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"This second edition of the popular reference and textbook outlines the historical developments in computing technology. The book describes historical aspects of calculation and concentrates on the physical devices used to aid people in their attempts at automating the arithmetic process.
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New edition of a text/reference which describes the development of arithmetic and calculation tools from Egyptian stone carving to the IBM/360 computer. It includes discussion of important stages such as the invention of the zero, logarithms, the Babbage machines, analog, and the Zuse machines, and provides interesting stories about both the machines and the people who produced them. Annotation c. by Book News, Inc., Portland, Or.
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A History of Computing Technology


By Michael R. Williams

John Wiley & Sons

ISBN: 0-8186-7739-2


Chapter One

In the Beginning ...

1.1 Numeration

Our system of numeration, if not a machine, is machinery; without it (or something equivalent) every numerical problem involving more than a very limited number of units would be beyond the human mind.

One of the first great intellectual feats of a young child is learning how to talk; closely following on this is learning how to count. From earliest childhood we have been so bound up with our system of numeration that it is a feat of imagination to consider the problems faced by early humans who had not yet developed this facility Careful consideration of our system of numeration leads to the conviction that, rather than being a facility that comes naturally to a person, it is one of the great and remarkable achievements of the human race.

It is now impossible to learn the sequence of events that led to our developing a sense of number. Even the most backward tribe of humans ever found has had a system of numeration that, if not advanced, was sufficient for the tasks they had to perform. Our most primitive ancestors must have had little use for numbers; instead their considerations would have been more of the kind Is this enough? rather than How many? when they were engaged in food gathering, for example. When early humans first began to reflect about the nature of things around them, they discovered that they needed an idea of number simply to keep their thoughts in order. As they began to live a settled life, grow plants, and herd animals, the need for a sophisticated number system became paramount. How and when this ability at numeration developed we will never know, yet it is certain that numeration was well developed by the time humans had formed even semi-permanent settlements.

It is very popular, in works dealing with the early history of arithmetic, to quote facts about the so-called primitive peoples and their levels of numeration. These facts generally note that the primitive peoples of Tasmania are only able to count one, two, many; or the natives of South Africa count one, two, two and one, two two's, two two's and one, and so on. Although often correct in themselves, these statements do not explain that in realistic situations the number words are often accompanied by gestures to help resolve any ambiguity. For example, when using the one, two, many type of system, the word many would mean, Look at my hands and see how many fingers I am showing you. This type of system is limited in the range of numbers that it can express, but this range will generally suffice when dealing with the simpler aspects of human existence.

The lack of ability of some cultures to deal with large numbers is not really surprising. Our own European languages, when traced back to their earlier versions, are very poor in number words and expressions. The translation of the Gospels made by Bishop Ulfilas in the fourth century for the Goths uses the ancient Gothic word for ten, tachund, to express the number 100 as tachund tachund, that is, ten times ten. By the seventh century the word teon had become interchangeable with the tachund or hund of the Anglo-Saxon language, and the Gospels of that period denote 100 as hund teontig, or ten times ten. The average person alive in seventh-century Europe was not as familiar with numbers as we are today. The seventhcentury Statute of Shrewsbury laid down the condition that, to qualify as a witness in a court of law, a man had to be able to count to nine. To apply such a condition today would seem ludicrous.

Perhaps the most fundamental step in developing a sense of number is not the ability to count, but rather the ability to see that a number is really an abstract idea instead of a simple attachment to a group of particular objects. It must have been within the grasp of primitive humans to conceive that four birds are distinct from two birds; however, it is not an elementary step to associate the number 4, as connected with four birds, to the number 4, as connected with four rocks. Associating a number as one of the qualities of a specific object is a great hindrance to the development of a true number sense. When the number 4 can be registered in the mind as a specific word, independent of the object being referenced, the individual is ready to take a first step toward the development of a notational system for numbers and, from there, to arithmetic. As was noted by Bertrand Russell:

It must have required many ages to discover that a brace of pheasants and a couple of days were both instances of the number two.

Traces of the very first stages in the development of numeration can be seen in several living languages today. Dantzig, in his book Number, describes the numeration system of the Thimshian language of a group of British Columbia Indians. This language contains seven distinct sets of words for numbers: one for use when counting flat objects and animals, one for round objects and time, one for people, one for long objects and trees, one for canoes, one for measures, and one for counting when no particular object is being numerated. Dantzig conjectures that the last set of words is a later development while the first six groups show the relics of an older system. This diversity of number names is not confined to obscure tribal groups-it can be found, for example, in widely used languages such as Japanese.

Intermixed with the development of a number sense is the development of an ability to count. Counting is not directly related to the formation of a number concept because it is possible to count by matching the items being counted against a group of pebbles, grains of corn, or the counter's fingers. These counting aids must have been indispensable to very primitive people who would have found the process impossible without some form of mechanical aid. Such aids to counting, although in different form, are still used by even the best educated professionals today, simply because they are convenient. All counting ultimately involves reference to something other than the things being counted. At first it may have been grains of corn but now it is a memorized sequence of words that happen to be the names of the integers. This matching process could have been responsible for the eventual development of the various number bases that came into existence because the act of counting usually takes the form of counting into small groups, then groups of groups, and so on.

The maximum number of items that is easily recognizable by the human mind at one glance is small, say five or less. This may be why initial groups consisted of about five items, and would account for the large number of peoples whose number systems were of base five. The process of counting by matching with fingers undoubtedly led to the development of the different number systems based on ten.

By the time that a number system has developed to the point where a base such as 5,10, 20, or even 60 has become obvious to an outside observer, the eventual development of its use in higher forms of arithmetic and mathematics has probably become fixed. If the base is too small, then many figures or words are required to represent a number and the unwieldy business of recording and manipulating large strings of symbols becomes a deterrent to attempting any big arithmetical problems. On the other hand, if the number base is too big, then many separate symbols are required to represent each number, and many rules must be learned to perform even the elementary arithmetical operations. The choice of either too small or too large a number base becomes a bar to the later development of arithmetic abilities.

A study of various forms of numeral systems yields the fact that a great variety of bases have been used by different peoples in various places over the globe. By far the most common is, of course, the number systems based on ten. The most obvious conclusion is that a very large percentage of the human race started counting by reference to their ten fingers. Although 5, 10, or 20 was the most popular choice for a number base, it is not uncommon to find systems based on 4, 13, or even 18. It is easy to advance a possible explanation of systems based on 5 and 20 because of the anatomical fact of there being 5 fingers on each hand and a total of 20 such attachments on both hands and feet. It is not quite so easy to see how the other scales may have developed in such a natural way.

If modern linguistic evidence can be trusted, the scale of 20 must have been very widespread in ancient times. It has been pointed out by several authors that some Eskimo people have a well-developed system which uses terms such as one-man for the number 20, two-men, for 40, and so forth. This obviously implies that a base 20 number system was in use at one time, but it is difficult to see how an early Eskimo could have had access to his toes for counting, unless he was inside a relatively warm igloo. This could imply that the Eskimos brought their number system with them when they moved into North America. In fact, it is possible to trace remnants of various number systems based on 20 all the way back to the very early people living in the tropical regions of southern Asia.

The European languages also show a marked preference for the grouping together of 20 objects. It is entirely possible that the general prevalence of base 10 numbers among the Indo-European peoples developed later from an original base 20 system. The most modern example of this is the French use of quatre-vingt (four-twenty) instead of huitante for 80, and quatre-vingt-dix (four-twenty-ten) instead of nonante for 90. If we are willing to look at forms of the language which died out in the thirteenth century, then the terms six-vingt (120) sept-vingt (140), huit-vingt (160), and even quinze-vingt (15-20 for 300) show that the base 20 system was no stranger. The English word score, as in the Biblical three score and ten years or Lincoln's famous Four score and seven years ago ... is another modern example of Europeans dealing in groups of 20. The term score will be discussed further in the section dealing with tally sticks.

Once the sense of number, as an entity separate from the thing being counted, has developed, there arises a need to assign names to the integers. This sequence of names, once decided upon, often becomes one of the most stable parts of a people's language. Thus, although languages may evolve so that almost all the words acquire vastly different forms, the sequence of integer names remains almost intact. The original meanings of the names of the integers are likely, therefore, to be quite obscure. The similarity of number names across related languages is easily seen by examining a table of these names in the family of Indo-European languages. Although the actual names differ from one language to another, the basic form remains constant (languages are Ancient Greek, Latin, Sanskrit, French, German, and English).

This stability of number names has been a good tool of the philologists. They have made extensive collections of the number names in many languages in an attempt to see which languages have common roots. Care must be taken in any exercise of this sort because a common set of names could have resulted from simple mixtures of languages, trade between two peoples, or simple coincidence.

George Peacock, in his Arithmetic, points out the situations that can arise by simple coincidence. He compares the number words of the Nanticocks (a tribe of Indians who used to reside on the south bank of the Chesapeake) with those of the Mandingoes (of Africa). The similarity is striking but can only be attributed to coincidence because any mixing of the languages due to geographic proximity or cultural contacts via trade is ruled out.

The opposite side of the coin can be shown by comparing the number words from languages which are known to be related. In Europe, the languages spoken by the Finnish and Hungarian people can be traced back to common root, yet the number words in these languages have very little in common.

The ability to count must soon have led to the need to record the results of counting. This probably first took the form of setting aside the pebbles used in the matching process, but would soon lead to the use of tally sticks, knotted cords, and the actual invention of numerals.

1.2 Written Number Systems

There appear to be two distinct stages in the development of written record keeping systems, the pictorial stage and the symbolic stage. The inscriptions done by people in the pictorial stage will correspond with the earliest era in the development of a number sense. The inscriptions will have a picture of ten cattle to represent ten cows or ten tents may indicate ten family groups. This stage is most easily seen in some records made by North American Indians just about the time they came into contact with Europeans.

The symbolic stage, on the other hand, will show a picture of a cow followed by five strokes to represent five cattle. At this stage the strokes no longer represent objects but have become a determinative (a sign used to qualify the meaning of the object sign). In other words, the strokes have become adjectives rather than nouns. In many societies this step must have come at the same time as the development of numbers as abstract ideas. This stage is best illustrated by some early stone carvings left by the Egyptians.

Once a particular society has reached the symbolic stage of recording numbers, the notation system which it develops will be almost entirely dependent on cultural influences. The use of fingers or pebbles for counting, the number of items counted into a group before a new group is started (the number base), and the materials available for making a lasting record of the result are all culturally determined. Once these variables have been set, the result will lead to one of two different types of notational systems: the additive system or the positional system.

1,2.1 The Additive Number System

In this system there is a distinct symbol for each kind of group made during the counting process, and this symbol is repeated as often as necessary to indicate how many of each group are needed. The Egyptian number system is the classical example of an additive system; however, most people are more familiar with the additive system used by the Romans. In the Old Roman system (before the subtractive forms of IV for 4 and IX for 9 were in use) it was possible to express any number less than 5,000 by a sequence of symbols in which no individual sign need be repeated more than four times. For example, the number 2,976 would be represented as MMDCCCCLXXVI. Although it was the custom to write down the symbols in decreasing order of value (M = 1,000, D = 500, C = 100, L = 50, X = 10, V = 5,1 = 1), this is by no means necessary. The value of a number in an additive system has nothing to do with the position of any symbol within the string representing the number. It is quite unambiguous to write the number 2,976 as ILVCMCXDMXCC but, of course, ease of reading always precluded its being written otherwise than in order of descending value.

The pure additive system is quite easy to use for simple calculations, although it does not appear so at first glance. Addition involves the two-step process of simply writing down the group symbols from each number, then collecting the sequences of smaller valued symbols to make larger valued ones so that the number regains its canonical form. For example:

2319 = MM CCC X VIIII +821 = D CCC XX I 3140 = MMDCCCCCCXXXVIIIII

The second step now takes over and, because IIIII = V, VV = X, CCCCC = D, DD = M, the final result is written as MMMCXXXX.

Multiplication, although slow, is not really difficult and only involves remembering multiples of 5 and 10. For example:

28 = XXVIII x12 = XII 336

XXVIII times I = XXVIII XXVIII times I = XXVIII XXVIII times X = CCLXXX CCLXXXXXXXVVIIIIII

which would be written as CCCXXXVI.

(Continues...)



Excerpted from A History of Computing Technology by Michael R. Williams Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

Chapter 1 In the Beginning 1
1.1 Numeration 1
1.2 Written Number Systems 6
1.2.1 The Additive Number System 7
1.2.2 The Positional System 8
1.3 The Egyptians 9
1.4 The Greeks 14
1.5 The European Number System 19
1.6 The Far East 27
1.7 Other Forms of Notation 32
1.7.1 Knotted Cords for Record Keeping 33
1.7.2 Tally Sticks 38
1.7.3 Other Methods of Numerical Notation 41
Further Reading 42
Endnotes for Chapter 1 44
Chapter 2 Early Aids to Calculation 46
2.1 Introduction 46
2.2 Finger Reckoning 47
2.3 The Abacus 53
2.4 The Quadrant 66
2.5 Two Legged Instruments 74
2.5.1 The Proportional Compass 75
2.5.2 The Sector 76
2.6 Napier's Bones 83
2.6.1 Napier and His Bones 83
2.6.2 Gaspard Schott and Athanasius Kircher 89
2.6.3 Early Versions of Napier's Bones 93
2.6.4 Genaille--Lucas Rulers 93
2.7 Logarithms 96
2.8 The Slide Rule 105
Further Reading 112
Endnotes for Chapter 2 116
Chapter 3 Mechanical Calculating Machines 118
3.1 Introduction 118
3.2 Wilhelm Schickard (1592-1635) 119
3.3 Blaise Pascal (1623-1662) 124
3.4 Gottfried Wilhelm Leibniz (1646-1716) 129
3.5 Samuel Morland (1625-1695) 136
3.6 Rene Grillet 142
3.7 Commercially Produced Machines 145
3.7.1 The Thomas Arithmometer 145
3.7.2 The Baldwin-Odhner Machines 146
3.7.3 Key-Driven Machines 149
Further Reading 152
Endnotes for Chapter 3 153
Chapter 4 The Babbage Machines 154
4.1 Charles Babbage (1791-1871) 154
4.2 The Need for Accuracy 160
4.3 The Method of Differences 161
4.4 Babbage's Difference Engine 163
4.5 The Scheutz Difference Engine 170
4.6 Other Attempts At Difference Engines 175
4.7 Babbage's Analytical Engine 177
4.8 Percy Ludgate (1883-1922) 186
Further Reading 188
Endnotes for Chapter 4 190
Chapter 5 The Analog Animals 191
5.1 Introduction 191
5.2 The Astrolabe 192
5.3 The Antikythera Device 195
5.4 Tide Predictors 198
5.5 Differential Analyzers 201
Further Reading 207
Endnotes for Chapter 5 208
Chapter 6 The Mechanical Monsters 209
6.1 Introduction 209
6.2 The Zuse Machines 210
6.2.1 Konrad Zuse 210
6.2.2 The Z1 211
6.2.3 The Z2 214
6.2.4 The Z3 215
6.2.5 The Z4 218
6.2.6 The Other Zuse Machines 220
6.3 The Bell Relay Computers 221
6.3.1 The Situation 221
6.3.2 The Complex Number Calculator 222
6.3.3 The Relay Interpolator 225
6.3.4 The Models III and IV 227
6.3.5 The Model V (The Twin Machine) 229
6.3.6 The Model VI 233
6.4 The Harvard Machines of Howard Aiken 235
6.4.1 Introduction 235
6.4.2 The Harvard Mark I 235
6.4.3 The Harvard Mark II 243
6.4.4 The Harvard Mark III and Mark IV 246
6.5 The IBM Calculators 248
6.5.1 The Punched Card Systems 248
6.5.2 The Large IBM Calculators 254
6.5.3 The Selective Sequence Electronic Calculator (SSEC) 255
Further Reading 258
Chapter 7 The Electronic Revolution 261
7.1 Introduction 261
7.2 John Atanasoff, Clifford Berry, & the ABC 262
7.3 The ENIAC 266
7.3.1 Introduction 266
7.3.2 The Place and the Problem 267
7.3.3 The People 268
7.3.4 The Machine 270
7.4 The Colossus Machines 284
7.4.1 The Enigma 284
7.4.2 Alan Turing (1912-1954) 288
7.4.3 The Robinsons 289
7.4.4 The Colossus 291
Further Reading 294
Endnotes for Chapter 7 295
Chapter 8 The First Stored Program Electronic Computers 296
8.1 The Genesis of the Ideas 296
8.2 Computer Memory Systems 301
8.2.1 Introduction 301
8.2.2 Thermal Memories 303
8.2.3 Mechanical Memories 304
8.2.4 Delay Line Systems 306
8.2.5 Electrostatic Storage Mechanisms 311
8.2.6 Rotating Magnetic Memories 316
8.2.7 Static Magnetic Memories 319
8.3 The British Scene 321
8.3.1 Introduction 321
8.3.2 The Manchester Machine 322
8.3.3 The Cambridge Machine--EDSAC 329
8.3.4 The NPL Pilot Ace 336
8.4 The American Scene 336
8.4.1 The American Background 344
8.4.2 The Electronic Discrete Variable Arithmetic Computer (EDVAC) 347
8.4.3 The Institute for Advanced Study Machine (IAS) 351
8.4.4 The Eckert/Mauchly Machines, BINAC and UNIVAC 358
8.4.5 The SEAC and SWAC Machines 365
8.4.6 Project Whirlwind 370
Further Reading 376
Endnotes for Chapter 8 379
Chapter 9 Later Developments 381
9.1 Introduction 381
9.2 The Early Machines of IBM 383
9.2.1 The NORC 383
9.2.2 The 700-7000 Series Machines 385
9.3 Early Super Computers 391
9.3.1 The Stretch 391
9.3.2 The LARC 395
9.3.3 The Ferranti Atlas 397
9.4 The IBM/360 Series of Machines 400
Further Reading 405
Endnotes for Chapter 9 406
Appendix 407
Index 416
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