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Building a 5-Ton Calculator From 19th-Century Plans 218

Posted by kdawson
from the steampunk-on-steroids dept.
alphadogg writes "Starting in May, many will have the opportunity to see computing done the old-fashioned way: with lots of gears, a big crank, and some muscle. The Computer History Museum in Mountain View, CA, will unveil a new construction, the first in the US, of the 19th-century British mathematician Charles Babbage's Difference Engine No. 2, an improved version of his earlier design for a mechanical digital calculator. It weighs in at two tons more than the Difference Engine built in 1991 at London's Science Museum. Microsoft millionaire Nathan Myhrvold commissioned and paid for the US model."
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Building a 5-Ton Calculator From 19th-Century Plans

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  • It's cool (Score:4, Funny)

    by kampangptlk (1252914) on Monday April 14, 2008 @10:08PM (#23072648)
    But does it run linux?
  • frock (Score:5, Funny)

    by Missing_dc (1074809) on Monday April 14, 2008 @10:09PM (#23072654)
    Does this mean as a sysadmin that I should start wearing my Frock and Tophat and subscribe to the local Victorian club???? :)

  • ...an improved version of his earlier design for a mechanical digital calculator. It weighs in at two tons more than the Difference Engine built in 1991 at London's Science Museum.

    Well - there goes Moore's Law then, I guess. Although, this was invented in the century before Moore himself was.

    Microsoft millionaire Nathan Myhrvold commissioned and paid for the US model."

    Hmm. Microsoft's upcoming answer to viruses, rootkits, worms, etc?

    • ...an improved version of his earlier design for a mechanical digital calculator. It weighs in at two tons more than the Difference Engine built in 1991 at London's Science Museum.

      Well - there goes Moore's Law then, I guess. Although, this was invented in the century before Moore himself was.

      Being a Microsoft product it has to have one extra ton of DRM and another ton of UI tweaks.

  • by calebt3 (1098475) on Monday April 14, 2008 @10:19PM (#23072744)

    Babbage's Difference Engine No. 2, an improved version of his earlier design for a mechanical digital calculator
    Hence the 2...
  • What if... (Score:5, Funny)

    by DigitAl56K (805623) on Monday April 14, 2008 @10:19PM (#23072752)
    What happens when you divide by zero on a calculator using a physical engine?

    Does it explode? Will it create a black hole? Could this be the next doomsday device?
    • by jellomizer (103300) on Monday April 14, 2008 @10:34PM (#23072886)
      Being boring I would expect it would Jam. A gear may break off if you force it.
    • by creimer (824291) on Monday April 14, 2008 @10:46PM (#23073010) Homepage
      Universe 1.0 will come to an end. God -- or the designated higher being of your choice -- will shake His divine head, and create Universe 2.0 with better error handling routines.
      • by jamstar7 (694492)
        I coulda swore I read someplace that a theory was, anytime somebody got close to understanding the Universe, it rebooted into something more incomprehemsible.

        The theory also mentioned that this has happened a few times already...

    • Re:What if... (Score:5, Informative)

      by Anonymous Coward on Monday April 14, 2008 @10:46PM (#23073012)
      As I recall from some of the mechanical calulators I used several decades ago, division was performed by repeated subtraction. I don't remember trying to divide by zero, but my guess is that you'd have to keep turning the crank forever . . .
      • by Whiteox (919863)
        On the old mechanical calculators, if you subtract 0, then it just whirs and shows you the same number.
        EG National cash registers and even the solenoid powered electric adding machines with paper tape printing.
        It's only microprocessors that can't handle div by 0 errors.
      • Re: (Score:3, Funny)

        by Torvaun (1040898)
        Or not turn the crank at all.
    • Re:What if... (Score:5, Informative)

      by evanbd (210358) on Monday April 14, 2008 @10:47PM (#23073020)
      It's far more specialized than that. It basically computes values of a polynomial from a starting set (interpolate / extrapolate). It doesn't have an explicit fexible divide operation. Exactly what sort of error you get out is going to depend on how you carry out the division, but most likely you would do exp(log(a) - log(b)), which would produce a very large negative number for log(b) (an incorrect result, obviously), and a very large number for the result. It might or might not overflow, depending on the precision of your approximating polynomials for log and exp at the values of interest.
    • I've done that. (Score:5, Interesting)

      by Ungrounded Lightning (62228) on Monday April 14, 2008 @10:50PM (#23073046) Journal
      What happens when you divide by zero on a calculator using a physical engine?

      I've done that.

      The particular calculator in question would spin madly, with the result digit dials working like a cross between an odometer and a clock movement, until you hit the button that aborts the process. (The abort apparently consisted of changing the divisor to a large number. It took close to a minute as the machine would do a trial subtraction, undo it, shift the register bar one to the left, and repeat until it got to the last digit.)
    • Re:What if... (Score:5, Interesting)

      by Tenebrousedge (1226584) <tenebrousedge&gmail,com> on Monday April 14, 2008 @11:07PM (#23073190)
      To start, a famous quote:

      "On two occasions I have been asked, "Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."


      What truly happens to an impossible sum?

      Does it dry up

      like a slashdotter in the sun?

      or does it fester like sco

      and then run?

      does it stink like an overused meme?

      or crust and sugar o'er--

      like a deferred dream?

      maybe it just sags like a 5-ton calculating machine under a heavy load

      or does it explode?

      • Perhaps you've drawn excessively from the parent poem in your parody, but I liked this a lot. A fine fusion of literature and geekery. You've earned my admiration (and I've marked you as a friend.)
      • GIGO (Score:3, Funny)

        by Tablizer (95088)

        a famous quote: "On two occasions I have been asked, "Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."

        I remember reading that one of them was a congressman. If so, things haven't changed in 150 years.
               
        • by Moraelin (679338) on Tuesday April 15, 2008 @03:53AM (#23074616) Journal
          Actually, it is at least possible that it was intended as a trick question. You know, one where if you say "yes" then you've just said "yep, I'm a con artist." Admittedly, it's a stupid one even as trick questions go, but still, there might be some purpose behind it.

          To put things into perspective Babbage got funding for one machine, never finished it, decided he's rather begin designing the version 2 model, asked for more funding, repeat ad nauseam. Pretty much it was _the_ original computing vapourware. Pretty soon he got no more funding, but that never stopped him from asking for more and hyping his unproven creation to the parliament.

          He also seems to have descended into a nerd-like bitterness, in which he took such questions out of context as proof that everyone else is a drooling idiot and that's why they don't see he's right. And in that he also included such questions as, basically, "well, what _can_ it do?" and "what's the business advantage for making one of these?" Stuff that you'd get asked by any business nowadays too. He took them as proof that his contemporary Englishmen were narrow minded and lacking in vision.

          It may seem obvious in retrospect that his design was right, but at the time it was everything except obvious. It was a _monumental_ expense with the economy and technology at that time, even compared to paying armies of people to calculate those by hand. And it was anything but proven. Noone knew if it would even work at all. Again, the first round of funding he got, produced nothing tangible.

          Also regarding the parliament at the time, they were not as obtuse as you (or Babbage) seem to think. They funded a lot of research, actually. The nautical clock, for example, was paid for by the parliament, and that was quite the iterative development. The first couple of versions not only were too inexact to be any use, but at least the first one didn't even compensate for the ship's rolling around. But nevertheless, that guy had _something_ working to show for his work, and kept getting more money to keep working. Babbage had nothing except his claims.

          Now before I sound too damning to Babbage, it wasn't only his fault. He got into a conflict with the company actually building it, and that was the chief reason why the V1 was never completed. But, still, seen from outside, he never had anything working to show, and even more damning he just unilaterally scrapped the design in the middle of the project and began designing an even more overengineered V2 instead.

          So, anyway, given that he was technically hyping vapourware, I can see a smart-arse member of the parliament trying to catch him with a trick question. Again, it _is_ a dumb one, but it's not the same class of dumb as actually thinking that a machine can magically guess the right answers when fed wrong data.

          (But then again, I see a ton of PHBs and businesses nowadays believing just that about electronic computers, so maybe it was just a dumb question after all.)
    • by kylehase (982334)
      You get black holes and strangelets.
    • What happens when you divide by zero on a calculator using a physical engine?

      "Careful, Babbage, you could put out somebody's pi with that thing."
           
  • Does this mean that they are re-releasing Vista? I mean most people consider it a oversized calclator anyway...

    (Yes, even Microsoft users can poke fun at themselves too...)
  • Meh.... (Score:5, Interesting)

    by mark-t (151149) <`markt' `at' `lynx.bc.ca'> on Monday April 14, 2008 @10:23PM (#23072792) Journal
    When you can make an difference engine out of LEGO [woz.org], it really doesn't seem that impressive to build a five ton one. Babbage's analytical engine, however... that would be an interesting piece.
    • Re: (Score:2, Funny)

      by Tablizer (95088)
      Article: Andrew Carol, an Apple software engineer who built a simpler difference engine, entirely of plastic LEGO pieces...

      It appears Mr. Babbage should have invented Legos first.
             
    • Re:Meh.... (Score:4, Insightful)

      by Jeremy Erwin (2054) on Tuesday April 15, 2008 @01:02AM (#23073892) Journal
      From Carol's site:

      Babbage's design could evaluate 7th order polynomials to 31 digits of accuracy. I set out to build a working Difference Engine using standard LEGO parts which could compute 2nd or 3rd order polynomials to 3 or 4 digits
      You can compute 3rd order polynomials by hand without too much strain. Seventh order polynomials are too difficult to reliably compute by hand--the mind numbing tedium might get to you after a bit.

      Nor can you build a seventh order difference machine out of legos.

      Plastic gearing and axles are subject to large amounts of flex and gear lash, which can be a significant problem where any level of precision is required.
      Babbage's machine weighs five tons because it was designed to be precise. The museum's machine weighs five tons because it is intended to be a replica of what Babbage created, not just an amusing simplification.
  • by jdb2 (800046) * on Monday April 14, 2008 @10:36PM (#23072906) Journal
    With the money this guy has surely he could afford to build a version of the Analytical Engine. It's not a giant leap for the machinists involved in such a project, given that the fine specifications for the various gears, wheels and cogs is a no-brainer for today's technology -- all the parts could be laser cut by a robot. It would be truly awe-inspiring to see the first computer functioning in all its glory, for indeed it is Turing complete and lays out many of the concepts used in modern digital computers.

    Here are some links :

    [fourmilab.ch]http://www.fourmilab.ch/babbage/ [fourmilab.ch]

    The obligatory 99-bottles-of-beer-on-the-wall in punched card Analytical Engine assembly language :

    [99-bottles-of-beer.net]http://99-bottles-of-beer.net/language-babbage's-analytical-machine-79.html [99-bottles-of-beer.net]

    Hmmm, I dare say that's shorter than the C# version, if you remove the comments. Oh and it will run Linux, if you have enough coal and are willing to wait a few years for X to load. ;) (it does have a graphical output device) As for a beowulf cluster, that might help performance, although your interconnect mechanism would probably be pneumatic ie. tubes (that's what the Internet is made of anyway right?) and the cluster size would require a few tens of millions of units. ;)

    jdb2

    • Re: (Score:2, Informative)

      by Sir Nimrod (163306)

      The problem is that there are no complete plans for an Analytical Engine. Drawings and diagrams, yes, but nothing complete. For Difference Engine No. 2, the Science Museum had a (reasonably) complete set of plans. (They had to make a few tweaks, but they did everything they could to keep it in the spirit of the original design.)

      Doron Swade's book The Difference Engine: Charles Babbage and the quest to build the first computer is a marvelous read; it was published in the U.K. as The Cogwheel Brain. You may

    • With the money this guy has surely he could afford to build a version of the Analytical Engine. It's not a giant leap for the machinists involved in such a project, given that the fine specifications for the various gears, wheels and cogs is a no-brainer for today's technology -- all the parts could be laser cut by a robot. It would be truly awe-inspiring to see the first computer functioning in all its glory, for indeed it is Turing complete and lays out many of the concepts used in modern digital computer

  • [a manager grumpily storms into a room full of smoke and dust with gaping holes in the walls and light fittings hanging from the ceiling]
    Manager "What happened here I heard this unearthly explosion ? "
    [a pallid skinned, slightly chubby man is sitting in the corner wearing shredded clothes and has black burn marks on his face]
    BOFH "I tried to port Quake II to the Babage machine and I needed to over clock it a bit and well one of the gears on the number 5 stack jammed when it reached 24,000 rpm"
  • Picture it (Score:2, Interesting)

    by snikulin (889460)
    Here is the pic of the UK version [sciencemuseum.org.uk].
  • by Nimey (114278) on Monday April 14, 2008 @11:11PM (#23073224) Homepage Journal

        WELCOME TO THE BABBAGE ANALYTICAL TIMESHARING SERVICE

        PLEASE NOTE THAT THE INTEGRATOR IS CURRENTLY UNAVAILABLE
        DUE TO THE WEEKLY GREASING SCHEDULE. WOULD ALL USERS KINDLY
        RETURN ANY UNUSED PLUGBOARDS, AS THE PROGRAMMING TEAM ARE
        RUNNING LOW. DIVISION UNIT 3 WILL BE OUT OF ACTION UNTIL
        THURSDAY DUE TO EMERGENCY COG REPLACEMENT - PLEASE ENSURE
        THAT YOUR PROGRAM DOES NOT ATTEMPT TO DIVIDE BY ZERO AS
        THIS CAN CAUSE SEVERE DAMAGE (INCLUDING SHAFT BREAKAGES).
    .
    .
    SYSTEM READY.
    ?
    • Bugger. Used all my mod points yesterday :o(

      Being British, I'd have liked a reference to the Memory Hole - I'm sure that Mintrue would have run some variant of the Analytical Engine...

  • I get the "nostalgia" and "historical interest" thing, but don't waste 5 tons of material doing it! If anything, miniaturize it. It'd be just as cool. Even better? Make an OpenGL version of it and turn it into a screensaver.
    • Re: (Score:3, Interesting)

      by Jerry Smith (806480)

      I get the "nostalgia" and "historical interest" thing, but don't waste 5 tons of material doing it! If anything, miniaturize it. It'd be just as cool. Even better? Make an OpenGL version of it and turn it into a screensaver.
      Personally I'd think it's 5 tons of material well-spent. It was things like these that made me think "How does it work?" when I was a wee lad.
  • by Fnord666 (889225) on Monday April 14, 2008 @11:27PM (#23073324) Journal
    From the FA:

    Carol gives the example of multiplying 5 by successive numbers, such as 6, 7, 8. "In simple terms, the method of differences is based on the observation that if the work has already been done to multiply 5 by 5, [then] that work can be reused to multiple 5 by 7 with the addition of another 5 into the previous total," he writes.
    I guess that's why the author went into journalism instead of computers.
  • I don't know how the engine works, but assuming it has the equivalent of adders, registers and some boolean bit-ops, might it be possible to extrapolate the size/weight of a machine such as this that emulates some simple RISC processor of today?

    I have visions of a multi-storied, block-sized, brass behemoth, with hundreds of workers scurrying around its innards "de-bugging" (and de-ratting) it, and keeping it lubricated.

    Just interested to hear peoples guesses.
  • See it in action! (Score:5, Interesting)

    by JoeCommodore (567479) <larry@portcommodore.com> on Monday April 14, 2008 @11:29PM (#23073346) Homepage
    See what one (difference engine #2) looks like running, impressive!

    This one is in mechano parts (Erector Set for us Americans)

    http://www.meccano.us/difference_engines/rde_2/index.html [meccano.us]
  • by chmguy (1273222) on Monday April 14, 2008 @11:39PM (#23073388)
    I'm am one of the Docents for the Difference Engine #2, and although the team making it work is WAAAAY more competent to comment, lemme put out a few FACTS, at the risk of "flame wars of death"... The Engine is a single function calculator that can iterate the values of a 7th order polynomial approximation to an arbitrary mathematical function. After about an hour of VERY careful setup, any set of coefficients could be entered, allowing almost any function to realized. It uses a technique called "finite differences" that allows the calculation to be performed using only addition (and 10's compliment coefficients to represent negative numbers). Our working plan is to set it up to do a table of logarithms, much like Babbage's own table, produced well before he thought of Difference Engine #2. The polynomial approximation for logarithms is quite accurate over the space from 1.0 to 1.6, 6000 iterations of the Engine. (It takes four turns of the crank or about 6 sec. per iteration.)
    The calculation section has about 4,000 parts, and a very elaborate printer mechanism has another 4,000, and was designed to produce sterotype molds of a complete page of a book of tables.
    It is a WONDEROUS device to behold! There are 52 distinct stages in it's control graph (EXACTLY like a modern timing diagram, just vertical...) An elaborate nest of 14 cams control the complex sequence of events to do an iteration, which is !pipelined!. The sinuous ripple carry mechanisms on the back side are HYPNOTIC, as are the forward and backward movements of the intra-column sector gears.
    Avoid CHM on May 10, it's gonna be a madhouse! But this is pretty close to the top of the list of "1000 Geeky Things to See Before You Die", oh, and by the way, there's all the other ABSOLUTELY WAY COOL stuff at CHM, wanna see an Apple I signed by "the Woz"...
    YOU GOTTA SEE THIS! chmguy
  • by Anonymous Coward on Tuesday April 15, 2008 @02:40AM (#23074336)
    The Difference Engine is a specialized device which was designed to automate the calculation of tables of values of complex formulae. Such as trigonometric functions, logarithms, etc. The Difference Engine works by using a variant of the Taylor method to approximate complex functions using high order polynomials. It then calculates successive values of the polynomial function using the difference method. It's quite elegant in terms of making the most out of limited computing ability.

    Consider a simple polynomial like x^2 + 3*x. Now, take a few initial values of that function like so:

    f(0) = 0
    f(1) = 4
    f(2) = 10
    f(3) = 18
    f(4) = 28

    Now, take the difference between each value where x is increased by the same amount (equivalent to a crude approximation to the derivative of f):

    g(1) = f(1)-f(0) = 4
    g(2) = f(2)-f(1) = 6
    g(3) = f(3)-f(2) = 8
    g(4) = f(4)-f(3) = 10

    Now do the same with these differences (equivalent to taking the 2nd derivative):

    g(2) - g(1) = 2
    g(3) - g(2) = 2
    g(4) - g(3) = 2

    Now we see that the 2nd differences are all the same value, this is because this is a 2nd order polynomial. For a cubic polynomial it takes 3 sets of differences. Now, we can calculate the value of f for x=5 and higher values without the formula by adding the differences.

    g(5) = 2 + g(4) = 12

    f(5) = f(4) + g(5) = 28 + 12 = 40
    f(5) = 5^2 + 3*5 = 40

    etc.

    We can use exactly the same process to merely approximate functions based on a table of values, given we calculate the differences to a high enough order (i.e. produce a polynomial approximation of high enough order) to give reasonably accurate values. Meaning, taking differences as above to some nth degree from n initial input values and then calculating successive values has the effect of approximating that function with an nth degree polynomial.

    Babbage's Difference Engine No. 2 design is capable of calculating 7th order polynomials with 31 decimal digit numbers, which is sufficient to calculate trigonometric and logarithmic functions to very high precision. Using the Difference Engine one would need to manually calculate only 7 initial values, then use the Engine to automatically produce tables for the remainder of the values needed. Compared to the methods of the 19th century (where the term "computer" referred to a person given that job, not a device) this represented an enormous savings of labor, as well as an enormous increase in accuracy of the output, under the right conditions.
  • but you have to wear the special trousers.
  • The parts shown in the photos look pretty hefty, almost large enough to be used in an automotive gearbox. I'd think that good precision machining could make the machine less than 1 cubic foot and a couple hundred pounds, and still be plenty robust. Even smaller if wristwatch-sized gears were used.
  • between the one in the Science Museum and this new machine? TFS states "two tons heavier", but the article doesn't mention it, nor the CHM website. The London machine weighs 5.5 tons including its printer, the CHM machine also is listed at 5 tons. What gives?
  • by hcdejong (561314) <hobbes@@@xmsnet...nl> on Tuesday April 15, 2008 @03:56AM (#23074624)
    According to this article [news.com] (which also contains more detail on building and shipping the Engine), the machine will be on display for 6 months, then it will be moved to Myhrvold's home. So if you want to see it, don't wait too long.

    (I found another article [wired.com] which claims the Engine will be at the museum for a year. The CHM website doesn't have definitive data.)

    I saw the one at the Science Museum a few years ago, and it's awesome. Well worth a trip.

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