Computations Computerized

How to solve e without really trying

The arrival of the Elliot 503 Computer marks an historic occasion in the life of the Victoria University of Wellington.

It has been obtained by the Applied Mathematics Division of the DSIR, who are responsible for its operation. As well as providing a computing service for several Government departments it will be available for use by the university in various research programmes.

What then can it do? The computer is capable of doing anything it is told to do. The problem here lies in the fact that it does not speak English, not English as we know it.

Early computers were fed their instructions in the form of a series of ones and noughts. This method, however, has been superseded by a compressed, precise language, formed of words and numbers called Algol. It is readily learnt and has gained international acceptance.

The following is an Algol programme for the Elliot 503 computer to calculate "e" from e

Problem Solving

Many of the problems solved by the computer will involve numerical calculations such as the calculation of functions, the solution of differential equations and the evaluation of integrals.

For example, in the solving of simultaneous equations, the computer is capable of handling 40 linear equations in 40 unknowns (1600 coefficients on the left-hand side alone), this operation occupying the computer for only a few minutes.

Linear programming forms a large percentage of the work handled. This essentially involves solution of simultaneous equations for which there is no unique solution but will provide maxima and minima amenable to further computation.

Indexing and analysis of texts by various authors is also feasible but language translation, although possible, is not likely, as the memory circuits would have to be stocked to form a huge dictionary that would be beyond the reasonable capacity of the machine.

The actual translation will sometimes be wrong due to the differing meanings of words in different contexts.

Speed

The speed of operation of the Elliot 503 is quite impressive. Input is normally performed by photo-electric paper tape readers which read 1000 characters per second, two of these readers being provided. It is also fitted with a card reader operating at 340 cards per minute.

The average instruction time is around 10 microseconds, although it can be as short as 4.5 microseconds. Output from the computer can be line printed at up to 1000 lines per minute or on punched paper tape at 100 characters per second. Output can be plotted graphically also, the pen of which can be moved in increments of 1/100th of an inch relative to the paper and makes 300 steps a second.

A by-product of the innovation of the computer is that of the housing of Dsir's Applied Mathematics Division with the University's Mathematics Department within the same building. This will provide a mathematical centre unparalleled elsewhere in New Zealand and the stimulating effect of each department on the other could be more permanent than the sharing of the computer.—Reprinted with the permission of "Mosaic."

The "absent-minded professor" has become a classic, and The Oklahoma Daily tells of a campus incident which reinforces the basic truth of the epithet:

At the first fall meeting of his Oklahoma University class, a mathematics professor walked into the classroom, strode to the blackboard and wrote his name.

"Now," he said, "just to make sure there isn't anyone in this class that shouldn't be here, is there any person who doesn't belong in Math 104?"

Several students responded that the room was filled with persons enrolled for Math 103.

"Oh," said the embarrassed professor, and hastily left to search for his proper room.

South—Man and Nature in the Antarctic, by Graham Billing and Guy Mannering. A. H. and A. W. Reed, Wellington: 86pp text and 207 plates. £2/2-. Our copy from the publishers.

In many countries throughout the world men of many kinds are preparing themselves for the southern summer. They are going to the Antarctic, one of the world's last remaining frontiers. They go to find and to conquer.

Yet this is not a war of ideological conquest. but a conquest of the elements and a crusade of inquiry. It is a peaceful campaign in a silent land, where men demonstrate international cooperation by acknowledging the necessity of mutual trust and harmony for survival.

Twelve nations work on the continent. While New Zealand's effort may seem small, it is by no means lacking in endeavour and significance. South sets out to record many facets of this endeavour.

Antarctic Correspondent

While the purist may quibble at the lack of depth and the traps of generalisation, this is not meant to be a technical book. It is a book about a strange environment and, in an often racy style, provides a broadly painted scenario of New Zealanders in the 20th century developing frontiers, as did their forebears 100 years ago.

Helicopters and snowcats have replaced the horse and cart, but foot-slogging is still an essential mode of transport. In spite of its deficiencies in content and production—some of the colour tends toward the lurid—it has brought to the public at a reasonable cost a readable account of an exciting place, a place inaccessible to most.

As a record of the pioneering endeavour of New Zealanders, this book has a definite place on the shelf of the well-informed student of man in his environment.

For those who have been lucky enough to have been there. South serves as a reminder of hardships, pleasures, companionship and intellectual endeavour. For those who prefer warmer climates, its pages may be offset by turning up the radiator.

Answers to problems on page 18 in this issue.

1. Prime number problem

2. Columns answer is a total of four + and − signs:

98 — 76 + 54 + 3 + 21 = 100

3. The triangle has zero area.

As 18 + 13 = 31

4. Wrong.

5. The fish describes two sides of a right-angled triangle 600 and 800 feet respectively. The diameter is the hypotenuse of this triangle—1000 feet.