Analytical Engine (1837): Babbage, Ada Lovelace and Computing

The Analytical Engine was a mechanical general-purpose computer designed by the English mathematician Charles Babbage, who began work on it in 1834 and set out its principles in detail in 1837. Never built, it nevertheless anticipated the essential parts of a modern computer. In 1843 Ada Lovelace published notes on the engine that included the first algorithm intended to be carried out by such a machine.

Background: from tables to engines

In the early 19th century, navigators, engineers, astronomers and insurers relied on printed tables of logarithms, tides and other values. These were calculated by hand by people called “computers” and were full of errors. Charles Babbage (1791–1871), a Cambridge-educated mathematician and later Lucasian Professor of Mathematics, set out to calculate and print tables by machine.

In 1822 he demonstrated a small model of a Difference Engine, a calculator that produced tables using the method of finite differences, which needs only addition. With government funding, his engineer Joseph Clement began building a full-size version. The project grew slowly and expensively, and in 1833 it stopped after a dispute with Clement. By then the government had spent about £17,000, a vast sum.

Designing a general-purpose machine

While the Difference Engine stalled, Babbage conceived something far more powerful. From 1834 he designed an engine that would not be limited to one method but could perform any sequence of arithmetic operations it was given. He called it the Analytical Engine and refined the design, in hundreds of drawings and thousands of pages of notes, for the rest of his life.

Its main parts closely resemble those of a modern computer:

• The store held numbers on columns of geared wheels; Babbage’s designs allowed for hundreds of numbers of up to about 40 or 50 decimal digits, and at one point he envisaged 1,000. This was the machine’s memory.
• The mill carried out addition, subtraction, multiplication and division. It is the equivalent of today’s central processing unit.
• Punched cards, borrowed from the Jacquard loom that wove patterns in silk, supplied both the instructions (“operation cards”) and the addresses of numbers in the store (“variable cards”).
• Output was to come from a printer, a card punch and a curve-drawing device.

Crucially, the engine could repeat a series of cards in a loop and could take different paths depending on the result of a calculation, the features now called iteration and conditional branching. In principle this made it what computer scientists call a general-purpose, or universal, machine. It was to be driven by steam and would have been the size of a small room.

Menabrea and Lovelace

Babbage published little about the engine himself. In 1840 he explained it to scientists at a meeting in Turin, and a young Italian military engineer, Luigi Federico Menabrea, later Prime Minister of Italy, wrote it up in French in 1842.

Augusta Ada King, Countess of Lovelace (1815–1852), was the only legitimate child of the poet Lord Byron and Annabella Milbanke. Her mother had her tutored in mathematics, and she had known Babbage since 1833, when she saw part of the Difference Engine. At the suggestion of the scientist Charles Wheatstone she translated Menabrea’s paper into English, and with Babbage’s encouragement added seven notes, labelled A to G, that were about three times as long as the paper itself. The translation appeared in 1843 in Taylor’s “Scientific Memoirs”, signed only with her initials, A.A.L.

Note G and the first published program

The last note, Note G, set out step by step how the engine could calculate Bernoulli numbers, a sequence important in mathematics. It was laid out as a table of operations, the variables used and the results at each stage, and is widely described as the first published computer program. It contained a small error in one step; it was never actually run, because the engine was never built.

Lovelace’s notes are remembered above all for their ideas. She argued that the engine could manipulate any symbols whose relationships could be expressed formally, not just numbers, and suggested that it might one day compose music. In a well-known phrase, she wrote that the Analytical Engine “weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.” She also cautioned that the engine could only do what it was ordered to do and could not originate anything, a point Alan Turing discussed a century later as “Lady Lovelace’s objection”.

Why it was never built

Babbage never obtained the funding to build the engine. The British government, burned by the Difference Engine, declined further support, and Babbage’s constant redesigns and quarrelsome manner did not help. At his death in 1871 only a trial portion of the mill and printing mechanism existed. His son Henry Prevost Babbage later assembled part of the mill, which was demonstrated in 1910.

Legacy

Babbage’s work was largely forgotten as a practical line of development, and the builders of the first electronic computers in the 1940s reached similar ideas mostly independently. Howard Aiken, who designed the Harvard Mark I, did learn of Babbage’s work and came to regard him as a forerunner. The theoretical idea of a universal machine was set out in modern form in Alan Turing’s 1936 paper on computable numbers, and the first large programmable electronic machines, such as ENIAC, followed in the 1940s.

Between 1985 and 1991 the Science Museum in London built Babbage’s later Difference Engine No. 2 from his drawings, completing it for the bicentenary of his birth; it worked as designed. Lovelace’s reputation also grew: in 1980 the US Department of Defense named its programming language Ada after her, and Ada Lovelace Day, first held in 2009 and now marked each October, celebrates women in science and technology.

Myths and facts

Myth: Babbage built the first computer. Babbage designed the first general-purpose computer, but he never completed it. The machines that actually ran programs came a century later and used relays and electronic valves rather than gear wheels.

Myth: Lovelace wrote the program entirely alone, or contributed nothing. Both extremes are wrong. Babbage supplied ideas and checked her work, and he had sketched earlier examples of programs for the engine in his own unpublished papers. Their surviving letters show a genuine collaboration in which Lovelace wrote the notes, chose to include the Bernoulli example and developed its working in detail.

Fact: the engine was decimal, not binary. Unlike nearly all modern computers, Babbage’s machine stored numbers as decimal digits, each held by the position of a wheel with ten settings.

Fact: Babbage’s interests were wide. He also wrote on manufacturing, campaigned against street musicians, studied code-breaking and helped found the Royal Astronomical Society and the Statistical Society of London.

Timeline

• 1822: Babbage demonstrates a small model of his Difference Engine.
• 1833: Work on the full Difference Engine stops; Lovelace meets Babbage.
• 1834: Babbage begins designing the Analytical Engine.
• 1837, December: Babbage writes a detailed description of the engine’s design and powers.
• 1840: Babbage presents the engine to scientists in Turin.
• 1842, October: Menabrea’s paper on the engine is published in French.
• 1843, September: Lovelace’s translation and notes appear in Scientific Memoirs.
• 1871, 18 October: Babbage dies with the engine unbuilt.
• 1991: The Science Museum completes Difference Engine No. 2.

Why it matters

The Analytical Engine was the first design for a machine that could be programmed to carry out any calculation, with a separate memory, processor and input and output. Together with Ada Lovelace’s notes, which glimpsed computing beyond arithmetic, it shows that the core ideas of the computer age were already imagined in the 1830s and 1840s, a century before electronics made them practical.