# NATS 1700 Lecture Notes - Fujifilm, Manchester Small-Scale Experimental Machine, Analytical Engine

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Published on 13 Oct 2012

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Lecture 5. The Dawn of Automatic Comput-

ing

Informal and unedited notes, not for distribution. (c) Z. Stachniak, 2011.

Note: in the case when I was unable to ﬁnd the primary source of an image or

determine whether or not an image is copyrighted, I have speciﬁed the source as

”unknown”. I will provide full information about images and/or obtain reproduc-

tion rights when such information is available to me.

Introduction

By the 1930s, mechanical and electromechanical calculators from Burroughs,

Felt & Tarrant, Marchant, Monroe, Remington, Victor, and other manufac-

turers had penetrated all aspects of a modern oﬃce operations. It seemed

that the mathematical tables could handle the rest in science and engineering.

However, certain branches of science and engineering reached a calculat-

ing barrier that prevented further progress unless an automated method of

dealing with complex operations, such as solving linear equalities, diﬀerential

equations, etc. could be found.

What was needed was a new type of a calculating machine that could per-

form large-scale error-free calculations by following, in a mechanical way, a

predeﬁned sequence of operations, that is, by following a program.

The 1930s was a crucial period in the development of computing. Not only

the ﬁrst designs of computers started to appear in Europe and the US but

also a groundbreaking theoretical research on computing was initiated.

In this lecture we shall take a look at the pioneering work on digital com-

puters. We shall discuss the origins of the ﬁrst computers and their intended

use. We shall talk about people and events leading to the ﬁrst designs and

their impact on society and on the development of future computer industry.

1

Alan Turing on Computing

Fig. 1. Alan Turing. Source: unknown.

We begin with our discussion on computer pioneers with a portrait of Alan

Turing who was not an engineer by training but a British mathematician,

logician, and cryptanalyst whose contributions to the science of computing

were not only large in scope but also groundbreaking.

Turing is perhaps best known for his outstanding contributions to cryptog-

raphy during the WWII when at Bletchley Park–the wartime headquarters

of the UK Government Code and Cypher School–he (and others) worked

successfully on breaking German ciphers.

However, we shall concentrate on his work on the mathematics of computing

that led him to the discovery one of the most powerful computing devices

ever conceived. One can safely claim that the ﬁrst general-purpose and uni-

versal computer ever devised was that created by Turing out of a few symbols

written on a piece of paper. In honour of its inventor, that device is now

called the Turing Machine.

In spite of the fact that Turing did his groundbreaking research on ”ab-

stract” computing machines at a time when there were no ”real” computers

(he published his results in 1936-37), his work is considered among the most

signiﬁcant contributions to the discipline of computing for this day.

2

The Hilbert Program

To appreciate Turing’s contributions fully, we have to temporarily switch the

focus of our narrative to another outstanding scientist David Hilbert, who

was among the most inﬂuential mathematicians in the ﬁrst decades of the

20th century.

In 1928, Hilbert suggested that the entire mathematics could be ”mecha-

nized”. Speaking very(!) informally, according to Hilbert, the entire math-

ematics could be done on some sort of an algorithm-following calculating

machine and the job of a mathematician would be to discover the appropri-

ate algorithms.

Many mathematicians agreed with Hilbert but not all. In 1936, Turing

published a paper ”On Computable Numbers, with an Application to the

Entscheidungsproblem” (‘Entscheidungsproblem’ in German means ‘decision

problem’).

In his paper, Turing demonstrated that, informally speaking, there are math-

ematical problems that are unsolvable, that is, putting it diﬀerently and in-

formally, could not be solved in an algorithmic way as envisioned by Hilbert.

We shall postpone a detailed analysis of Turing’s result until the next semester.

For now, let us only mention that to prove his result Turing designed an ab-

stract computer – a simple mathematical concept but a powerful computing

device sketched in Figure 2. Turing proved on paper that a computing ma-

chine could perform very complex tasks but not all such tasks.

3

## Document Summary

Informal and unedited notes, not for distribution. (c) z. stachniak, 2011. Note: in the case when i was unable to nd the primary source of an image or determine whether or not an image is copyrighted, i have speci ed the source as. I will provide full information about images and/or obtain reproduc- tion rights when such information is available to me. By the 1930s, mechanical and electromechanical calculators from burroughs, Felt & tarrant, marchant, monroe, remington, victor, and other manufac- turers had penetrated all aspects of a modern o ce operations. It seemed that the mathematical tables could handle the rest in science and engineering. However, certain branches of science and engineering reached a calculat- ing barrier that prevented further progress unless an automated method of dealing with complex operations, such as solving linear equalities, di erential equations, etc. could be found.