Babbage Difference Engine #2

Just got back from the opening weekend of the newest exhibit at the Computer History Museum in Mountain View, CA. The museum’s in the old SGI building, for locals, and it’s a lovely little place. The exhibit is a working Babbage Difference Engine! The following is based on my memory of what transpired, so if there are errors in this posting, blame me, not the display. Also, all photos are thumbnails you can click on for a larger version, which will open in a new window.

The Difference Engine we saw is only the second ever built, and it was built to prove (or disprove) the validity of Babbage’s design. Consequently it was constructed very precisely according to Babbage’s instructions, or according to other projects Babbage had done. So (for example) where the current engineers discovered they needed a system of springs at the bottom of the machine to support the weight of the gears, so that the individual turning the hand crank wasn’t required to do so, they used a spring system which Babbage had used on other machines he’d built. The only other change they made was to include a printer, and that also was crafted according to a printer designed by Babbage to use on one of his later machines.

A lower rear view of Difference Engine #2, showing the cast-iron springs (from 4 to 5 o’clock; the printer is partially visible on the right)
Apparently Babbage first created a set of plans for the Babbage Difference Engine #1, and built a prototype that was only a seventh of the size of the intended completed machine. It would do (effectively) addition and subtraction up to, I think, a seventh level polynomial. He called it the “Beautiful Fragment,” and that’s what Ada Byron Lovelace saw and was entranced by when she was only 17 years old. It was only she, in fact, who understood the Engine could do more than simply play with numbers mathematically — she saw the Engine’s potential for manipulation of symbols, such as in algebra, music, and language, as well. Alas, her ideas weren’t really listened to or understood, and the government never really comprehended the true potential of what they had on their hands.

Many intrigued computer geeks in front of a banner of the Analytical Engine plans
Upon her brilliant mathematical notes (some of which you can find on line!) and inspiration, Babbage next created plans for an Analytical Engine, which could do actual mathematical calculations past simply addition and subtraction. Fascinatingly, creating the plans for the Analytical Engine taught Babbage enough that he revised the plans for the Difference Engine, creating the more precise, compact, and effective Difference Engine #2. Those plans — the ones for Difference Engine #2 — are what were used for the machine we saw. Only two complete working machines have been made from these plans; ours is the second, and benefited from experience gathered in the crafting of the first one, which is in London.

The higher back of the Difference Engine (from 5 o’clock; the printer is to your immediate right off-camera)
The machine itself is surprisingly lovely: all gleaming steel and machined bronze and glowing wood precisely synchronized, whirring and clunking and moving in elegant symmetry. You can see a short snippet of video of the machine actually working at the Museum’s web site. In the video they also show the back of the Difference Engine, with the precisely machined pieces whirling gracefully around the metal columns like a metal DNA helix. Standing there in person, watching the levers and wheels and numbers and cogs all dancing perfectly interlinked, is like watching visual mathematical prose.

The printer is amazing as well — it has a simultaneous paper printout and two stereotype trays. Those trays are what you use to set up the lead sheets for printing books. Amazingly, you can apparently program the printing into the stereotype trays in a wide variety of ways: changing margins, number of columns and row widths; using word wrapping or two different font styles; and so on. Frankly, the entire thing is breathtakingly advanced for its time.

One of the elegantly attired gentlefolk present
In retrospect, though, I’d have to say what made the Difference Engine truly wonderful to me was the stories of the people involved. There were several individuals there in lovely period dress, which was a nice reminder of just how different the times were in which Babbage lived. They also showed a fascinating movie about Ada Byron Lovelace, which nicely demonstrated just how indispensable she was to the entire project. As Dr. Doron Swade (the curator whose passion spearheaded this project) pointed out, it’s a sad truism that women are usually simply painted out of history, and their brilliance and efforts forgotten. Well researched movies like this help us remember them, and grant them the immortality they truly deserve.

In some ways the movie and the talk given by Dr. Swade showed me very clearly that as much as things change, they always stay the same. The Babbage Difference and Analytical Engines were classic computer projects, at least in my experience: the brilliant man of vision who’s a dreadful manager, the military funding and increasingly hostile oversight, the hot-shot “rock star” programmer who delivers amazing code that never gets used, the political machinations and back-stabbing, the budget overruns and increasingly missed deadlines, the projects with a similar “look and feel” done by other groups as bits of the original amazing vision leak despite everyone’s best efforts, the furious and insulted engineer walking off the project, the amazingly cool idea that ends up languishing as vaporware… it was all there, all in the story!

Difference engine programmers surrounded by their fascinated audience, with Babbage in “grumpy Beethoven” pose on the back banner
Also enjoyable was contemplating the cast of characters which existed today: the brilliant and driven museum English curator, the American philanthropist who made his money with computers, the various engineers and historians — and, perhaps most of all to me, the wonderful, geeky audience itself. It amused me to reflect on the sheer magnitude of tiny computers and toys that were probably present in the auditorium during the speech, and to look out over the crowd at the faces. Most of them were white males, true, but there were many women as well, and many of those had that same slightly absent look in their eyes, or the same casual indifference as to how they dressed and looked. There were a surprising number of gray-haired folks there too, and I was fascinated to hear several different languages as well as see several different ethnicities.

I’m not holding my breath, but I’d love to see our subculture better comprehend Ada’s ability to meld poetry and science. As she noted in a letter to her mother, “You will not concede me philosophical poetry. Invert the order! Will you give me poetical philosophy, poetical science?” I think the computer industry will have matured into something really amazing once it can grasp that particular complexity. I hope a wider variety of voices in the field will help that occur.

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The Difference Engine itself

The Difference Engine’s crank (from about 10 o’clock, on the far end of the Engine)
I’ve got a couple of nice shots of the Difference Engine to share here. First, imagine yourself standing in the same plane as the Engine, facing forward with it. Then imagine a clock face under the machine, with the 12 directly ahead and the 6 directly behind, and with 3 on the immediate right and 9 on the immediate left. I’ll use those facings to try and make clear which side of the Engine you’re viewing in my photos. So if I say, for example, that a photo is from 7 to 8 o’clock, that means I (the photographer) am standing between what would be the 7 and the 8 on the clock face centered under the machine. Hope this helps! :)

This first shot (above) is looking at the front of the machine from about 10 o’clock. You can clearly see the wooden-handled crank on the far end. The two Difference Engine programmers are setting up a seventh degree polynomial equation to be solved, and once they’d done so they turned the crank and the Engine clanked and whirred and…

The entirety of the printer, along with agog passers-by (from about 12 o’clock and looking at the opposite end of the Engine from the crank)
…then the printer started moving! Very cool looking. This shot is from the same angle as the above shot, but of the other end of the front of the Engine. I loved the fascinated expressions on the crowd as well, and the variety of people you can see.

The printer has actually been used to print — we got to see a page with two neat columns of numbers that looked quite nice — but it apparently takes something like two hours to clean the goopy ink out, so this time it was running ink-free. The sort of curvy gold colored tray is where the ink is poured, and where the roller emerges out of, to touch the metal segments which present the numbers of the calculated answer.

Below and tucked back behind the shiny-clean ink roller you can just see the segmented roller of numbers. Hanging a little below the ink roller is the paper roll, and below that is the front tray (currently empty) for the plaster mould imprinting. All three pieces swing and lift and roll smoothly, neatly weaving in and out with each other like clockwork. It’s amazing to see, and “still” photos just don’t do this lovely Engine and printer justice.

A “straight-on” view looking directly into the printer
Here’s another view of the printer, although I accidentally missed the ink rollers in this shot. You can better see the numerical keys, like typewriter keys, just above the paper roll in this shot. The big tray underneath is for the plaster mould. Amazingly, as noted earlier, the printer is programmable — for how many columns, how much white space between the numbers, which font to use… it’s incredible, and an amazing testament to Babbage’s dedication to the supposed infallibility of machines. He went to an awful lot of effort to eliminate any human error by removing humans from the equation as much as possible. Curiously, I still find the entire Engine and printer to be more wonderfully about humans… than just machines and Babbage’s much-vaunted “steam.” ;)

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The Informational Displays & Movie

The lower, printer end of the Difference Engine, showing the mix of lovely, exactingly crafted wood, bronze, and steel work (from 3 o’clock)
The hour-long movie shown was titled “To Dream Tomorrow,” part of a series called “Women of Power.” The intent of the filmmakers is to finally give credit where it is due to some of the amazing women in science history who have been mostly forgotten due to their gender. This particular one was about Ada Byron Lovelace, the only legitimate child of the noted poet Lord Byron. Her mother was an avid mathematician, and made sure Ada studied mathematics, which she greatly enjoyed, for almost all of her life.

I still find it amazing and personally dismaying when I read of the contradictions of the times in which Ada lived. As an example, a then-popular conceit was that women’s brains were too “frail” and could be injured by doing any sort of serious scientific work, such as mathematics. Amusingly, at the same time one of her more brilliant tutors was the author of many of the mathematics books used at Cambridge University — a remarkable and brilliant scientist who was actually not allowed into the great library at Cambridge (or any other university)… because she was female. That woman was Mary Somerville, the individual who introduced Ada to Babbage.

The Engine as visible from the crank end (from 9 o’clock) — what I love most about this photo is the cheerfully calculating computer geeks! (here’s what they’re working on)
Ada herself, as another woman, struggled for much of her life to access training and teachers which the male university students of the time doubtless took for granted. Despite her intellectual brilliance she was married off at 20 (as was “proper” for the times) and had three children, which (of course) seriously interrupted her mathematical studies. Perhaps unsurprisingly, all the remaining pictures of her focus on her beauty, with none showing her writing or working on math.

Further, since her significant inheritance became the property of her husband upon their marriage (as was also “proper” for the times), the poor woman had little to no money of her own with which to pay for teachers. Worse, she got to watch her inheritance frittered away by her husband’s obsession with building incredibly, unnecessarily intricately decorated additions to their houses.

It is unfortunate some of the indignities heaped upon her gender by the times are (weirdly) still prevalent today. For example, Babbage is renown for not giving credit to others regarding the work on his engines. Despite this knowledge of his often irascible personality, many modern historians are positively gleeful in their denigration of Ada Lovelace as nothing more than Babbage’s mouthpiece, based on one paragraph written by Babbage where he mentions suggesting he do a particular piece of mathematical work for her. Amazingly, in that same paragraph he also notes her sending some of his work back to him for re-checking — because she caught a significant error in his original math! How one could deduce thereby that Ada was simply copying Babbage’s work is beyond me. I feel one would have to be very intent indeed on refusing credit to a woman to come up with that conclusion.

The Displays

A close-up of one of the plaster moulds created with this Difference Engine
One of the displays contained the “test” plaster mould created with the machine, as well as a book of the same style of trigonometric tables used in navigation which first caused Babbage to exclaim in anguish over the dismaying number of human errors in them. Considering Napoleon was a huge threat at the time, and the British lived on their navy, and the books of tables were of critical importance to navigators… Babbage’s horror at the number of errors can perhaps be forgiven.

If I’m remembering correctly, the plaster mould is what printers would use to pour the lead into in order to create the plates off which the pages of books would be printed. While this mould is simply two columns of very long numbers, as I mentioned above, the printer was programmable for a variety of printing and page styles. Babbage was obsessed with removing as much human error as he could from the printing of the various books of tables so critical to British commerce, so he insisted the Difference Engine had to be able to put its answers directly into the moulds used by the book printers themselves.

The text on the little display next to the mould reads (faithfully transcribed with spelling errors included):

Stereotype mold from Difference Engine No. 2
This is the first full mould produced by Difference Engine No. 2. The engine impresses results on soft material, in this case, Plaster of Paris. Such molds, called stereotype molds, were used in the 19th century to produce printing plates for use in a printing press. This mold is experimental. The alignment of the numbers and the line heights appear to be erratic. The experiment was used to make adjustments to reduce these irregularities.

The text on the little display next to the book of tables reads:

Table of Logarithms by Charles Babbage, 1827
Babbage’s logarithm tables, first published in 1827, had a reputation for exceptional reliability. Babbage did not computer the tables from scratch but used reputable tables by Francois Cailet as the starting point. Nine separate stages of painstaking checking were used to verify correctness. The results were stereotyped and the volume remained in print for over a century. The last printing was published in 1912.

I’ve transcribed the text of the first photo, in case it’s not large and clear enough. The second photo has nice pictures in it, and the graphic is quite large!
Here’s a photo and the text of the big photo display:

(under the portrait of Babbage)
Charles Babbage 1860 Aged 69 taken in London. Last known portrait.

(the text:)
“Another age must be the judge.”
— Charles Babbage, 1837

Charles Babbage (1791 – 1871), an English mathematician, is known as the first computer pioneer. His designs for vast mechanical calculating engines rank as one of the startling achievements of the 19th century.

Babbage failed to build a complete engine despite lavish government funding, decades of design and development, the best of British engineering, and the social advantages of a wealthy well-connected gentleman of science. His designs remained on the drawing board for nearly 150 years.

This Engine, Difference Engine No. 2, is one of only two Babbage engines ever build. It was completed in March 2008 at the Science Museum, London, and is faithful to Babbage’s original plans drawn up between 1847 and 1849. It is the second of two identical machines built one after the other.

The Engine consists of 8,000 parts in bronze, cast iron and steel. It weighs five tons and measures 11 feet long and 7 feet high. It was designed to calculate and print mathematical tables. Babbage’s early vision was that the ‘unerring certainty’ of machinery would eliminate the risk of human error in the production of printed mathematical tables.

The Engine automatically calculates and tabulates a class of mathematical expressions called polynomials. It calculates to 31 digits of precision and automatically prints an inked hard copy as a record. It also impresses results on soft material, plaster for example, to be used as a mold for casting printing plates, and the format of the results on the printed page is programmable. The Engine works exactly as Babbage intended.

Babbage died embittered and unacknowledged. He had failed to convey his vision of automatic computation by completing a machine. This Engine is a sight no Victorian ever saw. It both memorializes the invention of automatic computing devices and vindicates Babbage’s work. The completion of the Engine closes an anguished chapter in the history of computing.

In Closing

The electric bike, its trailer, and its creator
As I left the display hall I noticed what I first thought was a recumbent bicycle with, curiously enough, a trailer with two seats on it, and what looked like a Persian carpet for footing. Closer investigation revealed it to be an electric recumbent bike, and its owner/creator was quite happy to invite me and one of my friends for a ride around the parking lot! Here’s a close-up of the bike itself and its owner, Mike.

The blue flaring cloth on the front shield is the remains of his initial obsession with streamlining the bike against wind drag, but he noted once he figured out how to put enough batteries on the bike it really didn’t matter any more, so he cut that off. It still looked oddly pretty fluttering in the wind. The bike (carrying three adults, all the batteries, and the trailer) can go up to about 35mph, and the trailer hugged the ground quite nicely even on the wide turns — I didn’t feel any fishtailing at all. The rearmost passenger faces forward, while the passenger closer to the bike faces back. We had quite a bit of fun waving at the grinning observers coming out of the Computer Museum.

So I guess innovation still lives in the Valley. Yay! ;)