Tag Archives: Calculator

The Museum of Mathematics in the Collegius Maius

Photography by Carlos Dorce

Photography by Carlos Dorce

Another interesting museum located in the Collegius Maius of the Jagiellonian University is an exhibition about mathematics where children can play and learn a lot! There are old calculators from the 20th century…

Photography by Carlos Dorce

Photography by Carlos Dorce

…abacus and slide rulers:

Photography by Carlos Dorce

Photography by Carlos Dorce

Children can play with Geography and learn that straight lines in a map are not the shortest ways for the planes:

Photography by Carlos Dorce

Photography by Carlos Dorce

They can also learn the theorem of Pythagoras scrolling this interesting figure:

Photography by Carlos Dorce

Photography by Carlos Dorce

There are polyhedra and a lot of geometrical and topological games:

Photography by Carlos Dorce

Photography by Carlos Dorce

The museum is very small but all the tourist are inside Collegius Maius so you can be very quiet watching all the exhibited objects and toys, like the Rodin’s Thinker:

Photography by Carlos Dorce

Photography by Cristina Martínez

Finally… here you have my two children playing with Eulerian graphs! They are lovely! Aren’t they?

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Collegius Maius (map)

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Kircher’s Organum Mathematicum

Photography by Carlos Dorce

Photography by Carlos Dorce

Yesterday I didn’t remember to show Kircher’s Organum Mathematicum:

Organum Mathematicum was invented in 1661 by the Jesuit astronomer and mathematician Athanasius Kircher. This device is a comprehensive portable encyclopedia and is designed for the following disciplines: arithmetic, geometry, fortifications, chronology, gnomonics (sundials), astronomy, astrology, steganography (encoding) and music. The case contains tables for calculations without ‘tiring the mind’. Each of the nine disciplines contains 24 flat boards of different colours, with definitions and information.

This is Athanasius Kicher:

Athanasius Kircher (1602-1680) pictured in the book Mundus Subterraneus (1664) by Cornelius Bloemart (1603-1680). Source: Wikimedia Commons

Of course, in the exhibition you can also find compasses, rules, abacus, slide rules, the Napier bones,…

Photography by Carlos Dorce

Photography by Carlos Dorce

…and calculators from the 20th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationNational Technical Museum in Prague (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)

The Pascaline

Pascaline (1652). Musée des arts et métiers (París).

When Blaise Pascal (1623 – 1662) was only 17 y.o., his father Etienne Pascal (another great mathematician) was appointed chief of the taxmen in Normandy, France. What did this clever teenager think when saw his poor father calculating everytime? Well, as good son as he was, he decided to give him the best present which Etienne could receive: a calculating machine (1652) which was recalled with the name Pascaline a lot of years later. This analogic machine was only able to add numbers but Etienne’s work became easier than before. Pascal introduced several improvements to his invention and the Pascaline was patented. Unfortunately, the manufacturing of the machine was too expenseive and Pascal’s small business could only make fifty calculators and one of them still survives in the Musée des arts et métiers in Paris.

In addition , we also report the visit to see some of the instruments that Pascal used to study the atmospheric pressure.

Location: Musée des arts et métiers in Paris (map)

Whipple Museum of the History of Science (and V)

Photography by Carlos Dorce

Photography by Carlos Dorce

The last post dedicated to Whipple Museum is for the calculators and their predecessors. All these objects are located in the next room which contains a lot of things in shelves and drawers as if they were in a store. There are calculators and a drawer dedicated to the Napier’s rods or bones:

Photography by Carlos Dorce

Photography by Carlos Dorce

There also are some interesting abacus like this one:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, different slide rules fill some drawers. You must be very patient and it’s a pity that this museum isn’t located in a larger building. 

WM27

Photography by Carlos Dorce

I have more pictures but you must go there if you want to have a real idea of the exhibition. It’s impossible to summarize it in some photos!

LocationWhipple Museum of the History of Science in Cambridge (map)

Babbage in the Science Museum

Photography by Carlos Dorce

Photography by Carlos Dorce

My last post about the Science Museum is about Charles Babbage. We’ve seen that there is a difference machine in the groundfloor of the museum but in the mathematical section there is a special space dedicated to him and his machines:

Charles Babbage (1791-1871) is widely regarded as the first computer pioneer and the great ancestral figure in the history of computing. Babbage excelled in a variety of scientific and philosophical subjects though his present-day reputation rests largely on the invention and design of his vast mechanical calculating engines. His Analytical Engine conceived in 1834 is one of the startling intellectual feats of the nineteenth century. The design of this machine possesses all the essential logical features of the modern general purpose computer. However, there is no direct line of descent from Babbage’s work to the modern electronic computer invented by the pioneers of the electronic age in the late 1930s and early 1940s largely in ignorance of the detail of Babbage’s work.

Apart of his portrait from 1860, we can see in the exhibition the right sagittal section with cerebellum of his brain. Babbage’s son donated it for research to the Hunterian Museum at the Royal College of Surgeons in England. There also are extracts from his diary (1844):

Photography by Carlos Dorce

Photography by Carlos Dorce

Charles Babbage invented the Difference Engine in 1821 but never built a full example. The only complete Difference Engine built during Babbage’s lifetime was made by Swedish engineers George and Edvard Scheutz. Inspired in Babbage’s ideas, and encouraged by Babbage himself, they printed the first ever mathematical tables calculated by machine. The Scheutz brothers went on to sell two further Difference Engines of which this is the second:

Photography by Carlos Dorce

Photography by Carlos Dorce

Practical and finantial problems meant that Babbage and his engineer Joseph Clement completed only about a seventh of Babbage’s original mechanism, which is on display in the ‘Making the Modern World’ gallery on the ground floor. Known as Difference Engine No. 1, it is one of the finest examples of precision egineering from 19th-century England.

The world’s first mechanical computer was also invented by Babbage in 1834. He never saw his Analytical Machine finished and this small section was under construction when he died:

Photography by Carlos Dorce

Photography by Carlos Dorce

There is also a model of the Difference Engine No. 2:

Photography by Carlos Dorce

Photography by Carlos Dorce

Charles Babbage designed this mechanical calculating machine, called Difference Engine No. 2, between 1847 and 1849. He aimed to print mathematical tables that were much more accurate than the hand-produced versions available to Victorian engineers, scientists and navigators.

Babbage called his machine a Difference Engine because it calculated tables of sums automatically using ‘the method of finite differences’. This mathematical method involves only addition and subtraction, and avoids multiplication and division, which are more difficult to mechanise.

I have a picture in front of this machine with my students from our visit to the museum in February 2012:

Who took this picture for us?

Who took this picture for us?

Nowadays, the machine is part of this section dedicated exclusively to Babbage.

I am going to visit the Science Museum again next February and I am sure that another post will be written because there are a lot of pictures and things that I don’t have time now to share with you!

LocationScience Museum in London (map)

The Science Museum in London (V)

Photography by Carlos Dorce

Photography by Carlos Dorce

I must finished this wonderful walk for the calculating machines going downstairs to the groundfloor again and showing some instruments more. Number 41 is a calculating machine from c.1955 made by Bell Punch Company Limited and number 42 is the ‘Eckel dial rule’ from the same year. The calculator number 51 is from 1955-1965.

Among the instruments which made our life more confortable there is also space for the sundials, clocks and quadrants. For example, look at this Gunter’s quadrant from the beginning of the 19th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

One example of sundial is this inclining sundiel from 1800:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, we notice this universal ring dial from the mid-eighteenth century. Sundials were still needed to set the clocks and watches that had superceded them as timekeepers:

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationScience Museum in London (map)

The Science Museum in London (III)

Photography by Carlos Dorce

Photography by Carlos Dorce

A lot of calculating machine from different times are on display and John Napier and his arithmatic inventions are part of this trasure. There is his Rabdologia (1617) where he described his famous Napier’s bones or rods and we have also some examples of them.

Photography by Carlos Dorce

Photography by Carlos Dorce

The box located in the bottom of the picture is Napier’s own Napier’s bones. There other sexagessimal bones are also very curious:

Photography by Carlos Dorce

Photography by Carlos Dorce

Napier’s bones were very popular and they were used until the 19th century as we can see them in this wooden box:

Photography by Carlos Dorce

Photography by Carlos Dorce

The exhibiion continues with “The Art of reckoning”:

As the level of trade increased throughout the Renaissance, the European counting boards and abacusses were gradually replaced by the use of pen and paper. Merchants andgentlemen taught themselves and their sons the new method.

In England, during the 16th and 17th centuries, many books were written encouraging people to learn arithmetic, and many gadgets invented to aid the beginner. By the 18th century, ready reckoners, devices to simplify calculation, were available to many tradesmen.

These words introduces all the calculating machines world but it’s also the moment of the former counting methods. For example, what do you think about this replica of a 16th century counting cloth?

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationScience Museum in London (map)

The Science Museum in London (II)

Photography by Carlos Dorce

Photography by Carlos Dorce

There is asection dedicated to Mathematics and it’s a paradise for the mathematical freaks! It’s full of calculators, Klein’s bottles, polyhedra,… and it’s possible to learn a lot of things only reading the information next to them. Shall we begin?

After the Second World War, the teaching of arithmetic to children in Britain became less focussed on repeated sums and tables, and more orientated towards understanding through experience. The use ofcalculators was always controversial.
In 1971, the rapid introduction of silicon chips ushered in the age of the pocket electronic calculator. However, in Japan, use ofthe ‘soraban’ or Japanese abacus was so instilled that, even a generation later, older people relied on them.

Educational toys became increasingly popular during the 20th century as parents realised they could improve their children’s performance and manufacturers realised there was a large potential market. For example, we can see the ‘Tell Bell’ educational toy from c.1930 in the first picture of this post.

All these first calculators also have their space in the museum. Here we can see some examples. The first one is the ‘Addiator’ mechanical adder from 1924. Until the 1970s mechanical adders remained essentially the same as those made in the 19th century but used new materials and designs:

Photography by Carlos Dorce

Photography by Carlos Dorce

The ‘Alpina’ mechanical adder was produced in Germany in c.1955:

Photography by Carlos Dorce

Photography by Carlos Dorce

From c.1950 we find the ‘Baby’ and the ‘Exactus’ mechanical adders and the ‘ Magical Brain’ mechanical adder is from c.1960:

Photography by Carlos Dorce

Photography by Carlos Dorce

But… when did everything begin? The first known attempt to make a caclulating machine was by Wilhelm Schickard (1592-1635), Professor at the University of Tübingen. Sketches of the machine appear in two of his letters written to Johannes Kepler in 1623 and 1624. Unfortunately the machine was destroyed by fire and there is no record of a replacement. Two decades later, Blaise Pascal completed a calculating machine in 1642 when he was 19 y.o. It was designed for addition and subtraction, using a stylus to move the number wheels:

Photography by Carlos Dorce

Photography by Carlos Dorce

The crude constructional methods of the time resulted in unreliable operation. Although several machines were later offered for sale, the venture was not a commercial success.

Photography by Carlos Dorce

Photography by Carlos Dorce

Sir Samuel Morland was the first Englishman to venture into the field of calculating machines designing this one (1666) on Pascal’s invention.

Photography by Carlos Dorce

Photography by Carlos Dorce

Gottfried W. Leibniz continued the construction of new calculating machines with this new one which wasn’t on display when I was in the museum. The mechanism was based on the stepped reckoner which eventually became the foundation of the Arithmometer:

Photography by Carlos Dorce

Photography by Carlos Dorce

It is unworthy of excellent men to lose hours like slaves in the labour of calculation, which could be safely relegated to anyone else if machines were used.

Leibniz, 1671

Finally, we must take a look to the Facit:

Photography by Carlos Dorce

Photography by Carlos Dorce

Was it really the World Champion in its class?

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationScience Museum in London (map)

The Science Museum in London (I)

Photography by Carlos Dorce

Photography by Carlos Dorce

The groundfloor of the Science Museum is full of technical and scientific objects which change our world in the last centuries and we find some mathematical objects (of course!). For example, we can see some slide rules: Fuller’s slide rule from 1890 (nr.25), Boucher circular rule from c.1885 (nr.26), a celluloid slide rule for triangle-mesh-reinforced concrete slabs from c.1912 (nr.27) and an engineer’s combination rule from c.1870 (nr.28).

We also find the calculating machines which became popular after 1850 among bookkeepers, astronomers and engineer like this Trinks Brunsviga (c.1908-1914):

Photography by Carlos Dorce

Photography by Carlos Dorce

In 1870 the General Register Office purchased a DeColmar arithmometer -an early mechanical calculator- of this type, to analyse the census. By the end of the century, staff were also using slide rules:

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationScience Museum in London (map)