Kha's protractor

Kha was an architect at Deir El-Medina, Egypt, supervisor of some projects completed during the reigns of three kings of the 18th Dynasty (approximately 1440-1350 BC). Buried with his wife Merit, the items of their tomb are exposed at the Egyptian Museum, Torino. The papers at http://arxiv.org/abs/1107.4946 describes some devices of the ancient Egypt masonry (cubits, cords, plumb, levels and squares), that Kha used during his activity. An object among those found in his tomb could be used a protractor.

The figure shows an object from the Kha’s Tomb supposed to be the case of a balance scale, or the scale itself as reported by the corresponding label. In a previous preparation of the items of Kha’s Tomb, it was possible to see the front and back of the object. They are the same, with the same complex decoration.

The tool has a complex decoration, that suggested me the case could be used as a protractor, to determine directions and measure angles. The detail of decoration is shown in the following figure. 

 We see the 16-fold symmetry of a compass rose with 16 leaves as an inner decoration. Outside this rose there is a polygonal line with 18 corners and then 36 sides. In the inner decoration we can see the fraction 1/16 corresponding to one leaf. The Egyptian knew  and used the fractions as the sum of distinct unit fractions. That is, a fraction was written as a sum of fractions, each fraction having a numerator equal to 1 and a denominator equal to a positive  integer. Every positive rational number can be represented by an Egyptian fraction. In this ancient system of calculus, the Eye Of Horus defined the Old Kingdom number one, such as, 1 =  1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64, rounded-off at the six-term. A 1/64 is needed to have the exact value 1. The separated parts of the Eye of Horus were used to write describe the fractions. May be, Kha used the balance case for calculations, or simply as a protractor when he was using a plumb, a level or a scale, to find vertical or equilibrium positions, but also to measure the deviation from vertical or horizontal directions. 

Is there anything we can tell about number 36, the number of corners of the external decoration of the architect’s case? Let us remember that the Egyptians has the Decans, 36 groups of stars which rise in succession from the horizon due to the earth rotation. The rising of each decan marked the beginning of hours of the night. In the ancient Egypt, the decans were used as a sidereal clock beginning by at least the 9th or 10th Dynasty (ca 2100 BC). Probably, the object found in the Kha’s tomb had simply a geometrical decoration, such as that on another object of the tomb, which seems to be a “rose of direction”. 

The use of 1/16 fraction, the coincidence of the number of corners with that of decans, and the fact that the decoration was engraved on the instrument of an architect, suggest me that this object had been used as a protractor instrument with two scales, one based on Egyptian fractions, the other based on decans. Assuming this tool used to evaluate angles, let me show a possible set-up to measure the angle of an inclined plane. Note that the case has a lid. Let us imagine to remove the lid; the case has a perfectly linear side, that can be put on a smooth surface, as shown in the following figure.

 

(http://arxiv.org/abs/1107.4946)

When the surface is horizontal, using a plumb to have the vertical direction, one of the directions of the rose of the case coincides with the direction of the plumb (the line between leaves 1-16 or 8-9 seems to be perpendicular to the side of the case). If the surface is inclined, the direction of the rose is inclined forming a certain angle with respect to the vertical. This angle has the same value of the angle of the inclined plane.  Geometry originated as a practical science, to measure lengths, surfaces and volumes. In my opinion, Kha could have used his tool, with the contemporary use of a plumb to have a reference direction, to create a set-up able to provide a practical measurement of inclination. The Kha’s protractor could be one of the first devices to measure angles. 

References 

TT8, http://en.wikipedia.org/wiki/TT8

Turin Egyptian Museum: the tomb of Kha 

Deir El Medina: The Painted Tombs, Christine Hobson, Exploring the World of the Pharaohs: A 

complete guide to Ancient Egypt, Thames & Hudson, 1993. 

Building in Egypt; Pharaonic Stone Masonry, Dieter Arnold, Chapter 6, Tools and their 

applications, New York and Oxford, 1991 

Cubits, http://en.wikipedia.org/wiki/Cubit

E. Robens and R.S.H. Mikhail, The ancient Egyptian balance, Thermochimica Acta, Volume 

82(1), 1 December 1984, Pages 63-80. 7. Egypt Plumb Bobs, Wolfgang Ruecher, Wolf’s Plumb Bob News, Issue 02, Feb.2010, 

http://www.plumbbob.de/media//DIR_42117/DIR_120101/309a7eac7359df18ffff818cac14422e.pdf

http://en.wikipedia.org/wiki/Eye_of_Horus

http://en.wikipedia.org/wiki/Egyptian_fraction

http://en.wikipedia.org/wiki/Decans

Longobard Necropolis near the Asti-Cuneo motorway

The largest Longobard necropolis in Italy, having 760 tombs -  and one of the most important in Europe because being of a specific century, the VII -  emerged at Sant'Albano Stura, during the works for the Asti-Cuneo motorway. A great discovery, because of the many tombs have funerary items. The necropolis was discovered in the spring 2009; just today the supervisor of Archaeological Studies, Egle Micheletto, gives the announcement, a few weeks after the conclusion of  excavations.
 http://torino.repubblica.it/cronaca/2011/07/25/news/una_necropoli_longobarda_negli_scavi_della_asti-cuneo-19567203/

Necropoli longobarda sulla Asti-Cuneo

"La più grande necropoli longobarda in Italia, ricca di 760 tombe, una tra le principali anche in Europa in quanto ascrivibile a un unico secolo, il VII, e’ emersa a Sant’Albano Stura, durante i lavori per l’autostrada Asti-Cuneo. Un ritrovamento eccezionale – anche perché più della metà delle sepolture è dotata di corredi funerari - venuto alla luce a partire dalla primavera 2009, ma di cui la soprintendente ai Beni archeologici Egle Micheletto dà notizia solo ora, a poche settimane dalla conclusione degli scavi"
http://torino.repubblica.it/cronaca/2011/07/25/news/una_necropoli_longobarda_negli_scavi_della_asti-cuneo-19567203/

The decreasing level of Toshka Lakes seen from space

The decreasing level of Toshka Lakes seen from space
by Amelia Carolina Sparavigna, Dipartimento di Fisica,
Politecnico di Torino, Torino, Italy
Abstract

Toshka Lakes are lakes recently formed in the Sahara Desert of Egypt, by the water of the Nile, conveyed from the Nasser Lake through a canal in the Toshka Depression. From space, astronauts noticed the growing of a first lake, the easternmost one, in 1998. Then additional lakes  grew in succession due west, the westernmost one between 2000 and 2001. In fact, sources of  precious information on Toshka Lakes are the pictures takes by the crews of space missions and  the satellite imagery. They show that, from 2006, the lakes started shrinking. A set of recent  images displays that the surface of the easternmost lake is strongly reduced.
More
http://arxiv.org/abs/1107.4430

 

The easternmost of the Toshka Lakes in 2005 (NASA imagery)

 

The same lake in 2011 (NASA imagery, March 31, 2011)

 

Superposition of the two images. Note the strong decreasing of the surface of the lake. 

Read the detailed discussion at Toshka Lakes  on this blog.

100 años de Machu Picchu

100 años de Machu Picchu a 100 km de indígenas aislados - ConNuestroPeru
"El 24 de julio se celebra el centenario del "descubrimiento" de Machu Picchu, la ciudadela inca en lo alto de los Andes peruanos, por el explorador y académico estadounidense Hiram Bingham. Pero al tiempo que Perú celebra el legado de los indígenas incas, también planea garantizar a las empresas de hidrocarburos el acceso a las tierras de los indígenas aislados en la reserva de Kugapakori-Nahua-Nanti, lo que supondría un riesgo extremo para sus vidas. "

More

100 años de Machu Picchu a 100 km de indígenas aislados

Un reactor que convierte la luz solar en combustible

"Investigadores estadounidenses y suizos han creado un pequeño reactor capaz de producir rápidamente combustible a partir de la luz solar, utilizando para ello agua, dióxido de carbono y óxido de cerio. El proceso es semejante al que utilizan las plantas para crecer y de él da cuenta la revista Science en su última edición. El prototipo ha sido desarrollado por un equipo formado por investigadores del Instituto de Tecnología de California (EE.UU) y de la Escuela Superior Eidgenössische Technische y el Instituto Paul Scherrer de Suiza. Opera captando los rayos del sol y concentrándolas en un cristal de cuarzo, proyectando el haz de luz sobre un óxido de metal conocido como óxido de cerio o cerio."

Desarrollan un reactor que convierte la luz solar en combustible

Shoemaker Impact Structure

"The Shoemaker (formerly Teague) Impact Structure—located in Western Australia in a drainage basin south of the Waldburg Range—presents an other-worldly appearance in this astronaut photograph. The Shoemaker impact site is approximately 30 kilometers (19 miles) in diameter and clearly defined by concentric ring structures formed in sedimentary rocks (brown to dark brown, image center). The rocks were deformed by the impact event approximately 1.63 billion years ago (as reported by the Earth Impact Database). Other age-dating analyses of granitic rocks at the core of the structure call this age into question (Pirajno et al. 2003)."
http://eol.jsc.nasa.gov/EarthObservatory/Shoemaker_Impact_Structure.htm
"Beginning with the Mercury missions in the early 1960s, astronauts have taken photographs of the Earth. Our database tracks the locations, supporting data, and digital images for these photographs. We process images coming down from the International Space Station on a daily basis and add them to the 1,101,059 views of the Earth already made accessible on our website."

The gospel according to Judas

The gospel of Jesus's favourite disciple, Judas, was on show before its return to Egypt where it was found 30 years ago. "The fragile codex -- made up of 13 papyrus leaves -- has been restored with a two-million-dollar fund from the National Geographic Society (NGS) and the Waitt Institute for Historical Discovery. Its most recent owners, the Basel-based Maecenas Foundation for Ancient Art (MFAA), will now hand the codex over to the Coptic Museum in Old Cairo. The gospel, written in Coptic in the third or fourth century, is believed to be a translation of an original Greek text belonging to an early Christian sect sometime before AD180. The document offers new insights into the relation between Jesus and Judas, whose betrayal led to his capture and crucifixion. Unlike the gospels of Matthew, Mark, Luke and John, in which Judas is portrayed as a reviled traitor, the new gospel depicts him as acting on a request by Jesus to hand him over to the Romans."

The gospel according to Judas - Coptic - Heritage - Ahram Online

The first ever ancient Egyptian epigraphy

"Following the relocation of the artefacts, a team from Yale University, the University of Bologna and the Provinciale Hogeschool Limburg, Belgium, has completed the first epigraphic and digital record of a site near Nag El-Hamdulab on the west bank of the Nile, north of Aswan. The site was discovered nearly half a century ago by the famous Egyptian Egyptologist Labib Habachi. Minister of State for Antiquities Zahi Hawass said this new and thorough study has brought to light a previously unknown Early Dynastic cycle of royal images and an early hieroglyphic inscription. This work was carried out by the Aswan-Kom Ombo Archaeological Project (AKAP)..., lead by Maria Carmela Gatto and Antonio Curci, ... Now in its seventh season, the project aims to survey and rescue the archaeology of the region between Aswan and Kom Ombo, in the southern part of Upper Egypt. Gatto said that this group of images and the short inscription—carved around 3200 BCE, at the dawn of the dynastic period—record the earliest depiction of a royal Jubilee complete of all the elements known from later documents: an Egyptian ruler wearing a recognizable crown of Egypt; “the following of Horus”; and the royal court as known it is known to have been in Early Dynastic accounts such as the Palermo Stone."

The first ever ancient Egyptian epigraphy - Ancient Egypt - Heritage - Ahram Online

Cocoons

"...a new finding of ancient wasp cocoons hidden inside the fossilized egg of a titanosaur sauropod.
The research, published July 15 in the journal Palaeontology, suggests the ancient wasps played an important role in certain food webs during the Age of Dinosaurs. The clutch of five eggs ... belonging to a titanosaur (among the largest creatures to ever walk the Earth), was discovered in 1989 in the Patagonia region of Argentina; only recently did scientists discover that one of the broken eggs contained tiny sausage-shaped structures. The size and shape of the structures, which are about an inch long and 0.3 inches wide (2-3 cm by 1 cm), most closely matched cocoons made by some species of modern wasp ...".
http://www.cbsnews.com/stories/2011/07/15/scitech/main20079883.shtml

Appelli del Santo Padre per la Somalia e il Corno d'Africa

«Con profonda preoccupazione seguo le notizie provenienti dalla regione del Corno d`Africa e in particolare dalla Somalia, colpita da una gravissima siccità e in seguito, in alcune zone, anche da forti piogge, che stanno causando una catastrofe umanitaria». Lo ha detto papa Benedetto XVI durante l'Angelus da Castel Gandolfo, ricordando le «innumerevoli persone stanno fuggendo da quella tremenda carestia in cerca di cibo e di aiuti».
«Auspico - ha poi detto facendo un appello - che cresca la mobilitazione internazionale per inviare tempestivamente soccorsi a questi nostri fratelli e sorelle già duramente provati, tra cui vi sono tanti bambini. Non manchi a queste popolazioni sofferenti - ha concluso Benedetto XVI - la nostra solidarietà e il concreto sostegno di tutte le persone di buona volontà».
http://www.ilsole24ore.com/art/notizie/2011-07-17/somalia-appello-papa-mobilitazione-143930.shtml?uuid=AaeT6toD
http://www.vatican.va/holy_father/benedict_xvi/angelus/2011/documents/hf_ben-xvi_ang_20110717_it.html

Biofuel for flights

"Lufthansa, Europe's second-largest airline, became the first carrier in the world to offer regular scheduled flights running on biofuel, with four daily round trips between Hamburg and Frankfurt.
The airline will use a biofuel blend using 50 per cent so- called hydrotreated renewable jet fuel, Lufthansa said. The fuel is made from feedstocks including inedible plants and wood chips. Lufthansa will fly an Airbus A321 on the services." Read more
http://www.smh.com.au/travel/travel-news/lufthansa-begins-worlds-first-regular-biofuel-flights-20110718-1hks1.html

Harappa

An interesting problem concerning the development of  writing systems, is the following: where had they first appeared? Probably, writing systems developed independently in at least three places, Egypt, Mesopotamia and Harappa. In places where an agricultural civilization flourished, the passage from the use of symbols to a true writing system was early accomplished. It means that, at certain period in some densely populated area, signs and symbols were eventually used to create a writing system, the more complex society requiring an increase in recording and communication media.

On Harappa culture see http://www.mongabay.com/reference/country_studies/india/all.html

 and http://en.wikipedia.org/wiki/Indus_Valley_Civilization 

The earliest signs of human activities in India go back to the Palaeolithic Age, roughly between 400,000 and 200,000 B.C. Stone objects and cave paintings from this period have been discovered in many parts of the South Asia. Evidence of domestication of animals, agriculture, permanent village settlements, and wheel-turned pottery, dating from the middle of the sixth millennium B.C., has been found in Sindh and Baluchistan, (both in Pakistan). One of the first great civilizations--with a writing system, urban centers, and a diversified social and economic system--appeared around 3,000 B.C. along the Indus River valley in Punjab and Sindh.

The remains of two major cities - Mohenjo-daro and Harappa - reveal remarkable urban planning, systems of water supply and drainage. Excavations at these sites and later archaeological digs at about seventy other locations in India and Pakistan provide the knowledge of what is now generally known as the Harappan culture (2500-1600 B.C.).

The major cities contained a few large buildings including a citadel, a large bath, flat-roofed brick houses, fortified administrative or religious centers having meeting halls and granaries. Essentially a city culture, Harappa civilization flourished  because it was supported by a solid agricultural production and by the commerce, which included trade with Sumer inMesopotamia. The people made tools and weapons from copper and bronze but not iron. Cotton was woven and dyed for clothing. Wheat, rice, and several vegetables and fruits were cultivated. A number of animals, including the humped bull, were domesticated. The scholars consider the Harappan culture as conservative, because it seems that it remained relatively unchanged for centuries: for instance, when the villages were rebuilt after flooding, the new constructions closely followed the previous ones. Stability seems then  to have been one of the features of this civilization, but it is not yet clear who had the power, whether an aristocracy of priests or the community of traders.

Interesting artifacts of Harappa are steatite seals. These small, flat, squared objects with human or animal motifs provide a picture of the Harappan life. They also have inscriptions generally thought to be in the Harappan script, which has eluded the scholarly attempts at deciphering it. There is a large debate whether these signs represent numbers or are an alphabet. If there is an Harappan alphabet is proto-Dravidian or proto-Sanskrit?

A possible reasons for the decline of civilization of Harappa was the invasions from central and western Asia,  destroyers of Harappan cities. Other causes were several  recurrent floods, earthquakes, the increases of soil salinity and desertification.

Let me compare in  the following figures, a small terracotta elephant head from Harappa and a representation of Ganesha (Museo Arti Orientali, Torino), and a small statue form Mohenjo-Daro with a statue of Parvati.

For more references on the problem of Harappa writing system, see

“Icons and signs for the ancient Harappa”, http://cogprints.org/6179/

Volcanoes under Antarctic waters

"Scientists from British Antarctic Survey (BAS) have discovered previously unknown volcanoes in the ocean waters around the remote South Sandwich Islands. Using ship-borne sea-floor mapping technology during research cruises onboard the RRSJames Clark Ross, the scientists found 12 volcanoes beneath the sea surface — some up to 3km high. They found 5km diameter craters left by collapsing volcanoes and 7 active volcanoes visible above the sea as a chain of islands."
More http://www.antarctica.ac.uk/press/press_releases/press_release.php?id=1541

The Lady of Introd

Notizia ANSA
Trovato in Valle d'Aosta scheletro donna di 5.000 anni fa. Contemporanea di Oetzi, l'uomo del Similaun, ritrovato nel '91 l confine tra l'Italia e il Tirolo austriaco. E' ora chiamata la Signora di Introd, 16 luglio, 2011.
Found in Valle d'Aosta the skeleton of a woman, lived 5,000 years ago. She was contemporary of Oetzi the Iceman, discovered in '91 at the Italian border with Austria. She is called the "Lady of Introd", July 16, 2011.

"La Stampa"
http://multimedia.lastampa.it/multimedia/in-italia/lstp/65668/

E' stata soprannominata la "Signora di Introd" e dopo 5000 anni la sua sepoltura è ancora perfetta. Lo scheletro di questa donna ancora misteriosa e ancora senza età, è stata ritrovato all’interno di una tomba ad Introd, paese alpino di poco più di 600 abitanti, non lontano da Aosta. Rannicchiata sul fianco destro e con il capo rivolto a nord ovest, non ha attorno nessun oggetto di corredo funebre. I resti della signora sono già stati trasferiti in laboratorio, dove nei prossimi giorni saranno oggetto di analisi approfondite per determinarne l'età, le abitudini alimentari e la causa di morte. L’Assessore all’Istruzione e Cultura Laurent Viérin esprime“grande soddisfazione per questo importante ritrovamento, unico nel suo genere, che testimonia la ricchezza e la qualità del patrimonio archeologico valdostano e della nostra storia.”

She is the "Lady of Introd" and 5000 years after the burial her skeleton is still perfect. This woman is a mystery and her age has yet to be determined. She was found in a tomb, at Introd, a mountain village with 600 inhabitants, not far from Aosta. Huddled on her right side and with the head facing west, no objects had accompanied her burial place. The remains of the woman have already been transferred in a laboratory, where, over the next few days, it will be determined the age, habits and cause of death. The Head of the Education and Culture Council, Laurent Vierin, told that there is a great satisfaction for this important and unique discovery, demonstrating the abundance and quality of the archaeological heritage of the Aosta Valley.