# Combined operations

Mathematical picture in an Estonian Bar
Photography by Carlos Dorce

The first think that I made after arriving at Tallinn was going to the hotel and looking for a restaurant to have lunch. I didn’t want towalk a lot because I was tired and I decided to go to the first bar or restaurant which I’d find. Once again I was lucky because I had lunch in a very good and cheap restaurant! While Michael Phelps was winning his series in the Olympic Games of London and all the people in the restaurant were talking about the swimming machine, I noticed this advertisement hanging on one of the walls. I am sure that the two Estonian drunk men who were discussing about the Olympic results haven’t noticed it and I understood that the Beauty of Mathematics is only reserved for not so much people.

# Parabolic lights

Parabolic lights in Tallinn
Photography by Carlos Dorce

This curious illumination system is located in the main entrance of Foorum mall in Tallinn. The light is projected on a parabolic surface from which the entrance is very well illuminated. Of course this is a good excuse to get out of the Old City and approach to the new buildings of the Estonian capital.

Location: Foorum (map)

# And… is 2 equal to 1?

Photography by Carlos Dorce

I found this other mathematical advertisement  walking through the streets of Tallinn. Are there good mathematicians in Tallinn? I’m sure that the answer is “yes” but I wanted to check it and I came into the Labor Baar and I could enjoy two very good cocktails paying only one so… is important if there are good mathematicians? Of course not after two good cocktails .

Location: Labor Baar (map)

# 2 is equal to 3? Of course not

Photography by Carlos Dorce

2 is equal to 3? I found this is the advertisement travelling in the ferry from Helsinki to Tallinn. It probably means that if you buy 2 bottles of Fresita Piccolo, you’ll receive three bottles so you’ll get one free bottle. Nevertheless, a good mathematician knows that 2 won’t never be equal to 3, doesn’t he? If we have

a = 3a – 2a

and we consider that a = b + c, then we have:

3a – 2a = 3 (b + c) – 2 (b + c) = 3b + 3c – 2b – 2

⇒ 3a – 3b – 3c = 2a – 2b – 2

⇒ 3 (a – b – c) = 2 (a – b – c)

And dividing by (a – b – c) in each sides, we obtain 3 = 2. Have I made a mistake?

# A Runic calendar in Tallinn

Estonian Runic Calendar (1819)
Estonian History Museum (Tallinn)
Photography by Carlos Dorce

A Runic calendar is a perpetual calendar based in the 19 year Metonic cycle of the Moon. The Greek astronomer Meton of Athens (Vth century BC) observed that a period of 19 years was equal to 235 synodic months and 6.940 days which is almost equal to 19 solar years except for a few hours. This cycle was used in the Babylonian calendar and Meton computed all the necessary parameters and the intercallary months to adjust the periods of the Sun and the Moon.

Runic calendars were written on parchment or carved onto staves of wood (as the one of the Estonian History Museum), horn or bone. It appears to be  a medieval Swedish invention and the Nyköping staff, believed to date from the 13th century, is the oldest one which is preserved. The Runic calendar preserved in the Museum is dated in 1819 and its first line is made up of the first seven letters of the Runic alphabet (runes). 52 weeks of 7 days were laid out using 52 repetitions of this first seven runes and each rune corresponded to each weekday varied from year to year. On another line, many of the days were marked with one of the 19 symbols representing the 19 possible positions of a year in the Metonic cycle (called “Golden Numbers”).

This kind of calendars were used until mid-19th century.

# Estonian History Museum

Estonian History Museum (Tallinn)
Photography by Carlos Dorce

The Estonian History Museum is one of the most interesting attractions of Tallinn. We can read in the official web site that the story of the Museum began in 1802, when Tallinn’s town hall pharmacist, Johann Burchard (1776–1838), started a collection called Mon Faible (“My weakness”).  The first exhibit was a Chinese opium pipe and Burchard put on the exhibition “Antiquities and rarities” at the House of the Brotherhood of the Blackheads in 1822. Twenty years later, the Estonian Literature Society was founded in Tallinn and one of its aims was to establish a museum “to broaden our knowledge of this country by studying its history, art, manufacturing, technology and nature”. Extensive collections were compiled over the following twenty years, which formed the basis of the Provincial Museum of the Estonian Literature Society, founded in 1864 at the house of St. Canute’s Guild.

In 1911, the Estonian Literature Society purchased premises on Toompea at 6 Kohtu Street, where the museum’s innovative activities could flourish. As the only museum in the city, it became an important focal point in Tallinn’s cultural life with educational lectures and exhibitions. The Museum retained its important position through its valuable collections although the Estonian National Museum in Tartu (founded in 1909) became the most important museum in the Republic of Estonia. In 1940 Estonia was incorporated to the U.S.S.R. and  The museum was nationalized and the History Museum of the Estonian Soviet Socialist Republic was established in its place. Overbearing ideological pressure ruined the museum in the following years. In addition to subjugating the museum employees, items that were deemed harmful were eliminated, which meant destroying everything that reminded people of the republic of Estonia. The Museum preserved the greater part of the main collection and it moved to its current location at the Great Guild Hall in 1952. Finally, in 1989 the Museum was renamed the Estonian History Museum and many important exhibitions that introduced the contemporary history of Estonia were held in the late 1980s and early 1990s.

Estonia is a very young country and in the main exhibition we find a lot of references to its former background and to the Soviet occupation. Among all these interesting object there also are some references to mathematical objects. For example, we can see different scholar material as two geometrical figures…

Two geometrical figures (1920-1930)
Photography by Carlos Dorce

and a mathematical ruler:

Mathematical ruler (c.1950)
Photography by Carlos Dorce

The this section of the exhibition about the schools we can read that the first educated Estonians were said to be monk Nicolaus, who was appointed by the Pope to carry out missionary work in Estonia in 1170, and the parish priest Johannes, who worked with the Livonians at the beginning of the 13th century. In the mid-13th century cathedral schools were established in Tartu, Pärnu, Tallinn and Haapsalu. Next to the monasteries, there were monastic schools, and in the 15th and 16th centuries, town schools were founded. The 17th century was of great importance to Estonian cultural history because it was when that high schools, along with print shops, were first founded in the country. The University of Tartu was founded in 1632. In the 1680s a network of village schools was created but regular school education in rural areas only took hold in the early 19th century. Peasant schools were mandatory, and students were taught in the native language; however, most of the children were allowed to study at home. Writing and arithmetic were taught starting in the mid-19th century. The 1897 census revealed that 94% of Estonians were able to read, which was the highest percentage among the nations of the Russian Empire. The Imperial University of Tartu reopened in 1802 and became a centre of science and intellectuals in the Baltic provinces. In 1803 the university employed an Estonian and a Latvian-language lecturer. On December 1, 1919, the University of Tartu of the Republic of Estonia was opened, marking the beginning of regular higher education in the Estonian language.

Another interesting object is in the lower lever: it’s an abacus which was taken from Ivan Mazepa’s (1639-1709) tent after he Battle of Poltava in 1709. The wooden box has a framed mirror and an abacus with beads made of white and red bone. Mazepa wanted to unite the Ukranian terriories into a single state. During the Great Northern War he initially supported Russia but later changed sides and lost the Battle of Poltava alongside Swedish troops.

Mazepa’s abacus
Photography by Carlos Dorce

Finally, there is a three-dimensional wooden puzzle made in 1920s or 1930s. It consists in 16 pieces. Different wooden puzzles were made in Estonia already in the 19th century:

Estonian Puzzle (c.1925)
Photography by Carlos Dorce

As we can see, the Estonian History Museum is very interesting for a Mathematical lover. Furthermore, there is another object which must be mentioned but I’m going to talk about it in the next post.

Location: Estonian History Museum at Tallinn (map)