SwADE | 2 51
For all his wide interests the centre of his life was a near obsession with his calculating
engines, and it is for these that he is most widely known. Their design was his great reward, his
ill-fated attempts to build them was his downfall. He famously never completed an engine in its
entirety and, not without bitterness, saw himself as having failed.
Babbage’s epiphany is captured in a well-known vignette in which, in London in 1821, he and
John Herschel were checking astronomical tables calculated by human computers. Babbage,
dismayed at the number of errors, recalled that he exclaimed:^4
I wish to God these calculations had been executed by steam.
The appeal to steam can be read as a metaphor for the infallibility of machinery, as well as for
the idea of mechanized production as a means of solving the problem of supply. The ‘unerring
certainty of mechanical agency’ would ensure error-free tables as and when needed.^5 Babbage
immediately launched himself on his great venture—the design and construction of machines
for mechanized computation—a mission that occupied him for much of the rest of his life.
By the spring of 1822 Babbage had made a small working model of a Difference Engine
powered by a falling weight. His Difference Engine, so called because of the mathematical
principle on which it was based (the method of finite differences), would, in intention at least,
eliminate all sources of human error at a stroke. Calculation, transcription, typesetting, and
verification—manual processes used in the production of mathematical tables and therefore
susceptible to error—would now be unfailingly correct, ensured as they were by the certainties
of mechanical action.
Up to that point Babbage’s main interest and experience had been in mathematics, and his pub-
lished output to this time consisted entirely of mathematical papers, thirteen in all between 1813
and 1821. So in 1822, when experimenting with his new model, we have a mathematician aged 30
running the first practical automatic computing machine and reflecting for the first time on the
implications for machine computation. With his first experiments fresh in his mind he articulated
these early reflections in five papers written in the six months between June and December 1822.
Their content is as revealing as it is remarkable, although it has been largely overlooked.
The first model completed in the spring of 1822, known as ‘Difference Engine 0’, has never
been found. But a demonstration piece, completed in 1832, representing one-seventh of the cal-
culating section of Difference Engine No. 1, has all the essential features of its lost predecessor
and is used here to illustrate Babbage’s earliest recorded reflections on machine computation
(Fig. 24.1a). The ‘beautiful fragment’, as the piece was referred to by Babbage’s son,^6 is perhaps
the most celebrated icon in the pre-history of automatic computing. It was the first successful
automatic calculating device, and the significance of it being automatic cannot be overstated.
Number values were represented by the rotation of geared wheels (figure wheels) engraved
with the decimal numbers 0–9. These were arranged in columns with the least significant digit
at the bottom. Initial values, from a pre-calculated table, were entered by rotating individual
figure wheels by hand to the required digit value. The engine was then operated by cranking
a handle above the top plate to and fro (see Fig. 24.1b). Each cycle of the engine produced the
next value of the mathematical expression in the table, and this could be read from the last col-
umn on the right. In this way the engine tabulated a class of mathematical expressions (called
polynomials), using repeated addition of the values on the columns, and the results appeared
in turn on the last column.
In contemplating his first working model, Babbage was struck by the prospects of solv-
ing equations by machine computation. An equation, say y = x^2 – 1, defines the relationship