Hypatia's Street Theatre: Act II



Scene 1. Cyril with Hierax, later with Hypatia. Cyril's Study -- which is furnished soberly, but with more opulence that the Prefect's Office.


Hierax: You summoned me, my lord.
Cyril: Yes, Hierax. It's about a criminal investigation ... a break-and-enter at Hypatia's house two weeks ago.
Hierax: Do they have suspects?
Cyril: Not yet, but it's too close for comfort. It happened on the day the two of us were watching the rehearsal of Hypatia's Meno-skit. What do you know about the incident?
Hierax: That day, a group of boys were going to Hypatia's house, in order to convince her that her skits were blasphemous. When I realized that she'd gone to the Prefect's Office, I ran to intercept them -- but I came too late: they'd already ransacked the house.
Cyril: Hierax -- for the last time! -- you must reign in those so-called boys. You have their confidence -- now use it.
Hierax: They listen to me only when I prod them on.
Cyril: Try threatening them with excommunication -- in my name.
Hierax: Their fury's blind as a sand-storm. They would blow me down like a dry weed -- and even these venerable walls (waving his hand around the room) would not resist them.
Cyril: (pacing around) Then we must pull the scorpion's stinger -- identify the criminal elements in their ranks and neutralize them.
Hierax: I could not be involved in this, or else I'd lose their trust -- and any hope of control.
Cyril: Leave it to me: the archbishop of Alexandria does have a few discrete, reliable men at his command. You'll see: in a month or two, your pit-bulls will be tamed ... (Hierax makes threatening grimaces and gestures to Cyril, who has his back turned) ... Now tell me: what's the latest from the street?
Hierax: That witch Hypatia and her foul-mouthed friends have set up shop downtown and treat the gaping passers-by to various Satanic satyr-plays: drums and screeches within earshot of my church -- and in this time of Lent.
Cyril: Real satyr-plays -- with nudity and all?
Hierax: I did not watch every detail. They've filled the air with incubi and demons -- who'd lustily slip into any orifice and take possession of a body. My church is almost empty, the parishioners are scared.
Cyril: Come, come, now -- and remember that you are their shepherd: if you just stand your ground, your flock will overcome its fear; but if you run, they'll panic. That's a law of nature.
Hierax: Can you do nothing to prevent this devilry?
Cyril: What do you expect?
Hierax: I thought the Church ...
Cyril: O yes, the Church is powerful -- as long as acts wisely. It cannot start a quarrel with the Prefect every time a certain pastor and his flock are spooked by things that go "bump" in the night. Especially with nothing else to go on -- no details ...
Hierax: I have some details of their odious skit: it is about a pagan sect called... let me see ... o yes, Pythagoreans.
Cyril: My, my -- good old Pythagoras. His harmless sect's been dead almost a thousand years!
Hierax: Pagan and harmless, sir?
Cyril: Before the coming of our Lord, this was a pagan world, my friend -- and yet we need to study it, if only to appreciate the present. It's part of the quadrivium -- you know: the studies following the trivium at the University.
Hierax: The University? Excuse my boldness, but it's said that you did all your studies with Theophilus, your illustrious and most saintly uncle.
Cyril: (with a bitter laugh) Is that what's being said? Well, between you and me, Hierax: my saintly uncle and illustrious predecessor was a celebrity -- a personal friend of Emperor Theodosius the Great -- he had no time for a mere boy. He sent me to a monastery ... but not before I'd had a few secular teachers ... like Hypatia's father Theon -- a kind old man, who drew me in with games and stories. Theon was no sorcerer, I'm absolutely sure, and Hypatia -- his daughter -- is probably no witch ... although admittedly she is an awful nuisance.
Hierax: Another detail just occurred to me.
Cyril: What is it?
Hierax: They prove some mathematical result and say that even Zeus is powerless to change it.
Cyril: Of course he is powerless -- since he does not exist.
Hierax: (grimly) They speak of Zeus but mean to slander God the Father.
Cyril: Their tongues are forked -- and their thoughts inflammatory, I agree. But legally there's nothing we can do when they malign a non-existing god.
Hierax: (Triumphantly) One pagan idol actually appears in their performance.
Cyril: (Startled) A pagan god on stage? That is enough to nail her!
Hierax: So, shall I contact the authorities?
Cyril: Leave it to me, I have a meeting with Hypatia this very morning. Maybe I can persuade her to cease and desist. But listen, Hierax -- though we can invoke decrees against them, the pagan gods no longer really threaten us. The common people need a place to congregate, and they will go to church just as their parents went to pagan sacrifice. Don't get me wrong: I very much respect this continuity which encompasses birth, marriage, death from one generation to the next ... and I am saying that beliefs don't really erode customs. But thoughts can undermine both -- and that's where Hypatia is so dangerous. Thoughts can stray like sparks and start a conflagration.
Hierax: All I can see is that she's arrogantly reaching for the stars.
Cyril: When we spoke to her collaborator, you said it well: the stars are out of bounds for Man -- and that's where we will have to draw the line.
Hierax: You stopped me then -- and I was worried I had made a mistake.
Cyril: Relax, my friend: arguing with the nephew of a rabbi just isn't my idea of casual conversation. I didn't want to follow through -- but you were absolutely right.
Hierax: You are so gracious, sir, pax vobiscum (turning to leave) ... but, if you'll forgive me, I would like to ask a question. It is unseemly to trouble you with trifles -- yet, try as I may, I cannot curb my curiosity.
Cyril: You make me curious to know what you're so curious about.
Hierax: A word, my lord.
Cyril: Goodness, Hierax, words are legion -- and most of them are innocent enough. Which word are you curious about?
Hierax: What exactly is the trivium?
Cyril: (proudly) It's what they teach you before you have hair on your chin. The language arts: grammar (extends his right thumb)... logic (index) ... rhetoric (middle finger).
Hierax: And the quadrivium follows that?
Cyril: Yes, it's a higher form of torture (using fingers of the other hand): arithmetic ... music ... geometry ... astronomy. An awesome foursome, isn't it -- but it all makes sense to the pagan mind: (repeating his finger display) : number at rest ... number in motion (yes, that's music) ... space at rest ... space in motion (that is, the celestial spheres). Never mind it, Hierax, it's all useless knowledge.
Hierax: But you said we needed it to appreciate the present.
Cyril: Only some of us still do -- the pilots of this great ship, Our Holy Church, in these times of change. Future generations will not need it any more. (A knock at the door)... yes, what is it?
Usher: A lady's here to see you, sir.
Cyril: Let her in. Please leave me now, good Hierax -- thanks for your vigilance ... and do try to control those boys of yours, the Guardians.

(Exit Hierax, bowing and limping. Enter Hypatia.)


Cyril: Good morning, madam, thank you for accepting my invitation. I think, this place is good and comfortable for a friendly chat.
Hypatia: I 'm pleasantly surprised to see so many books around your walls -- it makes me feel at home.
Cyril: This library belonged to my illustrious uncle -- and this is just its "public" part: most of the rarer volumes -- for instance, mathematics and astronomy -- are in another wing.
Hypatia: What a collection! (Throws up her arms in amazement.)
Cyril: We cannot always be as simple in our thoughts as we must be in our sermons...
Hypatia: ... or in our lectures -- oh, I know.
Cyril: You're famous for making complex theories seem simple and straightforward.
Hypatia: Some say, I relish complexity.
Cyril: Don't you -- a little?
Hypatia: My favourite state of mind is wide-awake tranquility. But, as you know, the mind is naturally restless -- call it Original Sin if you like -- and I would rather exercise it in a graceful way than leave it to its spastic worries.
Cyril: I quite agree. Please sit down. You see, we do have things in common -- and at a different time or place, we might ... For instance, if we were in Athens ...
Hypatia: You mean Athens now? Or in the time of Socrates?
Cyril: No, even now! In Athens we might still find opportunities for open philosophical debate in public -- no one would take offence.
Hypatia: (Pensively) I loved my years in Athens -- but I was younger then, and took its openness for granted.
Cyril: Have you ever thought of going back?
Hypatia: I have -- but it is just a dream.
Cyril: You'd find the Church less militant, and its Patriarch a kinder man than me.
Hypatia: I find it strange to hear you say such things.
Cyril: Hypatia, I am not blind. A new world order being born is not all light and sweetness: there is much struggle -- and even though I am among the mid-wives, and have to push and pull relentlessly, and without compromise, I'm still aware that this is messy business. When all is done and tidied up, I'm confident that you will look on us more kindly. In the meantime there is still Athens: it is a bit out of the way, and the Church is not pressing its case as strongly there as here.
Hypatia: My father's buried here in Alexandria.
Cyril: (startled) Your father! Now I see! (Gets up and paces around) Your father would be furious to see you tethered to his grave.
Hypatia: I am not tethered to his grave -- I am continuing his life.
Cyril: You need not stay in Alexandria for that. If you wish to remain on this shore, why not consider Ptolemais -- where your admirer Synesius of Cyrene is bishop. He'd welcome you with open arms. I hear he's ill and lonely.
Hypatia: What irks you so about my presence here?
Cyril: It's not your presence, nor what you think or do in private, it's what you do in public that offends. Your stock-in-trade is doubt, the enemy of faith.
Hypatia: How else can people separate the truth from falsehood?
Cyril: Learn to trust a little.
Hypatia: Trust any prophets -- true or false?
Cyril: Just now you've asked three questions in a row! In automatic imitation of that ancient trouble-maker Socrates, you question, question, question -- everything! I'll tell you what: the little people, whom you've never known, the ones who carry this whole Empire on their battered backs, the poor, down-trodden beasts of burden -- they have no time for questions, they want and need their answers pure!
Hypatia: But the root of any answer is a question, isn't it? Oops, I guess that was another question.
Cyril: My sheep need grass, their stomachs are not made for roots.
Hypatia: With due respect, my lord, it seems to me, your sheep should have a word to say in this: they might resent to be so firmly guided -- and rebel! I can't imagine a society that persists for any length of time without a healthy give-and-take of information -- including searching questions. My own concern is to revive the art of questioning in mutual respect and tolerance.
Cyril: Before it can afford such fancy ornaments, society needs concensus. Don't forget that your great model Socrates -- as well as Plato, Aritotle, Stoics, Epicureans, and so on -- did blossom in a context that was centuries old, and sure of its consensus. When our new order reaches that maturity, it will be even more respectful of dissenters -- and indeed will love them like lost sheep.
Hypatia: I hear the message, but -- alas -- my doubts remain.
Cyril: Doubts -- doubts! Have you no faith?
Hypatia: Of course I do!
Cyril: In what?
Hypatia: Faith has no object.
Cyril: Is there anything you believe without knowing it?
Hypatia: Yes -- for instance that the universe is harmonious and ultimately understandable.
Cyril: And people naturally good?
Hypatia: Naturally imperfect -- but perfectable.
Cyril: An ivory tower fantasy! In real life, greed and deceit are everywhere -- goodness is the exception. As for your harmonious universe, you ought to spend a couple of days hungry and barefoot in a stony desert -- as I have done.
Hypatia: I did visit your desert, Cyril, and your market crooks -- they did not shake my simple faith. Unlike you, I am not burdened by dogmatic armor-plate. Don't let it crush you, Cyril ...
Cyril: Then let me change the subject: in your latest skit, a pagan god appears, I'm told.
Hypatia: It is Apollo, god of light and harmony -- a theatrical device, which we could easily omit.
Cyril: Too late -- the felony has been committed. I'll have to ask the Prefect to review your permit.
Hypatia: So be it, Cyril: both of us have strong convictions -- neither can back down, because we each are public symbols. You aim for correctness, while I strive for clarity -- and the two don't mix. It's easier for me to fight all out because I have no power -- I could not crush you. Your part is more difficult: one swipe of your paw and I am dead. However, come what may, I will not hate you -- I'll always see you as a boy in Father's study -- so full of life and curiosity. In my poor pagan way I, too, do recognise lost sheep.

(Exit Hypatia. Cyril follows her toward the door. Alone, he kneels and prays with fervent concentration.)


Scene 2. The Pythagoreans.

There are two panels hanging in the back-ground. The one on the right shows a dissection proof of the Pythagorean Theorem, with five colours. The one on the left shows the Pythorean triangle with its three surrounding squares -- all equally tiled, but coloured yellow (the smallest), blue, and green (the one on the hypotenuse), respectively.


Hypatia: Welcome spectators! Today we'll take a long step back in time -- over nine hundred years -- and visit the Pythagoreans. They were a small community, a kind of sect, with strange beliefs and customs, such as: sharing things communally, not eating meat -- in fact not even beans -- and leading simple, truthful lives. More strangely yet, they thought the universe was based on mathematics.

We want to show you something that unsettled their beliefs -- in fact, it still has repercussions in our time -- but we also wish to entertain. So to make you smile, we'll make them look a little more ridiculous than they were ... Look, here they come, led by Pythagoras himself.

They march in to the strains of Beethoven's Turkish March (from The Ruins of Athens), and singing.

Chorus: All is number, number is all, there's nothing that cannot be quantified;
           all is number, number is all, reality is just a dream;
           all is number, all is number: earth, and sky, and stars, and thunder;
           all is number, number is all, things aren't as messy as they seem.


           Come live with us and share what you have -- shed your belongings,
           study, study, wonder -- study, wonder, wonder.
           Come live with us and share what you have -- shed your belongings,
           purify your soul and body: study, study ...


           All is number, number is all, there's nothing that cannot be quantified;
           all is number, number is all, reality is just a dream;
           all is number, all is number: earth, and sky, and stars, and thunder;
           all is number, number is all, things aren't as messy as they seem.

Samuel: (As Pythagoras, paces, hops, and skips) Even space is ruled by number -- look at how we measure it. We even track the stars by their degrees and minutes (manipulates an astrolabe). And time as well: hours, minutes, seconds -- and even finer intervals: show us, my lad (a drummer beats out 4/4 time, then 3/4, then the two together, then rapid polyrythms).
Dario: This could become too rapid for a proper count.
Samuel: Yes, so it seems, and yet the drummer's hands are perfectly at ease: somewhere in him the proper count is made... And even melody -- the stuff of dreams -- is just a dance of numbers. Look: here's a pipe that's 60 notches long, a shorter one of 48, another one of 40, and the smallest one of 30. Listen! (Plays a major triad). In hearing this as harmony, our ear is recognising a numerical relation. Here: let more skilfull players show us how it works.

More explanations may be given: the tonic (do) has 60 "notches", then follow: 54 (re), 48 (mi), 45 (fa), 40 (sol), 36 (la), 32 (ti), 30 (do'). It is a matter of ratios. A simple round ("Row, row, row your boat..."?) is hummed with pan-flutes and harp accompaniment.

     Toward the end, a moan is heard which gradually becomes a wail.

Lydia: (cries out) I can't stand it any more!!
Several: What's bugging her? -- Shh, don't disturb the Master. -- What's troubling you, sister?
Lydia: Let me out of here! I can no longer take this idiotic incantation: "all is number". It is so sterile, stupid, narrow-minded. The shadow moving on the sun-dial knows no hours or minutes -- and neither does the sun. Numbers are imposed on these grand spectacles by your sterile, petty minds.
Dario: No -- numbers are behind it all, but our imagination dresses them in pretty costumes -- to satisfy its thirst for thrills and grandeur. Haven't we just seen how music is but numbers set in motion, while we are blissfully adrift in melodies?
Lydia: My bliss is not a number -- brother -- nor is my pain. I came to this community so full of confidence and hope. (Facing Samuel) O Pythagoras, I hate this tunnel-vision!!
Samuel: I understand, my child, but please remember: bliss and pain are private. We don't presume to meddle with that sphere. What we attempt to grasp with numbers is the outside world, where we must find patterns to explore.
Lydia: Do all patterns need numbers? Look at the space we move in (takes some graceful dancing steps), that mysterious medium (grabs a yard-stick), which by your tunnel-vision is reduced to this! (Brandishes the stick, flings it toward Dario, and stomps out.)
Dario: (picks up the stick) Alas, poor yardstick, clumsy metaphor -- crude, material echo of the ideal number-line.
Samuel: (rhapsodically) O infinitely slender line -- crowded with points -- infinitesimal dew-drops, in infinitely many perfectly spaced arrays.
Dario: Not as sparse as on this poor stick, whose gaps could be divided into ten ...
Several: ... or sixty ... or nine hundred fifty-one ... or a zillion ...
Dario: ... equal parts. And even the minutest gap is filled with infinitely many points, each having its own name. No number is left out, and no gaps remain.
Samuel: That, my friends, is plenitude -- a truly cosmic yardstick.
Hypatia : (steps forward) Your line has numbered points so plentiful it staggers the imagination. However, though it has no gaps, could it not have cracks -- I mean, unnumbered places?
Several: Cracks in the number-line? She's cracked herself! A wise-cracking crack-pot!
Samuel: She is no novice, let her explain herself!! Our task -- remember -- is to listen carefully, and show her where she's wrong or see where she is right. There is no other road to truth. Speak, sister, tell us what you think.
Dario: But stay away from smoke and mirrors: we can't accept phantasmagoria from the world of senses and illusion.
Hypatia: Then what about geometry? Look over there: the Master's favourite theorem. The two upper squares (points at them) make up the same area as the lower one. That's all it says -- no more, no less -- and nothing about numbers.

The Dissection Pantomime. The five coloured shapes (cardboard) shown in the right panel are first displayed as the two squares on top of a right triangle, and then reassembled to form the square under its hypotenuse -- with gestures indicating why the fit is perfect .


Several: She's changing the subject! I want to see those cracks. She's wasting our time.
Samuel: Please pay attention! And let there be music.
Hypatia : Patience: we'll get back to the number-line.

While the pantomime continues, another round is hummed. Re-enter Lydia, remaining on the side-lines, drying her eyes, but listening attentively

Samuel: We are not conscious of the numbers in this music -- yet we know they are there. Likewise we shall, in time, discover them behind the theorem we just saw.
Hypatia: If I want to make a set of pipes, I do need the numbers. But that theorem stands by itself, without numbers.
Dario: No numbers -- and no use! But over here (points at the other panel) we have them both.
Hypatia : The venerable 3 - 4 - 5, as ancient as the Pyramids: 3 times 3 plus 4 times 4 equals 5 times 5. A mathematical cliché.
Dario: And eminently practical. Yes, the Pyramids themselves were built with it. But we have gone much further. Look at this (pulls off the top layer of the left panel, revealing an analogous diagram with 39 - 80 - 89) -- the numerical version of that shape over there: 39 steps along one side, 80 along the next, and 89 on the bottom. We have long lists like that. No airy-fairy theorems to gape at -- but solid information digitalised for error-free transmission.
Lydia : I prefer digitalis on a mountain slope to you obsessive digitalisation. Why must everything be so rigid? Why not allow a little softness?
Dario: Approximations are inevitable at the interface between our theory and the world -- but inside the theory, they're intolerable. Would the Treasury accept an abacus which sometimes lost a bead or two? Would you accept to drift off course and end in shipwreck on your cruise to Syracuse?
Hypatia : In your example there, the 39 is almost half of the 80 -- but not quite. You'll never get one side exactly half the other -- or two the sides exactly equal.
Dario: It's true we'll have to cut things very fine, take many tiny steps along each side. We still need more research -- that is all.
Hypatia : It isn't possible.
Dario: Go try to prove us wrong!

Hypatia : Alright then. Shall we take the case in which two sides are equal? This one here (pulls down the panel on the right, revealing another one underneath). It is the simplest case of the great Theorem. You'll never digitalise it.
Dario: Why not? Look here (reveals another panel on the right): this has 20 and 21 -- that's almost equal -- and 29 along the bottom. And we can do better by cutting it finer -- to 119, 120, and 169, for instance.
Hypatia : You'll never get them perfectly equal. Some triangles are simply incommensurable.
Dario: What is that supposed to mean?
Hypatia: You cannot go around them with equal steps and without cutting corners -- no matter how you tip-toe ...

Lydia: (stepping forward) How can you say "no matter how"? Do you have a crystal ball? Can't you imagine that scientists -- by parallel computing with thousands of abaci or as yet unknown devices -- will one day figure out how many steps it takes to go around your silly triangle?
Hypatia: It cannot be today and cannot be tomorrow. Even Zeus is powerless to change that.
Lydia: Thus speaks a narrow mind. For me tomorrow has no limits.
Dario: Hold it, sister! We don't want to lose the argument by over-stating our case. For instance, there will never be a biggest of all numbers -- not even in a thousand years.
Hypatia: And likewise there will never be a number counting steps around this triangle -- which happens to be half a square. (Holds up a yellow square and folds it along the diagonal.)
Dario: Why not?? I can imagine coming home one day and saying to my wife: "today we did it!" "What? she'd say" daubing more powder on her nose. "We've made a square," I'd say, "with blah-blah units on each side and yada-yada of the same units along the diagonal. All whole numbers, no loose ends."
Hypatia: "Poor darling", I would say, if I were she, "come, have another beer. I've heard you talk about your project many months, and I've been telling you it cannot work. But you won't listen to a woman."
Dario: Hey, this is fun! Can we continue in this vein? I'd say: "today I'll listen, 'cause we have the answer".
Hypatia: "The answer is blah-blah and yada-yada"?
Dario: "The actual numbers are a secret. My assistants wrote them down -- they're huge. The boys computed endlessly -- grinding through case after unsuccessful case, until they found the smallest one that worked."
Hypatia: "You're sure you have the smallest case?"
Dario: "Absolutely! All the lesser ones were rejects."
Lydia: (to Hypatia)Why are you beating round the bush?
Hypatia : To corner him -- just watch. (Holds up a blue square with twice the area of the yellow one.) Here is your blah-blah square and this one is the yada-yada -- exactly fitting the diagonal of blah-blah. Now we take a ruler with yada-yada units marked on it (picks up a yardstick and sweeps it across the blue square) and draw yada-yada horizontal lines across the square -- and then once more but vertically.
Dario: "That's very entertaining, dear, but what's the point?"
Lydia: She's put a grid of lines over the square. So what?
Hypatia: Please don't keep butting in on our marital debate.
Dario: You'll see, fair lady: right or wrong -- my wife will win the argument.
Samuel: No sarcasm, please -- neither ad hominem nor ad feminam: we're all listening to make sure the game is fair.
Hypatia : Thank you, Master. (To Dario) Now the blue square's covered by a myriad of tiny tiles -- and we can do the same, with tiles of the same size, for the yellow square, which -- having half the area -- will have exactly half as many tiles. Do you agree?
Dario: "You're brilliant, dear," I'd say, "you've turned my little steps along the edges into little tiles covering the areas. Yes, I agree: the blue one would have twice as many as the yellow one. Is dinner ready?"
Several: This isn't going anywhere. She's teasing us. No -- she is boring us.
Hypatia : (tears the blue square down the middle) Each of these pieces has as many tiles as does the yellow square. Do you agree?
Dario: Alright, alright.

(Hypatia folds one of the blue rectangles in half to make a smaller square, which she holds up together with the yellow one.)


Hypatia : This little blue one has exactly half as many.
Dario: What are you trying to say?
Hypatia : (emphatically) Your example was not the smallest! This one here (shakes the yellow square) is now the double square, and it has fewer tiles than yours.
Dario: (startled) Could it be the boys have overlooked this case?
Samuel: No! What she just did could be done with each of your examples. She'd always make a smaller one. It would mean that there is no smallest one.
Several: This is insane. How can you pare them down ad infinitum? If there is no smallest, there ain't any.

Lydia: But she cheated!
Dario: Where?
Lydia: When she tore the yada-yada square in two, she could have ripped right through a row of tiles instead of neatly separating them.
Hypatia: Good try, sister -- but I've come prepared for this objection. (Spreads out a square kerchief as shown on the right.) This would be your scenario -- but remember: the yada-yada square had twice as many tiles as the blah-blah. So, they would have to be divisible into 2 equal parts.
Dario: Your model seriously underplays the size of yada-yada.
Hypatia: The principle is still the same: if we omit the red tile in the centre, we can easily divide the rest in two -- but then the red tile is left over. So, this scenario would not apply to your example.
Dario: I'll be darned.

Samuel: (jumps up and starts pacing around) Now, by Apollo, I begin to see the light -- and it is blinding me!!
Dario: What's wrong?
Samuel: There is no such example!
Lydia: Why is that so important?
Samuel: We can't even measure sides and diagonal of a simple square with the same yardstick. And this is just the tip of the iceberg! Our whole digitalization programme will founder on this. (Slaps his forehead with his palm.)
Lydia: When the Master acts like this, he's totally upset.
Samuel: Of course, a double square number cannot itself be a square. How could I've been so blind -- not seen this simple connection? (Drops on his knees and hides his face in his hands).
Lydia: O brothers, sisters, come! The Master is not well. (Commotion among the Pythagoreans).
Dario: (to Hypatia ) Now look what you have done! (to Samuel) But she hasn't shown the so-called cracks in our number line.
Samuel: (still kneeling, shaking his head) Yes, by Zeus, she has!
Dario: I don't get it.
Hypatia: If blah-blah's on the number-line, there is a crack where yada-yada should have been.
Samuel: (lifting his arms) Help, Apollo, help, what shall we do?
Apollo: (appears in radiant light) Switch to geometry! (Paces, hops and skips) All number is geometry, but not all geometry is number.

As the dissection pantomime starts up again, the Pythogoreans rise and march out singing. Pythagoras goes last, scratching his head.

Chorus: Geometry, o geometry, Apollo will show us the way to thee;
           geometry, o geometry: new mysteries to be explored.
           number is all geometry, but not all geometry is number
           geometry, o geometry, we'll never ever will be bored.


           Come live with us and share what you have -- shed your belongings ...

Enter Hierax, shouting, running on stage. He tears off Apollo's sun-crown.


Hierax: Vade retro, Satanas! Down with idolatry!
Dario: Hey, take it easy. (Hierax attempts to pull down the back-ground panels). Stop this man!
Hierax: (over-powered) Pagan scum, you'll pay for this!

Hierax exits cursing. Two cops appear.


Cop 1: Everybody freeze. Stay where you are. Who is your director?
Hypatia: I am the one responsible.
Cop 2: Then you're in trouble, madam.
Hypatia: We have a permit to perform here -- look.
Cop 1: Our orders are to take you into custody. Please do not resist.




Scene 3. Hypatia and Orestes.

Orestes sits at his desk in the Prefect's Office. Enter Hypatia in prison garb. He gets up and goes toward her. She remains stiffly distant.


Hypatia: (resentfully) Look at me, sir! Your permit did me no good.
Orestes: This should not have happened. I'm very, very sorry -- but I must assume responsibility. All I can do now is resign ...
Hypatia: No, no, Orestes -- don't make matters worse. Responsibility obliges you to stay -- and endure setbacks like this.
Orestes: What did they do to you, Hypatia?
Hypatia: Tore up my dress while searching me for arms. (Pauses) That place was horrid -- full of stench and screams -- my heart goes out to its poor inmates -- one day in there atones for many crimes.
Orestes: (softly) Believe me, Hypatia, I did all I could. The night I spent was not as horrible as yours, but it was torture too.
Hypatia: (after a pause) I do believe you, friend -- I'm too worn out to think straight.
Orestes: (holding out a small chalice) Take one of these, Hypatia. It will make you feel stronger.
Hypatia: (Takes a candy) How did you get me out?
Orestes: I had you brought here for interrogation -- that's what I told police.
Hypatia: O yes -- it made them quite excited to have a prisoner going directly to the Prefect's Office. They gave me breakfast and allowed me to clean up; they even made me change into a brand new prison dress. (Strikes a fashion model pose) Now shoot!
Orestes: (eyes rivetted on her) Shoot what?
Hypatia: Start the interrogation.
Orestes: I have revoked your street performance permit.
Hypatia: That is not a question, it's a statement -- an unwelcome one at that.
Orestes: It's either this or there'll be riots -- and you, Hypatia, might get hurt.
Hypatia: So, does that mean my acting career is over?
Orestes: Not necessarily. I've spoken with the management of our civic theatre: they say they'd be delighted to try your mathematical comedies -- at least they're something new and different. And I assured them that there is a lot of interest in your plays, that they elicit controversy...
Hypatia: ... yes, demonstrations against "blasphemy" and for "freedom of expression", and even fisticuffs -- did you tell them that as well?
Orestes: I don't think that they need to be concerned. The university, the library, and the beach protect the theatre on three sides; the fourth side points toward the merchant-quarter. It is a quiet place, far from the crowds.
Hypatia: And from my audience ... I don't like it -- I must stay close to the people: that's the whole point.
Orestes: Your audience will follow you. Those skits of yours have really made a splash -- no one can quite explain it. One of my scribes overheard young people in a tavern argue about incommensurability -- imagine that -- and my cook told me of a woman selling "Doctor Lovestrength's Earthy Girth Tea".
Hypatia: Such effects will quickly fade when we are are tucked away in the Theatre. I do not like it.
Orestes: You have no choice.
Hypatia: Are you pulling rank on me?
Orestes: No I'm admitting defeat ... Don't you see that I have no one backing me up? The Emperor is just a kid -- his mother and sister are lunatics. The power of this State is in the hands of bishops. They rail against government -- except when it helps them -- and in their Councils hammer out the rules we all must live by ... All I have going for me is a little shred of Roman Law.
Hypatia: Yes, I've seen this coming -- while not wanting to believe it. What about my project then?
Orestes: Those who are curious about your plays will not mind going to the Theatre. And yes, I forgot to say that there'll be free admission, sponsored by the City -- to keep disorder off the streets.
Hypatia: O my, I never thought I'd cause disorder. How did it come to that? (Straightens up and resumes her seductive pose). This is a strange interrogation, Governor: the prisoner asks most of the questions.
Orestes: Okay, now it's my turn. The whole world knows that Alexandria is a crazy place, but if you'd told me a few months ago that we'd have civil unrest caused by mathematics, I wouldn't have believed it. Are you a sorceress after all? What is your special magic?
Hypatia: No magic and no sorceress, my lord. I like to contemplate, to dream, to understand -- and share the fun of it with others.
Orestes: But some of them don't think it's fun -- apparently they think it's dangerous.
Hypatia: Or simply scary. There's been a lot of change in recent years, and -- as the Bishop says -- most people have no time to sort it out and get acclimatised.
Orestes: So, knowing that, why do you play with fire?
Hypatia: To help you regulate it, Governor. The fire is there anyway, it's spreading underground -- and if we cannot harness it, it will one day engulf us.
Orestes: Let's be concrete. Why does your latest skit -- the Pythagorean one -- inflame the minds instead of calming them?
Hypatia: It isn't black and white like that: only the flaming minds are visible, while the cool ones go home quietly -- the will become more numerous in time.
Orestes: By emulating the Pythagoreans?
Hypatia: Why not? They were models of virtue. They lived communally -- much like the Christians of two hundred years ago -- and were concerned with purity and wisdom.
Orestes: They also worshipped Reason.
Hypatia: Not exclusively. They realized that reason is necessary -- but knew as well as you and I that it will never be sufficient. Besides, Reason is a tolerant Goddess, imposing but few -- albeit ironclad -- constraints. The rest is freedom.
Orestes: Alexandrians hate all constraints.
Hypatia: But seem to love dogma ... The Pythagoreans, on the other hand, were free to shed their dogma -- that the whole world could finally be understood in terms of numbers.
Orestes: Many people still believe that -- and pride themselves in being practical.
Hypatia: It is a reasonable working hypothesis.
Orestes: And you are undermining it in particular and dogma in general. The solid ground on which our daily lives are built -- yes, yours and mine too -- is turned to quicksand by you sorcerer's apprentices.
Hypatia: No, Orestes -- we're masons broadening a bridge over the quicksands of fear. Our latest skit exposes the hard texture of the stones we use; and shows that those who cross the bridge -- like the Pythagoreans -- are not just swallowed up by chaos.
Orestes: So, why and how does it inflame the passions?
Hypatia: As I said before: not all passions are inflamed. As for those who are, your guess will more astute than mine.
Orestes: Quite frankly, anything that happens in this town without the blessing of the Bishop is anathema to him -- no matter what it is -- and his obedient flock will tear it down.
Hypatia: Doesn't it need specific irritants to rouse its wrath?
Orestes: Of course, and they must be rubbed under its noses. For your latest skit, here are a few that might be relevant: Pythagoras holds a staff, in mockery of a bishop's -- he lifts an astrolabe, a well known instrument from hell -- his followers recant their credo, encitement to apostasy -- their way of life is reminiscent of the Gnostic heresy -- but worst of all, you are involved in it: the whole thing smells of pitch and sulphur.
Hypatia: I am amazed.
Orestes: You are so innocent, Hypatia. To converse with you makes me feel twenty years younger. What would I do without you?
Hypatia: Come, come now -- don't exaggerate.
Orestes: (shaking his head) If you but knew what trash is normally discussed within these walls! ... But listen: Cyril's letter to me mentions a more serious matter. The notion that the human mind can see constraints which even the Almighty must obey ... smacks of Promothean arrogance, he says. It undermines the people's simple faith.
Hypatia: Does he think the Almighty can make 2 plus 2 equal 5? Or that it pleases the Creator to tease us with nonsense?
Orestes: I cannot speak for Cyril, but I know him well enough to make a guess. He does not fault your reason, but your morals: certain ideas are for adults only -- it is immoral to let children play with them. (Pauses, sighs) Please forgive my cancelling that permit -- you know I had no choice.
Hypatia: (steps closer, lightly puts her hand on his head) Poor Roman Prefect!
Orestes: No -- poor Roman Empire!
Hypatia: (resolutely) I also have no choice: I have to carry on my public work.
Orestes: Who forces you?
Hypatia: I made a sacred vow.
Orestes: You mean that solemn promise at your father's death-bed ...
Hypatia: The whole truth is much heavier, Orestes: I am atoning for betrayal.
Orestes: How can that be?
Hypatia: I failed my father when he needed me -- abandoned him, refused to help and comfort him, because in childish spite I felt abandoned.
Orestes: As I see it, you just soared into spheres he was too old to enter: the novelties of Diophantus and -- in your own words -- the old mysteries of Apollonius. It's wonderful when children can outstrip their parents, and I know that he was very proud of you.
Hypatia: I was proud of myself as well -- too proud. You see, throughout my childhood, Theon was my teacher and my play-mate; later he became my closest friend, but still remained my play-mate. We had such fun rewriting Euclid's Elements, and penetrating into Ptolemy's Syntaxis.
Orestes: Although I saw it only from afar, you did appear to have a lot of fun.
Hypatia: And I was very hurt when it was over.
Orestes: Did that happen suddenly?
Hypatia: Yes, and you witnessed it. You were sixteen when the Serapeum was torched and razed to the ground on orders of Archbishop Theophilus.
Orestes: I do remember how apalled I was to see monks behave so arrogantly. How they gutted that gem of architecture, and left the city scarred. You were away -- in Rome, I think...
Hypatia: ...that's right. The trip had been my twenty-first birthday present.
Orestes: Your father had friends among the defenders inside the temple. He did not sleep for days. My lessons didn't start again till you'd come back and taken over.
Hypatia: Yes, you became my charge -- my son, as it were -- but I was left a waif.
Orestes: I must admit I liked the change: at day I studied the quadrivium with the most beautiful woman in the world; and at night ran secret errands for her father to the bishop's residence. I took me years to figure out what I had been involved in.
Hypatia: What do you think it was?
Orestes: Smuggling pagan books -- from the Serapeum's collection of a hundred thousand volumes. The Archbishop and your father had cooked up a book salvaging scheme. Theophilus loved pagan books, but this adulterous love had to be kept secret ... The packages were always sealed -- I was kept ignorant of the crime.
Hypatia: You were just a boy ... but there was more to it.
Orestes: What was it?
Hypatia: The artifacts in the Serapeum -- especially the giant statue of the bull -- were stuffed and spiked with precious stones and metals -- the wealth of rural Egypt, scraped from villages up and down the Nile. (angrily)Theophilus controlled most of this loot and used it -- through my father -- to buy back books from other looters. Thus at least some of the library was reassembled.
Orestes: Where is it then? (sarcastically) I bet, Cyril has it now.
Hypatia: (spitefully) And some of it is in my house...
Orestes: (startled and uneasy) What? How did you get it?
Hypatia: My father learned to bargain. He came back with more than he delivered to Theophilus. Useless books: written in Egyptian, Aramaic, Sanskrit, and other useless languages; and worthless artifacts: trinkets, statuettes, masks, urns, and chalices made of wood, clay, and other worthless materials.
Orestes: But that's State Property -- you can go to jail for keeping it!
Hypatia: (exploding) I have just been to jail, my lord, and spent the night in urine, excrement, and vomit. State Property -- you meat-head! (tugs at her prison garb) Look what your rotten state has done to me -- and I did have a permit. Our saintly Cyril needs no permits for his machinations -- he's naturally immoral -- nobody bats an eye. You've all gone crazy -- let me out of here! (storms toward the door)
Orestes: (runs after her and catches her by the arm) You can't go on the street like that -- they'll arrest you again.
Hypatia: (immobile, with head bowed) Orestes, let us count to ten before we speak again.

They silently count, looking in opposite directions. Then (Orestes first) they turn toward each other.


Orestes: Hypatia, you are right: this job is driving me insane -- I have internalized the double standard. (Sighs)What can one do when lawlessness reigns in the highest circles?
Hypatia: (sits down) Keep all those things in trust until our rulers can be trusted.
Orestes: So ... Theon fed Theophilus with books, and greedy monks with precious stones -- while building his collection...
Hypatia: ...for a future popular museum.
Orestes: And he gave lessons to the bisop's nephew Cyril, while leaving me with you.
Hypatia: He never had more than one private student.
Orestes:Theophilus must have wondered why this distinguished scholar was doing him such favours.
Hypatia: He was too vain to wonder why the world lay at his feet ... but he did offer something in return. (Pauses) He promised to protect the scholar's daughter -- and he kept is word. (Pauses, eyes down-cast) I did not know about this until recently.
Orestes: So you were free to reach for the stars. It's like fairy-tale!
Hypatia: Without the happy ending... (Hesitates) One evening I found my father lying on the floor: he was already dead.
Orestes: And your vow?
Hypatia: That's when I made it -- but it was too late for him to hear. (After a long silence she gets up) I think I'd better go now.
Orestes: You can't go on the street like this (points to her prison garb). They'll put you back into the slammer right away. Here, take this hooded cloak -- and may the force be with you.
Hypatia: (puts on the cloak) What force?
Orestes: (gets up) Need I name it?
Hypatia: (softly) I love you too, Orestes -- but it is too late for us. (Exit Hypatia)




Scene 4. Hierax's Rant.

Evening on the market square. Juggler, flower-girl, belly-dancer, Dario, two or three monks. Hierax comes limping in, climbs on a box and starts a public speech. Hypatia scurries across the scene dressed in her cloak, stops in a corner of the stage and listens intently.


Hierax: Friends, Alexandrians, lend me your ears; I 've come to call for freedom, not oppose it. You may have heard it said by evil tongues that I and those who think and feel like me are enemies of freedom. I know you don't believe such calumnies -- but please allow that I defend our cause, and tell you who conspires to slander us and why. Whenever anyone stands up for decency these days, he gets his knuckles rapped by self-anointed champions of "liberty". What liberty? we ask -- and for whose benefit? Is liberty for all of us or just for them? To raise your children in the fear of God and chastity and righteousness -- do you still have that freedom? Or must you cover up their eyes and ears, evade their questions with embarassment, in order that some maniacs may freely flaunt their fantasies?
Juggler: What if we have no children?
Hierax: Then you have yourselves, your brothers, sisters, parents, friends. Look at yourself, young man: your manual dexterity is equal to a goldsmith's. But did you have the freedom to apprentice in that trade? Or did you find all doors were shut and all positions taken?
Juggler: Shut and taken! But who cares: I'm waiting for my place in Heaven. (Laughter).
Hierax: Which you will have, my friend. But let us not forget that God put us upon this earth to show our mettle. It's here the grain is separated from the chaff.
Dancer: And pain is separated from a laugh. (Laughter).
Voices: Hear, hear.
Hierax: Well said. The pain of multitudes is separated from the laughter of the few, by a great smoke-screen labelled "freedom" -- allowing those who laugh to do as they please with those who suffer. Who cares about the freedom of the latter -- from hunger, misery, pain, or anguish?
Juggler: Or persecution?
Hierax: Yes, persecution was a unimaginable scourge -- a bloody monster, mangling men and women, devouring children, violating virgins. We owe it to the victims' sacred blood, never to let it stalk this earth again -- give it no room to grow, no liberty to spread. It is so easy and convenient to forget, become complacent, say "the past is past". But what was once reality, remains forever possible. There are still people in our midst whose grandparents were persecuted under Diocletian -- when martyrs were obliged to walk, with their already wounded feet on thorns and nails, and then were whipped until their veins lay bare, and after suffering the most excruciating tortures were destroyed by the most horrid deaths -- when brave Eulalia's sides were ripped with shards, and her breasts burnt till she expired by the violence of the flames -- when pious Vincent's limbs were dislocated, his skin torn up with hooks, and he strapped to a gridiron, with fire underneath and spikes on top -- and when Julitta's child was killed before her face while she had boiling pitch poured on her feet, her body slashed with steel -- do not they and all the others merit our remembrance?
Voices: They do! They do! Their blood cries for revenge!
Florist: Irene, my namesake, was chased naked down the street and burnt alive next to the city wall.
Hierax: What are we doing to avenge their sacrifice? We clench our fists, we grit our teeth -- but our hearts are faint. We're cowards -- cowed by the wealthy and their spittle-lickers. We're suckered by the very scoundrels who hide blasphemy behind the mask of "freedom", and are cynical enough to holler "persecution" at every sign of righteous wrath. They labour to confuse us, lull us to sleep -- to have free reign -- indeed that's what they mean by freedom -- to help Satan control the world. Their previous brutal methods have been stalled. A mighty bulwark has arisen: the Holy, Catholic, and Apostolic Church -- so they have changed their tune. To undermine this bulwark they encourage heresies -- Satan's little helpers -- which they protect with whining calls for "tolerance". And to corrode this bulwark from inside they try to poison our minds: replace the sturdy cloth of common sense with silken finery of double-talk, straight-forward rules of right and wrong with quibbling equivocation, and a wholesome sense of beauty with an anxious respect for twisted ugliness. Thus they aim to enslave us, make us dim-witted pawns of their designs -- while they carouse and dine in their rich mansions and despise us. Shall we oblige them, go along with it, do as they have planned? Or shall we resist?
Voices: Resist! Let's burn their houses! Burn the bastards!
Hierax: Then arise! Break your chains, reclaim your freedom, show them who is master!

Hierax climbs down. One of the monks hands him a burning torch. He leads the procession off stage. The juggler goes last, backward, still juggling. Music: the gods' ascent to Valhalla (from Wagner's Rheingold ). Dario and Hypatia leave sideways in opposite directions, but hypatia stops and comes back to centre stage.

Hypatia: (alone) Like shimmering tears the stars are scattered through the night. There must be a great sorrow in the eye that wept them.

Curtain

Scene 5. Heavenly Bodies. On the stage of Alexandria's civic theatre.

Samuel: (clapping his hands) Good. Let's do it again. Dario, take care to hit those chalk-marks with each down-beat. Remember: three steps to each bar of music. Hypatia, make that reversal of your head-movement a bit more deliberate -- and you, Lydia, take care to keep your arm as close to parallel to Hypatia's beak as possible. You are our weather-vane.

Left stage: to 16 bars of the Blue Danube waltz, Hypatia and Dario do part of the ``Martian Dance''. Hypatia (as Earth) in a bluish cape wears a raven mask, whose large beak stays aimed at Dario. He (as Mars) wears a reddish cape. Under their capes, they wear the costumes of Phyllis and Jerry from the first skit. Samuel is in his Eratosthenes garb, but with a bright shiny cape -- Lydia in the costume of Dora from Skit One plus a green cape.

Hypatia starts and ends N (north -- the back of the stage) and does a circle around Samuel. During the same time, Dario does a 41% wider semicircle starting W and ending E. He is passed by her when both are south. Lydia is standing E facing the dancers, keeping her left arm parallel to Hypatia's beak.

Hypatia: (laughing, frees her face by pushing the mask upward) Hey, Mars, we're getting there. The music really helps us synchronize. Isn't astronomy fun? And this stage is wonderful. It's been a quarter century since I've stood on it.
Dario: It seems you're almost glad they kicked us off the street. (Slumps to the floor)
Lydia: What happened, Dario?
Dario: Mighty Mars fell on his arse. Serves him right: the world is going to the dogs, and we are fiddling with celestial triangles.
Lydia: Yes, fiddling while Rome goes up in smoke.
Samuel: What else is there to do? Rush out onto the street and shout?
Hypatia: Dario, this is political: encouraging a search for sense and harmony in a time of turmoil.
Dario: It's relatively safe to ruminate on distant trifles.
Samuel: More urgent matters are mired in such verbiage as makes thought unthinkable.
Dario: But what do shopkeepers and housewives care about Mars? They've likely never recognised it -- it's in the night-sky only every other year.
Lydia: The Moon is much more present in their lives. Let's show how Aristarchos found the distance to the Moon during a lunar eclipse.
Samuel: We could incorporate that -- but by itself it is too meagre. I'd stand out here and shine a light on you, the Moon, and Hypatia, the Earth -- whom you'd be slowly circling.
Hypatia: Let's do it. Come over here, Lydia ... a little closer, and now walk around me ... slower.
Samuel: See? Now you enter the Earth's shadow ...
Dario: Hypatia is eclipsing you.
Samuel: ... now you emerge again. According to Aristarchos, this passage took three hours -- one eighth of a day. And how long does it take you to go once around?
Lydia: Twenty-seven days and twelve hours -- two hundres and twenty times my passage through the dark.
Hypatia: Hence the Moon's circuit has the length of 220 earth diameters -- and anybody can now estimate its radius.
Dario: Thirty-five earth diameters -- and there we have distance to the Moon.
Lydia: But wouldn't the shadow be wider than the Earth?
Samuel: Not by much: the Sun is so much farther than the Moon that I -- as the Sun -- would have to dive into the harbour to present the distance true to scale. Anyway, the triangle Earth-Moon-Sun makes lousy choreography -- it's a very slim sliver.
Dario: Not many people are aware of that.
Lydia: Fie, Dario, are you suggesting that we cozy up to ignorance?

Door pops open. Enter Chrysostomos.

Hypatia: Welcome to our workshop! (to the others) Please meet Chrysostomos -- playwright in residence -- who'll string our skits together into one organic whole.
Chrys.: Just call me Chrys (giggles) but don't forget to spell it with a Y ... Yes, one orgiastic whole -- with lusty lads and winsome wenches -- including Cleopatra and her lover, the inimitable Julius ... A juicy play for today's lecherous public: a learned eunuch at Cleopatra's court is putting on these skits for her intellectual sport.
Hypatia: A eunuch?
Chrys.: A doubly tragic hero! Eunuchs: a belittled and despised minority -- unjustly neglected by earlier playwrights.
Samuel: They seem to lack a certain something.
Hypatia: And this is Samuel, my friend and colleague ... Lydia ... Dario ... friends of more recent years -- former students.
Chrys.: Welcome all! (effusively) We are so glad to have you back, Hypatia. The older members of this theatre still rave about your Antigone from twenty years ago.
Hypatia: Twenty-seven years, I think ...
Chrys.: ... and I am honoured to be your designated scribe. I've seen all of your street performances: Eratosthenes, Socrates, and the Pythagoreans. They'll work well in the play -- after a bit of polishing.
Hypatia: That's where we count on you, Chrys. And we need help on this last one too: it is to be the grand finale -- music, stars, geometry, and numbers.
Chrys.: Ah, the quadrivium!
Samuel: Say, Chrys, what do you think: are Sun and Moon about equally far, or is one farther than the other?
Chrys.: Is this a test, Professor? Of course the sun is much, much farther than the moon.
Hypatia: How do you know?
Chrys.: Today the moon is half -- a silvery finger-tip high in the southern sky -- pointing, not at the setting sun which gives it light, but at the passive blue above. How can that be? (Kneels beside Lydia) The answer's clear -- the moon is near -- like you, my dear -- the sun's a blazing ball of fire -- upon a lofty distant spire.
Hypatia: (applauds) Poetry is so succinct!
Samuel: Did you just make this up?
Chrys.: It's from a play by Plautus: "Madam Flutterby".
Dario: Dismal doggerel -- even the clumsy Latin tongue has been known to do better.
Chrys.: 'Tis a farce, my critical friend: a love-smitten swain bares his heart to a harlot -- and in the end she bares even more.
Lydia: Was I the harlot?
Hypatia: Don't take offence, Lydia. This is the theatre world: all bark and no bite.
Chrys.: So what's this skit about? You're dressed like for the first one -- except for those colourful capes.
Hypatia: We wear those to remind you that you promised us four dancers. Once we've worked out the choreography, they will do the dancing, and we'll be the same characters as before: Eratosthenes, Dora, Jerry, and Phyllis. Professor Lovestrength will explain the vision of his older friend and colleague Aristarchos -- about the great distances between the planets ...
Dario: ... a veritable television ... (Gets a friendly slap from Lydia)
Hypatia: ... and about their movements. That's where we need the dancers.
Chrys.: We have one with a very pale round face. She'd make a perfect Moon.
Samuel: We're not so sure about the Moon. It is too close for comfort.
Chrys.: Ah, that's why you asked that question ... But we can't leave out the Moon: it is so ever-present, so romantic. Why don't we follow up on the Plautus-scene? Put our moon-dancer over here, the sun over there -- shining a light on her face.
Lydia: Let's try it, Dario. You'll be my sun. (They take up positions.)
Hypatia: Good, but hold that light exactly at the height of her face. The moon is half, remember, and this is a right angle -- that's important.
Samuel: And where is the Earth?
Hypatia: At Lydia's navel. (Fastens a string to Lydia's belt and gives the other end to Dario) This the Earth's line of sight to the Sun.
Dario: You're staring at me with your belly button, Lydia.
Chrys.: Bravo! I love improvisations.
Hypatia: (Pointing at the string) This is the hypotenuse of a right triangle. Pay attention to the angle it makes with the floor. The farther the sun is away -- move a bit farther, Dario! -- the smaller the angle.
Samuel: Now I see what you're doing. Yes, Chrys, Aristarchos measured it as three dregrees -- a 120th of a full circle. That means, the distance between Lydia's nose and navel is about one nineteenth of the distance between her and Dario's lamp.
Chrys.: Are you saying the circumference of a circle is 120 nineteenths of its radius?
Hypatia: Yes, we give a small discount just for poets.
Chrys.: So, the Sun is nineteen times as far as the Moon. I thought it was more.
Samuel: You're right. Such small angles are very difficult to measure -- Aristarchos didn't get it right, and didn't really care: he only wanted the sun far enough to fit his planetary model. And that is what our skit is mainly about.
Chrys.: I must admit, this little episode is a bit dry. It would be more gripping if the moon-dancer were stark naked, and the string came out of ...
Hypatia: Don't be naughty, Chrys.
Chrys.: In Cleopatra's court, it wouldn't be impossible. Sorry -- I have the nasty habit of thinking out loud.
Hypatia: Chrys is a lamb in wolf's clothes, I've known him for years.
Samuel: Perhaps you can help us, Chrys. How would you motivate an interest in the planet Mars?
Chrys.: Astrology, of course. Caius Julius would not dare get out of bed when Mars is retrograde -- this may not be historical ...
Hypatia: Nobody would believe it even if it were. Superstition isn't in the character of Caesar... But what about Mark Antony?
Chrys.: He came later ...
Hypatia: ... only six or seven years.
Chrys.: The play revolves around the teenage Cleopatra's royal education: she speaks nine languages -- but hasn't even heard of the quadrivium.
Samuel: Couldn't it revolve around Mark Antony's enlightenment? That fearless warrior may have had an anxious eye on Mars, I think, especially its retrogression.
Hypatia: Cleopatra could have wanted to demystify it for him -- show its naked innocence.
Chrys.: The warrior's naked innocence -- hmm, let me think about it ... But now, please let me see the main part of your skit.
Hypatia: Please, Lydia, go and say your introduction -- and don't forget to curtsy: in the play, you'll be addressing royalty.
Lydia: (stepping forward) Your Majesty, most noble Romans, honoured guests. Today's performance imitates the dance of Mars across the sky -- as Ra, the ancient sun-god, would have seen it. One of the dancers is the Earth itself -- please bear with us, and remember that it's Ra's point of view: to himself he is immobile, everything turns around him.
Samuel: I am Ra, (pointing) this is Gaia, and that is Mars. Keep a sharp eye on Gaia's beak, and watch the movement of yon lady's lovely arm.

They dance as before to 16 more bars of waltz.

Chrys.: Gaia and Ra -- a splendid couple! She leaves Uranus for a hot Egyptian lover ... and rounds out the ménage à trois with fiery Mars.
Hypatia: No, Chrys, this isn't myth -- but math. It's Aristarchos's perspective on planetary motion -- which Eratosthenes will expound to his friends Jerry and Dora. Did you watch my beak?
Chrys.: I did. What is that dreadful mask of yours?
Hypatia: A raven mask from far away. I found it in my father's attic. All the label said was "raven -- north of sixty". That means 60 degrees up from the equator.
Chrys.: There's more up there than ice and snow, I guess.
Hypatia: I kept the beak trained on Dario, and looked past him to the farthest row of the theatre. First I saw him over there, then he moved toward the centre and through it to the left, but there he stalled and slid backward to the other side, and finally resumed his path from right to left until the end. Lydia's arm was always pointing in the same direction, showing the audience what I saw. It went like this. (Imitates Lydia's arm movement)
Chrys.: So you and Dario were just circling Samuel, but you saw Dario doing this ... switch-back. (Imitates the same movement)
Hypatia: Yes, and that's how we earthlings see Mars moving through the Zodiac. Aristarchos says that Mars and Earth are just circling the Sun.
Lydia: That's from the Sun's point of view.
Dario: It's even worse: as Ra looks down on us, he will see India, then Persia, Egypt, Italy, and Spain -- in other words, he sees the whole thing turning on itself as well as circling through the Zodiac.
Chrys.: A dancing earth -- ridiculous! If this be science, count me out. The earth is rock-solid -- the most immobile object known to Man. We'll be the laughing stock of Alexandria.
Samuel: Aristarchos did work for a while right here in Alexandria -- in old Euclid's time. Many great scholars heard his theory, and nobody laughed.
Chrys.: Whichever Muse presides at mathematical symposia must lack a sense of humour. I can accept this only as theatre of the absurd.
Lydia: It's just Ra's point of view -- no one is saying what's really standing still, if anything.
Dario: We leave that question to philosophers. In mathematics we are free to choose our perspective.
Chrys.: In your illustrious science anything goes -- is that it? What a surprise!
Hypatia: Not at all, Chrys. Once you choose a hammer you cannot use it as a sickle. Remember the Pythagoreans and their digital perspective.
Chrys.: Alright, I'll choose the allegorical perspective. Your dance is just an allegory -- call it "Ra's Egocentric Dream". We can put signs of the Zodiac on the top row of the theatre, so people know what you are pointing at. But let the dancers be gods instead of planets.
Dario: That's illegal -- let's call them heavenly bodies ...
Lydia: ... and the dance a mathematical model.
Chrys.: I prefer "allegory", darling -- believe me, it sells better; and leave out "mathematical" -- that has the opposite effect. What is so mathematical about it anyway?
Hypatia: The whole idea of turning what you call "switch-backs" into orderly concentric motion is like the shift from square to diamond in the Meno Skit -- but much more radical. And all ingredients of the model -- circles, triangles, etc. -- are mathematical.
Chrys.: I only see a dance.
Lydia: Then let's forget the planets for a while -- and imagine the following scenario ... Three of us are on Lake Mareotis -- each in a small boat. The night is starless, moonless -- and no wind is stirring. The water is like a mirror, and our boats glide silently. They have lights on their masts: yellow, blue, and red. Each sees the other two as points of light, no one can tell who's moving and who's still. The question is: how does each of us see the others move?

Samuel: In my yellow boat, I see the red and blue lights circling me -- the red one farther than the blue, and slower.
Hypatia: The three lights form an evolving triangle -- which is the mathematical foundation of this dance. From its blue corner I watch the other two. The yellow light is orbiting me. But how do I see the red one move, and how does it see me?
Dario: I think we need to show Chrys the ropes. Ta-daa! Look at these, Chrysostomos.
Chrys.: Knotted ropes -- how primitive! Now we're really in the past -- with the pyramid builders.
Dario: We use these just for theatrical effect.
Samuel: (Takes one of Dario's ropes).) This is Number 6: our position after 6 bars of music. Would you hang on to the blue knot, Hypatia, and you the red one, Dario? (Dario and Hypatia obey.) And let's step over here on our chalk marks. Do you do see, Chrys?
Chrys.: Yes, if you say so I'll accept that they reached that position after 6 bars. And that you have triangles of different shapes for the other positions. What will you do with them?

Samuel: We could put them over there in the same order and orientation, but with the blue knots all on the same peg -- to show how Gaia sees the others move.
Chrys.: Why not show that version right away? I like it: Gaia stands still and Mars does a curlicue. The ballet would be snappier.
Hypatia: But then we can't put Mars and Venus on together -- they'd surely bump into each other.
Chrys.: How can a simple change of view-point cause collisions?
Hypatia: Now look who is scoring mathematical points! The choreography is harder, Mister Playwright! The dancers' senses will more readily grasp concentric motion. And -- by the way -- so will the geometer's brain. That is the ultimate advantage of this model: our minds, not tangled up in messy curlicues, have room to stretch farther ... Here, let me show you something. (Whispers in Dario's ear) We'll do our dance again with Dario's orbit twice as wide as mine. Lydia, please, be the weather vane.

Hypatia now stays inside her former track, Dario outside his. 16 bars of waltz.

Chrys.: Wow! No switch-back. He is too far away from you, so -- even though you pass him on the inside track, he stays within your field of vision.
Dario: That's not quite right, but almost.
Lydia: It's a very succinct way of putting it.
Hypatia: You see, Chrys, the width of that retrograde loop depends on how close he is. Our first version was a bit too close: four bars of music -- a quarter year. To match reality he should be slightly further out. See how we can play with these switch-backs? That's how we reckon that Jupiter's orbit is five times as wide as ours, and Saturn's twice as wide again.
Samuel: The power of abstraction: one model fits all.
Chrys.: Bravissimo -- but you've forgotten something ... What does the red boat see?
Hypatia: An excellent question, Chrys. (To the audience) Does anybody know the answer?
Chrys.: Don't look at me, Hypatia. You'd find my anwer opposite to excellent.
Hypatia: You got it, Chrys! The key word is "opposite".
Chrys.: You're mocking me.
Hypatia: I wouldn't think of it. Look: if red moves toward blue, it will see blue approaching. Similarly, when they move apart, each will see the other fleeing. And if red moves to the right of blue by so many degrees, what does blue see?
Chrys.: (observing his forearm as he rotates it sideways) It will see blue doing likewise.
Hypatia: Each sees the movements of its opposite in exactly the same way.
Chrys.: How obvious -- yes -- and I do see it! Mars would see Gaia as she sees him.
Samuel: As long as he disregards all else -- the sun's blinding light, for instance.
Lydia: That's why we cannot see much of Venus's retrograde loop.
Chrys.: Ah -- Venus! Aphrodite -- born from the foaming sea where Chronos flung his father's jewels. I'm all for Venus, but how does she get into the act?
Dario: Venus is to Earth as Earth is to Mars.
Chrys.: Oh good -- we're back to gibberish: math is to me as water's to my cat.
Hypatia: Math is to philosophy as fencing is to war: mere preparation for some -- an art in itself for others.
Chrys.: I hasten to admit: for all its strict obedience to Logic, math might turn out to be the last remaining bastion of freedom.
Hypatia: If you draw such conclusions, Chrys, you'll have the literati snickering that such-and-such philosopher had said it all much better ...
Samuel: We have no hidden messages: the medium is the message.
Usher: Please pardon the intrusion. A messenger is here for Lady Hypatia.

Messenger appears at door, hands a letter to Hypatia.

Chrys.: One of the Bishop's men ...Well friends, this was an excellent beginning, but I must now vamoose. Let's meet again tomorrow. (Exit Chrysostomos)

Hypatia comes back, tucking the letter into her dress.

Samuel: Why don't we finish up the day by trying out the full-blown Planet Dance?
Hypatia: Yes, let's -- I feel like dancing.

As Lydia adjusts her dress a sizable crucifix falls to the floor. The others stare at her, perplexed.

Lydia: (touching the crucifix) I was afraid you'd be perplexed. My ailing mother put it round my neck -- it had come down to her through many generations, mother to daughter, from the time of martyrs in the reign of Daecius. Who am I to break this chain?
Dario: I do think that all younger generations must break certain chains.
Samuel: And then go on to forge their own ...
Dario: Forsooth -- but we were set to frolick with voluptuous Venus -- and suddenly our blood runs cold, because a tortured body's dangling between her breasts ... I'm sorry, Lydia, I'm just reacting -- I've not had the time to think.
Lydia: I knew this would be hard to take, and will not ask you to get tangled in my destiny. (hides the crucifix under her cape)
Hypatia: (taking Lydia in her arms) Lydia, please do not hide. Seeing you bear your pain so quietly -- makes all of us feel less afraid.
Lydia: I am young, Hypatia, life has been good to me -- but I would never want to turn my back on those in pain. This (touches her crucifix) will remind me not to forget them.
Dario: (sits down on the floor and stares straight ahead) ... not to forget them ...
Hypatia: What are you thinking of, Dario?
Dario: Of faces I'd forgotten...
Samuel: (scratching his head) Perhaps we could learn from astronomy. It's a question of perspective: are we flesh with bones inside or are we bones clothed in flesh?
Lydia: (laughing through tears) Doctor Lovewell's speaking like an oracle again -- so everything's alright. O dear Professor, please, please, please, explain.
Samuel: I mean that ... if we took offense at Lydia's crucifix, we might as well shrink from her smile -- because it is more of her skull than of her flesh.
Hypatia: What ghoulish thoughts, Professor, fie! No wonder honest folk don't want to read your books!
Dario: But he's dead on -- our skulls will still be grinning long after we are gone.
Hypatia: Here is material for several ponderous seminars. Shall we schedule them now?
Dario: It's getting late, but I would say -- if Lydia is up to it -- we should attempt the planet dance. Just so she doesn't feel she's spoiled the party...
Hypatia: What do you say, Venus?
Lydia: Yes, Mother Earth, I'd love to try this dance.

She goes toward Samuel with outstretched arms. A joyful waltz ("Libiamo" from La Traviata?). Dario and Hypatia dance as before, except that now Hypatia's beak is following Venus. Lydia is halfway between Samuel and Hypatia, orbiting the sun in double time. Music and lights fade out together. Curtain.


Scene 6. Samuel's Dream.

Hypatia is having breakfast in her house . Enter servant.

Servant: Madam, a visitor is here to see you -- your colleague Dr. Samuel.
Hypatia: He must have urgent business to be up so early ... Do let him in.

Enter Samuel.

Hypatia: Good morning, Samuel. What brings you here so early?
Samuel: (embarrassed) This might sound foolish, but I had the urge see that all was well with you -- I'd had a nightmare...
Hypatia: ... in which all was not well with me?
Samuel: The dream still gives me goose-bumps when I think of it.
Hypatia: What did you dream of? Tell me.
Samuel: As I was walking to the university -- in the dream, that is -- the sun was shining, and the sea was sparkling in the distance. Then clouds appeared and it began to rain, first gradually but soon in heavy drops. When I looked at my hands, I realised ... that it was raining blood!
Hypatia: How awful -- it's enough to make me shudder too! But what's it have to do with me?
Samuel: Somehow I knew -- though nothing told me -- that it was your blood.
Hypatia: My blood ... And that is why you came to see me?
Samuel: Yes, and it has helped: I feel relieved. Have you never done a silly thing like that?
Hypatia: I guess so, but I have forgotten. A cup of this warm milk will reassure you further. Here take some. I'll get dressed and we can walk together to the library. The sky is cloudless -- there will be no rain.
Samuel: Hypatia, please don't go today.
Hypatia: Come on, let's not go overboard! It's good to banish nightmares by exposure to reality -- it's bad to let them run our lives. We'll go together, and all will be well.
Samuel: Hypatia, please don't go.
Hypatia: O stop it, Samuel! This is not like you. Maybe you have a fever.
Samuel: I know it's not like me, but I can't help myself: please do not go.
Hypatia: Just drink your milk, and I will show you something. (Picks up a letter) This is a letter from Archbishop Cyril: he's coming to my office at the library today.
Samuel: That is amazing! I thought he shunned the place.
Hypatia: Officially he does -- but privately he comes occasionally. Remember we have the original Septuagint and various treatises by Doctors of the Church.
Samuel: So, you are meeting him today?
Hypatia: Yes. He says he wants to try and settle our differences amicably. How could I not go?
Samuel: Last night, some of his thugs were roaming in the Jewish quarter. That's not far from the library!
Hypatia: They've cleaned it out last year -- there's nothing left to loot! Please, Samuel, calm down. There is no danger: this letter will protect me!
Samuel: Most of the Guardians cannot read.
Hypatia: They'll recognise the bishop's seal.
Samuel: Don't count on their intelligence, Hypatia.
Hypatia: Look what you are doing, Samuel: you're dragging me into your nightmare. I simply have to keep such an appointment -- and if it's the last thing I do ... Now wait for me while I get dressed, okay?

Exit Hypatia. Enter Dario and Lydia, dishevelled and out of breath.

Dario: Fancy meeting you here, Samuel. Where is Hypatia?
Samuel: She's getting dressed... What's up? You seem distraught.
Lydia: You know the little synagogue in Dario's street? The bishop's thugs...
Dario: ... the socalled Guardians ... they are trashing it. The cops were called but didn't come.
Samuel: So you expect Hypatia to help? What can she do?
Dario: Alert the governor, for instance, he is a friend of hers.
Samuel: Not even he could stop the Guardians. But I'll go over there to see if some things can be salvaged -- or some people helped.
Dario: I'll come along.

Exeunt Dario and Samuel. Enter Hypatia.

Hypatia: Look who is here! (Goes to hug Lydia) What a morning of surprises -- I almost feel as though it were my birthday. Where is Samuel?
Lydia: He went with Dario to see about a synagogue the Guardians are "shutting down".
Hypatia: I hope they won't get into trouble -- Samuel had a strange foreboding.
Lydia: He's very sensible and experienced, remember he's an army veteran. If Dario had gone alone I would be worried.
Hypatia: All we can do is keep our fingers crossed.
Lydia: Couldn't you alert your friend Orestes?
Hypatia: I'm sure he's been alerted and will do his best. But even he can't stop the Guardians.
Lydia: So you'll do nothing?
Hypatia: I'll do what I am best at: think and persuade. I am going to the library and later to the university.
Lydia: I'm afraid they could harm you, Hypatia -- very afraid.
Hypatia: Fear is the greatest enemy of life, Lydia. Fate can strike anyone any time. If it should strike me soon, don't weep for me -- but tell yourself: Hypatia was a fruit ripe for the plucking -- she did not wish to shrivel on the vine. I'm going to the library.
Lydia: Oh Hypatia! May I come along?
Hypatia: Of course -- but straighten out your hair a bit (hands her a comb).
Lydia: (combing her hair) Thank you, Hypatia.

Exeunt Hypatia and Lydia. Blackout. Dark music. When lights come on again, Lydia is alone on stage, dishevelled, clutching her crucifix. Enter Dario limping, obviously beaten up.

Dario: Where is Hypatia?

Lydia weeping silently -- answers after a long pause with a simple gesture.

Lydia: They stripped her -- she just stood there silently with pleading hands, and tears streaming over her face. When the shards cut into her flesh, she only moaned a little. When they tore off her limbs, it was no longer Hypatia who screamed -- it was all tortured creation -- and in my head it cried "Eli, Eli, lama sabachthani".

This is echoed by the same words in Bach's St. Matthew Passion, with their German translation (?). Music fades into a kind of spoken fugue (as in Gould's "Idea of North") of their translation into many languages, starting with English.

Lydia slowly drops to her knees and buries her face in her hands. Dario crouches beside her, trying to comfort her.

As the music changes to the final chorus of the St. Matthew Passion, Samuel comes in, looking roughed up and carrying a menorah. Moving slowly (timed to the first stanza of the chorus), he puts down the menorah, takes a cape off the table, puts it on, and re-assumes the role of the narrator.

Samuel: (as narrator) This is how Hypatia was murdered by a fanatical mob in March 415 AD. The brutality and impunity of the crime shocked Alexandria's scholars and scientists into silence and eventual exile -- heralding the end of classical civilization and the beginning of a dark millennium. This happened long ago -- but what was once reality, remains forever possible.

Blackout. Curtain.