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Zeta #AtoZAprilChallenge

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The Zeta function ζ(s) is defined as above, for example :

ζ(2) = 1/12 + 1/22 + 1/32 … = π2 / 6.

This converges for s>1 (i.e. tends towards a limit), but diverges for anything else. The Riemann Zeta function extends this range to allow us to compute the result for any complex number. The Riemann Hypothesis claims that the ‘zeros’ or ‘roots’ of this extended function, i.e. solutions for which ζ(s) = 0, have the form 1/2 + ai, i.e. where the real part of the complex number is always 1/2 (as well as certain ‘trivial’ roots which don’t have this form).

Unsolved! Proposed by Bernhard Riemann in 1859. This is one of the 7 ‘Millennium Prize’ problems, for which there is a $1m reward.

Get cracking!

There’s a number of consequences if this is true, but perhaps the most important is that it reveals the distribution of the prime numbers. The Prime Number Theorem allowed us to estimate the number of primes up to a given number. If armed with all the roots of the Riemann Zeta function, then we can work out the exact number!

Yawpa #AtoZAprilChallenge

Mocking Bird (Audubon).jpg

Yawpa is the Hopi name for the Mockingbird. “The mockingbird fluttered around the bamboo, calling out, ‘Pashumayani! Pashumayani! Be careful! Be careful!’ This is the way the people departed from the Lower World” (from The Four Worlds: the doorway to the Fourth World, in ‘The Fourth World of the Hopis’, by Harold Courlander.)

From Wikipedia, the Northern Mockingbird:

It also features in the title and central metaphor of the novel To Kill a Mockingbird, by Harper Lee. In that novel, mockingbirds are portrayed as innocent and generous, and two of the major characters, Atticus Finch and Miss Maudie, say it is a sin to kill a mockingbird because “they don’t do one thing for us but make music for us to enjoy. They don’t eat up people’s gardens, don’t nest in corncribs, they don’t do one thing but sing their hearts out for us”.[47]

Hush, Little Baby” is a traditional lullaby, thought to have been written in the Southern United States, its key first lines, “Hush, little baby, don’t say a word, Mama’s gonna buy you a mockingbird. And if that mockingbird don’t sing, Mama’s gonna buy you a diamond ring.”

The song of the northern mockingbird inspires much of classic American folk song of the mid-19th century, “Listen to the Mocking Bird“.[48]

Mockin’ Bird Hill is a popular song best known through recordings by Patti PageDonna Fargo, and by Les Paul and Mary Ford in 1951.

Thomas Jefferson, the third President of the United States, had a pet mockingbird named “Dick.”

The sound of the Mockingbird

Image: By 21_Mocking_Bird.jpg:
John James Audubon (1785–1851)

Alternative names
Birth name: Jean-Jacques-Fougère Audubon
Description
American ornithologist, naturalist, hunter and painter
Date of birth/death
26 April 1785
27 January 1851
Location of birth/death
Les Cayes (Haiti)
New York City
Work location
Louisville, Kentucky, New Orleans, New York City, Florida
Authority control
VIAF: 14765625
LCCN: n79018677
GND: 11865098X
BnF: cb118895048
ULAN: 500016578
ISNI: 0000 0001 1040 5229
WorldCat
WP-Person21_Mocking_Bird.jpg, Public Domain, https://commons.wikimedia.org/w/index.php?curid=13259783

X #AtoZAprilChallenge

nascent love like –

the new moon turns

its face away

Beginnings glow, and often fail to spark much longer. When we met we knew a few things, that experience was not measured in promiscuity, that love is for most of us a mirage, that looks and bodies change – over time – and “bien fol qui s’y fie”, as le bon Roi Henry reputedly said…

Our geometry evolved, by trial and error, infinite patience, a shared belief in waiting, respect, and, yes, tenderness, without which physical love declines into hell. Early on you decided you’d be on top, mostly. I respected your will to be in control, to decide when, in the end, to rely on this man to be what he claimed to be – nowhere to hide, the armour-less knight. One night we became what we are now: lovers for the long haul, interminable foreplay, exploring the far away shores. Once, I could have made the mistake of dreaming to tame the panther, and was saved by humour, and you showing me the way to understand myself, the feminine side of me.

For now, every time, we discover more, those secret paths that lead to new delights, the beautiful corners of ourselves we have not yet explored, in new geometries of body and soul…

mountain summit

how easily reached

by the autumn wind

– Johnny Baranski

Original Post

Walpi #AtoZAprilChallenge

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We leave Flagstaff on the I89 direction North. Soon we see the sign for the Sunset Crater and Wupatki, but today we are heading further up in the Navajo country. Shortly after Cameron we cross the Little Colorado River, theatre of many migrations over two millennia of Native American history.

We turn off East, toward Tuba City, named for Tuuvi, a Hopi Indian who converted to the Mormon faith. A small sign shows us the way to the Dinosaurs footprints. A young Navajo man welcomes us and gives us a guided tour of the prints: mind-blowing, 65-million-year-old tracks on the red rocks and sand. He explains the discovery, and that in due course more prints will appear as erosion does its work. We understand the sanctity of the place, and the due regard to time’s work: no hysterical digging here! On the horizon we see a green line following presumably a river bed: there is water there for sure, and the guide explains that farmers have been cultivating corn and other plants there for a thousand years. For $100 we could have an extended guided tour of the Western Navajo Reservation. But today we want to continue our exploration further East. We thank him, leaving a gift of $40, and after a long look at one huge footprint, we resume our voyage.

We are now travelling on Highway 264 in the direction of the Black Mesa. Traffic becomes rarer, mainly the occasional pick up trucks. We miss the Gold Mine canyon (no sign!) and soon we see the settlement of Old Oraibi. We are in view of the Third Mesa, in Hopi country. We pass the Second Mesa, and we drive up to the Hopi Cultural Center, it is lunch time already.

After we have sampled some delicious Hopi cooking, my partner Gorgeous goes negotiating with the lady in charge of the gift shop. After half an hour of diplomatic exchange, always cheerful, we receive authorisation and detailed instructions for a visit to the ancient village of Walpi on the First Mesa. Our guide, Chucky, will wait for us there.

We drive past the I87 junction, admiring the new Hopi Health Center on the South side of the Highway. We drive over Wepo bridge and shorty afterwards turn left toward the First Mesa villages. We drive slowly and carefully through Tewa and Sitsomovi, children wave at us, we wave back. We park the car on the gap, just before the village of Walpi. Our guide appears, we exchange greetings.

The site of Walpi, at the tip of the First Mesa is a wonder: high above the plateau, with 360 deg. views all round: to the North toward the Navajo Reservation and the immensity up to Utah, to the South toward the Painted Desert and the Petrified Forest (which we will visit the following day.)

In sober words, and with smiling eyes, our guide explains the village, its old houses (most of them it turns out were built in the 17th century.) He points out the patient works of maintenance to repair roofs and walls, visible on several houses. Some of the carpentry must be more than ancient. The village is immaculate: wood and stones, under the cloudless blue sky. The guide points out a steep staircase going down to the ground far below. Occasional fences protects pedestrians from falling off the street which is circular around the village. We see ancient stone ovens, clearly still in use. We see a well! We are told about the kivas, the underground ceremonial chambers much mentioned in the tradition, recognisable by the long pole merging from the opening. We are told about the kachinas, the Spirits and their representation, in ceremonial dances and in the special sculpted dolls, that are one Hopi speciality.

The village seems deserted, but it is not as we soon find out. Our guide points out his house, and we soon arrive at the Plaza, the center of village life, social and ceremonial. Walpi is special and the plaza the center also of a deep mystery: the Sipapuni, or, traditionally, the place of  emergence from the Lower World. We are told that when time comes, boys are sent to the desert to collect snakes. They are then to spend the night before the ceremony, in the kivas, with the snakes. The medicine men ensure no-one is hurt, even if a snake bites! Our guide undertook the rite as a fifteen-year old and still smiles about it…

We are shown the Sipupani, in the center of the plaza, where all tribes, including our own, came from. Is there an opening? Or the symbol of it? This is the special meaning of Walpi, and the reason why, twice a year, for the arrival and departure of the Spirits (in their own migration from and to the Sacred mountain white people called the San Francisco peaks, near Flagstaff) the main ceremonies are held in Walpi. Hopis are summoned nowadays by the Hopi radio station and the Internet. Our guide has spoken to the village chief before our arrival: we are authorised to take a picture of the plaza: awesome!

We slowly continue our walk: then our guide knocks at the low door of a small house. We are invited to enter. The room is spotless, strangely light despite the size of the very small window, and immediately its owner introduces himself. This is the workshop of a master carver of kachinas. A wood stove is burning but the room is cool. On a low table we are shown a collection of beautiful kachinas. One tall sculpture represents the gods and dancing ceremonies, with the village at the base, two eagles surveying the scene: a marvel. Our guest explains that it took him ten years to carve. Other kachinas represent spirits and dancers, there seems to be a kachina for all occasions. We see a beautiful dancing Butterfly maiden, dressed in the customary dress of the Butterfly dance: a delicate and beautifully coloured doll – what a present for a young daughter (we negotiate the price, and both of us feel good about the transaction.) The craftsman explains that such a doll is used for the education of the girls, to teach them the ways of the Hopis, their role and responsibilities.

We could listen to our guest for a long time, but we have been in the village for two hours already! We thank our guest and guide, who makes sure we are back to our car.

Slowly we drive back through the villages, children wave, we wave back. Our minds are full of images from this magic village. We take the I87 southwards, in the direction of old Homolovi, and the modern Winslow. The three os us are now four, with the Butterfly maiden, silent and smiling.

Image: the plaza at Walpi, First Mesa, courtesy of the Walpi village chief, and our guide Chucky.

Snap

#VisDare 135: Negotiating

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At long last I found you again my darling, after all those months of anxiety! Where could you be? And you are there, just in front of me, in the middle of those inert little dolls… When your turn comes be sure that fellow will notice your guy, I’m a good head above the others.

Yes, those idle folks will be surprised, such a small woman, with that huge fellow! We will laugh too, and cry a little. You will hug me, me holding you in those strong arms, my little beauty.

Then we will take the long road home, away from this city, no more auctions for you. You won’t leave my sight, on the way you’ll tell me your story. And I will tell you how much I love you, cherish you, how I feared to have lost you, and won’t let you go away again, without me…

Image source: Doll Auction at Caledonian market, 1920s.

 

Crossroads #TheDailyPost

Write a new post in response to today’s one-word prompt.

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We came to many, sometime as one, more often from different roads: yet we kept trying.

This is different, the land is elsewhere, the colours of the desert, and we only have a choice of two, for this is no cross, only a fork.

So which one do you want?

On the left is the unknown, there we have to trust, more than ever, obscure destiny…

On the right is certain death, a sweet reassurance, all in good time…

She chose obscurity.

 

Image: Shao Wenhuan – Crossroads, No. 4, 2010, via regardintemporel

 

Vanished #AtoZAprilChallenge

Dedicated to the Native American tribes, victims of the greatest genocide in history, who knew agriculture, and the art of living, when Europe was starving, crawling in medieval darkness.

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He stands on the red rocks, alone with ghosts, his sight on the painted horizon.

Slowly they appear in his vision: the millions, slaughtered by disease, hunger, the swords and bullets of the invaders.

He remembers: a people in tune with nature, who understood the path of Mother Earth, as no-one since has understood Her.

And, now, he, the white scientist, knows the end is near: his own tribe will have to leave the Fourth World, and find solace in hell.

Then the braves will rise from their forgotten graves, as trees from the desert.

Written originally for the #FiveSentenceFiction prompt “Abandon”

Photo: 12th century Wupatki ruins, Wupatki National Monument

Unlucky #AtoZAprilChallenge

Tuareg2.JPG

Captain Le Guen was a Muslim, a faith he had inherited from his mother, who, as a young child, had been rescued by the Franj from her burning village in the Aurès, during that war. He had been born in Qimper in Brittany, where Le Guen père, an officer in the Navy, had wanted to respect his wife’s wishes to bring up the boy in the faith of the Prophet. His side of the bargain was to send young Le Guen to Saint-Cyr. His religion made Le Guen a rarity in his regiment, although not in the army. A veteran of Chad, Somalia and Afghanistan Le Guen spoke Arabic fluently, and moreover the dialects of the Tuareg. At Saint-Cyr, the Franj’s officers school, he had been a distinguished linguist.

He had stopped his column in the early evening, letting the men relax, and was consulting the old Tuareg who was his guide. Their advance had been rapid, perhaps too rapid, and they had met little resistance, and recovered few weapons. As they moved further North and to the East the maps had proven less accurate, and the satellites’ positioning coordinates at time unreliable, as if someone was warning him. They were now in the desert, having left the relative moisture of the Sahel hundreds of kilometres down South.

“Two kilometres from here, said the old man, you will see an expense of darker sands, towards the North.” He paused, and Le Guen was silent, knowing better than interrupt the old man’s story. His help had been invaluable, telling him when to steer his convoy away from mine fields and other vicious traps.

The indigenous troops – Southerners who suffered a lot in the searing heat – were afraid of the old Tuareg, and had begged Le Guen to disarm him: that is to take away the ornate and ancient knife he wore at the belt of his woollen robe. Le Guen had refused, explaining in sober words that the old man was his guest, God willing. The Southerners were Muslim too and they understood, keeping their disapproval to themselves.

“Those are moving sands, resumed the guide, make sure your men understand they must not approach them”. There was a long silence. The Tuareg’s deep blue eyes, the only part of his face visible through the blue headgear, were scanning the dunes.

Le Guen exchanged a few words with his NCO’s on the short range radio, and waited. He knew the story may be continuing. “Our tradition says that a Pharaoh’s army disappeared here, many years before the Prophet himself came here. They were swallowed by the sands, men, horses, chariots, all of them.” Le Guen was listening intently. Was the story a parable?

“At night, if one is very quiet, one can still hear the horses, and men shouting.” Images of ancient warriors haunting the dunes came to Le Guen’s mind. His father had told him similar stories, from the high plateaux of Laos. He waited. “You see, the track you are now following is very old, and my people know its history…” concluded the guide.

It would be much colder tonight, and the captain had warned the men from the start. As they moved deeper into the desert the nights would get to temperature thirty or forty degrees below those of daytime. Further North Saharian nights before dawn could reach Siberian temperatures of −30 or -40 degrees centigrade.

“You asked me why you haven’t found any weapons”, said the old man in a soft voice modulated by the wind, “but you see, the weapons are here, the raiders have no need to hide them.” The guide, Le Guen noted, had used the name for cattle thieves to describe the insurgents. The captain was now looking straight at the old man. The deep blue eyes held his stare: “If you are unlucky, God forbid, you will be bringing those weapons to them, mon capitaine”. The old man lifted his arm, and turning back pointed at the long convoy, behind them, bristling with the best Franj weaponry.

Image: Algerian Tuareg, By GarrondoOwn work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=4613636

Original post

The Guardian Angel

Hopi Tawa Mural.jpeg

The old man looked out of the window into the familiar expense of the suburban garden, taking in the brightness of the tulips, the now fading bluebells and the impertinent grass, absurdly green. What a contrast with the arid plateau at the foot of the mesa!

There, on his desk, near the photograph of the assembled family – the one he’d taken on his terrace the summer before – she stood, her delicate silhouette arrested in the position of the butterfly dance, the colours of her wings shimmering in the morning light. “You are a beauty,” he thought, “And I am lucky to have you: my inspiration, my living companion…”

Soon, a cup of steaming coffee to his side, he went back to work. “This novel will never be finished,” he said to himself; “Not that I don’t want to, but now I am so slow, and I know… I will run out of time!” It was true that since his wife’s departure (he never thought of her death, merely of a delay in them being reunited) he had become very slow, as if he’d adopted a different rhythm of life. Yet he was waking up at the same time, as if she was still there, and carefully brewed coffee, as if she was waiting for her first cup, upstairs, in their room. But, now, he had gone back to long hand writing, and he was lucky to get a few hundred words into shape during his morning work.

Behind her mask, the kachina was observing him. “You are a good man,” she was saying to herself, “and, you are right, your end is near. But since you have led a good life, and understand the meaning of your life, I will do something for you…”

The old man put his pen down, and looked at her: he knew she was talking to herself, but could hear the soft voice, and he could sense the imperceptible motion of her fingers, holding the pahos, the ceremonial prayer sticks.

“Maiden, do you miss the mountains?” He asked, smiling at her, perhaps not expecting an answer. He resumed his work, the pen scratching the paper, honing words.

Later, as he was feeling more light-headed than usual, he heard her voice again.

“When the time comes, you will know what has to be done,” she said slowly, “and your people will bury you according to your rites,” she continued, “but later, you will take the trail to Maski, the Land of the Dead, and on your way there you will find me: I will wait for you, and guide you, have no fear.”

Image: A mural depicting Tawa, the sun spirit and creator in Hopi mythology. Painted Desert Inn, Petrified Forest National Park, Arizona. By Fred Kabotie, National Park Service – http://www.nps.gov/common/uploads/photogallery/20140223/park/pefo/BBBAA541-155D-451F-6780A798473458A3/BBBAA541-155D-451F-6780A798473458A3.jpg, Public Domain, https://commons.wikimedia.org/w/index.php?curid=23228610

Hopi mythology at Wikipedia

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