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The reality is that Ada’s contribution was both profound and inspirational. More than Babbage or any other person of her era, she was able to glimpse a future in which machines would become partners of the human imagination, together weaving tapestries as beautiful as those from Jacquard’s loom. Her appreciation for poetical science led her to celebrate a proposed calculating machine that was dismissed by the scientific establishment of her day, and she perceived how the processing power of such a device could be used on any form of information. Thus did Ada, Countess of Lovelace, help sow the seeds for a digital age that would blossom a hundred years later.
I. It was in a review of this book that one of Babbage’s friends, William Whewell, coined the term scientist to suggest the co
II. Specifically, he wanted to use the method of divided differences to closely approximate logarithmic and trigonometric functions.
III. Named after the seventeenth-century Swiss mathematician Jacob Bernoulli, who studied the sums of powers of consecutive integers, they play an intriguing role in number theory, mathematical analysis, and differential topology.
IV. Ada’s example involved tabulating polynomials using difference techniques as a subfunction, which required a nested loop structure with a varying range for the i
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Alan Turing (1912–54), at the Sherborne School in 1928.
Claude Sha
CHAPTER TWO
THE COMPUTER
Sometimes i
Some of those advances seem almost trivial, but progress comes not only in great leaps but also from hundreds of small steps. Take for example punch cards, like those Babbage saw on Jacquard’s looms and proposed incorporating into his Analytical Engine. Perfecting the use of punch cards for computers came about because Herman Hollerith, an employee of the U.S. Census Bureau, was appalled that it took close to eight years to manually tabulate the 1880 census. He resolved to automate the 1890 count.
Drawing on the way that railway conductors punched holes in various places on a ticket in order to indicate the traits of each passenger (gender, approximate height, age, hair color), Hollerith devised punch cards with twelve rows and twenty-four columns that recorded the salient facts about each person in the census. The cards were then slipped between a grid of mercury cups and a set of spring-loaded pins, which created an electric circuit wherever there was a hole. The machine could tabulate not only the raw totals but also combinations of traits, such as the number of married males or foreign-born females. Using Hollerith’s tabulators, the 1890 census was completed in one year rather than eight. It was the first major use of electrical circuits to process information, and the company that Hollerith founded became in 1924, after a series of mergers and acquisitions, the International Business Machines Corporation, or IBM.
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In the case of computers, there were many such incremental advances made by faceless engineers at places like IBM. But that was not enough. Although the machines that IBM produced in the early twentieth century could compile data, they were not what we would call computers. They weren’t even particularly adroit calculators. They were lame. In addition to those hundreds of minor advances, the birth of the computer age required some larger imaginative leaps from creative visionaries.
DIGITAL BEATS ANALOG
The machines devised by Hollerith and Babbage were digital, meaning they calculated using digits: discrete and distinct integers such as 0, 1, 2, 3. In their machines, the integers were added and subtracted using cogs and wheels that clicked one digit at a time, like counters. Another approach to computing was to build devices that could mimic or model a physical phenomenon and then make measurements on the analogous model to calculate the relevant results. These were known as analog computers because they worked by analogy. Analog computers do not rely on discrete integers to make their calculations; instead, they use continuous functions. In analog computers, a variable quantity such as electrical voltage, the position of a rope on a pulley, hydraulic pressure, or a measurement of distance is employed as an analog for the corresponding quantities of the problem to be solved. A slide rule is analog; an abacus is digital. Clocks with sweeping hands are analog, and those with displayed numerals are digital.
Around the time that Hollerith was building his digital tabulator, Lord Kelvin and his brother James Thomson, two of England’s most distinguished scientists, were creating an analog machine. It was designed to handle the tedious task of solving differential equations, which would help in the creation of tide charts and of tables showing the firing angles that would generate different trajectories of artillery shells. Begi
That challenge of linking together multiple integrators was not mastered until 1931, when an MIT engineering professor, Va