Welcome!

Benvenuti in queste pagine dedicate a scienza, storia ed arte. Amelia Carolina Sparavigna, Torino

Thursday, September 27, 2012

Silbury Hill


Silbury Hill on Google Earth

More info
A possible role of Alpha Crucis in the astronomical landscape of Silbury Hill

Tuesday, September 25, 2012

Sunday, September 23, 2012

Robert Wilson's portraits

Robert Wilson's portraits of Brad Pitt and Johnny Depp


Robert Wilson: Portraits at Palazzo Madama

Video portraits by Robert Wilson, an artist, choreographer, painter, video artist, sound and light designer -http://robertwilson.com/about/biography, at Palazzo Madama, from 20th September to 06th January 2013.
Subjects of his video-portraits are among the others,  actors such as Brad Pitt and  Johnny Depp, and a  Nobel Laureate, the writer Gao Xingjian. His videoportrait is in the treasure tower of the Palazzo. We can see him on the bent glasses of  a showcase of  the tower.






Werewolf

Greg Weeks produced the following for
http://www.gutenberg.org/cache/epub/33730/pg33730.html

Lycanthropus, by C. EDGAR BOLEN

The jellied night has oozed its miry black
From out the hills to fill the valley floor.
Atop the ragged hills the torn cloud-wrack
Is lightning-limned into a hellish door.
A gust of wind across the sky is hurled—
The gods of old are loosed upon the world.

Age-old, the blood-lust wells within my throat;
Tensely I wait, and feel my body shrink;
My hairless hide becomes a furry coat.
Blood-hungry, through the opened door I slink;
I raise my head and howl in horrid glee—
And from the plain a howl comes back to me.



According to the TRANSCRIBER'S NOTE: This etext was produced from Weird Tales August-September 1936.

After the Fox


Dear Author (Rob Lee), thank you for this beautiful picture!

"I was lucky and had my telephoto lens (200mm) on the camera when he came for a visit. He's sporting his winter look. Here he is last spring when he was younger (same angle)" writes Rob Lee on 2006.
http://en.wikipedia.org/wiki/File:Fuzzy_Freddy.jpg
 www.flickr.com/photos/roblee/34957634/in/set-773976/
www.flickr.com/photos/roblee/11655198/in/set-1357853/
Author Rob Lee from Evergreen, CO, USA


Suricata suricatta


Suricata suricatta :  A group of Meerkats at Auckland Zoo, New Zealand.
Date 27 June 2009, Source originally posted to Flickr as Meerkats
Author Ashleigh Thompson


 Dear Author (Ashleigh Thompson), Thank you for this beautiful picture! 


Saturday, September 22, 2012

When America discovered Europe

A very remarkable book this one
The American discovery of Europe,  By Jack D. Forbes
 Let me suggest the reading of it. To stimulate the curiosity, here some small abstracts

What is Cornelius Nepos telling? And Pliny?



The world's first seismometer was Chinese


Who was the inventor of the first siesmometer?
 Zhang Heng. He was  (AD 78–139) a Chinese astronomer, mathematician, inventor, geographer, cartographer, artist, poet, statesman. He lived under the Han Dynasty (AD 25–220) of China. He was a  Chief Astronomer, Prefect of the Majors for Official Carriages, and then Palace Attendant at the imperial court.  He invented the world's first water-powered armillary sphere,  improved the inflow water clock by adding another tank and invented the world's first seismometer, which discerned the cardinal direction of an earthquake 500 km away. He improved previous Chinese calculations of the formula for pi. In addition to documenting about 2,500 stars in his extensive star catalogue. Some modern scholars have also compared his work in astronomy to that of Ptolemy (AD 86–161). (Adapted from Wiki)

 A replica of an ancient Chinese Siesmograph  (25-220 CE). Picture taken in July 2004  at Chabot Space & Science Center in Oakland California.
"In 132 CE, after several serious earthquakes in China, astronomer Zhang Heng invented this instrument to warn people of the next one. When the ground shook, it moved a pendulum inside the jug. The pendulum pushed a lever that opened one dragon's mouth. A ball rolled out and into the toad's mouth below, sounding an alarm. The open dragon mouth pointed in the direction of the earthquake, notifying the Emperor."
http://en.wikipedia.org/wiki/File:EastHanSeismograph.JPG

Friday, September 21, 2012

Ancient solar observatories: Stonehenge





This is Stonehenge. The image shows directions of sun during the day. “The lines on the drawing show the direction and height (altitude) of the sun throughout the day. Thicker and shorter lines mean the sun is higher in the sky. Longer and thinner lines mean the sun is closer to the horizon”, according to Sollumis.com http://www.sollumis.com/. The site is located in the Google Maps. The direction of the sun is given on the summer solstice, choosing an altar at the circle for observation. We see that, at sunrise, the sun is passing near the stone outside the circle.

Thursday, September 20, 2012

The qocha of Chuquiña

Chuquiña is a small town in Bolivia.
Near Chuquiña satellite maps show a huge "qocha".
A "qocha" (small lake, lagoon)  is an artificial pond used to gain water for cultivation.
Waru-warus, camellones, qochas were old pre-incaic cultivation techniques.





On Andean qochas you can find more info here
http://www.archaeogate.org/sperimentale/article/1396/1/qochas-on-andean-highlands-by-amelia-carolina-sparavign.html
http://stretchingtheboundaries.blogspot.it/2011/04/qocha.html
http://stretchingtheboundaries.blogspot.it/2011/04/raised-fields.html
http://stretchingtheboundaries.blogspot.it/2011/05/le-qochas-dellaltopiano-andino.html

Wednesday, September 19, 2012

Our Starman

Didn't know what time it was and the lights were low
I leaned back on my radio
Some cat was layin' down some rock 'n' roll 'lotta soul,  he said...
Then the loud sound did seem to fade
Came back like a slow voice on a wave of phase
That weren't no D.J. that was hazy cosmic jive

There's a starman waiting in the sky
He'd like to come and meet us
But he thinks he'd blow our minds
There's a starman waiting in the sky
He's told us not to blow it
Cause he knows it's all worthwhile
He told me:
Let the children lose it
Let the children use it
Let all the children boogie


I had to phone someone so I picked on you
Hey, that's far out so you heard him too!
Switch on the TV
we may pick him up on channel two
Look out your window I can see his light
If we can sparkle he may land tonight
Don't tell your poppa or he'll get us locked up in fright

Starman, by David Bowie


Our Starman, farewell


Neil Armstrong, Apollo 11, NASA

http://www.theatlantic.com/technology/archive/2012/07/the-apollo-11-journey-in-photographs/260125/

Wednesday, August 22, 2012

The legend of Cangjie

After unifying China, the Yellow Emperor, being terribly dissatisfied with his Quipu method  of recording information, charged Cangjie of creating characters for writing. Cangjie then settled down on the bank of a river, and devoted himself to the completion of the task at hand. ... One day, Cangjie  saw a phoenix flying in the sky above, carrying an object in its beak. The object fell to the ground directly in front of Cangjie, and he saw it to be an impression of a hoof-print. Not being able to recognize which animal the print belonged to, he asked for the help of a local hunter passing by on the road. The hunter told him that this was the hoof-print of a Pixiu. This conversation with the hunter greatly inspired Cangjie  ... From that day forward, Cangjie paid close attention to the characteristics of all things, including the sun, moon, stars, clouds, lakes, oceans, as well as all manner of bird and beast. He began to create characters according to the special characteristics he found, and before long, had compiled a long list of characters for writing. To the delight of the Yellow Emperor, Cangjie presented him with the complete set of characters.
Adapetd from Wikipedia http://en.wikipedia.org/wiki/Cangjie


Cangjie
Public domain image

Wednesday, August 15, 2012

Empresa destruye patrimonio cultural

Empresa destruye patrimonio cultural
"El observatorio más antiguo de América, es afectado por trabajos de empresa autorizada por el INC. Desconocen informes que dan cuenta de restos arqueológicos alrededor de área patrimonial."
http://www.connuestroperu.com/actualidad/miscelanea/22-miscelanea/22705-empresa-destruye-patrimonio-cultural

Ancient solar observatories: Syrian desert

The Syrian desert is covered by ancient stone structures created during Neolithic times, as I discussed in the paper, Stone circles on the harraat of Syrian desert, published at http://arxiv.org/abs/1106.4665
Some of these stone structures are circular, with radial lines of stones. These circles have been also compared with Stonehenge. Therefore, we can ask ourselves, are these solar observatories too, as Stonehenge is.
The answer is probably so, see my paper at http://arxiv.org/abs/1208.2591
I used a software for the solar energy applications to see the direction of sun on sunrise and sunset of solstice. It seems that there is a good agreement. Therefore, the Syrian stone circles are probably the Stonehenges of Middle East.

This is one of the stone structure of Syrian Desert. The image shows directions of sun during the day. “The lines on the drawing show the direction and height (altitude) of the sun throughout the day. Thicker and shorter lines mean the sun is higher in the sky. Longer and thinner lines mean the sun is closer to the horizon”, according to Sollumis.com http://www.sollumis.com/. On the left, the site as it appears in the Google Maps. In the middle, the direction of the sun on the summer solstice, choosing the center of the circle for observation. We see that, at sunrise, the sun is passing near the dot. At the sunset the direction is that of a line. In the image on the right, we see the direction of the sun on winter solstice. At sunrise, the lines is passing between dots. The sunset has the direction of a radius (images have been obtained from original provided by Google Maps and sollumis.com).

Circles and lines!
Alignemnt at the sunrise on the winter solstice


At the site http://www.dp-news.com/en/detail.aspx?articleid=97188
it is told that "He (David Kennedy) explains that they come in a huge variety of forms, some being ‘kites’, structures that funnelled animals, some being seemingly random meandering lines of stone and others being rectangular. None are believed to be aligned with the stars, which has added to the mystery surrounding their purpose." Well, in my opinion it is not so.

Thursday, July 19, 2012

Do dolphins think nonlinearly? - physicsworld.com

Do dolphins think nonlinearly? - physicsworld.com
"Unlike solid objects such as the sea floor or fish – which reflect acoustic signals linearly, as straight-forward echoes – bubbles reflect nonlinearly. This means that acoustic echoes from bubbles contain harmonic frequencies in addition to the fundamental frequencies of the outgoing signal – producing a "clutter" that is incredibly confusing to sonar. And to make matters worse, bubbles are extremely efficient at reflecting sound."

Tuesday, July 3, 2012

Rumors

Higgs Bosons Rumors: Hopes that Cern scientists have found the Higgs Boson were strengthened yesterday when rival American researchers announced their strongest evidence yet of its existence.
http://www.telegraph.co.uk/science/large-hadron-collider/9370677/Higgs-Boson-rumours-strengthened-by-Tevatron-data.html

Sunday, July 1, 2012

Huge and old crater in Groenlandia

Descubren cráter del asteroide más antiguo y grande en Groenlandia
"Un cráter de 100 kilómetros de ancho fue descubierto en Groenlandia y corresponde al impacto más antiguo y del asteroide más grande que se conoce hasta ahora, asegura un artículo publicado en la revista Earth and Planetary Science Letters."

Friday, June 29, 2012

Small oscillations...

"Researchers Terry Hunt and Carl Lipo test a new theory that suggests how ancient Easter Islanders may have used ropes to “walk” the moai to their platforms. Mystery of Easter Island"http://ngm.nationalgeographic.com/2012/07/easter-island/walking-statue-video

20,000 years old pottery in a Chinese cave

"BEIJING (AP) - Pottery fragments found in a south China cave have been confirmed to be 20,000 years old, making them the oldest known pottery in the world, archaeologists say."
New Jersey Herald - Pottery 20,000 years old found in a Chinese cave

Saturday, June 23, 2012

Roman jewelry in Japan

TOKYO —"Glass jewelry believed to have been made by Roman craftsmen has been found in an ancient tomb in Japan, researchers said Friday, in a sign the empire’s influence may have reached the edge of Asia."
http://www.japantoday.com/category/national/view/roman-jewelry-found-in-ancient-tomb-near-kyoto

A portrait of Julius Caesar


My image processing based on the Tusculum Bust, Museo Archeologico di Torino.
The Tusculum bust is considered a portrait of Julius Caesar

Friday, June 22, 2012

Alan Turing

Google celebrates the 100th birthday of a computer genius, Alan Mathison Turing (23 June 1912 - 7 June 1954) with a doodle. He is the founder of computer science. He broke the german Enigma-ciphered code.

http://timesofindia.indiatimes.com/tech/news/internet/Alan-Mathison-Turings-100th-birthday-Google-pays-tribute-with-a-doodle/articleshow/14353203.cms

Thursday, June 21, 2012

Silicene

Silicene pops out of the plane - physicsworld.com
"Researchers in Japan say that they have made 2D honeycomb crystals of silicon that resemble the carbon-based material graphene. This is the second potential sighting of the material dubbed "silicene"; the other was reported in April by an independent group in Europe. The Japanese research suggests it may be relatively easy to alter the structure of silicene by changing the substrate on which it is grown – which could allow different versions of silicene to be produced with a range of useful electronic properties. However, not all scientists agree that this latest material is actually silicene."

Tuesday, June 19, 2012

Arles, Turin and Caesar

The heart of the ancient history of Arles, this is what is on show at the Louvre Museum of Paris, until 25 June 2012. The Museum is  hosting an exhibition of spectacular Roman pieces recovered from the bottom of the Rhone! From March 9 to June 25, 2012, the Louvre Museum in Paris

On exhibition fifty of the most spectacular artifacts unearthed by archaeologists: columns and capitals, fragments of statues and reliefs, Roman jewelery, lamps, vases ... These pieces are coming from the museum of Arles, and other pieces from Avignon, Vienne and Turin.
Among the pieces from Turin, you can admire Julius Caesar's bust, unearthed in 1825,  long considered unique, until the discovery in 2007 in Arles of another bust of the Roman politician. At the Louvre, these sculptures will be presented for the first time side by side.


http://www.france.fr/it/arti-e-cultura/evenement/arles-gli-scavi-del-rodano-un-fiume-memoria

   Arles

Torino

Un altro ritratto interessante è quello del busto Farnese, a Napoli

 Napoli


Thursday, June 14, 2012

Blackwood and Lovecraft

Of such great powers or beings there may be conceivably a survival... a survival of a hugely remote period when... consciousness was manifested, perhaps, in shapes and forms long since withdrawn before the tide of advancing humanity... forms of which poetry and legend alone have caught a flying memory and called them gods, monsters, mythical beings of all sorts and kinds...

These words written by Algernon Blackwood introduce the The Call of Cthulhu, by H. P. Lovecraft. 

"The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age." 

Tuesday, June 12, 2012

Ancient Rainfall, Carved in Stone

"Stalactites grow from cave ceilings not as dull cones but often sporting elegant corrugations. In Physical Review Letters, two Italian researchers now explain these mysterious, wavy patterns using standard fluid mechanics. Their theory shows that the horizontal ripples form because spatially periodic patterns arise in the rate of mineral deposits from the water flowing down the stalactite. Starting from this model, climate scientists might in the future use stalactite surface structure to reconstruct variations in precipitation patterns over tens of thousands of years."
Ancient Rainfall, Carved in Stone

Friday, June 1, 2012

NGC 891

Another superb image at http://apod.nasa.gov/apod/ap120526.html
" This sharp cosmic portrait features NGC 891. .. At first glance, it has a flat, thin, galactic disk and a central bulge cut along the middle by regions of darkobscuring dust. The combined image data also reveal the galaxy's young blue star clusters and telltale pinkish star forming regions. And remarkably apparent in NGC 891's edge-on presentation are filaments of dust that extend hundreds of light-years above and below the center line. The dust has likely been blown out of the disk by supernova explosions or intense star formation activity. "

Here the NASA image after processing with AstroFracTool and Iris


Transit of Mercury

Very beautiful image at http://apod.nasa.gov/apod/ap120527.html Image Credit: SOHO - EIT Consortium, NASA
"The diminutive disk of Mercury, the solar system's innermost planet, spent about five hours crossing in front of the enormous solar disk in 2003 ... the horizon was certainly no problemfor the sun-staring SOHO spacecraft. Seen as a dark spot, Mercury progresses from left to right (top panel to bottom) in these four images from SOHO's extreme ultraviolet camera. The panels' false-colors correspond to different wavelengths in the extreme ultraviolet which highlight regions above the Sun's visible surface."

Here the image from NASA after processing with IRIS




Transit of Venus

"The next transit of Venus, where Venus appears as a dark spot in front of the Sun, will begin at 22:09 UTC on 5 June 2012, and will finish at 04:49 UTC on 6 June.[1] Depending on the position of the observer, the exact times can vary by up to ±7 minutes. Transits of Venus occur in pairs that are eight years apart: the previous transit was in June 2004, and the next pair of transits will occur in December 2117 and December 2125." from Wikipedia

Aristarchus proposed to measure the distance to the Sun using parallax. This approach based on the geometric principles of parallax last for two thousands of years, until Edmond Halley in 1716 proposed to observe the transit of Venus. The use of Venus transits gave an estimate of 1.53×10^13 cm, 2.6% above the currently accepted value, that of l.49 × 10^13 cm. More recently, in 1910, the parallax was measured using the asteroid Eros that passed much closer to Earth than Venus. A transit of Venus happens when this planet passes directly between the Sun and Earth, appearing as a small black disk moving across the Sun bright disk. The duration of such transits is usually measured in hours.
Read more "Two amateur astronomers at Berkeley", at http://arxiv.org/abs/1202.0950

Tuesday, May 8, 2012

An ancient rangefinder (Roman Dodecahedron)

According to Wikipedia, "a rangefinder is a device that measures distance from the observer to a target, for the purposes of surveying, determining focus in photography, or accurately aiming a weapon. Some devices use active methods to measure (such as sonar, laser, or radar); others measure distance using trigonometry (stadiametric rangefinders and parallax, or coincidence rangefinders). These methodologies use a set of known information, usually distances or target sizes, to make the measurement, and have been in regular use since the 18th century".
 It could be surprising, but probably the Roman Army had a rangefinder. It was the Roman Dodecahedron (I have already discussed it in some posts and papers: on arXiv, where I am explaining how  it can be used for measuring distance as a rangefinder, http://arxiv.org/abs/1204.6497 ).
For me, those dodecahedrons having a structure with holes of different sizes, are military instruments to evaluate distances for ballistics. It is simple to use. Of course, later, during the Middle Age, different instruments had been developed for surveying: the dodecahedron was of the Roman Army, and, probably, its use lost after the collpase of the Empire. See also "Ancient and Modern Rangefinders", on arXiv, http://arxiv.org/abs/1205.2078 and on SCIRP  http://www.scirp.org/journal/PaperInformation.aspx?PaperID=23245




Sunday, May 6, 2012

M R James - Casting the Runes

Montague Rhodes James, who used the publication name M. R. James, was an English mediaeval scholar and provost of King's College, Cambridge (1905–1918), and of Eton College (1918–1936). He is best remembered for his ghost stories. In his stories, James's protagonists and plots tend to reflect his own antiquarian interests. Among the "antiquarian ghost stories", there is the "Casting the Runes"

"One chapter in particular struck me, in which he (Karswell)  spoke of "casting the Runes" on people, either for the purpose of gaining their affection or of getting them out of the way--perhaps more especially the latter: he spoke of all this in a way that really seemed to me to imply actual knowledge. ...
By way of answer, Dunning had the episode in the Manuscript Room at the British Museum to relate. 'Then he did actually hand you some papers; have you examined them? No? because we must, if you'll allow it, look at them at once, and very carefully.'
They went to the still empty house--empty, for the two servants were not yet able to return to work. Dunning's portfolio of papers was gathering dust on the writing-table. In it were the quires of small-sized scribbling paper which he used for his transcripts: and from one of these, as he took it up, there slipped and fluttered out into the room with uncanny quickness, a strip of thin light paper. The window was open, but Harrington slammed it to, just in time to intercept the paper, which he caught. 'I thought so,' he said; 'it might be the identical thing that was given to my brother. You'll have to look out, Dunning; this may mean something quite serious for you.'
A long consultation took place. The paper was narrowly examined. As Harrington had said, the characters on it were more like Runes than anything else, but not decipherable by either man, and both hesitated to copy them, for fear, as they confessed, of perpetuating whatever evil purpose they might conceal. So it has remained impossible to ascertain what was conveyed in this curious message or commission. Both Dunning and Harrington are firmly convinced that it had the effect of bringing its possessors into very undesirable company. That it must be returned to the source whence it came they were agreed, and further, that the only safe and certain way was that of personal service; and here contrivance would be necessary, for Dunning was known by sight to Karswell. ...".

http://www.classicreader.com/book/1833/1/

Casting the dice

"Cleromancy is a form of divination using sortition, casting of lots, or casting bones or stones, in which an outcome is determined by means that normally would be considered random, such as the rolling of dice, but are sometimes believed to reveal the will of God, or other supernatural entities." Source: Wikipedia
"Alea iacta est (Latin: "The die has been cast") is a Latin phrase attributed by Suetonius (as iacta alea est) to Julius Caesar on January 10, 49 BC as he led his army across the River Rubicon in Northern Italy. With this step, he entered Italy at the head of his army in defiance and began his long civil war against Pompey and the Optimates. The phrase is still used today to mean that events have passed a point of no return, that something inevitably will happen." Source: Wikipedia

Saturday, May 5, 2012

On Roman and Etruscan Dodecahedra again

This morning I found the following link: http://sculpture.net/community/showthread.php?t=10801 having a quite interesting discussion on the " Roman Dodecahedron Mystery "
Let me report what SteveW wrote:
"This object is an on-the-fly surveying device. Worn on a chain around the neck, a military officer could hold it out to arms length and "fit" an enemy soldier or catapult, ballista etc between the opposing holes and then multiply by 100 (or whatever factor/number of links of the chain) to guage his distance. It would have been accurate enough to place a man within a few feet up to roughly a mile away. "
This is a quite good  reference for my paper  A Roman Dodecahedron for measuring distance
http://arxiv.org/abs/1204.6497

A figure from my paper http://arxiv.org/abs/1204.6497

Somebody is considering that there are also dodecahedra of stones. These were tools for gambling, please see An Etruscan Dodecahedron http://arxiv.org/abs/1205.0706 or the previously written post.

Friday, May 4, 2012

An Etruscan Dodecahedron

An Etruscan Dodecahedron, by Amelia Carolina Sparavigna
Department of Applied Science and Technology
Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, Italy
published on arXiv, http://arxiv.org/abs/1205.0706

The paper is proposing a short discussion on the ancient knowledge of Platonic solids, in particular, by Italic people.

How old is the knowledge of Platonic solids? Were they already known to the ancients, before Plato? If we consider Wikipedia [1], the item on Platonic solids is telling that there are some objects, created by the late Neolithic people, which can be considered as evidence of knowledge of these solids. It seems therefore that it was known, may be a millennium before Plato, that there were exactly five and only five perfect bodies. These perfect bodies are the regular tetrahedron, cube, octahedron, dodecahedron and icosahedron.
In his book on regular polytopes [2], Harold Scott Macdonald Coxeter, writes "The early history of these polyhedra is lost in the shadows of antiquity. To ask who first constructed them is almost as futile to ask who first used fire. The tetrahedron, cube and octahedron occur in nature as crystals. ... The two more complicated regular solids cannot form crystals, but need the spark of life for their natural occurrence. Haeckel (Ernst Haeckel's 1904, Kunstformen der Natur.) observed them as skeletons of microscopic sea animals called radiolaria, the most perfect examples being the Circogonia icosaedra and Circorrhegma dodecahedra. Turning now to mankind, excavations on Monte Loffa, near Padua, have revealed an Etruscan dodecahedron which shows that this figure was enjoyed as a toy at least 2500 years ago."
Before Plato, Timaeus of Locri, a philosopher among the earliest Pythagoreans, invented a mystical correspondence between the four easily constructed solids (tetrahedron, icosahedron, octahedron and cube), and the four natural elements (fire, air, water and earth). “Undeterred by the occurrence of a fifth solid, he regarded the dodecahedron as a shape that envelops the whole universe.” [2].
It is interesting that Donald Coxeter is reporting the existence of an Etruscan dodecahedron, that is, an object having the shape of a Platonic solid found in Italy, not of Greek origin. In Refs.3 and 4 too, it is told that there exists an Etruscan dodecahedron made of soapstone found near Padua and believed to date from before 500 BC. Another book referring to this dodecahedron is Ref.5, is that written by György Darvas.
György Darvas discusses in [5] the Platonic solids and their use as dice. He tells that the best known of them is the cube. We use it in gambling, “because of its symmetries, it is equally likely to fall on any of its sides. … In truth, any regular body satisfies this condition of falling on any side with the same probability, not just the six-sided cube, that we in contemporary Europe are accustomed to call dice in this context.“. The author continues telling that etymologically, “the noun dice does not even refer to a cube. This is the plural of the noun die, here meaning a surface with a relieved design forming one of the facets of polyhedron.
In principle, any of the five regular polyhedra can be used as a die. “There is an evidence to suggest that in Italy of old, dodecahedra were used in games, while in Etruscan cultures, they can have a religious significance (Figure 6.9a)". This is what reference 5 is telling.
In fact, this figure 6.9a of Ref.5 (Fig.1 shows a snapshot of what we can see by means of Google Books) is showing a Roman dodecahedron, not an Etruscan dodecahedron as the caption is telling. The book continues: "In Japan, for example - where the number five is considered a lucky mascot - a dodecahedron delimited by regular pentagons is still used for this purpose to this day. Sometimes it is customary to write the digits from one to twelve on its faces, sometimes the names of the twelve months.”.


Fig.1 The image shows a snapshot of a page of Ref.4 that we can see by means of Google Book.

Fig.1 shows that Figure 6.9a of Ref.[4] can be misleading. This is a Roman dodecahedron of the second or third century AC (see Ref.6), having probably a use quite different from that of dice.
What was then the shape of the Etruscan dodecahedron? Let us report the original discussion and illustration of the researcher that found it. He was Stefano De' Stefani. In the Proceedings of the Royal Venetian Institute of Sciences, Arts and Letters ([7], 1885), the author tells where the dodecahedron was found and reports about the existence of an icosahedron in Turin. The paper is entitled “On an almost regular dodecahedron of stone, with pentagonal faces carved with figures, discovered in the ancient stone huts of Monte Loffa“.
The place of discovery belongs to Sant'Anna del Faedo village of Breonio, in the region of the western Lessini Mountains, called by the ancient historians as the region of Reti and Euganei, who were destroyed and scattered by the Gauls. De’ Stefani is in agreement with several ancient writers, who considered Reti an ancient Italic people of Etruscan origin, that under the Gauls pressure had to find refuge on Alps [8].
The author continues telling that Gauls, “people of wild and fierce aspect”, leaved in the same huts of Monte Loffa the manifest evidence of their presence, shown by tools, weapons and ornaments. “This village or encampment of prehistoric times shows objects of human industry that are represented by flint tools and weapons from the Neolithic period, of Etruscan bronzes type or Euganeo and Gaulish coins and other objects.
The paper has an illustration showing the dodecahedron (see Fig.2).


 Fig.2 Etruscan dodecahedron from Monte Loffa (from ref.7).

The paper continues with a deep discussion of the nature and use of the dodecahedron in Fig.2. Several scholars were interviewed by De’ Stefani, and he came to the conclusion that this dodecahedron was a die.
The paper [7] reports the opinion of Ariodante Fabretti [9], that De’ Stefani received in a letter written by Carlo Cipolla [10]. Fabretti says that it is a die. The signs are conventional, perhaps a sort of numerals. In this case, this specimen is interesting because it seems to show a mixture of dots, as in our modern dice, and Etruscan numbers, adapted from the Greek numerals. On one of the face we can see “IV”, may be, for “four”.
There is also another interesting fact. Fabretti showed to Cipolla an icosahedron that could had some link with this dodecahedron. The icosahedron was made of blue-glazed earthenware. On each face there were impressed some Greek letters. Cipolla asked Fabretti if he knew anything about the origin of the icosahedron. He replied that it was owned by the city of Turin, before coming to the Museum of Antiquities, on occasion of an exchange. It was therefore supposed that this object was found in Piedmont.
It seems that in 1885, the existence of the icosahedron was unpublished. Unfortunately, I do not know where the Turin icosahedron is. Probably it is like that shown in Fig.3, from the second century AD, sold at auction for about $18,000 [11]. In my opinion, the Turin icosahedron could be older.

 Fig3. The icosahedron die of Ref.11.

We could conclude that the ancient people in Italy, trading with Greeks, imported some numerals, and, among the first applications, used them on dice for gambling. In any case, they developed their own numeral system that evolved in the Roman numeral system.

References
1. http://en.wikipedia.org/wiki/Platonic_solid
2. Regular Polytopes, by Harold Scott Macdonald Coxeter, 1973, Dover, ISBN 0-486-61480-8.
3. The number of things: Pythagoras, geometry and humming strings, by Evans G. Valens, Methuen, 1964.
4. A History of Mathematics, by Carl B. Boyer, Uta C. Merzbach, 1968, John Wiley and Sons
5. Symmetry: Cultural-historical and ontological Aspects of Science-arts relations; the natural and man-made world in an interdisciplinary approach, by György Darvas, 2007, Birkhäuser Verlag, Basel, Switzerland
6. A Roman Dodecahedron for measuring distance, A.C. Sparavigna, 2012, arXiv,
arXiv:1204.6497v1
[physics.pop-ph], http://arxiv.org/abs/1204.6497
7. Intorno un dodecaedro quasi regolare di pietra a facce pentagonali scolpite con cifre, scoperto nelle antichissime capanne di pietra del Monte Loffa, Stefano De' Stefani, Atti del Reale Istituto veneto di scienze, lettere ed arti (1885).
8. Reti http://it.wikipedia.org/wiki/Reti; Euganei, http://it.wikipedia.org/wiki/Euganei, http://en.wikipedia.org/wiki/Euganei
9. Ariodante Fabretti (1816 - 1894) was an Italian politician and historian. He was senator of the Kingdom of Italy in the sixteenth legislature. In 1860 he became professor of archaeology at the University of Turin. From 1871 to 1893 he was director of the Egyptian Museum of Turin. In 1876 he became Emeritus Member of the Accademia dei Lincei.
10. Carlo Cipolla (1854 - 1916) was an Italian historian, Professor of Modern History at the University of Turin, 1882-1906, and later at the Institute of Higher Studies in Florence.
11. http://www.georgehart.com/virtual-polyhedra/dice.html

Wednesday, May 2, 2012

A dodecahedron of a Roman soldier

In a recent  post (April 2012) I have discussed about Roman Dodecahedra.
After preparing a model of a Roman Dodecahedron, I was able to investigate it as an optical instrument.
In the  paper "A Roman Dodecahedron for measuring distance", published in arXiv, http://arxiv.org/abs/1204.6497 you can find how a Roman soldier could had used it to determine the distance of a target.The dodecahedron is quite simple to use and portable. Someone could tell (or is telling)  that it is more complicated compared to a simple cross-staff. Well, a cross-staff is rather long. In the case it were of bronze, the instrument turned out to be too heavy. Moreover, it seems that the cross-staff had been developed during the 14th century, therefore it was an instrument of the Middle Age in Europe.
(http://en.wikipedia.org/wiki/Jacob's_staff)



Thursday, April 26, 2012

Roman Dodecahedra

Recently I have read a very interesting paper entitled "The magic dodecahedron of Gauls, that saved Roman legions: Mirror of Universe  and gauge of seasons." by Cinzia di Cianni, published on La Stampa,   in Italian  (Il dodecaedro magico dei Galli che salvò le legioni romane: Specchio dell’Universo e misura delle stagioni:, July 28, 2010). Here I  shortly discuss this article.
It starts with the following questions. Was is it, "a sacred symbol for Druids or the tip of a scepter? A gauge or a candlestick? Nobody knows what it is really, in spite of the fact that in museums and private collections, we find over than a hundred of them. It is a small hollow object of metal, dating from the fourth century and having a Gallo-Roman origin." The object exists in a variety of designs and sizes, always consists of 12 regular pentagons and this is known as "Roman dodecahedron". All the found "Roman dodecahedra"  have a diameter between 4 and 11 cm. and have at the center of the 12 faces holes of different sizes. Each of the 20 vertices is surmounted by one or three knobs, may be to fit them on some surfaces.
"The Roman dodecahedron is a simple object, actually a "time capsule", containing an incredible density of history and myth. By itself it does not reveal anything relevant because it has no inscriptions on patterned surfaces. No document  speaks about it."  The article continues telling that, in fact,  there are 27 theories about its use, ranging from a game for divination to surveying or military purposes. Scholars gave up probably until some new finds: however, some amateur archaeologists, among them Sjra Wagemans, continue to study this mystery, that is "what was it used for?"
Cinzia di Cianni tells that the first description of the geometrical volume of this object is in the "Timaeus" by Plato. It is a solid as the tetrahedron, octahedron, cube and icosahedron, that is, one of the five Platonic solids. Before Plato, it was also described in the fifth century BC by the Pythagorean Hippasus of Metaponto. "Harmony of proportions and mathematical properties, has continued to captivate artists and scientists, from Euclid to Poincare, from Leonardo to Luca Pacioli, to Escher. So, during several centuries, the dodecahedron had accumulated magic and symbolic features, from Greeks to Celts, from Renaissance to modern times." Di Cianni continues reporting the interest on dodecahedra by  Francesco Maurolico, a Greek mathematician and astronomer of Sicily, who lived in the XVI century, and the contemporary astronomer Jean-Pierre Luminet, who works with data provided by the scientific probe "WMAP" (Wilkinson Microwave Anisotropy Probe), used to observe the cosmic background radiation in the microwave range.
For what concerns the Roman dodecahedra the article tells that all of them, collected in several European museums, always came from Gaul and the lands of the Celts: Great Britain, Belgium, Holland, Germany, Switzerland, Austria and Eastern Europe. A defined scholar theory about their use is still lacking. Recently Sjra Wagemans, of the Dutch multinational DSM Research and amateur  archeology, proposed a theory which assigns an astronomical feature to these objects. Sjra used a bronze copy of a dodecahedron to see that it is possbile to determine the equinoxes of spring and autumn. "The dodecahedron is therefore linked to the agricultural cycle, both sophisticated and simple at the same time, to determine  without a calendar, the most suitable period of time during the autumn for sowing wheat."  And crops were of vital importance for the Roman legions. At the site www.romandodecahedron.com, Wagemans introduced the research and waiting for comments.

Courtesy: DieBuche, Wikipedia

I like very much the discussion by Cinzia di Cianni about this mistery of archaeology.
For what concerns the measurement of time, we know that Romans used gnomons (the Vitruvian equinoxial gnomons) to determine the latitude and that they had very good meridians. In fact, Vitruvius deeply describes in his De Archtectura, how to prepare the analemma. See my Measuring times to determine positionshttp://arxiv.org/abs/1202.2746
It is possible that the dodecahedron was used to determine more precisely the time during the equinoctial period. According to Cinzia, there are  many proposal for their use.
In my opinion it is necessary to study how they can move, since they are biased structures, in order to understand whether they could have been used as dice for divination or bowls for simply playing with them. In a static use of them, the hypothesis for measuring time is quite interesting.
However there is the possibility to use it to measure distances as in the following approach:


Monday, April 23, 2012

Phonons and Auxetics

About me.
One of my researches is on dispersions of phonons.
Quite interesting are the new auxetic materials, providind phononic band-gaps

2011 SPARAVIGNA A.C., Vibrations of a One-Dimensional Host-Guest System, MATERIALS SCIENCES AND APPLICATIONS, Scientific Research, pp. 5, 2011, Vol. 2, pagine da 314 a 318, ISSN: 2153-117X, DOI:10.4236/msa.2011.25041

2007 SPARAVIGNA A., Phonons in conventional and auxetic honeycomb lattices, PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS, APS, pp. 6, 2007, Vol. 76, ISSN: 1098-0121, DOI: 10.1103/PhysRevB.76.134302

2007 SPARAVIGNA A., Phonons dispersions in auxetic lattices, JOURNAL OF PHYSICS. CONFERENCE SERIES, 2007, Vol. 92, pagine da 012100-1 a 012100-4, ISSN: 1742-6596, DOI: 10.1088/1742-6596/92/1/012100

2007 SPARAVIGNA A.C., Phonons in lattices with rod-like particlesarXiv:0706.4076, 2007

2007 SPARAVIGNA A.C., Phonons in honeycomb and auxetic two-dimensional lattices arXiv:cond-mat/0703257, 2007

Sunday, April 22, 2012

Ale's stone boat

Ale's Stones (or Ales stenar) is a megalithic monument in Kaseberga,  southern Sweden. It is a boat of stones,  67 meters long formed. There are 59  boulders of sandstone,  up to 1.8 tonnes each. According to the local  lores,  King Ale lies buried there.
http://en.wikipedia.org/wiki/Ale's_Stones