Prior to the invention of electronic computers, tables of logarithms used for calculating mathematical equations were published using large teams of human “computers”. Back then computers tabulated the results in reference books. Even with exhaustive quality control, errors were common.
For example, the computation of data point D1 was made in error. The computation of data point D2 used the value of D1 in the calculation of the value of D2. D1 and D2 were published in a table containing 2,000 other calculations whose accuracy depended on the correct value of D1.
Bugs in the process and computation go hand in hand!
Why is this important?
The error could result in navigation tables charting the ship to a wrong course or a wrong time for the time of low tide.
A entire branch of mathematics – Numerical Analysis – revolves around the use of sequences and series to calculate the values of square roots, exponentials and logarithms. I share the human computer’s pain as estimation of a square root was an exam question.
Charles Babbage was a founder of the Royal Astronomical Society, Cambridge University professor and inventor.
In 1822, Babbage published to the paper “Note on the application of machinery to the computation of astronomical and mathematical tables“. His big idea is that machines can do the calculations faster and more accurately than a room full of human computers.
The British Government funded Babbage with £1,500 and £6,000 more by 1827 on the hope that the engine would generate precision tables at a lower cost. By 1842 after £17,000 (£1.2 M in today’s money) had been sunk into the difference engine with no tables produced. The British government pulled out of the project. Babbage also changed direction on the design and focused on the Analytics engine which obsoleted the value of the difference engine.
Just like issues faced with today’s start-ups, the Difference Engine’s failure is familiar. The concept:
- challenged the Victorian era’s ability to manufacture high precision parts
- failed to manufacture a working prototype
- ran out of funding and
- became obsolete and
- the project no longer held the founder’s attention.
Babbage updated the design as Difference Engine 2 to use fewer parts and perform calculations faster.
The Difference Engine was actually built in Sweden by Per Georg Scheutz and sold to the British and American Governments in 1859. Another Swede Martin Wiberg built a “compact” device in 1875 to produce logarithmic tables. The device included a printer.
The difference engine’s limitation was that the device only did one thing – produce tables of numbers.
The Analytics engine was more flexible. It used punched card input to external instruct the device what to calculate. Punched cards are an old idea going back to the Jacquard knitting machines first produced in 1804. Electronic computers built between the 1940’s to the late 1970’s used punched card input. By the time i moved on to second year University in 1981, video display terminals thankfully replaced them.
Babbage worked on the Analytical Engine between 1833 to 1842.
The engine contained a “store” or memory of data that could be called up to save intermediary results and use them in subsequent calculations. The store could save 100 digits and measured 25 feet long.
The mill component was analogous with the modern computer’s CPU. Using the instructions encoded on the punched cards. The mill measured six feet in diameter and 15 feet tall.
The first programmer was Ada Augusta, Countess of Lovelace – the poet Lord Byron’s daughter. Ada was an eminent mathematician and linguist. It was Ada who, in 1843, suggested using codes to represent letters and symbols. She also invented the concept of looping to perform repetitive calculations.
Like the Difference Engine project, the Analytical Engine project ran out funding – no one was willing to invest and work ceased.
Charles Babbage is one of many who had a vision of creating X and, with dogged determination, gave it a go. Whether the implementation was realized or not – it does not matter. The main thing in Babbage’s case is that his designs showed the analytics engine will work using today’s manufacturing technology.
Babbage’s’ London address was at 5 Devonshire Street, Portland Place, Marleybone. Average home prices on Devonshire Street are £1,708,557 or CAD$2.8M. Site is now a doctors office.
It would appear that the buildings were rebuilt after the blitz.