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The Difference Engine

In 1790, shortly after the start of the French Revolution, Napoleon Bonaparte decided that the republic required a new set of maps to establish a fair system of property taxation. He also ordered a switch from the old imperial system of measurements to the new metric system. To aid the engineers and mathematicians making the change, the French ordinance survey office commissioned a fresh set of mathematical tables.

In the 18th century, however, computations were done by hand. A "factory floor" of be­tween 60 and 80 human computers added and subtracted numbers to fill in line after line of the tables for the survey's Tables du Cadastre project. It was grunt work, demanding no special skills above basic numeracy and literacy. In fact, most computers were hairdressers who had lost their jobs—aristocratic hairstyles being the sort of thing that could endanger one's neck in revo­lutionary France.

The project took about 10 years to complete, but by then the war-torn republic did not have the funds necessary to publish the work. The manu­script languished in the Academie des Sciences

for decades. Then, in 1819, a young British mathematican named Charles Babbage would view it on a visit to Paris. Babbage was 28 at the time; three years earlier he had been elected to the Roy­al Society, the most prominent scientific organi­zation in Britain. He was also very knowledge­able about the world of human computers—at various times he personally supervised the con­struction of astronomical and actuarial tables.

On his return to England, Babbage decided he would replicate the French project not with human computers but with machinery. England at the time was in the throes of the Industrial Revolution. Jobs that had been done by human or animal labor were falling to the efficiency of the machine. Babbage saw the power of mecha­nization and realized that it could replace not just muscle but the work of minds.

He proposed the construction of his Calcu­lating Engine in 1822 and secured government funding in 1824. For the next decade he im­mersed himself in the world of manufacturing, seeking the best technologies with which to con­struct his engine.


The year 1832 was Babbage's annus mirabi- lis. That year he not only produced a function­ing model of his calculating machine (which he called the Difference Engine) but also published his classic Economy of Machinery and Manu­factures, establishing his reputation as the world's leading industrial economist. He held Saturday evening soirees at his home in Dorset Street in London, which were attended by the front rank of society. At these gatherings the model Difference Engine was placed on display as a conversation piece.

A year later Babbage abandoned the Differ­ence Engine for a grander vision that he called the Analytical Engine. Whereas the Difference Engine had been limited to the single task of ta­ble making, the Analytical Engine would be ca­pable of any mathematical calculation. Like a modern computer, it would have a processor that performed arithmetic (the "mill"), memory to hold numbers (the "store"), and the ability to alter its function via user input, in this case by punched cards. In short, it was a computer con­ceived in Victorian technology.

Babbage's decision to abandon the unfinished Difference Engine was not well received, how­ever, and the government demurred to supply him with additional funds. Undeterred, he pro­duced thousands of pages of detailed notes and machine drawings in the hope that the govern­ment would one

The Dark Ages

Babbage's vision, in essence, was digital com­puting. Like today's devices, such machines manipulate numbers (or digits) according to a set of instructions and produce a precise numer­ical result.

Yet after Babbage's failure, computation en­tered what English mathematician L. J. Comrie called the Dark Age of digital computing—a pe­riod that lasted into World War II. During this time, machine computation was done primarily with so-called analog computers. These devices model a system using a mechanical analog. Sup­pose, for example, one wanted to predict the time of a solar eclipse. To do this digitally, one would numerically solve Kepler's laws of mo­tion. Before digital computers, the only practi­cal way to do this was hand computation by hu­man computers. (From the 1890s to the 1940s the Harvard Observatory employed just such a group of all-female computers.) One could also create an analog computer, a model solar system made of gears and shafts that would "run" time inro the future [see box on next page].


Before World War II, the most important an­alog computing instrument was the Differential Analyzer, developed by Vannevar Bush at the Massachusetts Institute of Technology in 1929. At that time, the U.S. was investing heavily in rural electrification, and Bush was investigating electrical transmission. Such problems could be encoded in ordinary differential equations, but these were very time-consuming to solve. The Differential Analyzer allowed for an approxi­mate solution without any numerical process­ing. The machine was physically quite large—it filled a laboratory—and was something of a Rube Goldberg construction of gears and rotat­ing shafts. To "program" the machine, research­ers connected the various components of the device using screwdrivers, spanners and lead hammers. Though laborious to set up, once done the apparatus could solve in minutes equa­tions that would take several days by hand. A dozen copies of the machine were built in the U.S. and England.

One of these copies belonged to the U.S. Ar­my's Aberdeen Proving Ground in Maryland, the facility responsible for readying field weaporis for deployment. To aim artillery at a target of known range, soldiers had to set the vertical and horizontal angles (the elevation and azi­muth) of the barrel so that the fired shell would follow the desired parabolic trajectory—soaring skyward before dropping onto the target. They selected the angles out of a firing table that con­tained numerous entries for various target dis­tances and operational conditions.

Every entry in the firing table required the in­tegration of an ordinary differential equation. A human computer would take two to three days to do each calculation by hand. The Dif­ferential Analyzer, in contrast, would need only about 20 minutes.

Date: 2015-12-11; view: 174

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