One of the most brilliant engineering concepts of the 19th century was almost lost forever. It’s the first mechanical calculator by Charles Babbage, which he gave the somewhat forgettable name of Difference Engine No. 2.
However, the final results are anything but forgettable.
The fact that Babbage was never able to construct this machine in his lifetime only serves to increase our appreciation for his vision, skill and attention to detail. Difference Engine No. 2, as realized first by the Science Museum in London in 2002, is considered one of the most beautiful machines ever built. It stands seven feet high, weighs in at five tons and is composed of 8,000 parts.
As awesome as it looks in repose, when set in motion, it’s a sight to be seen…
A Short History
The story of the Babbage difference engines is one of ingenuity, heartbreaking failure after heartbreaking failure and ultimate triumph, over a span of almost two centuries. In the first quarter of the 19th century, England’s Industrial Revolution was in full bloom. New inventions and methods were changing the landscape of society with innovations such as steam engines, iron ships, railways and telegraphic communications.
As scientists and engineers extended the dominion of industry through new processes, machines and social orders, an Achilles heel was readily apparent – the dependence on printed mathematical tables for a vast variety of activities. Whether navigating a ship, designing a building, tracking stars or calculating insurance rates, people had grown dependent upon printed numerical tables that often contained errors – with sometimes fatal results.
Babbage was frustrated by all the wrong numbers he constantly detected in printed tables and resolved to find a better way. His inspiration for building a mechanical calculating engine/printer is traced back to 1821 after a tedious encounter with error-filled printed tables. His resulting design, subsequently dubbed Difference Engine No. 1, had an ambitious brief:
- Eliminate calculation errors when solving polynomial equations
- Eliminate transcription errors in the typesetting process
- Eliminate errors that crept into repeated printings
- Built-in security elements to eliminate mathematical errors
The first design tackled the problem of calculating the solutions to polynomial equations (like x2 + 3) using a technique called the “method of finite differences” – a way to eliminate multiplication and division from the calculation. The design, if ever realized, would have resulted in a four-ton, 25,000-part behemoth.
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Government funding was lined up and development continued until 1833, when a dispute between Babbage and his chief engineer abruptly terminated the project. Babbage was able to salvage a working model of a part of Difference Engine No. 1 which demonstrated the feasibility of automated computation.
Eventually, Babbage went on to design Difference Engine No. 2, a streamlined and improved version. Between the two designs, Babbage created a design for much more powerful machine, the Analytical Engine. It would have been the world’s first general purpose computer with the capability to accept programmed instructions.
Neither it nor Engine No. 2 ever reached the build stage, although several prototype parts survive.
Babbage was betrayed by his own inflexibility (some would call it arrogance), political problems, inconsistent financing and bad marketing. When Babbage died in 1871, his life’s work was archived and forgotten, having no direct impact on the dawn of computing in the 20th century.
It wasn’t until 1980 that the saga of Charles Babbage re-emerged from obscurity.
Discovering the Difference
Our story picks up in the early 1980s when Prof. Allan Bromley at the University of Sidney started studying the Babbage archive, which is housed in the library of the London Science Museum. Bromley’s interest blossomed in 1985 into a project led by the museum’s Curator of Computing, Doron Swade, to construct a working example of Difference Engine No. 2.
The design is split evenly between the calculating and output subsystems, and the goal was to get the calculating engine operational by the 200th birth anniversary of Babbage, in 1991.
Swade and his team wanted to know whether Babbage ever had a reasonable chance of building his engine given the state of technology at the time, and if built, would it work?
Swade had a comprehensive set of twenty technical drawings left by Babbage. While fairly detailed, they were not complete in all aspects and even contained a few errors (which are speculated to have been purposefully placed to prevent piracy!). Swade had to extrapolate his knowledge of 19th century fabrication technology to come up with an authentic set of manufacturing methods, tolerances and materials.
New drawings of 8,000 parts, now updated to include the missing information, were used to construct the difference engine to the correct level of precision for the period.
Swade met his initial deadline and had the calculation engine working by 1991. It would take until 2002 and the funding provided by Nathan Myhrvold (more on him below) to complete the printing press and actually test the whole machine.
The task of building the output section fell to Richard Horton, the Metals and Engineering Conservator at the museum. Along the way, engineers encountered many of the same problems (financing, technical and logistic) that Babbage had encountered a century earlier.
In the end, the engineering team proved that the machine was buildable in Babbage’s time and would have worked.
The Workings of the Machine
The realization of Babbage’s design for Difference Engine No.2 is impressive by anyone’s standards. The two sections – one for calculating and one for printing – is a precision machine of flawless design.
The calculation section is a series of metal columns that can store digits, from zero to nine, on number wheels separated by sector gears of different heights. The first column is set to the initial value of a polynomial and column two is set to the polynomial’s first derivative for a given value of the variable (X). A crank is turned four times to calculate one iteration of an algorithm made up of addition, subtraction and carry operations. The crank is turned until the calculation is complete and ready to be printed.
The output section can print a mathematical table directly to paper, but it’s really nifty feature is its stereotyping apparatus. The machine can produce stereotype plates that can be used in printing presses. A plaster or paper-mache cast is first molded and then filled with the appropriate metal type.
This technique ensured uniform consistency of all printed copies of mathematical tables, one of the primary motivations behind the design of the original difference engine.
Serial Number 2
As former Chief Technology Officer at Microsoft, has always had an interest in inventions, and holds 17 patents on his own or with co-inventors. In 1991 he agreed to fund the construction of the output section of the Difference Engine No. 2 residing in London.
Myhrvold was so taken with the machine that he commissioned the construction of another copy for himself. It was delivered in 2008 and resides at the Computer History Museum in the Silicon Valley.
The builder of Serial Number 2, Richard Horton and his assistant, John Shuver, were on hand at the dedication ceremony on 1 May 2008. Horton has related some of the challenges he faced that extended the time necessary to complete the second machine’s fabrication.
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For instance, the 14 drum cams cracked and warped because they received the wrong heat treatment. This made the crank unworkable. It took six months to correct the error.
Another problem occurred when the project’s main contractor went bankrupt at the start of principal construction. Horton and his team had to create parts by hand and fix badly-formed components. This set back the project another four months.
With 248 figure-wheel gears to install, care had to be taken that each gear fit its bearings precisely in order to prevent friction and yet avoid loose fittings.
Serial Number 2 of the Babbage Difference Engine No. 2 went on display at the Computer History Museum on 10 May, 2008. Richard Horton summed it all up: “I don’t think any project…can compare — it was a once in a lifetime project”.
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