Charles Babbage was born on December 26, 1791 in Teignmouth, Devonshire, U.K., as the son of a wealthy banker. His father's money enabled him to receive an excellent education including private tutors when his health gave him problems at an early age. This resulted in Babbage developing a life-lasting love of mathematics. When he started at Trinity College, Cambridge in 1810, he was fairly disappointed in the level of mathematics taught at Cambridge as he found himself well in advance of his tutors in that field. Hence it comes as no surprise that he later started working as a mathematician and statistician. In those days, when calculators did not yet exist, most calculations were done by looking up the answers in long mathematical tables which had been manually calculated and subsequently printed. Babbage found many errors in these tables, something that annoyed him immensely as he was a perfectionist, and being familiar with the work on calculating machines done by Schickard, Pascal and Leibniz, this led him in 1822 to raise the issue of constructing a calculating machine with the president of the Royal Society. He basically tried to find a method of calculating and printing these tables mechanically thereby eliminating the many human-made mistakes he encountered so frequently.

Notice the * Difference Engine * in the background

In 1822
he presented a paper "Note on the application of machinery to the computation of
astronomical and mathematical tables" to the Royal Astronomical Society in which he
described his machine, called a *Difference Engine*. This machine could calculate
the values of polynomials using a method called the difference method.

To understand
this concept (for the less-mathematically inclined reader, it might be advisable
to skip this paragraph): consider the function *f*(x) = 3*x* + 5.
For the different values of *x* (i.e. 1, 2, 3, 4, etc.) the resultant *f*(x)
is 8 (3x1 + 5), 11 (3x2 + 5), 14, 17, etc. The difference between each resultant
value (8, 11, 14, 17…) is a constant 3. It was on this concept of differences
that Babbage managed to design a calculating machine for polynomials. For more complex
polynomials, like *f*(x) = 2*x*²
+ 7*x* + 6, one would have to follow a two-step approach and work out the differences
of the differences before a constant value was obtained.

The
*Difference Engine* could also print the results of its calculations, as Babbage had
realised that many errors in the printed tables were caused by the printers
themselves, so he tried to eliminate that possible source of errors by automating
the printing process as well.

In 1823,
the government gave him a grant of ₤1500 for the
construction of his *Difference Engine*. Babbage converted one of the rooms
in his home to be used as workshop and he managed to find an engineer, Joseph Clement,
to construct the machine parts for him. Five years later, a lot of brass, steel,
pewter and wooden machine parts had been built, most of them hand-made and
purpose-designed by Babbage himself, but Babbage was experiencing the same problems
that others before him (e.g. Pascal) had experienced, in that the level of technology
available at that time was insufficient to produce the machine parts with the
critical tolerances that his machines required. By now his funds had run out,
but he managed to receive one grant of ₤1500 in 1829 and solicit two further
grants of ₤3000 one year later. The project also started to raise concerns
with the government as rumours had it that the machine might never
work.

When
Babbage built a large workshop behind his house for the construction of the machine,
Clement refused to move to the new workshop. This resulted in a fall-out between
the two and ultimately Clement not only stopped working for Babbage but also refused
to hand over the drawings and his tools to build the *Difference Engine.*
Now fund-raising became even more problematic and Prime Minister Peel at one stage
commented sarcastically that maybe Babbage's machine could be set to calculate
the time when it would be ready for use. Peel expressed sincere doubts that he
could convince parliament to vote for "the creation of a wooden man to
calculate tables from the formula *x*²
+*x*+41". Work on the machine was halted in 1834 and a few years
later the government officially abandoned the project as well.

Even
an improved version, the *Difference Engine 2*, that Babbage had
designed between 1846 and 1849 could not entice the government to continue
funding him. The fact that Babbage was a notoriously bad public speaker did not
help either to further his requests for funding.

Babbage was told he could keep the drawings and the parts built so far, but as that was not what he had originally agreed when he received his first grant, he gave everything back to the government and today it can be found in the Museum of King's College in London.

One side-effect of Babbage's endeavours was that in the roughly ten years Clement had worked for him, his workshop had raised the standard of precision mechanical toolmaking in England to new heights and many expert toolmakers were trained in his workshop under Clement's tutelage.

Although
the *Difference Engine 2 *was never constructed by Babbage, the design
papers he left behind enabled the Science Museum in London in 1985 to commission
the rebuilding of the *Difference Engine 2*. A full-size working version
was completed by 1991 to commemorate the 200^{th} anniversary of his birth
and is now on display at the Museum in South Kensington. It is 11 feet long,
7 feet high, and 18" deep and weighs 2.6 tonnes.

In the meantime
Babbage had started thinking about a more general purpose calculating machine:
an apparatus that would be able to do any type of calculation, not just polynomials.
He called his latest design the *Analytical Engine.* This machine was
controlled by an external program – similar to our modern computers – which he
achieved by using the French loom maker Jacquard's idea of punched cards. He inter-connected
the punched cards by strings of ribbon so they could feed his *Analytical Engine*
continuously. The punched cards contained the values and the operations (add, subtract, etc) to
be executed.

In this
machine he used the concept of the *mill*, which today would be called the
Central Processing Unit (CPU) and which he used to process the operations on
the values which he retrieved from the *store,* which we today call the computer's memory.
England's computer manufacturer ICL - in honour of Babbage - has incorporated the
term *mill* in its modern computer design.

Again Babbage approached government (in 1834) for funding for its construction but considering the bad experience of the first Babbage machine, it was ultimately decided not to go ahead. A not altogether surprising decision considering "We got nothing for our ₤17,000 but Mr Babbage's grumblings", as the Secretary of the Royal Astronomical Society wrote in his letter to the Board of Visitors of the Greenwich Royal Observatory. "We should at least have had a clever toy for our money". What they had was a large bunch of intricate parts and lots of drawings but not the fantastic calculating machine that Babbage had promised them.

In 1842,
Babbage travelled to Italy to give some lectures on his *Analytical Engine*
which resulted in the Italian Luigi Menebrea writing an account of his lectures.
This was translated into English by one of Babbage's friends, Augusta Ada Byron, Lady Lovelace, the
daughter of the poet Byron. She was a mathematician who also had shown great
interest in Babbage's earlier *Difference Engine.* When Babbage asked her
to add some of her own notes on the *Analytical Engine* to the translated
article, her own notes were twice as long as the original article and
this "Sketch of the Analytical Engine" became the definitive work on the machine.
The letters between Ada and Babbage were many as she was one of the few people
who understood his machines and grasped its concepts and potential.
In her 1843 article she already predicted that this type of machine could be used
for composing music, producing graphics and for scientific use, all areas where
today's computers are applied indeed. She also suggested to Babbage a plan for
his *Analytical Engine* how to calculate Bernoulli numbers, a plan which is now regarded as
"the first computer program" which makes Ada the first computer programmer.
In 1979, the U.S. Department of Defence developed a new programming language and named it
"Ada" in her honour.

“*The Analytical Engine weaves
algebraic patterns just as the Jacquard loom weaves flowers and leaves. *”

Ada Lovelace on Babbage's mechanical computer; Luigi Menabrea “Sketch of the Analytical Engine

invented by Charles Babbage” (1843), translated and annotated by Ada Lovelace,
Note A.

Although
the *Analytical Engine* was never constructed by Babbage and only existed
by way of his drawings, his son Henry P. Babbage managed to construct the *mill *part
of it in 1906 using his father's designs. It calculated and printed the first 25
multiples of *π* (pi) and this replica can now be found in the Science
Museum in London.

Socially
Babbage did not fit in easily with acceptable society norms. His hate of music,
especially as it was played on the streets of London in his time, resulted in numerous
letters to the *Times.* This resulted in street fiddlers and other musicians playing
outside his windows just to annoy and ridicule him. Children and adults
followed and cursed him when he walked the street, his windows were broken and
at one stage a dead cat was thrown at his house. During one 80-day period
Babbage, ever the statistician, counted 165 such nuisances.

As a statistician he collected every fact because he thought it might ultimately be useful. He wanted to quantify everything and express his measurements in numbers, be it the heartbeat of a pig or the breath of a calf. He proposed to collect info on how much oak a man could saw in ten hours or how much an ox could plow in one day. In 1857 he published “Table of Relative Frequency of the Causes of Breaking of Plate Glass Windows” listing 464 breakages, 14 of which were apparently caused by drunkards. Babbage thought there would be much use for collecting statistical information like that.

Despite his sometimes odd behaviour, Babbage is remembered often as the “Father of Computing” but the failure to construct his calculating machines and more specifically, the failure of the government to support his endeavours, disappointed him greatly and had left him an embittered man when he died on October 18, 1871 in London.

In 2010
Great Britain issued a sheetlet of ten stamps together with a prestige booklet
to commemorate the 350^{th} Anniversary of The Royal Society. Babbage
was portrayed on one of the stamps - he became a member of the Royal Society in 1815 -
and two pages of the booklet were dedicated to him and his two machines,
the *Analytical Engine *and the *Difference Engine.*

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© Wobbe Vegter, 2006**