For once I would have to agree with my sisters. The manzana of Amecameca was the most extraordinary sight, though I’m not sure María or Josefa saw it quite the way I did. We arrived just before sunset.
The little zócalo was already crowded. In the arcades about the perimeter all the shops were still open, their lanterns lit. Amazingly, this was a nightly affair, the atmosphere less of excitement than of expectancy. At the plaza’s heart pulsed a fountain among the fig trees, beneath whose green eaves spread an array of tianguis offering elotes and tortillas, tacos and atole. The crowns of the trees were filling with urracas come to the fountain to drink, then squabble and gossip and roost for the night. The fountain basin formed a hexagon, and around it were benches, two to a side. Distributed across these—posed like rock formations or mineral accretions—were the village elders, among whom we had arrived in time to find Abuelo a seat. Finding an open seat was not the problem. Getting him to it was. “Don Pedro, ¡qué milagro! Don Pedro, tanto gusto en veros.” At first the men, then the women too, came to pay their respects as he settled in, these seamed and grey-headed ancients in black. They crowded in till he sat as beneath a small, stooped porch of goyles and caryatids.
It started out as a trickle, but soon what must be the region’s every last unattached male—anyone able to walk unassisted—had joined all the others in circling the plaza’s outer perimeter. Gradually fleshing out a ring just within the bachelor’s circle came an almost equal number of their female counterparts. And behind each virgin walked the family, proud and vigilant. In our group María and Josefa went first, holding hands, then Isabel and her lance-captain, then Amanda and I a good long way behind them.
The outer ring, los machos,† advanced right to left, cross-grain to the setting sun. The inner circle of las hembras circled left to right, or viewed from the top—north, east, south, west. It was as if each ring were a cog, but then what was the mechanism? At first I was reminded of the great Ptolemaic15 machineries of heavenly congress. Or no, a press, perhaps, for extracting cider† … And then it came to me. Here was just such a machine as Pascal had invented only a short time ago, the automatic arithmetical machine whose fame was spreading like a wildfire all across Europe, and even to us. Ha! Now I was truly beginning to enjoy myself, for it was clear that our own Iberian genius had long predated the new Gallic invention. In short, our manzana must certainly be a very ancient arithmetical machine for the calculation and apportionment of dowries.
Not just that. Here was a living breathing demonstration of double conic sections just such as I had seen diagrammed by the Alexandrians and emerging now from the swirl like an hourglass—yes, the double conic was just like an hourglass, why hadn’t I seen it? Two cones joined at their apex as though mirrored but in fact traced by the sightlines—fore and then aft—of any individual on the outer circle as he obsessively follows the progress of a special someone on the inner … follows her from the tangent of her appearance to that of her agonizing, if temporary, vanishing.
And I had seen enough of our lance-captain’s dowering to guess at the basic motives and parameters. We may call these Focus, Locus, Vertex, Directrix. F is the dowry—the focus. The directrix (D) is an obtuse, oblique or generally tangential pursuit of F by making a beeline to the means, that is, to the woman in view. The vertex (V), then, will be the true measure of the woman’s charms; and the locus (L) will equal the distance between the truth (V) of said charms and any statement praising them in the pursuit of F.
On the elliptical side of the field lies any understatement. But by far the more common of course will be the hyperbolic. Our lance-captain’s strategy usually consisted in paying the same compliments to all the females of our house. This, I now realized, executed a cunning double or even triple arc—hyperbolic toward us, and folded within that, a subtle ellipticism toward my mother. In my view, his praises of her beauty, if only from a poetic perspective, had for all his gusto fallen well short of their object. But then what of the parabolic? I wasn’t quite certain—surely even the great geometers did not work everything out at once.
To give rhetorical precision to all this romance, one may say that the elliptical comment, parting from the plane of the vertex at an angle shallower than the generator (the angle of first or last glance), will always be too soon, or too late. The hyperbolic comment, on the other hand, cuts the plane of the vertex along the axis at a sharper angle than does either the generator or the elliptic. The maximal amount that can be communicated by the seeker along the outer circle (where it intersects the directrix) will depend upon how close after tangency the woman is sighted, as well as upon distance, relative velocity, her hearing’s acuity and, above all, the man’s readiness of wit as conveyed by his speed of composition and clarity of elocution. This is speaking in the raw quantitative sense. Qualitatively of course, one word, one glance might suffice.
Though this particular wording may not have come to me then, the images did with very great precision as we went round and round the manzana of Amecameca. Eventually I found myself coming to an appreciation of roulette, another invention of this devilishly clever Pascal and of which I had only read vague descriptions. I now wondered if that cunning French monk was not a parodist as well, one who had closely studied the Iberian dowry machine in action in Spain, and had thus been led from mere mechanics to certain conclusions about the marriage of geometry, chance and finance in affairs of the heart.
By this time I found myself stopped inside the ladies’ circle, with Amanda tugging at my sleeve and the fortunes of so many lovers whirling in the camera combinatoria of my head, beginning to open out into an Archimedean spiral …
“You look drunk,” she whispered. “We’d better sit down.”
Our mother took Josefa and María off to Chalco in the morning. We could stay up at Ixayac as long as we liked. After failing to spear a fish in six tries each we generally agreed to return our spear to its hiding place and move on. But today something was holding me there.
The trout were, as Xochitl had said. Just not there. But maybe they were not there twice. If the new geometers were right, light was bent by its entry into a medium of different density, water being obviously denser than air…. And if I was right and the vent at the pool bottom was hot, then we had water at two different temperatures and densities. But though Aristotle argued that light followed the shortest route between two points, a refracted trajectory was obviously longer than a straight one. So either he was wrong about the geometry or wrong about the properties of light, or there was something I’d missed…. Had he actually meant shorter in distance? Couldn’t he have really meant shorter in time? If the light travelled at different rates—it might be like a traveller destined to arrive at a certain hour no matter what route he took. And though I knew I hadn’t quite unravelled it, I was irresistibly drawn to this riddle of something like Destiny in light….
“Ixpetz, come on.”
For the second time in less than a day here was Amanda tugging at my arm. My shoulder ached, my whole arm in fact. I must have thrown the spear twenty times and not given her a turn at all. But two throws back I was sure I had nicked one.
So, progress on refraction; and tonight we would just see about light and time. I had in mind some tests with candles and as many mirrors as I could connect in a line….
By noon Amanda and I were already on the upper bench, sitting on the dry stone on the south side of the teardrop pool. The view to the west was clear. We could see to the lake’s north shore and to the villages beyond. The parent falcons had returned, but rather than bringing food they had been roosting quietly atop one of the pines rising from the lower bench. Aside from the crash of water, which we hardly heard anymore, it was quiet. A cool spray drifted around and between us as we picked at the great mass of tamales con rajas we had brought all this way up for lunch.
Amanda wasn’t a bit hungry. What was wrong? We were very close to quarrelling. She hadn’t wanted to swim in the lower pool for two days now. Or tak
e a temazcal.
I was reading the Pinakes by Callimachus. So I’d brought her the Argonautica, a book by his student. But I could see she wasn’t really reading. It couldn’t be that she was bored—not now, with the falcons. We had everything we needed here. And what could be more fascinating than Jason and the Argonauts? And yet I felt it. High in my stomach a nettled sensation.
Alexandria was making it next to impossible to keep Greece and Egypt safely apart—the forms and the riddles, the now and then, the parallel lines of our mornings and my afternoons—to keep them from converging. It had even crept into the books I was picking for us to read. Callimachus and Apollonius, though they wrote in Greek, were librarians of Alexandria. I so wanted to tell Amanda of this white hunger that had awoken in my heart, this thing like hope, pushing to be born in me, to join in the great work of deciphering the emblems of universal knowledge, tracing its forms, charting its equations, its infinitesimal changes. In Alexandria the signs had been so hopeful, a revival that was like a foretelling of our own: Galileo, Descartes, Pascal, Bernouilli, Torricelli. Even now, this very day perhaps, Magister Kircher in Rome was adding new wonders to a universal museum not unlike Alexandria’s, and so resurrecting the dream of the Ptolemies. The great work was happening right now and yet an ocean away, in the studios of the artists and physicists of Italy, the mathematicians and philosophers of France. How could I even begin to tell Amanda of this, and yet how could I not?
Very casually I started in with Alexandria’s librarians, the poets Callimachus and Apollonius, the grammarian Aristarchus. Already Amanda was wrinkling her nose. Grammar was her least favourite subject.
“Seven hundred thousand volumes,” I put in hastily. Could it even be imagined, such a sum? What was our library here, next to that? With so many books coming in, another library was set up in the temple of Serapis. This new repository, they named the Serapiana—the daughter library. I asked Amanda if she did not find this lovely. She made no comment. Scholars began streaming in from all over the world to Alexandria, so the Academy of Athens founded a daughter Academy there too, under a librarian named Theon. Not a poet, this one, but a powerful mathematician, who taught astronomy and divination.
“Magic, Amanda. He must have been a wizard, like Pythagoras, like Ocelotl—”
She suggested we go down.
Was she even listening? Because this was the best part—this Theon had a daughter, Hypatia. He believed she could become a perfect being—a girl, NibbleTooth. Barely eight and she was already helping her father study an eclipse of the sun. I knew I’d caught Amanda’s interest, yet she was adamant about not staying. I felt a flush of anger but tried to calm myself by thinking thoughts that, if not altogether wise themselves, were about wisdom.
And then as she started to her feet there erupted a din of screeching falcons such as we had never heard. On the lip of the niche two fledglings were jostling to spread their wings and wildly crying out as if their wingtips were raw nerves in agony. An even greater commotion came echoing back from the uppermost branches of the pine opposite—swaying under the weight of two—but no three screeching falcons. A second of the fledglings vaulted now from the niche and came crashing awkwardly into the boughs. Only by clutching desperately at the branch with its talons did it keep from toppling backwards to the ground. The third, still back at the niche, flapped and lunged without letting go until at last overwhelmed by the sheer pitch of urgency of the other four beckoning with shrieks. No sooner had it leapt off the ledge but the parents launched themselves, soon followed by one, then two, then all three.
Amanda and I had come to a crouch, breathless, stunned and all but deafened as they wobbled then swooped screaming back and forth over the bench.
It was dusk when we came down.
In the morning I took the lead and kept it all the way up, with her straggling behind. We worked our way along the river towards the bracelet of stones where we crossed over. A flock of white pelicans was wheeling and diving at the trout pool ahead. From a trot I broke into a run. Each pelican following the next, they dove and rose again, dripping like the paddles of a waterwheel. Gaining height they merged a moment against the snowfields, then broke into the blue just in time to fold again and plunge to the water like spatulas after their handles.
I spotted an otter where it stood on the pool’s far bank, one forepaw raised delicately, muzzle uplifted to sniff the air. I could not have said whether in contempt of their proficiency—for not one pelican in five ever needed to break formation to actually swallow a fish—or in resentment of these interlopers fouling his larder on their way from the lake back to the sea.
By early afternoon we were close to quarrelling once more.
With Amanda refusing yet again to swim or take a temazcal, we’d spent the whole morning on the upper bench at flying lessons. She sat, distracted, hardly watching at all as the adults hovered above the fledglings, dipping and turning at the merest tremble of those beautiful wings. Wings the very shape of loveliness and power, tips tapering to an archer’s bow, to a single pinion of grace. I watched them now as if to save my life. I watched them with falcon’s eyes. As the adults led, all five soon dove and swooped and swept in widening relays and volleys. Wild shrieks like the clash of steel. What were they feeling? Was it joy? If so, how wild the heart to give such voice to joy. Shrieks and shrieking echoes—one after the other—terror, terror to wild exuberance, fierce exultation, to a joy like rage. Their echoes crashed against the face, careened off the water. Tears started from my eyes. I blinked the chill into my lashes. I was the one exalted, exulting in these echoes.
And what had been that terror if not the fear they might never fly at all?
By mid-afternoon Amanda wanted to start down.
We still had at least an hour. How could we leave even a minute early, with so much for us here? Two benches, two pools—five falcons. With her face so closed off from me, it felt as if all the secret shapes and silent tides of the world were trying to divide us. I began to tell her more about Hypatia, whose father had been teaching her about mathematics and stars, divinations in the flights of birds. But there were things even he did not know, so he let her go off to study in Athens, at the Academy, under the direction of Plutarch himself….
Amanda had collected her things in her satchel yet stood hesitating at the ledge where we climbed back down to the lower bench. I stood close behind her, looking out into the valley. Imagine that journey, Amanda. See, that was the Aegean down there—the near shore was Egypt, the city on the island was Athens. And see that canoe just entering the chinampas?—the galley taking her away from home. We had each other, Amanda, but Hypatia was alone. She missed her father terribly, but she was following her destiny. And did Amanda not think I missed Grandfather sometimes up here? Did she think I’d never felt bad about always being here, with her?
Still she wouldn’t look at me, as if convinced everything I said was only another trick to delay her. Which was true, but it wasn’t because of the falcons and it wasn’t just so we could stay late. It was because I was afraid. Could it be we no longer loved the same things—or no longer loved what we shared? This was my punishment for wanting to keep Egypt for myself, concealing it from her.
When she started down without another word I wasn’t even angry. I only followed her to the next bench, talking all the while, talking as we gathered up our things, and as we walked down the little stream and under the overarching bushes. I slipped ahead of her to slow her down.
“You know, Amanda, Hypatia became a teacher so famous that men came to her from everywhere, and so beautiful half of them grew sick with love of her. But she was a healer like Ocelotl. Like your mother.” Since I could not stop her I was walking backwards, talking quickly, unsure of the remaining distance to the ledge. “She cured one of these men with a therapy of music, a medicine of harmony—do you see? And to another of these lovesick men she showed her soiled undergarments—”
Amanda stopped. Suddenly, mystifyingly, I had
her full, angry attention. Her eyes narrowed.
“Why would she do that, Juana?”
Were things so bad between us? She seemed suspicious of everything I said or did.
“Tell me why you said that,” she demanded.
“I said it because she did it, that’s why! To show him his idea of beauty was not where true beauty lies.”
I stood facing her, my heels at the ledge, the whole Valley of Mexico—Athens and Alexandria—falling away behind me. I was desperate to talk to her and could not find a single thing she wanted to listen to. And now the tears did come.
Amanda looked at me for a long moment. Her eyes shimmered. But when she still said nothing I turned, embarrassed, to start down.
“Wait, Ixpetz,” she said. I felt her fingertips on my shoulder. “The other song. For the girl. Mother is teaching me….”
I turned back, watched her pause an instant to collect herself. On a ledge overlooking the city on a lake she sang me the song for the newborn girl. And still I did not understand yet why.
My beloved daughter, my little girl, you have wearied yourself, you have fatigued yourself.
Our lord, Tloque Nahuaque, has sent you here.
You have come to a place of hardship, a place of affliction, a place of tribulation.
A place that is cold, a place that is windy.
Listen now:
From your body, from the middle of your body, I remove, I cut the umbilical cord.
Your father, your mother, Yohualtecutli, Yohualticitl, have ordered, have ordained
that you shall be the heart of the house.
You shall go nowhere,
you shall not be a wanderer.
You shall be the covering of ashes that banks the fire,
you shall be the three stones on which the cooking pot rests.
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