The Universal History of Computing: From the Abacus to the Quantum Computer: From the Abacus to the Quantum Computer - Softcover

Über die Autorin bzw. den Autor

GEORGES IFRAH is an independent scholar and former math teacher.
E. F. HARDING, the primary translator, is a statistician and mathematician who has taught at Aberdeen, Edinburgh, and Cambridge Universities.
SOPHIE WOOD, cotranslator, is a specialist in technical translation from French.
IAN MONK, cotranslator, has translated the works of Georges Perec and Daniel Pennac.
ELIZABETH CLEGG, cotranslator, is also an interpreter who has worked on a number of government and international agency projects.
GUIDO WALDMAN, cotranslator, has translated several classic literary works.

Von der hinteren Coverseite

"A fascinating compendium of information about writing systems-both for words and numbers."
-Publishers Weekly

"A truly enlightening and fascinating study for the mathematically oriented reader."
-Booklist

"Well researched. . . . This book is a rich resource for those involved in researching the history of computers."
-The Mathematics Teacher

In this brilliant follow-up to his landmark international bestseller, The Universal History of Numbers, Georges Ifrah traces the development of computing from the invention of the abacus to the creation of the binary system three centuries ago to the incredible conceptual, scientific, and technical achievements that made the first modern computers possible. Ifrah takes us along as he visits mathematicians, visionaries, philosophers, and scholars from every corner of the world and every period of history. We learn about the births of the pocket calculator, the adding machine, the cash register, and even automata. We find out how the origins of the computer can be found in the European Renaissance, along with how World War II influenced the development of analytical calculation. And we explore such hot topics as numerical codes and the recent discovery of new kinds of number systems, such as "surreal" numbers.

Adventurous and enthralling, The Universal History of Computing is an astonishing achievement that not only unravels the epic tale of computing, but also tells the compelling story of human intelligence-and how much further we still have to go.

Aus dem Klappentext

A fascinating compendium of information about writing systems-both for words and numbers.
-Publishers Weekly

A truly enlightening and fascinating study for the mathematically oriented reader.
-Booklist

Well researched. . . . This book is a rich resource for those involved in researching the history of computers.
-The Mathematics Teacher

In this brilliant follow-up to his landmark international bestseller, The Universal History of Numbers, Georges Ifrah traces the development of computing from the invention of the abacus to the creation of the binary system three centuries ago to the incredible conceptual, scientific, and technical achievements that made the first modern computers possible. Ifrah takes us along as he visits mathematicians, visionaries, philosophers, and scholars from every corner of the world and every period of history. We learn about the births of the pocket calculator, the adding machine, the cash register, and even automata. We find out how the origins of the computer can be found in the European Renaissance, along with how World War II influenced the development of analytical calculation. And we explore such hot topics as numerical codes and the recent discovery of new kinds of number systems, such as surreal numbers.

Adventurous and enthralling, The Universal History of Computing is an astonishing achievement that not only unravels the epic tale of computing, but also tells the compelling story of human intelligence-and how much further we still have to go.

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Excerpt

HISTORICAL SUMMARY OF ARITHMETIC,

NUMERICAL NOTATION, AND WRITING SYSTEMS

The writing of words and the writing of numbers show many parallels in theirhistories.

In the first place, human life was profoundly changed by each system, whichallowed spoken language on the one hand, and number on the other, to be recordedin lasting form.

Further, each system answered marvellously to the universal need, felt by everymember of every advanced society, for a visual medium to embalm human thought -which otherwise would inevitably dissolve into dust.

Again, everyone became empowered to create a persistent record of what he hadexpressed or communicated: of words which were otherwise long silent, or ofcalculations long since completed.

Finally, and most importantly, each system granted direct access to the world ofideas and thoughts across space and time. By encapsulating thought, and byinspiring it in others, the writing down of thought imposed on it bothdiscipline and organisation.

Number and letter have often worn the same clothes, especially at times whenletters were used to stand for numerals. But this is superficial: at a muchdeeper level there is still a close correspondence between the alphabet and thepositional number-system. Using an alphabet with a fixed number of letters,every word of a language can be written down. Using our ten digits 1, 2, 3, 4,5, 6, 7, 8, 9, and 0, any whole number whatever can be written down.

So we perceive a perfect analogy between these two great discoveries, the finalstage in the development of writing and the final stage in the development ofnumerical notation. They are among the most powerful intellectual attributes ofthe modern human race.

The analogy is not limited to this, however. Throughout its history, eachwritten number-system evolved in a very similar way to the verbal writing systemthat it grew up with. This can be seen in the way that both reflected the spokenlanguage or the cultural traditions to which the language was adapted; or,again, in the mannerisms of local scribes, and in the influence of the verymaterials used for writing.

The main purpose of the chapter is to present a recapitulation of the history ofnumerical notation and arithmetical calculation. But so close is the parallelwith writing just noted, that we shall incorporate notes on the history ofwriting at relevant points; for clarity, these notes will be flagged with [W].

For all that, the writing of language and the notation of numbers differradically in one respect. For something to be called writing, its signs must berelated to a spoken language; it must reflect a conscious effort to representspeech: "Writing is a system of human communication which uses conventionalsigns, which are well defined and which represent a language, which can be sentout and received, which can be equally well understood by sender and receiver,and which are related to the words of a spoken language." [J.G. Février,Histoire de lécriture (1959)]

By contrast, numerical notation needs no correspondence with spoken numbers. Themental process of counting is not linked to any particular act of speech; we cancount to any number without speaking or even without thinking a single word. Weneed only create a "sign language for numbers", and in fact humankind devisedmany "number languages" before inventing even the word "number" andgoing on to use the human voice itself to measure concrete or abstractquantities.

While written characters correspond to the articulations of a spoken language,the signs in a numerical notation reflect components of thought, of a method ofthinking much more structured than the sounds of speech. This method of thinkingis itself a language (the language of numbers, no less), but to acquire thislanguage we need first of all to have a concept of distinct units and thecapacity to aggregate them. The language of number organises numerical conceptsinto a fixed order according to an idea which, on reflexion, we recognise as ageneral principle of recurrence or recursion [a principleaccording to which the evaluation of a complex entity is resolved by evaluatingits component entities of a lower degree of complexity, which in turn . . . ,until the simplest level is reached, at which each entity can be evaluatedimmediately. Transl.] It also makes use of a scale of magnitude (orbase) according to which numbers can be distributed over successivelevels called first-order, second-order, . . . units.

For a system of signs to constitute a written number-system, therefore, theymust in the first place have a structure which its user can conceive, in hismind, as a hierarchical system of units nested each within the next. Then theremust be a predetermined fixed number which gives the number of units on onelevel which must be aggregated together so as to constitute a single unit at thenext level; this number is called the base of the number-system.

In summary: a notation for numbers is a very special human communication systemusing conventional signs called figures which have a well definedmeaning, which can be sent and received, which are equally well understood byboth communicating parties [in other words, a code. Transl.] ,and which are attached to the natural whole numbers according to a mentallyconceived structure which obeys both the recurrence principle and theprinciple of the base.

Over the five thousand years which have elapsed since the emergence of theearliest number-system, of course people have not merely devised one singlenumber-system. Nor have there been an indefinite quantity of them - as can beseen from our Classification of the Written Number-systems of History inChapter 23, which brings together systems so separated in space and time as tobe effectively isolated from each other.

At the end of this chapter, we shall present the main conclusions of thisClassification in a series of comparative systematic tableaux which will exhibitthe mathematical characteristics of each number-system.

The order of succession of the number-systems in this series of tables will notbe purely chronological, but will follow a path which traces their evolution inlogic, as well as in time, from the most primitive to the most advanced.

The number-systems which are found throughout history fall into three maintypes, each divided into several kinds (Fig. 1.40):

A. the additive type of number-system. They are based on the additiveprinciple and each of their figures has a particular value which is always thesame regardless of its position in the representation of the number (Fig. 1.14to 16). Basically, they are simply written versions of more ancient methods ofcounting with objects (Fig. 1.1 to 13);

B. the hybrid type of number-system. These use a kind of mixedmultiplicative and additive principle ( Fig. 1. 28 to 32) , and are essentiallytranscriptions of oral number-systems of varying degrees of organisation;

C. the positional type of number-system. These are based on theprinciple that the value of a particular figure depends on its position in therepresentation of a number (Fig. 1.33 to 36) , and therefore need a zero (Fig.1.37) . Number-systems of this type exhibit the greatest degree of abstraction,and therefore represent the final stage in the development of numerical notation( Fig. 1.38 and 39).

In the tables at the end of this chapter, the letters A, B and C will thereforeindicate the above types of additive, hybrid, and positional number-systemsrespectively. The kinds within these types will be indicated by numbers attachedto these letters, such as A1 for an additive number- system of the first kind,and so on.

By classifying them in this way we shall be able to perceive clearly the truenature of our modern system of numerical notation, and therefore to understandwhy...