The mind-blowing conclusion to the chilling NUMBERS trilogy: Because everyone wants to live forever. No matter what it takes, Sarah's desperate to escape from the numbers. Always numbers. Sarah loves Adam, but can't bear the thought that every time he looks in her eyes, he can see her dying; can see her last day. It's 2029. Two years since the Chaos. Sarah and Adam are struggling to survive. She knows he always envisioned them together "'til death do us part." But will a child come between them? The child she loves. The child he saved. Little Mia was supposed to die that New Year's Day. The numbers don't lie. But somehow she changed her date. Mia's just a baby, oblivious to her special power. But ruthless people are hunting her down, determined to steal her secret. Because everyone wants to live forever.
Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition.
Author: John C. Stillwell
Publisher: CRC Press
Release Date: 2010-07-13
Winner of a CHOICE Outstanding Academic Title Award for 2011! This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is historical and partly informal, but with due attention to the subtleties of the subject. Ideas are shown to evolve from natural mathematical questions about the nature of infinity and the nature of proof, set against a background of broader questions and developments in mathematics. A particular aim of the book is to acknowledge some important but neglected figures in the history of infinity, such as Post and Gentzen, alongside the recognized giants Cantor and Gödel.
Author: Brian Clegg
Publisher: Hachette UK
Release Date: 2013-02-07
'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.
Author: Svetla Slaveva-Griffin
Publisher: Oxford University Press
Release Date: 2009-03-04
Plotinus on Number studies the fundamental role which number plays in the architecture of the universe in Neoplatonic philosophy. This book draws attention to Platinus' concept as a necesscary and fundamental link between the Platonic and the late Neoplatonic theories of number.
Author: Ian Stewart
Publisher: Random House
Release Date: 2011-06-30
Roundworld is in trouble again, and this time it looks fatal. Having created it in the first place, the wizards of Unseen Univeristy feel vaguely responsible for its safety. They know the creatures who lived there escaped the impending Big Freeze by inventing the space elevator - they even intervened to rid the planet of a plague of elves, who attempted to divert humanity onto a different time track. But now it's all gone wrong - Victorian England has stagnated and the pace of progress would embarrass a limping snail. Unless something drastic is done, there won't be time for anyone to invent spaceflight and the human race will be turned into ice-pops. Why, though, did history come adrift? Was it Sir Arthur Nightingale's dismal book about natural selection? Or was it the devastating response by an obscure country vicar called Charles Darwin, whose bestselling Theology of Species made it impossible to refute the divine design of living creatures? Either way, it's no easy task to change history, as the wizards discover to their cost. Can the God of Evolution come to humanity's aid and ensure Darwin writes a very different book? And who stopped him writing it in the first place?
Well known that mathematics and physics have problems in their development. Only one mathematician, Morris Kline, discovered illogicality of development of mathematics. Despite this, he attempted to justify illogicality in math by fruitfulness of usage of mathematics in physics, instead to stay problem about illogical development of physics. Here is discussing inconsistencies of undefined notions which are reasons of paradoxes. Main initial notion of mathematics is notion of infinity, and it has inconsistence and this inconsistency is distributed to derived notions of infinitesimal and continuity. Those notions related to almost all branches of mathematics which used physics. Also in work is considering miss inconsistencies of Euclid’s and non-Euclid’s geometries. A lot approaches like “physics is geometry or geometry is physics” was and is ignoring those inconsistencies of geometries.
Author: David R. Topper
Release Date: 2014-07-24
Some unwritten stories only exist in fragments. In this book, for the first time, the histories of the injunction against idolatry and the dread of infinity are uniquely woven into one. The spectre of idolatry has haunted the three Western religions since the biblical prohibition. The story of iconoclasm runs from ancient times, where Jews largely ignored the ban on images, through the iconoclastic episodes in Islam and Christianity, and into modern times during the French Revolution. A perhaps surprising thesis of this book is that a conceptual and secular form of iconoclasm continued as the revulsion of illusionism in Modern Art. More recently it flared-up in the dynamiting of two large statues of the Buddha by the Taliban in Afghanistan in 2001. The phobia of infinity arose from Pythagoras's discovery of irrational numbers and it runs through Zeno's paradoxes and Aristotle's philosophy, with only rare cases of defiance, such as Archimedes searching for pi. The angst over infinity continued through the Middle Ages with the theological encounter of an infinite God, as in the writings of Thomas Aquinas, only to be confronted in the Renaissance philosophy of Cusa. At the same time, infinity arose unexpectedly in visual art with the discovery of linear perspective where God was identified with the vanishing point. In the 17th and 18th centuries infinity further emerged not only in the very, very large (the cosmos itself), but in the very, very small (within calculus). This paved the way in the 19th and 20th centuries for the idea of different orders of infinity codified by Georg Cantor, where the concept mingled again with theology. Math and science buffs familiar with some aspects of infinity may first learn of its link with art, as well as a long association with theology - right up to the present. With lucid visual aids for the uninitiated, this book may likewise grant the Art lover access into a previously uncharted territory - a math venture to stretch the mind.
Author: Marius Coman
Publisher: Infinite Study
It is always difficult to talk about arithmetic, because those who do not know what is about, nor do they understand in few sentences, no matter how inspired these might be, and those who know what is about, do no need to be told what is about. Arithmetic is that branch of mathematics that you keep it in your soul and in your mind, not in your suitcase or laptop. Part One of this book of collected papers aims to show new applications of Smarandache function in the study of some well known classes of numbers, like Sophie Germain primes, Poulet numbers, Carmichael numbers ets. Beside the well-known notions of number theory, we defined in these papers the following new concepts: “Smarandache-Coman divisors of order k of a composite integer n with m prime factors”, “Smarandache-Coman congruence on primes”, “Smarandache-Germain primes”, Coman-Smarandache criterion for primality”, “Smarandache-Korselt criterion”, “Smarandache-Coman constants”. Part Two of this book brings together several papers on few well known and less known types of primes.
Author: Mark Edwards
Publisher: A&C Black
Release Date: 2014-04-10
Book 3 of Aristotle's Physics primarily concerns two important concepts for his theory of nature: change and infinity. Change is important because, in Book 2, he has defined nature - the subject-matter of the Physics - as an internal source of change. Much of his discussion is dedicated to showing that the change occurs in the patient which undergoes it, not in the agent which causes it. Thus Book 3 is an important step in clearing the way for Book 8's claims for a divine mover who causes change but in whom no change occurs. The second half of Book 3 introduces Aristotle's doctrine of infinity as something which is always potential, never actual, never traversed and never multiplied. Here, as elsewhere, Philoponus the Christian turns Aristotle's own infinity arguments against the pagan Neoplatonist belief in a beginningless universe. Such a universe, Philoponus replies, would involve actual infinity of past years already traversed, and a multiple number of past days. The commentary also contains intimations of the doctrine of impetus - which has been regarded, in its medieval context, as a scientific revolution - as well as striking examples of Philoponus' use of thought experiments to establish philosophical and broadly scientific conclusions.
Author: Nigel Lesmoir-Gordon
Publisher: Springer Science & Business Media
Release Date: 2010-10-20
A geometry able to include mountains and clouds now exists. I put it together in 1975, but of course it incorporates numerous pieces that have been around for a very long time. Like everything in science, this new geometry has very, very deep and long roots. Benoît B. Mandelbrot Introduction This enhanced and expanded edition of THE COLOURS OF INFINITY features an additional chapter on the money markets by the fractal master himself, Professor Benoît Mandelbrot. The DVD of the film associated with this book has been re-mastered especially for this edition with exquisite new fractal animations, which will take your breath away! Driven by the curious enthusiasm that engulfs many fractalistas, in 1994, Nigel Lesmoir-Gordon overcame enormous obstacles to raise the finance for, then shoot and edit the groundbreaking TV documentary from which this book takes its name. The film has been transmitted on TV channels in over fifty countries around the world. This book is not just a celebration of the discovery of the Mandelbrot set, it also brings fractal geometry up to date with a gathering of the thoughts and enthusiasms of the foremost writers and researchers in the field. As Ian Stewart makes clear in the opening chapter, there were antecedents for fractal geometry before 1975 when Mandelbrot gave the subject its name and began to develop the underlying theory.
". . . full of intellectual treats and tricks, of whimsy and deep scientific philosophy. It is highbrow entertainment at its best, a teasing challenge to all who aspire to think about the universe." — New York Herald Tribune One of the world's foremost nuclear physicists (celebrated for his theory of radioactive decay, among other accomplishments), George Gamow possessed the unique ability of making the world of science accessible to the general reader. He brings that ability to bear in this delightful expedition through the problems, pleasures, and puzzles of modern science. Among the topics scrutinized with the author's celebrated good humor and pedagogical prowess are the macrocosm and the microcosm, theory of numbers, relativity of space and time, entropy, genes, atomic structure, nuclear fission, and the origin of the solar system. In the pages of this book readers grapple with such crucial matters as whether it is possible to bend space, why a rocket shrinks, the "end of the world problem," excursions into the fourth dimension, and a host of other tantalizing topics for the scientifically curious. Brimming with amusing anecdotes and provocative problems, One Two Three . . . Infinity also includes over 120 delightful pen-and-ink illustrations by the author, adding another dimension of good-natured charm to these wide-ranging explorations. Whatever your level of scientific expertise, chances are you'll derive a great deal of pleasure, stimulation, and information from this unusual and imaginative book. It belongs in the library of anyone curious about the wonders of the scientific universe. "In One Two Three . . . Infinity, as in his other books, George Gamow succeeds where others fail because of his remarkable ability to combine technical accuracy, choice of material, dignity of expression, and readability." — Saturday Review of Literature
Author: E. H. Sondheimer
Publisher: Courier Corporation
Release Date: 2006
This fresh overview of numbers and infinity avoids tedium and controversy while maintaining historical accuracy and modern relevance. Perfect for undergraduate mathematics or science history courses. 1981 edition.
Author: L. Sweeney
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Throughout the long centuries of western metaphysics the problem of the infinite has kept surfacing in different but important ways. It had confronted Greek philosophical speculation from earliest times. It appeared in the definition of the divine attributed to Thales in Diogenes Laertius (I, 36) under the description "that which has neither beginning nor end. " It was presented on the scroll of Anaximander with enough precision to allow doxographers to transmit it in the technical terminology of the unlimited (apeiron) and the indeterminate (aoriston). The respective quanti tative and qualitative implications of these terms could hardly avoid causing trouble. The formation of the words, moreover, was clearly negative or privative in bearing. Yet in the philosophical framework the notion in its earliest use meant something highly positive, signifying fruitful content for the first principle of all the things that have positive status in the universe. These tensions could not help but make themselves felt through the course of later Greek thought. In one extreme the notion of the infinite was refined in a way that left it appropriated to the Aristotelian category of quantity. In Aristotle (Phys. III 6-8) it came to appear as essentially re quiring imperfection and lack. It meant the capacity for never-ending increase. It was always potential, never completely actualized.
Author: Eli Maor
Publisher: Princeton University Press
Release Date: 1991
Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. "Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates."--Los Angeles Times "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama."--Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science