# 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)

# William Herschel’s house in Bath

Herschel’s house in Bath
Photography by Carlos Dorce

Nowadays, Herschel’s house in Bath hosts the Museum of Astronomy of this beautiful city in Somerset. The house has a plaque indicating that it’s Herschel’s house in Bath:

Photography by Carlos Dorce

William Herschel was born in Hanover the in November 15, 1738. His father Isaak was oboist in the Hannover Military Band and after the defeat in the Battle of Hastenbeck, Isaak sent his sons to seek refuge in England in late 1757 (in those times, England and Hanover were ruled by the King George II of Hanover). In England, William began to study English and music and he is important because of his musical compositions. Herschel moved to Sunderland in 1761 and became member of the Newcastle orchestra as first violin for one season. Then, he moved to Leeds, Halifax and Bath, where he became organist of the Octagon chapel.

Portrait of Herschel in Herschel’s house in Bath
Copy of a portrait printed in Famous Men of Science (New York, 1889)
Photography by Carlos Dorce

The house is full of musical instruments as you can see in this rooum set as his office:

Photography by Carlos Dorce

His important  musical career allowed him to be intereseted in astronomy, optics and mathematics and he started to build his own reflecting telescopes. Around 1775 Herschel was a very experimented astronomer and he could spend more than 15 hours diary observing the heaven and pulling his lens. In March 1781, he was looking for double stars when noticed a new object in the night heaven. He thought that it was a comet but after a lot of series of observations, he determined that the new object was a new planet beyond the orbit of Saturn. He called it “Georgium sidus” (Georgian star) after king George III although the new planet was known as “Heschel” in France after becoming its name “Uranus”. Herschel was awarded the Copley Medal and elected fellow of the Royal Society of London in 1782. In that year, he and his sister moved to England where he was appointed to King’s Astronomer and continued making new and great telescopes. He constructed more than 400 telescopes with which he discovered two moons of Saturn (Mimas and Enceladus) and two moons and the rings of Uranus (Titania and Oberon) among several other discoveries. His first observation of Uranus was made in this house in Bath (19 New King Street). In fact, one of the most interesting parts of the museum is the garden from where he did this important discovery:

Garden of Herschel’s house
Photography by Carlos Dorce

There is an armilar sphere In the garden  and a plaque that says:

Here lived Scientist and Musician Sir William Herschel (1738-1822) from where he found the planet Uranus, march 13th, 1781. He also discovered Infrared radiation in 1800. And his sister Caroline Herschel, early woman scientist (1750-1848), hunter of comets.

The  museum has a humble collection of astronomical objects where you can find astrolabes, armilar spheres, an orrery,…

Photography by Carlos Dorce

The astrolabe of the picture is a brass planispheric Hindu astrolabe, inlaid with silver Sanskrit script. It was commisioned in jaipur, India, in 1836.

Photography by Carlos Dorce

We can also see a replica of Herschel 7-foot telescope next to the desktop in the main entrance:

Photography by Carlos Dorce

This is a very interesting mathematical visit in Bath. Furthermore, everybody is in the centre of the city visiting the Roman baths and the abbey so you can visit the museum accompanied only by a few number of people. Breathe the air of the science!

Herschel died in August 25, 1822 in Slough and he was buried in the St. Laurence’s Church in Upton.

Portrait of Herschel (1785) in the dinig room of Herschel’s house
Photography by Carlos Dorce

Location:  Herschel Museum of Astronomy in Bath (map)

# The British Museum

Photography by Carlos Dorce

Today we’ve been in the British Museum. If you visit London you must go there to understand the history of the World. t has been my third time there but I love it as our first time together! I am going to write two or three posts about it but today I am only going to talk about the Islamic astronomical instruments which are exhibited in floor -1 because in the frontispiece of the main entrance you can see an armilar sphere above which everybody must walk to enter the museum.

Some aspects of science in the Islamic world developed in the service of religion. The obligatory five daily prayers, performed facing Makka, and the times for fasting in the holy month of Ramadan for example, require accurate knowledge of time and direction. For many centuries Muslims used instruments, mathematical tables and certain practices of folk-astronomy to find this important information. In this way Muslim scholars reached a level of sophistication unparalleled in Europe until well into the modern age.

We have an example in this astrolabe by Abd al-Karim al-Misri (1241):

Photography by Carlos Dorce

Another important object is this astrolabe quadrant engraved by the timekeeper (muwaqqit) of the Umayyad mosque at Damascus (1334/4):

Photography by Carlos Dorce

Finally, we find this brass celestial globe with constellations by Muhammad ibn Hilal al-Munajjim al-Mawsili (Mosul, 1275/6):

Photography by Carlos Dorce

Celestial globes are representations of the night sky. They were already known in Ancient Greece. The 48 constellations described by the astronomer Ptolemy in the 2nd century AD were adopted by Islamic scholars, who then influenced European knowledge of the stars and their names. Constellations on globes are always shown in ‘globe-view’, as if seen from the outside of the sphere. In the Islamic tradition this means that human figures are represented from the front, but left-handed:

Photography by Carlos Dorce

LocationBritish Museum in London (map)

# The wonderful vault of a Royal Library

Library of the monastery
Source: Wikimedia Commons

The King Philip II of Spain decided in 1550’s that he wanted to have a great library near his court in Madrid and he chose the new Monastery of San Lorenzo de El Escorial to place it in spite of other bigger villages. He didn’t want that the new library was a regular room inside a monastery so it had to be a very important place. Therefore, the library was placed on the second floor of the monastery just above his royal chambers but never above the basilica. Between 1565 and 1576, the king bought almost 5.000 books and manuscripts and the library became one of the most important libraries in all Europe.

Imaginary portrait of Juan de Herrera (1791) from
the book “Retratos de Españoles ilustres
Source: Wikimedia Commons

The mathematician and architect Juan de Herrera (1530-1597) designed a large room (54 m. long x 9 m. wide x 10 m. high) with big windows in both sides under a great barrel vault. This vault had to be decorated by an important painter and Philip II decided that Peregrino Tibaldi (1527–1596) had to be the right artist to do the work. Philip II was advised by Juan de Herrera and other humanists and he decided that the main subject of the paintings of the vault had to be the Liberal Arts. Furthermore, the seven arts would be together with the Philosophy and the Theology on both ends of the room. The Philosophy represented the compendium of the Human knowledge and she is accompanied by Aristotle, Plato, Seneca and Socrates:

The Philosophy

The Theology is on the side next to the convent and she represented the Divine knowledge. Therefore the vault represented the way from the Human Philosophy to the Divine knowledge through the seven Liberal Arts: the Arithmetic, the Geometry, the Astronomy (Astrology), the Music, the Rhetoric, the Grammar and the Dialectic. We can see a mathematical detail on the fresco below the Philosophy: it represents the School of Athens and there is a discussion between the Academics leaded by Socrates and the Stoics leaded by Zeno of Elea.

The School of Athens

The scholars aren’t listening to the speakers because each of them is “playing” with something different. We can see at the lower left corner a man measuring something with a compass and two books, a sphere and an armilar sphere, a dodecahedron and a compass in the middle of the picture:

Detail of the School of Athens

Going from the Philosophy to the Theology, we arrive at the Arithmetic after admiring the Grammar, the Rhetoric and the Dialectic. The Arithmetic is a woman turned to a table with simple mathematical operations rounded by muscled young men with tablets with arithmetical operations ans counting with their fingers:

The Arithmetic

There is also a representation of the Queen of Saba talking with King Solomon  According to the Book of the Kings (I,10,1), the Queen of Saba went to meet Solomon to ask some enigmas to him so we can see a ruler, a balance and a tablet with some numbers written on it. In the red tablecloth we can read “Everything has number, weight and measure” in Hebrew:

King Salomon and the Queen of Saba talking about numbers

The other panel next to the Arithmetic represents the school of the Gymnosophists who lived near the Nile and thought their philosophical theories from the numerical computations. In the middle of the picture we can see one of the gymnosophist with a compass looking at a triangle with the word “Anima” and the arithmetic progression 1, 2, 3 and 4 and the geometric 1, 3, 9 and 27 written on it. The other gymnosophists are computing with numbers written on the sand:

The Gymnosophists

Finally, at both sides of the Arithmetic on the roof we find four people related with this subject: Archytas of Tarentum (c.428–c.347 BC) and Boethius (c.480-c.525) in one side and the Platonic Xenocrates (c.396/5 – 314/3 BC) and Jordan in the other. They are writing numbers in their tablets.

There is the Music after the Arithmetic and we find the Geometry after it:

The Geometry

She has a compass in one of her hands and the young men around her have different geometrical instruments. The two scenes which are on the corresponding walls next to her are dedicated to some Egyptian monks drawing geometrical figures on the sand…

Egyptian monks measuring the lands

and Archimedes’ death:

Archimedes’ death

Notice that Archimedes is drawing the demonstration of the Theorem of Pythagoras made by Euclid!

Finally, the four chosen figures are the Astronomer Aristarchus of Samos (IIIrd c. BC) and the Persian astrologer Abd del Aziz also known as Alcabitius (Xth century) in one side and Archimedes (c.287-212 BC) and Regiomontanus (1436-1476)  in the other. Aristarchus is measuring angles and has a dodecahedron at his feet, Alcabitius has a carpenter’s square, Archimedes has a compass and a sphere to measure the Earth and Regiomontanus is pointing at a dodecahedron.

The last Liberal Art is the Astrology. She is backed on a terrestrial globe and her eyes are looking at the sky. She has a compass in one of her hands and the little boys around her have an armilar sphere and some astronomical books:

The Astrology

In one of the two panels on the walls we can see Dionysius the Areopagite observing a solar eclipse the day of Jesuschrist’s death in Athens (Luke, 23,45) We can notice a quadrant and an astrolabe in the hands of the amazed men!

Dionysius the Areopagite observing a solar eclipse

The other fresco represents King Ezekiel resting in bed and looking how time is delayed 15 years by God because of the repentance of his sins:

Ezekiel resting in bed

The four famous men are Euclid, Ptolemy, Alfonso X and Johannes of Sacrobosco. Euclid is represented here meaning the relationship between Astrology and Geometry. He has drawn three geometrical schemes. One is a triangle and a square inscribed in a circle and another square. Another scheme seems to be two overlaid squares partially hidden by Euclid’s name. In the middle of both pictures there is a man measuring the stars. Johannes of Sacrobosco has a quadrant in his right hand.

Euclid and Johannes of Sacrobosco

King Alfonso X of Castile (XIIIth. c) is the author of the Libros del Saber de Astronomía (“Books of the Astronomical knowledge”) and on the tablet which he has in his hands we notice a compass and the Ursa Maior (the compass is anachronistic!). His left hand has an open book with a horoscope

Alfonso X

So you can see that this wonderful vault is an open mathematical book designed by Tibaldi and Juan de Herrera. I’ve been twice in the library and now I am waiting for the next time that I could enjoy this artistic part of the monastery of San Lorenzo de El Escorial.

Location: San Lorenzo de El Escorial (map)

# The Museo del Prado

Sight (1617)
Jan Brueghel “the Elder” and Peter Paul Rubens
Source: Museo del Prado

The Museo del Prado deserves a long time to enjoy all the masterpieces which can be found in it. There are a lot of very important paintings and we can also find some mathematical ones which aren’t the most important pieces of the museum but also deserve a moment in the time of a mathematical tourist. This is the case of Ruben’s Sight. According to the web of the Museum:

This set of paintings on the five senses was one of the most successful collaborations of Peter Paul Rubens and Jan Brueghel “the elder.”

Rubens placed his figures in the magnificent courtly scenes created by Brueghel as settings for these allegories of the senses, resulting in a series of enormous quality and esthetic appeal. The subject was widely employed in Flemish painting.

Sight was considered the most important of the senses since the time of Aristotle. Here, Cupid shows Venus a painting on a Christian therme, The Healing of the Blind Man, which alludes to the recovery of sight through one of Christ’s miracles and thus touches on both physical and spiritual vision.

The presence of a canvas with Saint Cecilia, a copy of Raphael’s original, alongside some Roman busts, recalls the soul’s introspective vision, an image of chastity and virtue.

Jan Brueghel was a protégé of the Archdukes Alberto and Isabel Clara Eugenia, and in this work he includes their portraits and a view of their Palace at Mariemont.

This work is signed on a paper close to the goddess’s seat.

The painting has a lot of mathematical details which I want to show to you. For example, there are a portable sundial, some compasses and a quadrant on the table in the lower left corner:

Detail of the painting

There also are one compass more on the floor next to the table with a homothetic ruler and an astrolabe next to it:

Detail of the painting

There is an armilar sphere on the cupboard behind the table at the left of Venus:

Detail of the painting

Between Venus and Cupid we find two telescopes, a compass and some coins:

Detail of the painting

Finally, in a central position there is a globe and a compass on the floor:

Detail of the painting

The other pictures of the serie are also interesting but not in our mathematical sense. Walking from Velazquez to Goya, the visitor must admire this masterpiece.

Location: Museo del Prado (map)

# Nasîr al-Dîn al-Tûsî’s doodle

Today is Nasîr al-Dîn al-Tûsî’s 812th birthday. Here yoy have his Doodle! It has been published today in a lot of Arabic countries and I don’t know the reason why there is a telescope in the picture. It was invented some centuries later!!!