Charles Howard Hinton: The Fourth Dimension (1904/1912); A New Era of Thought (1888)

In an 1884 article entitled “What is the Fourth Dimension?”, Hinton suggested that points moving around in three dimensions might be imagined as successive cross-sections of a static four-dimensional arrangement of lines passing through a three-dimensional plane, an idea that anticipated the notion of world lines, and of time as a fourth dimension (although Hinton did not propose this explicitly, and the article was mainly concerned with the possibility of a fourth spatial dimension), in Einstein’s theory of relativity. Hinton later introduced a system of coloured cubes by the study of which, he claimed, it was possible to learn to visualise four-dimensional space (Casting out the Self, 1904). Rumours subsequently arose that these cubes had driven more than one hopeful person insane.

Hinton created several new words to describe elements in the fourth dimension. According to OED, he first used the word tesseract in 1888 in his book “A New Era of Thought”. He also invented the words “kata” (from the Greek “down from”) and “ana” (from the Greek “up toward”) to describe the two opposing fourth-dimensional directions—the 4-D equivalents of left and right, forwards and backwards, and up and down.

Hinton’s Scientific romances, including “What is the Fourth Dimension?” and “A Plane World” were published as a series of nine pamphlets by Swan Sonnenschein & Co. during 1884–1886. In the introduction to “A Plane World”, Hinton referred to Abbott’s recent Flatland as having similar design but different intent. Abbott used the stories as “a setting wherein to place his satire and his lessons. But we wish in the first place to know the physical facts.” Hinton’s world existed on the surface of a sphere rather than a flat plane. He extended the connection to Abbott’s work with “An Episode on Flatland: Or How a Plain Folk Discovered the Third Dimension” (1907).

The Fourth Dimension
Third Edition
Published by London: George Allen & Co, 1912

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A New Era of Thought
Publisher London: Swan Sonneschen & Co, 1888

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Sluneční hodiny na pevných stanovištích (2005) [Czech]

Sluneční hodiny jsou pozoruhodné kulturní památky. Snoubí se v nich matematika, geometrie, astronomie s uměním, architekturou či řemeslem. Bývají krásnou ozdobou budov a veřejných prostranství, připomínkou spojení našeho života se Sluncem, jsou i vynikající učební pomůckou.
V knize najdete katalog 2339 slunečních hodin na pevných stanovištích v Čechách, na Moravě, ve Slezsku a na Slovensku. Jedná se o první soupis svého druhu a rozsahu. Dozvíte se o principech fungování slunečních hodin, jejich stavbě a obnově, gnómonických zajímavostech a nejhezčích (ne nutně nejznámějších) slunečních hodinách na celém zpracovaném území.Pro návštěvníky Prahy, domácí i zahraniční, je připojen námět na vycházku za pražskými slunečními hodinami.

Sluneční hodiny na pevných stanovištích. Čechy, Morava, Slezsko a Slovensko
Edited by Miroslav Brož, Miloš Nosek, Jan Trebichavský, Drahomíra Pecinová
Publisher: Academia, Prague, 2005
ISBN 80-200-1204-4
EAN 9788020012043
404 pages

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B. Jack Copeland (ed.): The Essential Turing: Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, and Artificial Life. Plus the Secrets of Enigma (2004)

Alan Turing, pioneer of computing and WWII codebreaker, is one of the most important and influential thinkers of the twentieth century. In this volume for the first time his key writings are made available to a broad, non-specialist readership. They make fascinating reading both in their own right and for their historic significance: contemporary computational theory, cognitive science, artificial intelligence, and artificial life all spring from this ground-breaking work, which is also rich in philosophical and logical insight. An introduction by leading Turing expert Jack Copeland provides the background and guides the reader through the selection.

Publisher Oxford University Press, 2004
ISBN 0198250800, 9780198250807
Length 613 pages

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Philip Mirowski: Machine Dreams. Economics Becomes a Cyborg Science (2002)

This is the first cross-over book into the history of science written by an historian of economics. It shows how ‘history of technology’ can be integrated with the history of economic ideas. The analysis combines Cold War history with the history of postwar economics in America and later elsewhere, revealing that the Pax Americana had much to do with abstruse and formal doctrines such as linear programming and game theory. It links the literature on ‘cyborg’ to economics, an element missing in literature to date. The treatment further calls into question the idea that economics has been immune to postmodern currents, arguing that neoclassical economics has participated in the deconstruction of the integral ‘self’. Finally, it argues for an alliance of computational and institutional themes, and challenges the widespread impression that there is nothing else besides American neoclassical economic theory left standing after the demise of Marxism.

• Highly controversial assessment of how economics has modeled itself on mathematical and computer theory and the consequences of this • Author is world-famous for his iconoclastic views, here combining history of technology, economics, and computer science • Truly brilliant, scathing analysis of postwar economics and economists

Publisher Cambridge University Press, 2002
ISBN 0521775264, 9780521775267
Length 655 pages

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Bruce Collier, James H. MacLachlan: Charles Babbage and the Engines of Perfection (1998)

Charles Babbage, “the grandfather of the modern computer,” did not live to see even one of his calculating machines at work. A dazzling genius with vision extending far beyond the limitations of the Victorian age, Babbage successfully calculated a table of logarithms during his years at Cambridge University, allowing mathematical calculations to be executed with extreme precision. Only the possibility of human error prevented complete accuracy, and Babbage understood that the only way to attain perfection is to leave the human mind entirely out of the equation. He devoted most of his life and spent most of his private fortune and government stipend trying to improve his difference engines and analytical engines.

Bruce Collier and James MacLachlan chronicle Babbage’s education and scientific career, his remarkably active social life and long string of personal tragedies, his forays into philosophy and economics, his successes and failures, and the biggest disappointment of his life– his ingenious inventions were centuries ahead of the primitive capabilities of Victorian technology.

Publisher Oxford University Press, 1998
Series: Oxford portraits in science
ISBN 0195089979, 9780195089974
Length 123 pages

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Stephen Wolfram: A New Kind of Science (2002)

This long-awaited work from one of the world’s most respected scientists presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments–illustrated in the book by striking computer graphics–Stephen Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe.

Wolfram uses his approach to tackle a remarkable array of fundamental problems in science, from the origins of apparent randomness in physical systems, to the development of complexity in biology, the ultimate scope and limitations of mathematics, the possibility of a truly fundamental theory of physics, the interplay between free will and determinism, and the character of intelligence in the universe.

Written with exceptional clarity, and illustrated by nearly a thousand original pictures, this seminal book allows scientists and nonscientists alike to participate in what promises to be a major intellectual revolution.

Publisher Wolfram Media Inc, 2002
ISBN 1579550193, 9781579550196
Length 348 pages

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Peter Weibel (ed.): Beyond Art: A Third Culture. A Comparative Study in Cultures, Art and Science in 20th Century Austria and Hungary (2005)

Austria and Hungary in the 20th century were nations that made enormous achievements in the formal sciences and arts: abstraction, logic, mathematics, physics, positivism, psychoanalysis, cybernetics, constructivism, economics, art, media art, and concept art. Art and science are usually divided into two different cultures, and nations, too, are seen as having separate ones. This book delivers a new model of consilience and convergence of art and science by closely studying in a material historical way by using a multitude of original papers and contributions, photographs, documents, bibliographies, biographies, and survey essays, the mutual influence of art and science in Austria and Hungary. In fields ranging from Gestalt psychology to Quantum physics, from constructivism to theories of vision, from holography to cyberspace, we discover a multitude of ideas, books, movements and personalities that have deeply influenced the world. Richly illustrated, the book is a nearly invaluable sourcebook, in which a new method, resembling more a CD-ROM narration than a dictionary, has been used to map an unknown horizon of knowledge. Those involved in the history of science or art and in the field of cultural theory, will find an incomparable frame of reference and information. They will discover not only genius, talents and themes they have not been aware of, but also a new model of culture, a third culture. The book is graphically and structurally user-friendly with a synopsis for each chapter, models, diagrams, images, corolaries and index etc.

Publisher Springer, 2005
ISBN 3211245626, 9783211245620
Length 616 pages

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Michele Emmer (ed.): Mathematics and Culture II. Visual Perfection: Mathematics and Creativity (2005)

Creativity plays an important role in all human activities, from the visual arts to cinema and theatre, and in particular in science and mathematics .

This volume, published only in English in the series “Mathematics and Culture”, stresses the strong links between mathematics, culture and creativity in architecture, contemporary art, geometry, computer graphics, literature, theatre and cinema. So this book is designed not only for mathematicians but for all the people who have an interest in the various aspects of culture, both scientific and literary, with a special emphasis on the visual aspects.

Publisher Springer, 2005
ISBN 3540213686, 9783540213680
Length 203 pages

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Helaine Selin (ed.): Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (1997)

Here, at last, is the massively updated and augmented second edition of this landmark encyclopedia. The electronic version of this two-volume work contains approximately 1000 entries dealing in depth with the history of the scientific, technological and medical accomplishments of cultures outside of the United States and Europe.

The entries consist of fully updated articles together with hundreds of entirely new topics adorned with full color pictures. This unique reference work includes intercultural articles on broad topics such as mathematics and astronomy as well as thoughtful philosophical articles on concepts and ideas related to the study of non-Western Science, such as rationality, objectivity, and method.

You’ll also find material on religion and science, East and West, and magic and science. This amazing resource even contains entries on fascinating esoteric topics such as Native American mathematics, Polynesian navigation, and African Metallurgy.There are also biographical articles for those cultures where individual scientists are known to us, such as China and the Islamic world.

Publisher Springer, 1997
ISBN 0792340663, 9780792340669
Length 1117 pages

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Gareth Loy: Musimathics, Vol. 1. The Mathematical Foundations of Music (2006)

“Mathematics can be as effortless as humming a tune, if you know the tune,” writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music—a commonsense, self-contained introduction for the nonspecialist reader. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science.

In this volume, Loy presents the materials of music (notes, intervals, and scales); the physical properties of music (frequency, amplitude, duration, and timbre); the perception of music and sound (how we hear); and music composition. Musimathics is carefully structured so that new topics depend strictly on topics already presented, carrying the reader progressively from basic subjects to more advanced ones. Cross-references point to related topics and an extensive glossary defines commonly used terms. The book explains the mathematics and physics of music for the reader whose mathematics may not have gone beyond the early undergraduate level. Calling himself “a composer seduced into mathematics,” Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The topics are all subjects that contemporary composers, musicians, and musical engineers have found to be important. The examples given are all practical problems in music and audio. The level of scholarship and the pedagogical approach also make Musimathics ideal for classroom use. Additional material can be found at a companion web site.

Publisher MIT Press, 2006
ISBN: 0-262-12282-0, 978-0-262-12282-5

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William Ross Ashby: Design for a Brain (1952/1954)

Landmark work of the pioneer of cybernetics.

Publisher: John Wiley & Sons, New York (1954)
ASIN: B0007IYC5Y
259 pages

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Norbert Wiener: God and Golem, Inc.: A Comment on Certain Points Where Cybernetics Impinges on Religion (1966)

The new and rapidly growing field of communication sciences owes as much to Norbert Wiener as to any one man. He coined the word for it—cybernetics. In God & Golem, Inc., the author concerned himself with major points in cybernetics which are relevant to religious issues.

The first point he considers is that of the machine which learns. While learning is a property almost exclusively ascribed to the self-conscious living system, a computer now exists which not only can be programmed to play a game of checkers, but one which can “learn” from its past experience and improve on its own game. For a time, the machine was able to beat its inventor at checkers. “It did win,” writes the author, “and it did learn to win; and the method of its learning was no different in principle from that of the human being who learns to play checkers.

A second point concerns machines which have the capacity to reproduce themselves. It is our commonly held belief that God made man in his own image. The propagation of the race may also be interpreted as a function in which one living being makes another in its own image. But the author demonstrates that man has made machines which are “very well able to make other machines in their own image,” and these machine images are not merely pictorial representations but operative images. Can we then say: God is to Golem as man is to Machines? in Jewish legend, golem is an embryo Adam, shapeless and not fully created, hence a monster, an automation.

The third point considered is that of the relation between man and machine. The concern here is ethical. “render unto man the things which are man’s and unto the computer the things which are the computer’s,” warns the author. In this section of the book, Dr. Wiener considers systems involving elements of man and machine.

The book is written for the intellectually alert public and does not involve any highly technical knowledge. It is based on lectures given at Yale, at the Société Philosophique de Royaumont, and elsewhere.

Publisher MIT Press, 1966
ISBN 0262730111, 9780262730112
Length 99 pages

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Manuel De Landa: Intensive Science and Virtual Philosophy (2005)

Intensive Science and Virtual Philosophy cuts to the heart of the philosophy of Gilles Deleuze and of today’s science wars. At the start of the 21st Century, Deleuze is now regarded as the most radical and influential of contemporary philosophers. Yet his work is widely misunderstood and misinterpreted. In this already classic work Manuel DeLanda does what the growing host of Deleuzians have falled to do – he makes sense of Deleuze for both analytic and continental thought, for both science and philosophy.

Publisher Continuum International Publishing Group, 2005
ISBN 0826479324, 9780826479327
Length 232 pages

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Doron Swade: The Difference Engine: Charles Babbage and the Quest to Build the First Computer (2001)

In 1821 an inventor and mathematician named Charles Babbage was reviewing a set of mathematical tables. After finding an excess of errors in the results, he exclaimed, “I wish to God these calculations had been executed by steam.” Thus began Babbage’s lifelong enterprise to design and build a mechanical calculating engine-the world’s first computer. Drawing on Babbage’s original notes and designs, Doron Swade recounts both Babbage’s nineteenth-century quest to build a calculating machine-the Difference Engine-and Swade’s own successful attempt to build a replica for the bicentennial of Babbage’s birth. Set against the tantalizing background of Victorian science and politics with a colorful cast of characters, The Difference Engineis a saga of ingenuity and will-and the dawning of a new age.

Publisher Penguin Books, 2001
ISBN 0670910201
Length 342 pages

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Zachary L. Frazer, Tzuchien Tho (eds.): Alain Badiou. The Concept of Model. An Introduction to the Materialist Epistemology of Mathematics (2007)

The Concept of Model is the first of Alain Badiou’s early books to be translated fully into English. With this publication English readers finally have access to a crucial work by one of the world’s greatest living philosophers. Written on the eve of the events of May 1968, The Concept of Model provides a solid mathematical basis for a rationalist materialism. Badiou’s concept of model distinguishes itself from both logical positivism and empiricism by introducing a new form of break into the hitherto implicated realms of science and ideology, and establishing a new way to understand their disjunctive relation. Readers coming to Badiou for the first time will be struck by the clarity and force of his presentation, and the key place that The Concept of Model enjoys in the overall development of Badiou’s thought will enable readers already familiar with his work to discern the lineaments of his later radical developments. This translation is accompanied by a stunning new interview with Badiou in which he elaborates on the connections between his early and most recent thought.

Publisher: Re.press
ISBN-13: 9780980305234
ISBN-ebook: 9780980666571
Publication date: 1 December 2007
Pages: 180
Format: 216×140 mm Paperback
Series: Transmission

Keywords and phrases
Alain Badiou, ontology, epistemological break, Althusserian, axiom of choice, formal system, Jacques-Alain Miller, model theory, mathematical logic, Michel Serres, ideology, deduction theorem, suture, Justin Clemens, free variable, semantic, logical positivism, mathematical production, Louis Althusser, Dialectical Materialism

This book is Open Access. This work is not simply an electronic book; it is the open access version of a work that exists in a number of forms, the traditional printed form being one of them.

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