Analytical Engine | Research & Encyclopedia Articles

Analytical Engine

History

The Analytical Engine was, or would have been if it had ever been completed, the world's first general-purpose computer. It was designed in the 1830s by the English mathematician and inventor, Charles Babbage. Babbage was a mathematician at Cambridge University where he received his Master of Arts in 1817, and later, like Sir Isaac Newton, whose mathematical principles he helped put forward, occupied the Lucasian chair in mathematics.

His stated intention was to create an Engine that "is a machine to calculate the numerical value or values of any formula or function of which the mathematician can indicate the method of solution. It is to perform the ordinary rules of arithmetic in any order as previously settled by the mathematician, and any number of times and on any quantities." From this description it is easy to see that the Analytical Engine is nothing short of a programmable computer.

Far ahead of its time the Analytical Engine introduced a number of fundamental concepts in computing that are still used today in modern digital computers. Later, in the 20th century, when technology had moved on and computers were being built first out of electromechanical and then electronic devices, the pioneers of modern computing realized that Babbage has foreseen and anticipated almost every aspect of the work.

Babbage's first computational engine was the Difference Engine, which he designed in the 1820s. Unlike the later Analytical Engine, which was designed to be what is essentially a Universal Turing Machine, the Difference Engine was intended for the single purpose of mechanically computing mathematical tables that, until then, were laboriously calculated by hand and were notoriously error prone.

With his design of the Difference Engine complete, he pulled strings in government to get initial funding for the construction of his Difference Engine, a task he expected to take 3 years. The project failed miserably, however, descending into farce as it was beset by crisis after crisis. Eventually in 1827, after the death of his wife, things came to a head and construction of the engine was temporarily halted. Babbage left England and went abroad and did not return for some years.

By 1834 Babbage was back and managed to get further funding for the Difference Engine. However, the project foundered a second time, and this time for good. In the meantime he began his work on the Analytical Engine. He envisaged the Engine to be constructed with brass fittings and powered by steam. He tried, but was ultimately unsuccessfully, to secure funds either to finish work on the Difference Engine or to begin building his new Analytical Engine. But by now it was the 1840s and the British government, which had already spent as much as 17,000 British pounds with little to show for it, declined his invitation to finance his Engines further.

The Engine

Input to and output from the Analytical Engine was to be provided using punched cards, based on the work of Jacquard in the early 1800s. It is interesting to note that over 100 years later, the first digital computers also used the punch-card system for input and output of data.

Babbage settled on three sets of punched cards that would serve to direct the machine in its calculations. One set of cards were to be used to input the given numbers or constants of a problem to the machine. He called these cards the "Number Cards." A second set of cards was to be used to direct the Engine to store these given numbers, or any intermediate numbers arising during calculation, in a particular place or "column" in the Engine. These were the "Directive Cards." There would also be other "Directive Cards" for general purposes of control when necessary. The third set of cards was the set of "Operation Cards," and these were to direct the actual operations to be performed. That is, they would mechanically put the engine into a state where it could perform the required operation. In combination these cards would comprise the computer program and its input data.

The operational features of the Analytical Engine included a "Store" and "Mill," which are analogous to today's computer memory and central processing unit. The store comprised a number of vertical columns that would receive the given numbers and any intermediate results, and the Mill was a complex arrangement of wheels, gears, cams, and levers that operated on the numbers from the Store using decimal arithmetic.

Babbage's 1837 description of the Engine specified a forty-digit capacity for columns in the store, as well as a mill capable of adding and subtracting forty-digit numbers, multiplying two forty-digit multiplicands to produce an eighty-digit product, and dividing an eighty-digit dividend by a forty-digit divisor to give a quotient and remainder, each also of forty digits. But in later descriptions of the Engine the store has a capacity of fifty digits and the mill is able to add and subtract fifty-digit numbers and hold one-hundred-digit products and dividends.

Also in later versions of the Engine Babbage specified a "1000-column store," which is very impressive considering the size of the memory in early electronic digital computers. For example, one early digital computer, the UNIVAC I, also had 1000 memory locations, but each location could store only 12 characters, with one of those characters being reserved to indicate sign, which made its memory less than a quarter of that Babbage specified for his Engine. Consider also that this electronic computer also stored its program in the same memory area that it used for data, whereas the Analytical Engine, stored its program on the three sets of cards rather than in the store, and the dimensions of the Analytical Engine seem all the more impressive.

The mill was the part of the machine where the numbers would be operated on. The arithmetical operations of the mill would work only with signed integer quantities; that is, the Engine had no means of handling real numbers or fractions. As most analytical formulae involve real numbers, the Engine employed a technique called fixed-point arithmetic to allow it to work with decimal fractions that have a precision limited only by the fifty-digit capacity of the store and mill.

Since the Engine was to be made of brass wheels and cams, and rods, gears, and pivots, it would have been slower by several orders of magnitude than even the most lethargic of modern electronic computers. Babbage estimated the speed of calculation in his 1864 description of the Engine as being somewhere in the region of one addition or subtraction per second, and one minute for a multiplication of two fifty-digit numbers or division of a one-hundred-digit dividend by a fifty-digit divisor. Because of the way the Mill worked, addition and subtraction were more or less constant regardless of the sizes of the addends and subtrahends; multiplication and division, however, were much faster for smaller dividends and multiplicands.

The Present Day

Babbage's Difference Engine was eventually built in 1991, the bicentennial of Babbage's birth, using the technology of Babbage's time as demonstrable proof that his designs were well-founded. A working model can be found now in the Science Museum in London, England.

The Analytical Engine is, however, still little more than a design on paper, although there is at least one computer program available that emulates the Analytical Engine and proves the design was sound. The eventual cost of building the Difference Engine was very high, and the Analytical Engine is a much more complex and ambitious undertaking (and therefore a much more expensive one), so it remains to be seen if anyone will ever build one.