Engineering a Difference: The Hows and Whys of the Difference Engine

This thesis explores the difference engine as created by Charles Babbage. A brief history of Babbage’s life is given as well as of the widespread use of mathematical tables at the time. This serves to give context to the creation of the difference engine and clarify what it was meant to do. The difference engine was a mechanical device created to quickly produce error-free tables of transcendental mathematical functions that were so prized by all mathematics users of the time. I also explore the reason why difference engines remain hypothetical throughout Babbage’s lifetime. Although Babbage’s name is universally associated with the “difference engine”, it is not widely appreciated that he did not actually design or build such engines. Rather, he invented a language to describe how all the parts could be put together to accomplish certain tasks, what he called “Mechanical Notation”. Actually working out how to link all these parts together in three dimensional space would have been extremely difficult and time consuming without access to the 3-D modeling software we have today. The mathematical method that the difference engine used to perform calculations is also discussed. The limits of this method are examined from a mathematical perspective and then tested through the use of a computer program meant to calculate the logarithm base ten