Publisher Summary

This chapter provides an overview of the history of the development of today’s computers, which can be traced back to three roots. The first of these was the development of systems of numbering and of calculation and the search for techniques to automate this, the second was the development of formal logic, and the third was the development of the electronic and mechanical technology without which the construction of computers would not have been possible. The development of electromechanical and then of electronic technology was the thing that finally made the construction of computers possible. The first machine to be built that would qualify as a computer by today’s definitions was the Electronic Numerical Integrator and Calculator (ENIAC). Valve computers are known as the first generation computers and the early transistor computers are known as the second generation machines. Printed circuits, the reduction in size of transistors and diodes, and the development of families of similar computers of varying power heralded a third generation of computers.

EASIER CALCULATION

‘VII plus XXI’ or ‘three-fifths of VL’ are extremely awkward operations if the only notation available for manipulating the quantities is the Roman numerical system. The adoption of our present day numbering system, in which each digit has a constant relationship to that on each side of it, was necessary before advances were made in mathematics, commerce and taxation. In 1642 Blaise Pascal, son of a French tax collector invented a device to perform mechanically addition and subtraction and, by repeated additions and subtractions, multiplication and division.

Charles Babbage (1792–1872) was an English mathematician who conceived of a mechanical device which could, by reason of the property of fixed differences, compute tables of mathematical functions, such as logarithms, tangents of angles and astronomical tables. He built a pilot model of this ‘difference engine’ which worked quite well, but before he had finished constructing a larger version of it he conceived of a grander idea, that of an ‘analytical engine’ which would have worked on a more fundamental set of principles and would have had a much wider set of operations. In 1842 the Italian, L. S. Menabrea wrote a paper based on a series of lectures given by Babbage in Turin. Lord Byron’s daughter, Lady Lovelace, translated this paper into English, adding to it extensive notes. In this we have the first exposition of many of the principles which underlie today’s electronic digital computers. Lady Lovelace became Babbage’s ‘senior programmer’ and was the most perceptive interpreter of his ideas (Babbage himself exasperated his friends by his inability to explain his thoughts to them). The construction of the difference engine and of the analytical engine on the scale envisaged by Babbage was beyond the engineering techniques of the day and although he made a number of significant advances in these, he died an embittered man after the support of the British Government for his difference engine had been withdrawn and he had spent much of his own personal fortune on the analytical engine.

Babbage wrote: ‘If, unwarned by my example any man shall succeed in constructing an engine embodying the whole of the executive of mathematical analysis… I have no fear of leaving my reputation in his charge, for he alone will be fully able to appreciate the nature of my efforts and the value of their results.’ When this was read by Professor Howard Aiken of Harvard University many years later in 1939 it appeared to him ‘like a voice from the past’, as he was then involved in the design of the first machine which worked by using the principles of Babbage’s analytical engine. In one of her many explanatory notes on Menabrea’s paper Lady Lovelace described the potential functions of the analytical engine in the following words.

These sentiments are as appropriate to current computers as they were to Babbage’s analytical engine. Well intentioned but ignorant over-enthusiasm for computers is often followed by disillusionment when it is discovered that the apparent failure of a computer to solve a problem is in fact a failure to specify to it an adequate method for that problem’s solution.

In 1909 an Irish accountant named Percy Ludgate described, in a paper published in the Scientific Proceedings of the Royal Dublin Society, an analytical machine of his own conception. This device was never constructed, Ludgate dying of pneumonia in 1922 at the age of 39. He paid tribute to Babbage although he did not discover his work until his own initial design was complete. Unlike Babbage’s machine Ludgate’s machine did not perform multiplication by repeated addition, but by the use of the properties of a set of ‘index numbers’ which are similar to those of logarithms. Similarly, Ludgate had a novel method of automating division.

Some twenty years before this time, Dr Herman Hollerith and his assistant, James Powers, were developing machines which manipulated data by using holes punched in cards. The first use of punched cards was by a Frenchman, Jacquard, to control the complex sequence of operations involved in weaving a pattern on a silk loom. Babbage also used punched cards as a means of putting instructions and data into his machines. Hollerith started work on automatic processing of data in 1889 for the American census of the following year and his inventions started a whole new industry. Punched card data processing machines are still in use today, but it was not for some time after the first computers were working that the principles of automatic data processing using punched card machines and those of numerical computing were brought together in the first truly general purpose computers.

FORMALIZED LOGIC

A further set of developments which were essential to the development of computers was the formalization of logic. The logic of philosophers over the centuries and the logic of mathematicians, pioneered by the English mathematician George Boole, were brought together in the first decade of this century by Bertrand Russell and Professor A. N. Whitehead in their magnum opus, Principia Mathematica. This shows that all of mathematics can be derived from a very few logical processes, which are recognized as being fundamental to philosophy as well. Thus, the validity of a form of reasoning known as a syllogism may be determined by knowing the properties of ‘conjunction’, the ‘AND’ relationship of Boolean algebra. The following are two syllogisms:

The two propositions above the line are the two premises and the proposition below the line is the conclusion. A valid syllogism is one in which the conclusion is true if both of the premises are true and the conclusion is false if either one of the premises or both of them are false. ‘Conjunction’, the relationship ‘AND’ states precisely the same thing. This is often expressed in a ‘truth table’, thus for the relationship ‘A AND B’ the following table applies.

Thus the expression ‘A AND B’ is true if, and only if, ‘A’ is true and ‘B’ is true.

In the second of the two syllogisms given above it is possible for both of the premises to be true and for the conclusion to be false. This syllogism does not, therefore, correspond to the required relationship of truth values of a valid syllogism, that is the relationship ‘AND’ between the first two and the conclusion, and the syllogism is therefore invalid. This form of invalid syllogism is known as the Fallacy of the Undistributed Middle.

Russell and Whitehead showed that ‘AND’ and a few other similar relationships could be used to describe the operations of mathematics. Computers embody these principles in their circuitry and they can therefore perform both logical and arithmetical operations. It is this fact which gives them great power in both data processing and...