Monthly Archives: July, 2014

The Long Market in Gdansk

Source: Wikimedia Commons

The Long Market (Długi Targ) is one of the most important touristic attractions of Gdansk. It was a merchant road in the 13th century. After the massacre of Gdansk citizens on 13 November 1308 by Teutonic Knights, the place became the main street of the city and is name “Longa Platea” was first written in 1331. Nowadays it’s a very beautiful long square full of typical shops and restaurants which are the soul of this cosmopolutan city. One of its most representative houses is the town hall from the 16th century and Neptune’s Fountain, the main symbol of the city, is also there. This fountain was constructed in 1617 from Abraham van den Blocke’s designs.

Photography by Carlos Dorce

Photography by Carlos Dorce

Thus, if you visit Gdansk, you must have time to take a beer or a coffee in one of the cafes or have a typican Polish dinner in one of the restaurants which fill all the beautiful houses which can be admire in the square.

Among all these houses we also find a lot of mathematical symbols which allow me to talk of them in this new post. For example, Radisson Blue hotel is located in number 19 and the allegorical paintings of the facade are a joy for the mathematical freak:

Photography by Carlos Dorce

Photography by Carlos Dorce

On both sides we have some of the most important men in the history of astronomy like Hipparcus of Rhodas,

Photography by Carlos Dorce

Photography by Carlos Dorce

Ptolemy:

Photography by Carlos Dorce

Photography by Carlos Dorce

Copernicus:

Photography by Carlos Dorce

Photography by Carlos Dorce

Galileo Galilei:

Photography by Carlos Dorce

Photography by Carlos Dorce

and Hevelius:

Photography by Carlos Dorce

Photography by Carlos Dorce

Approaching the town hall, there is another red house which is full of artists ans it’s coronated by a replica of Aristotle and Plato from Raffaello’s “School of Athens”:

Photography by Carlos Dorce

Photography by Carlos Dorce

In another house there also are the allegorical Astronomia rounded by Cellarius’ heliocentric systems:

Photography by Carlos Dorce

Photography by Carlos Dorce

And finally we find other allegories like the Architecture, the Geometry or the Geography in the opposite side of the square:

Photography by Carlos Dorce

Photography by Carlos Dorce

For example…

Photography by Carlos Dorce

Photography by Carlos Dorce

…or:

Photography by Carlos Dorce

Photography by Carlos Dorce

As you can see, this is an excuse to admire the beautiful facades of the houses in this square which I never tire of walking through it.

By the way, there is a beautiful sundial in the town hall:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Długi Targ in Gdansk (map)

Advertisements

Frombork castle: a gallery of portraits of Copernicus

Photography by Carlos Dorce

Photography by Carlos Dorce

Today we have been in the wonderful Frombork castle (after driving from Gdansk for a long time through these bad ways!). Frombork is a small town near Russia and the castle is its main attraction. Before arriving at the city, something similar to a heliocentric system welcomes the visitors announcing that we are approaching to one of the most important places in Copernicus life:

Photography by Carlos Dorce

Photography by Carlos Dorce

Copernicus moved permanently to Frombork after his uncle’s death on 29 March 1512 (his uncle was Lukas Watzenrode, Bishop of Warmia). He began to attend the Chapter meetings and was appointed to take up administrative functions. From the buildings of the castle he worked on the calendar’s reform and made a lot of observations of the planets’ movements which were the starting point of his De Revolutionibus. In 1516 he moved to Olsztyn but before August 1521 he finally came back to Frombork and remained there until his death. Two years later, he was appointed to General Administrator of Warmia until the election of a new bishop. So Copernicus wrote his main work in Frombork and the castle is one of the most important stages of the history of science. Furthermore, he died there and was buried in the cathedral.

The main entrance of the castle is introduced by a great monument dedicated to him:

Photography by Carlos Dorce

Photography by Carlos Dorce

The statue was designed by Mieczyslaw Welter in 1972 although it wasn’t the first monument dedicated to the astronomer in Fromborg: there was another one by Max Meckel and Julius Seitz from order of the German Emperor Wilhelm II of Prussia, which was destroyed in nineteen fifties by local authorities:

Source: Wikimedia Commons

After visitnig the cathedral we have gone to the the museum:

Photography by Carlos Dorce

Photography by Carlos Dorce

The museum is dedicated to the Polish astronomer and it’s full of statues and portraits of him:

Photography by Carlos Dorce

Photography by Carlos Dorce

For example, this great portrait welcolmes you to the museum:

Photography by Carlos Dorce

Photography by Carlos Dorce

After a lot of paintings dedicated to local authorities, you can go upstairs to the first floor and then you can enjoy the gallery of portraits. The first one is this painting made by an unknown author from the 18th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

This copy made in 1948 of the portrait of Copernicus epitaph (16th c.) located in St. John’s Cathedral of Torun:

Photography by Carlos Dorce

Photography by Carlos Dorce

Another copy is this one made by Anny Szymborskiej in 1948 of “Copernicus talking with God”. The original was painted by J.Matejko in 1873:

Photography by Carlos Dorce

Photography by Carlos Dorce

And the Torun portrait copied by J.Hoppena in 1948! The original was painted around 1580 and was in possession of the Municipal School of Torun:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, this copy was made by M.Majer in 1925. The original was painted by Tobias Stimmer in 1574.

Photography by Carlos Dorce

Photography by Carlos Dorce

Of course, there also are engravings and small sculptures…

Photography by Carlos Dorce

Photography by Carlos Dorce

…like this one designed by P.Patray in 1973:

Photography by Carlos Dorce

Photography by Carlos Dorce

I don’t know if there are more portraits of Copernicus but here we have a large collection of them.

To be continued…

Location: Frombork castle (map)

More in Olsztyn castle

Photography by Carlos Dorce

Photography by Carlos Dorce

But the expermiental table isn’t the only thing related to Copernicus in Olsztyn castle! I’m in Gdansk now but I can’t forget the room dedicated to the astronomer! First of all, a copy of his famous portrait (very bad illuminated!) so-called Torun portrait (the original is in Torun). And secondly, an sketch of this other “Copernicus lecturing mathematics in Rome” (or “Copernicus explaining his heliocentric system”) by Wojciech Gerson.

Photography by Carlos Dorce

Photography by Carlos Dorce

It was created in 1873 within the framework of the four hundredth anniversary of Copernicus birth. Unfortunately, the painting has not been preserved until the present day.

Photography by Carlos Dorce

Photography by Carlos Dorce

The exhibition is not so big but you can learn some facts about Copernicus’life and his works on astronomy, medicine or economies.

During the years 1516-1530 he worked on the reform of the currency system of Prussia which foundations were elaborated by him as administrator at Olsztyn castle. His economic interests resulted in the treatise of 1519 (on the left). He aslo worked on the appropiate prices of bread.

Photography by Carlos Dorce

Photography by Carlos Dorce

There also are explanations of Copernicus as defender of the castle and canon of Warmia.

Finally, next to the main entrance there are some steps that go directly to another famous Copernicus’ portraits:

Photography by Carlos Dorce

Photography by Carlos Dorce

Of course, this is not going to be my last post about Copernicus in Poland! I don’t know what I am going to find in Gdansk but my next step in the trip will be… Torun!

Location: Olsztyn castle (map)

Copernicus in Olsztyn castle: the experimental table

Photography by Carlos Dorce

Photography by Carlos Dorce

Olsztyn castle is a great building which you must visit if you want to know more things about Nicolas Copernicus’ life. He lived here between 1516 and 1520 and it’s possible to imagine his steps in the courtyard:

Photography by Carlos Dorce

Photography by Carlos Dorce

The museum of the castle welcomes the visitors with a very explict plaque:

Photography by Carlos Dorce

Photography by Carlos Dorce

But the main attraction of the castle is the expermiental table drawn by the astronomer which is the only surviving original astronomical device used by him:

Nicolaus Copernicus was the most prominent resident of Olsztyn castle. He held there the position of the administrator of th Warmia cathedral chapter common property. He resided at Olsztyn castle twice. First, when he served the three year term of the administrator; from 8 November 1516 until 9 November 1519. The second stay of Copernicus in Olsztyn was related to the last war with the Teutonic Order. After plundering Frombork by Teutonic knights, Copernicus found refuge in Olsztyn castle and next administered the property of the chapter from 23 January 1520 until the end of October 1521. Responsibilities of the administrator included managing the property of the cathedral chapter in the districts of Olsztyn and Melzack. In those districts the administrator managed the land, held the judiciary powers and was responsible for fiscal issues […]. Copernicus devoted the time in Olsztyn to the administrative duties, taking the inventory of the archives of the chapter as well as the first edition of the treatise on the coin that resulted in formulating the law that “the worse coins get the better ones out of circulation”. Also hre, within the walls of Olsztyn castle, he wrote the text of the first chapter of the work of his lifetime “De Revolutionibus” -the work taht “stopped the Sun and moved the Earth from its foundations”. The same walls hide the most valuable monument of Copernicus -the experimental table- the only original instrument that swerved Copernicus for studies. The table 705 x 140 cm in size was drawn on the plastered wall of the north wing gallery just above the entrance to the room in which the administrator lived. Large fragments of that exceptional monument have been preserved until the present day.

Photography by Carlos Dorce

Photography by Carlos Dorce

The story hasn’t finished yet!

The astronomical table was made by Copernicus probably at the turn of 1516 and 1517. It alowed graphic presentation of the spring equinox date, which in turn allowed determination of the dates of movable church holidays and first of all, conducting work on calendar reform. The reform was necessary as the difference between the length of the calendar year introduced by the Council of Nicaea in 325 and the astronomical year caused that celestial phenomena moved back in time in relation to the calendar dates. At the beginning of the 16th c. that difference was already 10 days and for that reason Pope Leon X ordered the calendar reform that was dealt by the Fifth General Council of the Lateran. Copernicus drafted seventeen lines corresponding to the movement of sun rays at five-day intervals. Sixteen of them reflect the superficial movement of the Sun across fragments of hyperboles while one is a traight line. That straight line reflects the moment of equinox. It was additionally highlighted by colouring it blue and providing the inscription of which fragments of letters T, I and C have been preserved. The computations presented in the table cover the days between 25 January and 24 April. Application of sunlight projection reflected from an object positioned on the window still of the third gallery window for the observations make the table not only a priceless monument of Copernicus but also the oldest example of gnomonic reflection application. The visible missing fragments of plaster represent consequences of the castle reconstruction of 1676. At that time the gallery, and consequently the table, were divided by partition walls that have been removed in mid-19th c. […]

We saw the replicas of Copernicus’ instruments in Warsaw but this original one is very important for the Science lovers!

Location: Olsztyn castle (map)

Monument of Copernicus in Olsztyn

Photography by Carlos Dorce

Photography by Carlos Dorce

This is the most important statue which you can find in Olsztyn!

The monument was commissioned by Urszula and Ryszard Szmyt to commemorate the 650th anniversary of the foundation of Olsztyn. Everybody wants to sit next to him and have a picture of this moment before visiting Olsztyn castle where we can find more about this Polish astronomer.

Location: Monument of Copernicus (map)

Enigma Machine in the Museum of Technology of Warsaw

Photography by Carlos Dorce

Photography by Carlos Dorce

The Museum of Technology of Warsaw is located in the Palace of Culture and Science of Warsaw. This building is the tallest one in Poland (231 m.) and one of the most polemical symbols in this country. The construction started in 1952 (to 1955) and it was a present from Joseph Stalin and the U.S.S.R. authorities to the Polish people so it’s easy to imagine why there are a lot of people who don’t like it.

The Palace is decorated with a lot of statues of different allegories and Polish women and men and among them…

Photography by Carlos Dorce

Photography by Carlos Dorce

I’ve been searching for the net but I’ve not been able to find the names and representations of all these sculptures but this image is very familiar for us, isn’t it? It’s Copernicus! And which book is he reading? Look at the orbits!

Photography by Carlos Dorce

Photography by Carlos Dorce

The museum is in one of its corners and it is not so big. There are a lot of old cars, bikes, motorbikes and some old objects as telephones, radios,… and, of course, a calculator:

Photography by Carlos Dorce

Photography by Carlos Dorce

The Enigma machine is in the first floor next to the telephones:

Photography by Carlos Dorce

Photography by Carlos Dorce

Machine cypher was introduced in Germany at the end of the 1920s, and in 1933-34 the cipher communication system was adopted by the Third Reich.

In 1929 the Cipher Department of the Polish Army’s Headquarters organized in Poznan a training for cryptologists, and some time later set up its agency there. Soon the agency’s most clever mathematicians were transferred to Warsaw. Among them were: Marian Rejewski (right), Jerzy Rozycki (left), and Henryk Zygalski (middle).

Photography by Carlos Dorce

Photography by Carlos Dorce

This team set to work on the Enigma’s cipher with the application of mathematical methods, permutations in particular, and their previous experience of working on German ciphers. Cooperation with French radio intelligence was helpful, too. The Enigma’s cipher was ultimately broken at the end of 1933 and the beginning of 1934. In the process of deciphering scientists employed machines of their own design (similar to Enigma) produced by the AVA Fadiotechnical Factory. They also built a cycle counter and a cryptological bomb which were used in solving alterating cipher keys.

Photography by Carlos Dorce

The Enigma Machine. Photography by Carlos Dorce

 In the face of the incoming war the method of breaking ciphers together with the machine and the whole documentation was in July 1939 passed on France and Britain, where Enigma’s cipher was still not deciphered.

In September 1939 secrets of the Cipher Department were scrupulous obliterated, and the whole staff was evacuated to France. Rozycki was killed there and after the war Zygalski remained in England and Rejewski returned to Poland.

The riddle of the Enigma remained unrevealed for a long time. The first publication concerning this subject appeared in 1967 in Poland (W.Kozaczuk’s “Battle for Mysteries”). However, it was a book by G.Bertrand, the former head of French radio intelligence, that won a widespread fame after its publication in France in 1973 and triggered many other publications all over the world. While Bertrand (advocate of the idea of the Polish-French cooperation in the 1930s and 1940s) pointed Polish scientists as the authors of the success in breaking the Enigma cipher, some time later the English credired themselves with this achievement.

So… WAS ALAN TURING THE ENIGMA BREAKER?

The Enigma machine on display dated back to the end of the 1930s and was used in the Wehrmacht.

Location: Museum of Techonolgy in Warsaw (map)

Copernicus and Hevelius in the Knights’ Hall

Photography by Carlos Dorce

Photography by Carlos Dorce

One of the main attractions in Warsaw is the royal castle. It was the royal residence of the Polish kings sincs the 16th century and the place where the first Parliament of Poland was located. It was destroyed during the Swedish wars in the middle of the 17th century but one hundred years later it regained its magnificence.

The castle was bombed by the Germans in 1939 and blown up by the German army five years later. So there wasn’t any castle in Warsaw after the Second World War until th Communist authorities decidied to rebuild it in 1971. It was reopened in 1984.

So we have visited this emblematic building of the city (before enjoying a very good ice cream!) and the mathematical tourist has found the Knights’ Hall (1786) which should be explaied in all the touristic guides.

Photography by Carlos Dorce

Photography by Carlos Dorce

It was the most important ante room leading to the Throne Room intended to perform the functions of a National Pantheon. During the royal audiences, all the senators and diplomats accredited to the Court gathered here.

Photography by Carlos Dorce

Photography by Carlos Dorce

The array of paintings and sculptures renowned Polish men and historic events and the statue of Chronos-Saturn symbolizes the lasting memory of great statesmen. And now… if you look at the painting on the great World… you can see…

Photography by Carlos Dorce

Photography by Carlos Dorce

Copernicus! But he is not the only important astronmer in the room. There also is a bronze bust of Johannes Hevelius (1611-1687), sculpted by Giacomo Monaldi. Hevelius was the founder of lunar topography and after Copernicus, he is the second most important Polish astronomer!

Photography by Carlos Dorce

Photography by Carlos Dorce

We also find the painting “The Establishment of Krakow Academy, 1400” by Marcella Bacciarellego (1783-1786) which is one of the set of paintings dedicated to the events of Polish History:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, we can enjoy some very beautiful mosaics represented on the floors like this one:

Photography by Carlos Dorce

Photography by Carlos Dorce

I would have never said that this castle hid these mathematica joys. Enjoy them!

Location: Castle of Warsaw (map)

Copernicus in Warsaw

Photography by Carlos Dorce

Photography by Carlos Dorce

Today is our first day in Warsaw! My wife, my son, my daughter and me are going to visit Poland for twelve days and I am sure that the mathematical tourist is going to see a lot of things!

This morning we have been in the city centre and we have walked through Krakowskie Przedmiescie and Nicolas Copernicus was there! His natural position is the middle of Copernicus square which is called with his name and he is rounded by his heliocentric system:

Photography by Carlos Dorce

We can read in wikipedia:

Nicolaus Copernicus (Polish: Mikołaj Kopernik ; German: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance mathematician and astronomer who formulated a heliocentric model of the universe which placed the Sun, rather than the Earth, at the center.

Portrait, 1580, Toruń Old Town City Hall Source: Wikimedia Commons

The publication of Copernicus’ book, De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), just before his death in 1543, is considered a major event in the history of science. It began the Copernican Revolution and contributed importantly to the scientific revolution.

Copernicus was born and died in Royal Prussia, a region of the Kingdom of Poland since 1466. Copernicus had a doctorate in canon law and, though without degrees, was a physician, polyglot, classics scholar, translator, governor, diplomat, and economist who in 1517 set down a quantity theory of money, a principal concept in economics to the present day, and formulated a version of Gresham’s law in 1519, before Gresham.

The bronze statue was designed by the Danish sculptor Bertel Thorvaldsen (c.1770-1844) in 1822 and was completed eight years later. The phiolosopher Stanislaw Staszic (1755-1826) made important donations for erecting it in Torun because he knew that Napoleon was very surprised for not finding a monument dedicated to the Polish astronomer in his birthplace.

The inscription says “To Nicolas Copernicus [from a] grateful nation” in Latin and Polish although during the German occupation of Poland in 1944, the inscription was translated to German saying “To Nicolaus Copernicus [from] the German Nation”.

copernic02

Photography by Carlos Dorce

In 2007, Copernicus’ solar system was represented rounding him representing an image from his revolutionary De Revolutionibus Orbium Coelestium (1543).

Photography by Carlos Dorce

Photography by Carlos Dorce

The statue is in front of Staszic Palace (1620), the seat of the Polish Academy of Sciences. In 1967, a bronze replica was erected in Chaboillez Square in Montreal during the World’s Fair:

Source: Wikimedia Commons

In 1973, on the 500th anniversary of Copernicus’ birth, another bronze replica was installed in front of Adler Planetarium in Chicago:

Source: Wikimedia Commons

Location in Warsaw: map

Location in Montreal: map

Location in Chicago: map

Ten Barcelonas!

The new advertising campaign in the city of Barcelona is so numerical. The city is divided in ten districts and the first ten numbers are the stars of the new posters which are in all the streets. Enjoy them!

1. The former Barcino which is the focus of the city where the Roman ruins are together with the Mediaeval Gothic architecture, was the origin of the first district: Ciutat Vella (Old Town). Their streets and squares are an open book to the history of Barcelona.

Districte 2 L’Eixample

2. Eixample is the Modernist district! At the end of the 19th century, Barcelona was expanded in this rectangular net with their new wide streets which nowadays are the focus of the urban movement of the city.

Districte 3 Sants-Montjuïc

3. Sants-Montjuïc offers a long walk from the mountain to the sea pointing our attention in the history of the comercial Barcelona.

Districte 4 Les Corts

4. Between Diagonal, full of shops and malls, and the noise of the Camp Nou, Les Corts is a Barcelona full of gardens where you can be lost in this residential town.

Districte 5 Sarrià-Sant Gervasi

5. Old Sarrià-Sant Gervasi is the most residential district of Barcelona. It’s like a quiet town rounded by gardens and museums which ends in Tibidabo mountain.

Districte 6 Gracia

6. Gracia is the opened town to all the cultures, the urban artists, the music, the theatre ans the cinema although the people whi lives here are proud of it and its past.

Districte 7 Horta-Guinardó

7. Horta-Guinardó is the great balcony in the city. It’s full of water and the old houses and “masias” and the gardens are the treasure and the image of this richness.

Districte 8 Nou Barris

8. This different and wide district called Nou Barris (Nine Towns) is the focus of a lot of gardens and green zones to walk and enjoy its cultural life which is independent form the rest of the city.

Districte 9 Sant Andreu

9. sant Andreu is like its neighbours: characters, fight and a deep respect for its traditions. From the Tres Tombs to the Esclat and other parties, tradition is the most important thing in this old town.

Districte 10 Sant Martí

10. Beside the sea, ubiquitous chimneys welcome the Sant Martí district recalling its industrial past. An industry that has led to innovation and new technology in the district and has become the engine of the new Barcelona.