this vision he was told that he was a prophet, basically, and that he had to go out and do the right thing. He didn't accept it immediately, but he did start telling friends about it. His wife died in 619 and also his uncle. These relatives were very powerful within the clan and had been protecting Mohammed from persecution for his heretic views in the context of Arabic religion, which is kind of an animistic and polytheistic religion. He was urging people to redistribute their wealth and saying that there is only one god.

When his protectors died, more and more violent persecutions began. In 622 he escaped to Medina where some of his disciples had gathered, and there he was made welcome and became a leader of the town. This is called the Hejra, and dates in Islam are in years A.H., Anno Hejra, the year of the Hejra, so this is 622, it's 622 A.D. and it's 1 A.H. They don't coincide exactly because the Hejra was in the summer and not on the first of January. In Medina, he unified the neighboring tribes around his ideas and became more and more a powerful military leader. Eventually the persecutors from Mukah followed him there and tried to stone Medina, and then the army of Mohammed went to Mukah to take it over, because Mukah was a pilgrimmage spot for the pagan Arabic religions long before Mohammed. In 629, an alliance between Medina and Mekkah was formed. That was the beginning of a United Arab -- I'd call it a kingdom, but I guess that's not the right word. Islam is really two things: a revolutionary political organization and a religion all in one.

In 632, in (Porshily?), Mohammed died. That precipitated the beginning of stage R and, as usual, a lot of bloody strife between the potential successors to the extraordinary military and financial power of such an organization. I'll continue with my tour to Bagdad next time, in the period of the early Califate and the Mirab Dynasty down to the beginning of the Odissids and the (??) of the mathematician.