Cranking the Difference Engine

10 responses to “Cranking the Difference Engine”

1. 

   gsikich1

   Oct 27, 2010 at 1:22 am

   Amazing that it could be done in the 1800’s and yet, look where we are today. Makes one wonder about the possibilities of the future.

   Reply
2. 

   jurvetson

   Oct 27, 2010 at 1:23 am

   There is another crank on the right side for the printer:

   

   The math behind the difference engine:
   "If the first few values of a polynomial are known, the rest may be calculated by simple addition of the “repeated differences” between these values. For example, if F(x) = x^2 + 4, begin by manually calculating the values F(1) = 5, F(2) = 8, F(3) = 13, and F(4) = 20 and their differences, as shown above the upper dotted line.

   

   For this particular polynomial, the second difference is a constant (2). It can be added to the first difference (7) to obtain the next first difference (9) (red), which can then be added to the last function value (blue) to yield F(5) = 29, without performing any multiplication. The process can then be repeated to yield the next first difference (11) which may be added to the last function value to get F(6) = 40, etc. Using this method, any second-degree polynomial can be computed this way and, more generally any nth degree polynomial can be computed, using only addition, starting with the nth difference.

   Babbage’s Difference Engine has registers to hold one number from each of the columns in the table (for example 20, 7, 2). It would add the second difference to the first , then add that result to the function value to compute the next entry in the table. There were enough registers for seven orders of differences, allowing it to compute 31-digit values for polynomials with terms up to x7." (from the CHM)

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3. 

   Astrocatou

   Oct 27, 2010 at 2:03 am

   Well…even your previous pictures had me thinking of the German WWII Enigma machine..
   That was pretty clever…whatever the bad stuff behind it.
   I think it used a mechanical variation of all this…

   Great image/info..as usual.

   Reply
4. 

   solerena

   Oct 27, 2010 at 2:38 am

   it seems that engineering back then required some physical strength – "cranking it":) – vs. just sitting in front of the computers … like we all do now… it was better for one’s posture… some sort of exercise… although if you do the same cranking all day long … ouch!
   oh, got it – they could maybe alternate between "cranking" and "literal debugging"… some fun:)

   Reply
5. 

   rocketmavericks

   Oct 27, 2010 at 4:31 am

   While we all love machinery, keep in mind that the first computers were actually humans. Wives, actually. Richard Feynmann describes the early work from Trinity, which was the first attempt at FEA with regard to estimating neutron flux from fission reactions. His book, "The Pleasure of Finding Things Out, he details the role many of the great physicists wives played in facilitating the early mechanical computers at the time. Los Alamos documents this well….

   "Computers were people using desk calculators when Los Alamos began. By the end of the war, Los Alamos scientists were using the first electronic computer. John von Neumann was the primary agent of this change, which led to the Laboratory’s strong program in computer science and technology, as well as making it possible to calculate the behavior of nuclear explosives.
   Early calculations relating to the diffusion of neutrons in a critical assembly of uranium were made by Eldred Nelson and Stanley Frankel, who were members of Robert Serber’s group in the Radiation Laboratory at the University of California, Berkeley, in 1942. When they came to Los Alamos in the spring of 1943, they ordered the same sorts of machines that they had used in California: Marchant and Friden desk calculators to make the calculations required in the design of nuclear weapons.

   To perform some of these repetitive calculations, a group of scientists’ wives were recruited to form a central computing pool. These "computers" included Stanley Frankel’s wife, Mary; Josephine Elliott; Beatrice Langer; Mici Teller; Jean Bacher; and Betty Inglis. This became group T-5 under New York University mathematician Donald (Moll) Flanders when he arrived in the late summer of 1943.
   The mechanical calculators tended to break down under heavy use by physicists and had to be shipped back to the manufacturer until physicists Richard Feynman of Princeton University and Nicholas Metropolis of the University of Chicago learned to repair them. Although Theoretical (T) Division Leader Hans Bethe at first objected that this was a waste of time, he relented when the number of working calculators diminished.

   IBM computer circa 1945
   Dana Mitchell, whom Laboratory Director J. Robert Oppenheimer had recruited from Columbia University to oversee procurement for Los Alamos, recognized that the calculators were not adequate for the heavy computational chores and suggested the use of IBM punched-card machines. He had seen them used successfully by Wallace Eckert at Columbia to calculate the orbits of planets and persuaded Frankel and Nelson to order a complement of them.
   In September 1943, von Neumann made the first of many visits to Los Alamos. A mathematician at the Institute for Advanced Study at Princeton, he had been asked by Oppenheimer to serve as a consultant in hydrodynamics, and during his visits he became aware of the work on implosion being conducted by Seth Neddermeyer and his group."

   Yet another technology brought to you by investemnt in pure worthless research not valued by capital markets. The problem is that free markets are extremely valuable in harvesting the low hanging fruit and bringing economies of scale to create industries and markets to leverage inventions. The only problem, is that once the low hanging fruit on the tree is gone, free markets are not much for watering and fertilizing the tree to produce more fruit. Instead, they would prefer to cut it down and sell it for firewood!

   Q.E.D.

   Reply
6. 

   solerena

   Oct 27, 2010 at 4:46 am

   to rocketmaverics: intersting thoughts, especially like the one about free markets and the vital tree of research and technology development… free markets role is a double edge sword in this regard…

   Reply
7. 

   vt_samdog

   Oct 27, 2010 at 1:17 pm

   " … before the era of standard screws."

   Maybe he should have invented that first and his computer might not have taken 27 years to build–just sayin’….

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8. 

   Astrocatou

   Oct 27, 2010 at 2:36 pm

   !!!

   Reply
9. 

   rwoodworkr

   Oct 27, 2010 at 4:26 pm

   The original Wii.

   Reply
10. 

    Drift Words

    Nov 8, 2010 at 5:48 pm

    Nice video. Also good to see an engineer getting himself a workout, this particular model looks unlikely to go down the gym.

    Reply