Charles babbage computer

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In [1] and [12], for example, his date of birth is given as 26 December and both give the place of his birth as near Teignmouth.

Also in [18] it is stated:-

Little is known of Mr Babbage's parentage and early youth except that he was born on 26 December

Given the place that his birth was registered Hyman says in [8] that it is almost certain that Babbage was born in the family home of 44 Crosby Row, Walworth Road, London.

Babbage suffered ill health as a child, as he relates in [4]:-

Having suffered in health at the age of five years, and again at that of ten by violent fevers, from which I was with difficulty saved, I was sent into Devonshire and placed under the care of a clergyman (who kept a school at Alphington, near Exeter), with instructions to attend to my health; but, not to press too much knowledge upon me: a mission which he faithfully accomplished.

After the school at Alphington he was sent to an academy at Forty Hill, Enfield, Middlesex where his education properly began. He began to show a passion for mathematics but a dislike for the classics. On leaving the academy, he continued to study at home, having an Oxford tutor to bring him up to university level. Babbage in [4] lists the mathematics books he studied in this period with the tutor:-

Amongst these were Humphry Ditton's 'Fluxions', of which I could make nothing; Madame Agnesi's 'Analytical Instructions' from which I acquired some knowledge; Woodhouse's 'Principles of Analytic Calculation', from which I learned the notation of Leibniz; and Lagrange's 'Théorie des Fonctions'.

I possessed also the 'Fluxions' of Maclaurin and of Simson.

Thus it happened that when I went to Cambridge I could work out such questions as the very moderate amount of mathematics which I then possessed admitted, with equal facility, in the dots of Newton, the d's of Leibniz, or the dashes of Lagrange.

I thus acquired a distaste for the routine of the studies of the place, and devoured the papers of Euler and other mathematicians scattered through innumerable volumes of the academies of St Petersburg, Berlin, and Paris, which the libraries I had recourse to contained.

Under these circumstances it was not surprising that I should perceive and be penetrated with the superior power of the notation of Leibniz.

Woodhouse was one of Babbage's teachers at Cambridge yet he seems to have taken no part in the Society that Babbage was to set up to try to bring the modern continental mathematics to Cambridge.

Babbage tried to buy Lacroix's book on the differential and integral calculus but this did not prove easy in this period of war with Napoleon.

When he did find a copy of the work he had to pay seven guineas for it - an incredible amount of money in those days. Babbage then thought of setting up a Society to translate the work [4]:-

I then drew up the sketch of a society to be instituted for translating the small work of Lacroix on the Differential and Integral Calculus.

It proposed that we should have periodical meetings for the propagation of d's; and consigned to perdition all who supported the heresy of dots. It maintained that the work of Lacroix was so perfect that any comment was unnecessary.

The Analytical Society was set up in and its members were all Cambridge undergraduates. Nine mathematicians attended the first meeting but the two most prominent members, in addition to Babbage, were John Herschel and George Peacock.

Babbage and Herschel produced the first of the publications of the Analytical Society when they published Memoirs of the Analytical Society in This is a remarkably deep work when one realises that it was written by two undergraduates. They gave a history of the calculus, and of the Newton, Leibniz controversy they wrote:-

It is a lamentable consideration, that that discovery which has most of any done honour to the genius of man, should nevertheless bring with it a train of reflections so little to the credit of his heart.

These are the English translation of Lacroix's Sur le calcul différentiel et intégral published in and a book of examples on the calculus which they published in

Babbage had moved from Trinity College to Peterhouse and it was from that College that he graduated with a B.A. in However, Babbage realised that Herschel was a much more powerful mathematician than he was so [12]:-

He did not compete for honours, believing Herschel sure of first place and not caring to come out second.

Babbage married in , then left Cambridge in to live in London. He wrote two major papers on functional equations in and Also in , at the early age of 24, he was elected a fellow of the Royal Society of London. He wrote papers on several different mathematical topics over the next few years but none are particularly important and some, such as his work on infinite series, are clearly incorrect.

Babbage was unhappy with the way that the learned societies of that time were run. Although elected to the Royal Society, he was unhappy with it. He was to write of his feelings on how the Royal Society was run:-

The Council of the Royal Society is a collection of men who elect each other to office and then dine together at the expense of this society to praise each other over wine and give each other medals.

He served as secretary to the Royal Astronomical Society for the first four years of its existence and later he served as vice-president of the Society.

Babbage, together with Herschel, conducted some experiments on magnetism in , developing methods introduced by Arago. In Babbage became Lucasian Professor of Mathematics at Cambridge, a position he held for 12 years although he never taught.

The reason why he held this prestigious post yet failed to carry out the duties one would have expected of the holder, was that by this time he had become engrossed in what was to became the main passion of his life, namely the development of mechanical computers.

Babbage is without doubt the originator of the concepts behind the present day computer.

The computation of logarithms had made him aware of the inaccuracy of human calculation around He wrote in [4]:-

I was sitting in the rooms of the Analytical Society, at Cambridge, my head leaning forward on the table in a kind of dreamy mood, with a table of logarithms lying open before me. Another member, coming into the room, and seeing me half asleep, called out, Well, Babbage, what are you dreaming about?" to which I replied "I am thinking that all these tables" (pointing to the logarithms) "might be calculated by machinery."

Such a machine would be able to carry out complex operations using only the mechanism for addition. Babbage began to construct a small difference engine in and had completed it by He announced his invention in a paper Note on the application of machinery to the computation of astronomical and mathematical tables read to the Royal Astronomical Society on 14 June

Although Babbage envisaged a machine capable of printing out the results it obtained, this was not done by the time the paper was written.

An assistant had to write down the results obtained. Babbage illustrated what his small engine was capable of doing by calculating successive terms of the sequence n2+n+

The terms of this sequence are 41, 43, 47, 53, 61, while the differences of the terms are 2, 4, 6, 8, .. and the second differences are 2, 2, 2, The difference engine is given the initial data 2, 0, 41; it constructs the next row 2, (0 + 2), [41 + (0 + 2)], that is 2, 2, 43; then the row 2, (2 + 2), [43 + (2 + 2)], that is 2, 4, 47; then 2, 6, 53; then 2, 8, 61; Babbage reports that his small difference engine was capable of producing the members of the sequence n2+n+41 at the rate of about 60 every 5 minutes.

Babbage was clearly strongly influenced by de Prony's major undertaking for the French Government of producing logarithmic and trigonometric tables with teams of people to carry out the calculations. He argued that a large difference engine could do the work undertaken by teams of people saving cost and being totally accurate.

On 13 July Babbage received a gold medal from the Astronomical Society for his development of the difference engine.

He then met the Chancellor of the Exchequer to seek public funds for the construction of a large difference engine. The Royal Society had already given positive advice to the government:-

Mr Babbage has displayed great talent and ingenuity in the construction of his machine for computation, which the committee thanks fully adequate to the attainment of the objects proposed by the inventory; and they consider Mr Babbage as highly deserving of public encouragement, in the prosecution of his arduous undertaking.

He set out to produce an engine with [3]:-

six orders of differences, each of twenty places of figures, whilst the first three columns would each have had half a dozen additional figures.

However the construction proceeded slower than had been expected. By the expenses were getting out of hand.

The year was a year of tragedy for Babbage; his father, his wife and two of his children all died that year. He own health gave way and he was advised to travel on the Continent. After his travels he returned near the end of Further attempts to obtain government support eventually resulted in the Duke of Wellington, the Chancellor of the Exchequer and other members of the government visiting Babbage and inspecting the work for themselves.

By February the government had paid, or promised to pay, £ towards the project.

In Babbage published Reflections on the Decline of Science in England, a controversial work that resulted in the formation, one year later, of the British Association for the Advancement of Science. In Babbage published his most influential work On the Economy of Machinery and Manufactures, in which he proposed an early form of what today we call operational research.

The year was the one in which work stopped on the difference engine. By that time the government had put £ into the project and Babbage had put £ of his own money. For eight years from to the government would make no decision as to whether to continue support.

Charles babbage.docx: His notion was to have sprung feeler wires that would actuate levers when card holes allowed them access. Social and Economic Impact Babbage saw the computer, if developed, as working hand-in-hand with industry to improve the lives of people with accurate and scientific knowledge of the world. Charles Babbage — , English mathematician, did pioneering work on calculating machines and in operations research and was active in winning public support for science. His machines served as the intellectual predecessor to a wide range of manufacturing control and computing techniques.

In the decision not to proceed was taken by Robert Peel's government. Dubbey in [6] writes:-

Babbage had every reason to feel aggrieved about his treatment by successive governments. They had failed to understand the immense possibilities of his work, ignored the advice of the most reputable scientists and engineers, procrastinated for eight years before reaching a decision about the difference engine, misunderstood his motives and the sacrifices he had made, and failed to protect him from public slander and ridicule.

His work on the difference engine had led him to a much more sophisticated idea. Although the analytic engine never progressed beyond detailed drawings, it is remarkably similar in logical components to a present day computer. Babbage describes five logical components, the store, the mill, the control, the input and the output.

The store contains [4]:-

all the variables to be operated upon, as well as all those quantities which had arisen from the results of other operations.

into which the quantities about to be operated upon are always bought.

It was operated by punched cards and the punched cards contained the program for the particular task [4]:-

Every set of cards made for any formula will at any future time recalculate the formula with whatever constants may be required.

Thus the Analytical Engine will possess a library of its own. Every set of cards once made will at any time reproduce the calculations for which it was first arranged.

This was done by outputting data to punched cards which could be read in again at a later stage when needed. Babbage decided, however, not to seek government support after his experiences with the difference engine.

Babbage visited Turin in and discussed his ideas with mathematicians there including Menabrea. During Babbage's visit, Menabrea collected all the material needed to describe the analytical engine and he published this in October Lady Ada Lovelace translated Menabrea's article into English and added notes considerably more extensive than the original memoir.

This was published in and included [7]:-

elaborations on the points made by Menabrea, together with some complicated programs of her own, the most complex of these being one to calculate the sequence of Bernoulli numbers.

See THIS LINK.

He wrote in (see [7]):-

The drawings of the Analytical Engine have been made entirely at my own cost: I instituted a long series of experiments for the purpose of reducing the expense of its construction to limits which might be within the means I could myself afford to supply. I am now resigned to the necessity of abstaining from its construction

if I survive some few years longer, the Analytical Engine will exist

to report upon the feasibility of the design, recorded their opinion that its successful realisation might mark an epoch in the history of computation equally memorable with that of the introduction of logarithms

The construction of modern computers, logically similar to Babbage's design, have changed the whole of mathematics and it is even not an exaggeration to say that they have changed the whole world.

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Last Update October