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Calculation in those days relied extensively on the use of tables. Moreover, I still have my tables, which I used while in college, until 1978. Basically, the least you had to calculate the better, it was tiring and error prone. The problem was that the tables themselves had errors, lots of them. Ship captains would use tables to calculate the position of his vessel at sea and an error might mean hitting a coast. Artillery officers used tables to calculate trajectories. Bankers used tables to pay interest, insurers to charge payments. Engineers used them to design bridges and steam engines. As science and technology progressed beyond the capabilities of simple estimates, and mathematics provided the formulas to do it precisely, the failure of the tables to provide accurate values became obvious.
Babbage himself calculated that the British government had lost more than 2 million pounds (of those days) because of errors in the tables used to calculate annuities
John Herschel, the astronomer, said, "An undetected error in a logarithmic table is much like a sunken rock at sea yet undiscovered, upon which it is impossible to say what wrecks may have taken place". Herschel visited Babbage with some calculations done by his computers (people who did calculations) to check them with his friend. After finding many errors, Babbage exclaimed, "I wish to God these calculations had been executed by steam", meaning by a mechanical device. Thus it was born the idea to build such a machine.
It is difficult to think of a machine meant to print tables as related in any way to a modern computer but, at the time, it was the perfect solution. It was inconceivable to carry a calculating engine on board of even the largest of ships, it didn't make any sense since all you needed could be contained in a table that could fit in your pocket. Thus, it has to be understood that the Engine was designed for that purpose. For example the printing mechanism was meant not to just print tables but to stamp soft metal strips to make printing plates from. Moreover, the printing mechanism (or more properly, stereotyping mechanism) produced not just one set of printing plates but two, of different size, plus a printed copy, possibly to have an immediate feedback.
Tables are still much in use, all high sea sailors know how to use nautical tables, no matter how well equipped they might be. When I went to college, not long ago (I wish to believe), there was nothing but tables. Even nowadays, most floating point processors use look-up tables to solve various functions. A table in silicon is a very regular structure, easy to make and pack into a chip, much more easier and compact than designing special circuitry for each function.
The first electronic computers, in the 1940s, with names such as Eniac, Edvac, Maniac, they all had the AC ending, meaning Automatic Calculator and they all were meant, basically, to print tables
Since tables are regular, that is, the same process is done over and over to produce a series of values, the Difference Engine was not made to give a particular value given a certain input, actually, the setup of the machine required you to give it an initial value. The Engine was able to calculate series of them, by adding differences.
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