Some mathematical objects also exhibited here like this Gunter’s square made in 1567. Gunter also invented his scale for computing adapting the new logarithms invented by Napier in 1614. Hence, it’s time to start our visit to all the Napier’s rods and slide rules of the exhibition. Let’s have a look to a couple of them, like these English Napier’s rods from 1720…
or this other ivory set made from the 17th century:
From Gunter scales the slide rules were invented and this spiral logarithmic scale by John Holland (1650) is a very good example of the great inventions of the men from the Renaissance:
After the slide rules and before the computers, ihis fragment of the ‘Difference Engine No. 1’ by Charles Babbage (1832-3) assembled by his son Henry Babbage (c.1880) must also be exhibited:
Finally, a very curious mathematical object: this magic cube made by A. H. Frost in 1877:
Each row, each column and each diagonal have the same sum!
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):
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:
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:
There is also a model of the Difference Engine No. 2:
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:
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!
This is not going to be the only post dedicated to Babbage in the Science Museum. I’ve visited this museum in my birthday and I am going to write some posts about the mathematical section. However, the first thing that I saw after the exhibition about Turing is this Babbage’s Difference Machine No. 1.
This trial portion of the Difference Engine is one of the earliest automatic calculators and is a celebrated icon in the prehistory of the computer.
Charles Babbage was a brillant thinker and mathematician. He divised the Difference Engine to automate the production of error-free mathematical tables. In 1823 he secured 1500 pounds from the government and shortly afterwards he hired the engineer Joseph Clement.
The Difference Engine was designed to perform fixed operations automatically. During its development Babbage’s mind leapt forward to the design of the Analytical Engine, which using punched cards could be programmed to calculate almost any function. This design embodied almost all the conceptual elements of the modern electronic computer.
The project collapsed in 1833 when Clement downed tools. By then, the government had spent over 17.000 pounds to build the machine -equivalent to the price of two warships. The collapse of the venture was traumatic for Babbage and, in old age, he became embittered and disillusioned.
Historians have suggested that the design was beyond the capability of contemporany technology and would have required greater accuracy than contemporany engineering could have provided. However, recent research has shown that Clement’s work was adequate to create a functioning machine. In fact, the scheme founderer on issues of economics, politics, Babbage’s temperament and his style of directing the enterprise.
Trinity College is a constituent college of the University of Cambridge. It was founded by Henry VIII in 1546 and soon became one of the best European colleges. I really wanted to visit it in my holidays in England because a lot of notable fellows studied there, like Barrow, Newton, Babbage, Maxwell, Ramanujan, Hardy, … lord Byron, Galton,… Hence I wanted to walk through the same ways and gardens where Isaac Newton walked once!
The main door of the college is always full of tourists attracted by the great names who worked here. However I think that the apple tree planted next to this entrance also contributes to the success of the college. The tree was planted here as a ‘son’ of the famous apple tree located in Newton’s Manor House in Woolsthorpe:
There is a sundial in the courtyard and it’s not difficult to imagine one of this great minds checking his clock with the shadow of the gnomon. Why not?
I’ve visited the chapel which was begun in 1554-55 by Queen Mary, the daughter of Henry VIII, although it was completed by her Protestant half-sister Elizabeth I in 1567.
There are six statues in the Ante-Chapel dedicated to Thomas Babington, Lord Tennyson, William Whewell, Sir Francis Bacon and, of course, sir Isaac Newton…
…and Isaac Barrow, “master of Trinity, mathematician and preacher, Newton’s tutor”:
We can read in web of the Trinity College:
Isaac Barrow (1630-77) distinguished himself in Classics, Mathematics and Divinity. He was appointed Regius Professor of Greek three years before becoming the first Lucasian professor of Mathematics -an illustration of the way of the elements of the quadrivium were closely connected in the 17th century. Best known for his discovery of the fundamental theorem of calculus, Barrow resigned the Lucasian chair in favour of his pupil Isaac Newton, and devoted the rest of his life to theology -writing and preaching- and to being the Master of Trinity (1672-77) who commisioned the Wren Library.
The statue of Barrow was commissioned in preference to one of Richard Bentley, who was a more influential but also highly controversial Master. “The foremost scholar and textual critic of his day”, Bentley was regarded, together with Newton, as one of the ‘intellectual founders’ of Trinity, but as Master he ‘ruled like an irresponsible despot’. The statues of Bacon and Barrow were given by William Whewell. Sculptor: Matthew Noble, 1858.
And what about Newton?
Louis-Frabçois Roubiliac’s 1755 statue of Isaac Newton, presented to the Ante-Chapel by the Master Robert Smith, “is the finest work of art in the College, as well as the most moving and significant. The lips parted and the eyes turned up in though give life to marble. The inscription, Qui genus humanum ingenio superavit, is a pun ennobled by its truth”. This inscription is a quotation from the third book of Lucretius’s De rerum natura, meaning ‘in intellect he surprassed/survived the human race’.
Newton (1642-1727) was the greatest English mathematician of his generation. Developing his teacher Isaac Barrow’s work he laid the foundation of differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known. His 1687 book Philosophiae Naturalis Prinicipia Mathematica lays the foundations for most of classical mechanics. He also excelled in the realms of astronomy, natural philosophy, alchemy, and somewhat unorthodox theology. Newton is buried in Westmisnter Abbey.
The stained glass windows of the chapel are mid-Victorian (1871-5) although the original ones were glazed in 1567 with white glass bearing inscriptions, heraldic badgets and coats of arms.
The present designs were elaborated on a scheme of religious and historical allegories and we can distinguish the portrait of Isaac Newton (the second on the left)…
…and also the portrait of Isaac Barrow in the same window:
There also are portraits of the Venerable Bede and Alcuin.
We can also find Newton’s coat of arms…
… Ramanujan’s brass located on the north wall of the Ante-Chapel with an inscription text by F. H. Sandbach:
Srinivasa Ramanujan discovered many extraordinary facts in Number Theory. G.H. Hardy recognised his exceptional talent, brought him to England, and encouraged his work. Ramanujan was the first Indian to be elected a Fellow of the Royal Society; later he was made a Fellow of the College After a long illness he returned to India for the sake of his health and died at an early age in 1920.
Then… where is Hardy? Hardy’s brass is located in the same north wall and his inscription says:
Godfrey Harold Hardy was Professor of Mathematics at Oxford and then at Cambridge, and was famous for reforming methods of teaching in both places. In his own field he was universally recognised as pre-eminent among the world’s best mathemati-cians. He had little time for the views of others, and he defended his own with energy and humour. He was a Fellow of the College for nineteen years, and for a further sixteen years after his return to Cambridge. He was much loved by his friends. He died on 1st December 1947
The last step in our visit to the Trinity College is the Wren Library. The library was designed by Christopher Wren and completed in 1695. Wren filled it with light comming through the rows of tall windows lining the east and west walls:
The positions of the windows are above the book shelves in order to optimizate the available wall space for storing books.
There are some marble busts by Louis-François Roubiliac and Isaac Barrow is looking after everything from his position in one of the paintings on the walls:
The portrait was painted by Valentine Ritz (c. 1695 – 1745).