A Female Genius: How Ada Lovelace Started the Computer Age by James Essinger

Byron and Babbage. It’s possible that Sophia (who says other visitors were there) had heard about the impression the Difference Engine had made on Ada the first time Ada saw it. But Sophia’s remarks are worth quoting, because even if she wasn’t there she would most likely have heard from a first-hand source, perhaps even from Ada or Lady Byron, just how entranced Ada was by the machine.
    While other visitors gazed at the working of this beautiful instrument with the sort of expression, and I dare say the sort of feeling, that some savages are said to have shown on first seeing a looking-glass or hearing a gun… Miss Byron, young as she was, understood its working, and saw the great beauty of the invention.
    Unlike her mother, she understood how Babbage’s brilliant innovation linked the world of mathematics to a physical machine. At its heart, lay his decision to build his machine from cogwheels. Babbage had made this important practical decision about the technology at the heart of his planned calculation machine early on in his deliberations. Although we don’t know exactly what drove his decision, it isn’t difficult to guess the reasoning as it was the only technology available.
    Babbage’s conception of the Difference Engine was based on the idea that teeth on individual cogwheels (described as ‘figure wheels’ by Babbage) would stand for numbers. The machine’s operation would be based around meshing independently-moving cogwheels arranged in vertical columns with each other. This meshing process would carry out an arithmetical calculation.
    Babbage decided to use our familiar, everyday counting system of base 10 for his machine. This derives purely from the fact that the normal human allocation of fingers and toes is ten of each. He arranged things so that the cogwheel at the bottom of a vertical column would represent the units, the cogwheel second from the bottom the tens, the cogwheel third from the bottom the hundreds, and so on.
    For example, the setting of a four-digit number such as ‘6,538’ would require the bottom cogwheel to be turned eight teeth to represent ‘8’: the second cogwheel from the bottom to be turned three teeth to represent ‘3’; the third cogwheel from the bottom to be turned five teeth to represent ‘5’; and the fourth figure wheel from the bottom to be turned six teeth to represent ‘6’. All the figure wheels above the fourth wheel would all be set to zero. The value of any number was therefore capable of being set in the machine in a vertical stack of cogwheels as long as there were enough wheels in the vertical stack to cover the tens, thousands, tens of thousands, hundreds of thousands, millions etc that were required to evaluate the calculation.
    Babbage had christened his first calculating machine the Difference Engine because its entire operation was based on a mathematical concept called the ‘Method of Differences’. This method was a technique for calculating mathematical tables by repeated regular additions of the ‘differences’ between successive items in a mathematical series. A mathematical series is a set of numbers (terms) in ordered succession, the value of each being determined by a specific relation to the preceding number. To take a simple example, the numbers 1,2,3,4,5 and so on to infinity comprise the series with a formula that requires 1 to be added to each previous number.
    The beauty of the Method of Differences is that it simplifies the process of calculating a long and complex mathematical series. It allows otherwise difficult multiplications to be replaced by numerous straightforward but monotonous additions. But of course, if a machine is carrying them out, their monotony does not matter.
    And the beauty of Babbage’s numbered cogwheels was that they could be made to do these additions because, firstly, a cogwheel is, by definition, a gearwheel. It facilitates the meshing with another cogwheel. Secondly, and equally importantly,