Roman gambling in MUHBA
Photography by Carlos Dorce
MUHBA (Museu d’Història de Barcelona) is one of the most interesting museums in Barcelona. Located in Plaça del Rei, it involves a journey through an area stretching over 4000 m2 under the actual square which reveal the Roman’s ruban structure of the city. The remains allow the visitor to take a look at the commercial life of the city and its craft production centres and the everyday life of Barcelona’s first Christian citizens.
The main focus of the exhibition is the Roman ruins through which you can explore the life of the citizens of the former Barcino. There is a lot of information about Roman life and… of course, gambling was very important for our ancestors. For example, look at these bone dice (1st-3rd centuries) and terra sigillata globets (1st-2nd c.) found in the ruins! One of them is a weighing one for the most cheating players!
Photography by Carlos Dorce
Although gambling was prohibited by law, Romans played a lot and traps were so common among them. When the lusoria tabula was not available, it was improvised by stripes on the ground or on stones, as we can see in this board from the 1st-4th c.:
Photography by Carlos Dorce
There also are improvised boards graved on ceramics:
Photography by Carlos Dorce
This latrunculus was also found in the ruins (1st-4th c.):
Photography by Carlos Dorce
The latrunculus was a very popular game derived from the Greek Petteia to which Homer quotes in his works. Varro (1st c. BC) wa sthe first Roman author who mentions this game.
Another popular game was the traditional coin flopping (navia aut caput) which was played with these coins:
Photography by Carlos Dorce
Finally, I must talk about the tali (knucklebones) of the first photography. They probably were the most popular game in the Roman Empire and we have a lot of witnesses of their use until the 19th century. For example, you can notice the knucklebones in this 18th century painting:
Girl playing knucklebones. Jean-Baptiste-Siméon Chardin (1734)
Forty years of Rubik’s Cube
Today Google celebrates puzzle’s 40th anniversary with an interactive Doodle. The game was invented by Hungarian professor of architecture Ernö Rubik in 1974 and won the German Game of the Year six years later. All the people born in the 70s had at least one of these cubes at home and tried to solve this almost impossible game.
To solve it, you must know taht there are 8!=40.320 ways to arrange the eight corner cubes and each of the seven first cubes can be orientated in 3 different ways (the eighth cube depends on the other seven!). So, you can arrange the eight corner cubes in 37 · 8! ways. For arranging the edges there are 12!/2 ways and there also are 211 ways to orientate these 12 edges.
So if you multiply the four quantities you will see that there are approximately 43.252.003.274.489.856.000 ways to solve Rubik’s cube.
A chess in Warwick Lane
Photography by Carlos Dorce
Go to Warwick Lane and you will see a frieze representing a chess! It’s just a curiosity but… enjoy it!
Photography by Carlos Dorce
Location: 8 Warwick Lane in London (map)
Egyptian Mathematics in the BM
Photography by Carlos Dorce
I am going to begin my Egyptian visit to the British Museum with the limestone game-board in the form of a coiled snake used for the game called “mehen” (2890-2686 BC). The body of the coiled snake is divided into rectangular spaces but the number of these spaces is not important for the game.
Game-boards in the form of coiled snakes are known from the Early Dynastic period whengames became a regular item of tomb equipment. Several examples were discovered in the excavation of the Second-Dinasty tomb of King Khasekhemwy at Abydos. The game for which the snake-board was used was called mehen and although the exact method of play is not known, later representations show that it involved two players. The game-pieces consisted of spherical stone marbles and small figures of lions and lionesses usually made of bone or ivory.
The other popular game in Ancient Egypt was the ‘senet’ and there is one ivory sene board with a drawer for storing the gaming pieces with the glazed gaming pieces. This second board is in the special exhibition dedicated to the tomb-chapel of Nebamun (1350 BC):
Photography by Carlos Dorce
The secnond mathematicl object found in the British Museum is this sandstone stela of the Egyptian Viceroy of Kush, Merymose, who served under Pharaoh Amenhotep III (c.1400 BC). A hieroglyphic text describes his campaign against the Nubians of Ibhet:
Photography by Carlos Dorce
The hieroglyphic text is full of numbers and figures:
Photography by Carlos Dorce
Other hieroglyphic numbers are found in the limestone relief of Rahotep (c.2600 BC) which was fixed in the offering-chapel of a brick mastaba tomb.
Photography by Carlos Dorce
The relief shows Rahotep seated before offerings which are detailed in a formal list on the right of the slab and all these offerings are accompanied of the number of them. We can see the ‘lotus’ for the thousands…
Photography by Carlos Dorce
and a lot of examples of units, tens and hundreds:
Photography by Carlos Dorce
It’s also interesting this bone identifying label from an item of funerary equipment (3100 BC). The front of the label bears the name of Queen Neithhotep and on the back is the numeral 135:
Photography by Carlos Dorce
Finally, the limestone false door stela of Niankhre (2450 BC) from Saqqara which comes from the mastaba-tomb of the superintendant of the hairdressers of the Palace Niankhre. You can see the number 4.000 in the top of the stela:
Photography by Carlos Dorce
Location: British Museum in London (map)
Mesopotamian Mathematics in the BM
Photography by Carlos Dorce
This is the famous Royal Game of Ur (2600-2300 BC). This wooden game board was in at least six graves in the Royal Cemetery so it’s an early example of a game that was played all over the ancient Near East for about 3.000 years.
The game is a race for two players using dice with seven identical pieces each. All playing squares are decorated, but on later boards only the five ‘rosette’ squares are marked. […] Pieces are ‘at war’ along the central path but turn off to their own side to exit.
Playing pieces were discs of shell or lapis lazuli. The tetrahedrical dice of the game are also exhibited.
Apart of the Royal Game of Ur, the only exhibited objects which are related with Mespotamian mathematics are the Archaic and Cuneiform tablets. For example, look at this tablet containing a five day ration list (Jemdet Nasr, 3000-2900 BC):
Photography by Carlos Dorce
Each line contains rations for one day and the sign for ‘day’ and numbers 1, 2, 3, 4 and 5 are easily identificable (at the beginning of the line!).
Photography by Carlos Dorce
This Gypsum tablet with Archaic numbers (Uruk, 3300 BC) has 3 units (round impressions) and 3 ‘tens’ (elongated impressions).
Photography by Carlos Dorce
This tablet above contains the daily barley beer ration for the workers (3300-3100 BC). Here there are also identificable all the marks representing units and tens and it’s the same in the next tablet containig food rations (3300-3100 BC):
Photography by Carlos Dorce
Finally, there is another tablet from the Late Uruk Period (3300-3100 BC):
Photography by Carlos Dorce
However, mathematical tables are not only clay tablets with figures and numbers. For example, the next tablet contains a set of problems relating to the calculation of volume, together with the solutions.
Photography by Carlos Dorce
You can see the details of the tablet in the next two pictures:
Photography by Carlos Dorce
Photography by Carlos Dorce
There is also a tablet recording observations of the planet Venus from c.1700 BC:
Photography by Carlos Dorce
Astronomical tablets were so common in Mesopotamia and here we have a representation of the heavens in eight segments which include drawings of the constellations.
Photography by Carlos Dorce
The next piece of cuneiform tablet contains a star chart which was found in Ashurbanipal’s library:
Photography by Carlos Dorce
According the British Museum’s web…
Ashurbanipal, whose name (Ashur-bani-apli) means, ‘the god Ashur is the creator of the heir’, came to the Assyrian throne in 668 BC. He continued to live in the Southwest Palace of his grandfather, Sennacherib, in Nineveh, which he decorated with wall reliefs depicting his military activity in Elam. He also had a new residence built at Nineveh, known today as the North Palace. The famous lion hunt reliefs, some of which are now in The British Museum, formed part of the new palace’s decorative scheme.
Throughout his reign, Ashurbanipal had military problems, mainly at the borders of the empire. He also continued his father’s policy of attacking Egypt. Campaigns in 667 and 664 BC led to the defeat of the Egyptian Twenty-fifth Dynasty and the appointment of a pro-Assyrian ruler in the Nile Delta. Assyria also attacked Elam, possibly in 658-57 BC, following the receipt of insulting letters from the Elamite king. In 652 BC Shamash-shum-ukin, Ashurbanipal’s brother, and ruler of Babylonia, revolted against Assyria with the support of the Elamites. The Assyrian army invaded Elam and Babylonia. Babylon was captured in 648 BC and the following year the Elamite city of Susa was destroyed. There is little surviving evidence that can help us to reconstruct the last years of Ashurbanipal’s reign. Ashurbanipal boasted of his ability to read the cuneiform script, and was responsible for the collection and copying of a major library of contemporary literary and religious texts
Location: British Museum in London (map)
The Pitt Rivers Museum
The Pitt Rivers Museum
Photography by Carlos Dorce
The Pitt Rivers Museum cares for the University of Oxford’s collection of anthropology and world archaeology. It is next to the Oxford University Museum of Natural History which was closed in August and it was very surprising for me and also for my kids (I think it’s an idela museum for children!).
Photography by Carlos Dorce
There are some interesting mathematical objects in the collection and I am going to list some of them. First of all, we must focus our interest in the showcase dedicated to “counting”:
Photography by Carlos Dorce
There are some old counting strings:
Photography by Carlos Dorce
and this “swampan”:
Photography by Carlos Dorce
“Swampan” or calculating board with sliding beads, used in casting accounts. The two upper balls on each bar = 5 each, the lower balls = units, similar to the roman abacus. China.
There also is the typical “soroban” which is next to a icture of a Roman abacus and in the upper right corner of the next picture:
Photography by Carlos Dorce
“Soroban” or calculating board for casting accounts, similar to and derived from the Chinese “swampan”. Japan.
There is also a picture of a “quipu”.
There also are astrolabes and clocks. For example, there are a brass astrolabe dated in 1673 and sme interesting portable sundials:
Photography by Carlos Dorce
Finally there is some showcases dedicated to games, dice, chess,… in the upper floor:
Photography by Carlos Dorce
Before finishing this post, look at the next picture and try to guess who is this great man:
Photography by Carlos Dorce
The Oxford University Museum of Natural History was closed but it was possible to walk around the inner yard and it was possible to see one of the famous statues dedicated to the great scientific men. So it was possible to take a photography of Gottfried Wilhelm Leibniz!
Location: Pitt Rivers Museum (map)
The Ashmolean Museum in Oxford (and IV)
Photography by Carlos Dorce
This astrolabe is the only one which I found in the Ashmolean Museum. It was probably made in Spain in 1260 and it’s lent by the Museum of the History of Science.
Finally, I noticed two game boards. The first is this bone, wood and horn board with chess on one side and backgammon on the other. It’s from Northern Italy (1420-1450):
Photography by Carlos Dorce
The second one is also from Northern Italy and the same period and it’s a chessboard on one side and a game involving moving pieces along the coiled body of a dragon on the other:
Photography by Carlos Dorce
And that’s all! I’m sure that there are more mathematical objects in the Ashmolean but… I didn’t find them. If you do, perhaps we can collaborate in another post!
Location: The Ashmolean Museum in Oxford (map)
THE MATHEMATICAL TOURIST 