Babbage's Difference Engine Ted Metcalfe

"I wish to God these tables had been calculated by steam!" Late in 1820 the Astronomical Society of London commissioned the production of an accurate set of tables of all the Greenwich stars They were however calculated by hand and full of errors

Babbage Builds a Machine He goes into semi-seclusion and shows almost no one his work By May 1822 the machine was ready to show his friends Not everyone believed in it but most were amazed by the speed and accuracy at which it could calculate tables

Many people with money also liked the idea Babbage showed how it was possible to produce math tables “as cheap as potatoes” People with influence, like Sir Humphry Davy, the then President of the Royal Society invited Babbage to publicize

The government gives Babbage backing to create his machine in the full scale In August of 1823 the Treasury gives Babbage a commission to "To bring to perfection an engine for calculating mathematical tables"

Work was started right away The first designs for the full-size engine were laid down shortly after receiving his commission. It was to use 5 columns or orders of Differences in its calculations and to print its results to 12 significant places of decimals

Babbage breaks down Due to several deaths in the family, his father and wife, he suffered a nervous breakdown and had to take a break from creating his Engine While others attempted to continue the work, not much was done

Phase II Babbage’s friends a colleagues get together at his house and make plans to move forward Drawings from this period indicate that a larger machine was being contemplated: calculating with up to 16 digits using 7 orders of differences

Engine No 1 fails While many think that the machine was too advanced to work in that time period it seems to be many other minor reasons that lead to this failure Many say it is related to many government changes in this time that cause the organization to fall apart It is also said that instead of making a guaranteed working engine Babbage tried to make it more complex

What it does Most machines of that time could only do simple calculations one at a time Babbage wanted a machine that could do whole tables quickly and accurately, as well as to print them out

What a Difference is What is a "difference"? A "difference", written Δf(x), is simply the difference between the values of a function taken at two different values of its variable, x. The Method of Differences is thus a method of integrating "differences". Babbage's Difference Engine was a machine specially and specifically designed to perform this task as efficiently as possible

The machine in the end While Babbage never finished this machine, but rather moved onto better machines this was what could be seen as the first computer, in a modern sense of the term. The engine was accurate to 32 decimal places It required that the user turn a crank hundreds or thousands of times, a lot of work, so for more complex equations it was not as practical as hoped. The machine was also enormous and would take up much of a room and be nearly impossible to move