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Lecture 34

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Origins of the Computer

Introduction

Due to the fact that the U.S. has a shortage of skilled labourers compared to Europe, there is a strong emphasis on labour-saving technology. At the same time there is a population explosion during the latter half of the 19th century which requires census-taking programs. It was Herman Hollerith (1859–1929) who started the Tabulating Machine Company (1896), which later became I.B.M., in order to sell equipment to the U.S. government to fulfill the need for a means of storing and tabulating census data.

Calculating Machines

Calculating machines come in two varieties:

Analog machines represent numbers as physical quantities, i.e. one creates a physical model of the thing you wish to compute. These machines reached their zenith from the 1920s to the 1940s. As an example consider the differential analyzer which was used to calculate the Fourier coefficients for systems of equations. These calculations involved integrals, so these devices were essentially fancy planimeters.

Analog computing devices have essentially disappeared because they lack:

  • flexibility
    • they cannot easily be reconfigured to tackle problems from different domains
  • precision
    • construction details of the computing device determine the available precision

Digital computers became prevalent because they do not suffer from these restrictions, i.e. by changing the stored program in a computer it can be reconfigured to solve a different problem, and by endlessly iterating the calculation an arbitrary precision in the solution can be achieved. Digital computers can be mechanical, electro-mechanical, and electronic.

Three Pioneers

Charles Babbage

Charles Babbage (1791–1871) was a mathematician interested in the problem of mathematical table construction, which were used in his day in order to arrive at numerical solutions to various problems, e.g. the motion of the moon, 3-body problems, etc. Babbage was looking for a way to assist in the construction of these tables, which otherwise had to be generated by hand by "computers" (clerical personnel) in execises of enormous drudgery.

I wish to God these calculations had been performed by steam…

Babbage's solution was to construct the difference engine, a completely mechanical digital machine that was able to calculate values of polynomial functions, where xn was computed as an iterated difference function. The ability to calculate the value of polynomial functions meant that, by virtue of Weierstrass' Approximation Theorm, that a large class of other functions could be computer by first representing them as polynomials.

The successor to the difference engine was the analytical engine, a computing machine that stored a program as punched cards (inspired by the design of Jacquard's loom, a mechanical weaving apparatus). Prototypes were built but were never successful. Further development was infeasible due to the enormous cost; once funding from the British Admiralty dried up the engine passed into history.

Alan Turing

John von Neumann

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