The Manchester Universal Electronic Computer

FERRANTI LTD are making electronic computers similar in design to the one developed and engineered by them and installed in Manchester University. This Manchester model incorporates ideas evolved by Professor Williams and Dr. Kilburn in the Electrical Engineering Department of the University of Manchester and has already proved itself a most versatile computing aid in many fields.

Digital computers, as the name implies, deal with numbers represented as a sequence of digits, as in the familiar desk computers. They differ in construction from "analogue" computers, such as slide rules, in which readings on a scale are made to represent numbers; they can be made to express the results of the particular computation which they are doing to as many places of decimals as are required. They can, therefore, give accurate answers to any arithmetic computation, and also handle problems in applied science involving calculations based on formulae containing continuous variables.

All machines of this type can do THREE things:

1. They can perform all the operations of arithmetic exceedingly rapidly. An operator with a standard desk calculating machine can do about 500 multiplications of pairs of ten-digit decimal numbers in an average working day. The Ferranti machine can do about the same amount of work in two seconds. In a day it could do more arithmetic than the average man could do in many years, and will make fewer mistakes.
2. They can remember a great many numbers, and also the long and elaborate series of instructions which have to be obeyed to enable a complicated calculation to be performed automatically. The Ferranti machine can hold in its memory more than 15,000 twelve-digit decimal numbers, or more than 30,000 six-digit numbers, and it can recall any one of them within, on the average, one-thirtieth of a second. These numbers are not lost when the machine is switched off, as they are held in a magnetic store. In addition, the machine holds 256 twelve-digit numbers in its temporary "fast" (electrostatic) memory; these figures are available virtually immediately for any calculation which is to be done with them.
3. They can make decisions. A machine can decide, at any stage in a calculation, which of two or more contingencies has occurred and determine its future course of operations accordingly. The alternative courses of action must have been prescribed by the instructions given to the machine, which then decides which course to take in the light of the results achieved so far.

To enable them to perform these operations and to make the results available, the machines have to have instructions prepared for them in code. Mechanisms are required for "reading" these coded instructions and the numerical information required for the calculation, and for printing out the answers.

In the case of the Manchester machine, the information is presented on punched teleprinter tape of standard pattern, which is "read" by photo-electric cells; the answers can also be given on punched tape or can be typed out by teleprinter. Results taken out on teleprinter tape can be kept and fed back into the computer whenever they are required for further calculations: it is therefore possible to deal with larger quantities of data than can be held in the machine at one time.

1. Inversion of matrices.
2. Solution of simultaneous equations (with particular reference to the automatic design of engineering steel structures and of power flow in electrical networks).
    
   
3. Evaluation of a certain kind of determinant and all its minors (calculation of atom-atom polarisation in certain organic molecules).

   The need for a rapid means of solving simultaneous equations and the inversion of matrices is of very great importance in the field of industrial and scientific research. Although so far we hase been concerned only with matrices of orders up to 32 x 32 it is expected to have to invert larger matrices for economics and other studies. The machine can deal with symmetric matrices up to 160 x 160.
    
   

4. The evaluation of the latent roots and vectors of matrices, and hence the solution of the eigenvalue problem of linear differential and integral operators.

   The eigenvalue problem of linear operators is of central importance for all vibration problems of physics and engineering. The vibrations of elastic structures, the flutter in aerodynamics, the stability of electric networks, the atomic and molecular vibrations of particle physics, are all diverse aspects of the same fundamental problems viz. the principal axis problem of quadratic forms.

The solution of ordinary differential equations, for open or closed boundary conditions, is a problem very well suited to the machine. Ordinary differential equations arise as the mathematical description of the continuous behaviour of physical phenomena. Those already solved by the machine have arisen in the following applications:

1. Binary star formation.
2. The steady state configuration adopted by a thread when whirled about an axis under the influence of air resistance and centrifugal force. This was part of an investigation into problems of high-speed ring spinning.
3. Flow in a laminar compressible boundary layer.
4. Poisson's equation for one (spherical) colloidal particle.
5. The solution of complicated trajectory problems in three dimensions involving over thirty first order equations.

In many cases the tabular representation of the solutions of such equations is needed and hence the storage of a large amount of numerical information. The Manchester Machine with its large magnetic memory is particularly suitable for this type of problem. Those already solved have arisen in the following applications:

1. Interaction of two colloidal spherical particles (Poisson's equations, elliptic type).
2. The distribution of growth hormone in biological tissue (an attempt to explain the chemical origin of biological form).
3. The rate of accretion of interstellar material by a star.
4. The distribution of a collection of matter under its self gravitation.
5. Shroedinger's equation for the Helium atom (elliptic type, three-dimensional case).
6. Hyperbolic partial differential equations.

The ability of the machine to solve problems of logical rather than of arithmetic nature is illustrated by a programme to solve chess problems (of the mate-in-two type) and to enable the machine to play draughts with a human opponent.

(e) TABULATION OF SPECIAL FUNCTIONS.

Tables of Laguerre polynomials and Laguerre functions (special cases of the hypergeometric series) are being computed at present.

(f) COMMERCIAL AND INDUSTRIAL SUBJECTS

• Wages. The machine has been programmed to compute details of tax, insurance, etc. deductions, automatically and to print out pay slips.
• Tabulation. Programmes have been prepared for automatic tabulation of market research, etc. data and calculation of secondary statistics.
• Statistical Functions. Programmes have been made to compute certain statistical functions of general utility.

(g) GEODETIC WORK.

A programme for the automatic computation of survey traverse reductions is being examined.

(h) PROGRAMMES FOR CHECKING AND FOR PROGRAMMING.

It is interesting to note that the machine can be made to assist in the diagnosis of its own faults; various programmes exist which help the maintenance engineer in the location of faulty components.

Similarly the machine can be used to simplify programming: one technique is that of "interpretive routines". These enable routines to be written in a code which will make programming as easy as possible. The machine "translates" a programme written in such a code into normal instructions before carrying it out.

(j) MISCELLANEOUS .

From time to time ad hoc problems arise which have little connection with real life. Two enumeration problems in pure mathematics are being coded.

The computer is serial in operation, and its basic pulse repetition frequency is 100 kc/s.; it operates with numbers of twenty or forty binary digits, i.e. six or twelve decimal digits. Some additional information is summarised below.

1. Overall dimensions. Two bays each 16 feet long, 8 feet high, and 4 feet wide -- and a control desk.
2. Power consumed ................ 27 kilowatts
3. Ventilation. The Electronic Equipment is continuously ventilated by means of a re-circulating air system with heat exchanger connected to an external cooling unit.
4. Number of Components. About 4,000 valves, 2,500 capacitors, 15,000 resistors, 100,000 soldered joints and 6 miles of wire.
5. Storage capacity. High speed -- 10,000 binary digits on cathode ray tubes; equivalent to about 3,000 decimal digits. Magnetic drum -- 650,000 binary digits; equivalent to about 15,000 twelve-digit decimal numbers or 30,000 six-digit decimal numbers.
6. Input. Punched teleprinter tape feeding in up to 200 characters per second.
7. Output. Punched teleprinter tape or direct printing by teleprinter. A high-speed parallel output printer is being developed.
8. Multiplication time ................... 2.2 milliseconds
9. Addition time ......................... 1.2 milliseconds
10. Typical times for sub-routines. Square roots and reciprocal square roots: 105 milliseconds. Cosines of angles to 11 decimal digits: 80 milliseconds. Reciprocals: 95 milliseconds. Inversion of matrix of order n x n: 0.04 n³ seconds. A matrix of order 80 x 80 is now well within the capacity of the machine.

The possibility of making such a machine was first suggested over a hundred years ago by Charles Babbage, who was at the time Lucasian Professor of Mathematics at Cambridge. Although parts were made, and can be seen in certain museums, he was unable to complete his "engine" owing to lack of financial support and because of the inadequacy of the techniques available to him. However, from the accounts of his work which were written by Lady Lovelace (the daughter of Lord Byron), it is clear that he had a more profound understanding of the principles and possible applications of these machines than anyone else achieved until a few years ago.

The first large-scale electronic digital computers were built in the United States during the war. Since then several other machines have been built on both sides of the Atlantic.

The Ferranti machine differs in detail from all other machines, as it makes use of two new and improved "memories" both of which were developed in Manchester. It is the first machine of this type to be built by an engineering firm and to be commercially available.