Calculating to Perfection: The Difference Engine
Human error, it’s not exactly a new concept. I’m sure we’re all aware of small mistakes we make everyday. Some of them may be tyops whil tping, or perhaps we forget to write something on the grocery list. Some mistakes are of much higher danger, like stopping at a stop sign or maintaining the speed limit.
Of all the mistakes we make, especially the grave life or death mistakes, math is usually not real involved, but that was different in the 19th century.
As mentioned a few weeks ago in my piece on the human computers of Halley’s Comet, humans often computed complex mathematical functions that provided new abilities for much of humanity. Their calculations were published in mathematical tables used for farming and planting, exploration and research, as well as navigation, especially on the high seas. Only, there were frequent errors. All of these tables depended upon human computers, or human-made calculations. As humans are prone to do, mistakes often accumulated upon well known mathematical equations and made their way into published tables and guides.
When these equations were wrong, ships could be navigating miles off course. These types of errors often resulted in life or death situations.
In 1822, one man decided it was time for a solution. He envisioned a machine which could compute mathematical equations perfectly every single time. The inventor was Charles Babbage and his invention was the Difference Engine (Garfinkel and Grunspan 42).
Charles Babbage was born into a wealthy family in 1791. His father was often considered a bully, perhaps pushing Charles to achieve more and aim towards higher and higher goals (Computer History Museum, “Charles Babbage and…”). He attended the University of Cambridge and quickly became a brilliant mathematician and inventor (“Charles Babbage.”). Unlike many inventors today, Babbage was a broad, multidisciplinary inventor, building such devices as the time clock, speedometers, and even the locomotive cow catcher. However, Charles Babbage has made his stamp on history as one of the earliest computer pioneers. His first venture into the world of computing was the Difference Engine, the world’s first digital automatic calculating computer (“Difference Engine.”).
Charles Babbage envisioned his Difference Engine as a device to provide a simple way for humans to complete math and build complex tables used primarily for nautical navigation and astronomical discovery.
Every calculation made by the Difference Engine would be 100% free from error (Garfinkel and Grunspan 42).
This was a lofty goal, but Babbage was accustomed to aiming high. He set to work designing the machine. The Difference Engine was designed on the principle known as the method of difference to solve polynomial functions (Park, “What a Difference…”).
Being the mathematician I am not, I won’t try to confuse you by explaining a complex mathematical operation I don’t fully understand myself. Just known that the Difference Engine operated on discrete digits (1, 2, 3, etc.) making it a digital device, the first digital calculating machine ever invented (“Difference Engine.”). Unlike some upcoming developments, the Difference Engine never operated on binary digits.
Such a machine was incredibly complicated and built from over 25,000 individual parts including multiple camshafts, gears, cranks, wheels, and a host of other mechanical parts. The machine was to be four tons in weight, stand over eight feet tall, and stretch over eleven feet long (“The Engines.”). As huge and as complex as the device was, it was simple to operate. An operator would input the starting values and turn the crank once, the problem was solved. The output would be displayed on a column of rotating gears, printed on a sheet of paper, and impressed into a stereotype for easy transfer to a printing press (Infinite Retina: Spatial Computing Strategy, “A demo of…”).
The Difference Engine was also an automatic calculator, meaning it could store the result of one calculation and use it as a value for another calculation (Garfinkel and Grunspan 42).
The Difference Engine was a behemoth, but so was the budget, which became a problem. Charles Babbage began by appealing to the British Government for funding (“Difference Engine.”). In one of the first government grants for research, the British crown agreed and Babbage had his money.
The next step was to find a skilled mechanic. Babbage didn’t possess the skills to machine such intricate parts and, to make matters worse, no formal process existed to make fine gears and mechanical parts (Infinite Retina: Spatial Computing Strategy, “A demo of…”). Eventually, Babbage found engineer Joseph Clement who agreed to build the Difference Engine according to Babbage’s plans (“The Engines.”). Charles Babbage even built a dust proof and fireproof workshop in which to test the device (“Difference Engine.”).
The construction process was plagued with problems. Babbage kept running out of funding and the device proved even more difficult to build than originally figured. Eventually, the inevitable happened. In 1832, Joseph Clement refused to continue work until he was provided additional pay. The project ground to a halt and the government officially cut funding in 1842 (“The Engines.”).
In short, the project had failed.
However, in 1840, Charles Babbage began plans on Difference Engine №2. This new device could compute numbers many times larger than №1 and used only one-third of the parts Difference Engine №1 required (“The Engine.”). Unfortunately, this second Difference Engine was also never completed.
Many concluded that Babbage was too far ahead of his time and such a device was impossible to build in the 19th century. Biographer Anthony Hyman remarked, “Babbage worked by himself, far ahead of contemporary thought. He had not only to elaborate the designs but to develop the concepts, the engineering, and even the tools to make the parts. He…stands alone: the great ancestral figure of computing” (Hyman as quoted in Park, “What a Difference…”).
Charles Babbage died in 1871 without ever seeing anything larger than a small demonstration model function (“Charles Babbage.”).
One would think that his death spelled the end for the Difference Engine, but that’s not the case. In 1985, curator for the London Science Museum held plans for Charles Babbage’s Difference Engine. He wanted to know if the engine would actually work if the device was built and finished. After a round of funding very much similar to Babbage’s own journey 130 years prior, the calculation half of the Difference Engine was completed in 1991, just in time for Charles Babbage’s 200th birthday (Infinite Retina: Spatial Computing Strategy, “A demo of…”).
Although this modern recreation could compute, it wasn’t finished, at least not according to Babbage’s original design. Charles Babbage went to extraordinary lengths to insure that errors were minimized, even human error. The result of a calculation was displayed on the final column of the calculation section of the Engine, however, if it was written by a human the human could reverse digits or make other errors. Therefore, Babbage designed a section that would print the result on paper, similar to a printing press, and then stamp the result into soft plaster from which to mold lead type. Once in operation, the result could be transferred to paper many times over without any human input or possible error (Infinite Retina: Spatial Computing Strategy, “A demo of…”).
To finish the machine in the London Science Museum, a generous benefactor, Nathan Myhrvold, former CTO of Microsoft, offered to fund the completion.
He had only one request, that the London Science Museum also build him a second Difference Engine for his private collection (Infinite Retina: Spatial Computing Strategy, “A demo of…”).
The Museum agreed and the Difference Engine Serial №1 was finished in 2002. Nathan’s Engine was finished in 2008. In all, it took seventeen years to finish one machine from plans to the first calculation (Infinite Retina: Spatial Computing Strategy, “A demo of…”). But the device worked! As long as the machine wasn’t broken, or otherwise jammed, it worked flawlessly and gave accurate results 100% of the time (Infinite Retina: Spatial Computing Strategy, “A demo of…”).
The Difference Engine is an amazing machine. Many of its pieces can directly translate to pieces in our modern computers, albeit much smaller and much less mechanical (Graham-Cumming, “Let’s build…”). Yet, it’s fascinating to learn that much of our computers today are grounded in an invention developed over 150 years ago. The Difference Engine is the fourteenth major milestone in the history of computing.
More on Math in the History of Computers:
More on the History of Computers:
Works Cited
“A demo of Charle Babbage’s Difference Engine.” YouTube, uploaded by Infinite Retina: Spatial Computing Strategy, 17 July 2010, https://youtu.be/BlbQsKpq3Ak.
“A Modern Sequel.” A Modern Sequel | Babbage Engine | Computer History Museum, www.computerhistory.org/babbage/modernsequel/.
“Babbage’s Difference Engine №2.” YouTube, uploaded by Wired, 2 May 2008, https://youtu.be/0anIyVGeWOI.
“Charles Babbage and His Difference Engine #2.” YouTube, uploaded by Computer History Museum, 5 May 2008, https://youtu.be/KBuJqUfO4-w.
Garfinkel, Simson, and Rachel H. Grunspan. The Computer Book: from the Abacus to Artificial Intelligence, 250 Milestones in the History of Computer Science. Sterling, 2018.
Graham-Cumming, John. “Let’s Build Babbage’s Ultimate Mechanical Computer.” New Scientist, 15 Dec. 2010, www.newscientist.com/article/mg20827915-500-lets-build-babbages-ultimate-mechanical-computer/.
Park, Edwards. “What a Difference the Difference Engine Made: From Charles Babbage’s Calculator Emerged Today’s Computer.” Smithsonian.com, Smithsonian Institution, 1 Feb. 1996, www.smithsonianmag.com/history/what-a-difference-the-difference-engine-made-from-charles-babbages-calculator-emerged-todays-computer-109389254/.
Swaine, Michael R., and Paul A. Freiberger. “Difference Engine.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 28 June 2017, www.britannica.com/technology/Difference-Engine.
“The Babbage Engine.” The Babbage Engine | Babbage Engine | Computer History Museum, www.computerhistory.org/babbage/.
The Editors of Encyclopaedia Britannica. “Charles Babbage.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 22 Dec. 2019, www.britannica.com/biography/Charles-Babbage.
“The Engines.” The Engines | Babbage Engine | Computer History Museum, www.computerhistory.org/babbage/engines/.
