In Search Of Infinity
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| Author | : N.Ya. Vilenkin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 151 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1461208378 |
The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At the time, many scientists ignored the paradoxes and used set theory extensively in their work, while others subjected set-theoretic methods in mathematics to harsh criticism. The debate intensified when a group of French mathematicians, who wrote under the pseudonym of Nicolas Bourbaki, tried to erect the whole edifice of mathematics on the single notion of a set. Some mathematicians greeted this attempt enthusiastically while others regarded it as an unnecessary formalization, an attempt to tear mathematics away from life-giving practical applications that sustain it. These differences notwithstanding, Bourbaki has had a significant influence on the evolution of mathematics in the twentieth century. In this book we try to tell the reader how the idea of the infinite arose and developed in physics and in mathematics, how the theory of infinite sets was constructed, what paradoxes it has led to, what significant efforts have been made to eliminate the resulting contradictions, and what routes scientists are trying to find that would provide a way out of the many difficulties.
| Author | : Brian Clegg |
| Publisher | : Robinson |
| Total Pages | : 185 |
| Release | : 2013-02-07 |
| Genre | : Mathematics |
| ISBN | : 1472107640 |
'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 | : Sarah C. Campbell |
| Publisher | : Astra Publishing House |
| Total Pages | : 34 |
| Release | : 2022-08-30 |
| Genre | : Juvenile Nonfiction |
| ISBN | : 1635928265 |
What is infinity? Explore this fascinating and complex math concept and its purpose in our world in this picture book that both demystifies and explains. Perfect for kids who grew up on Baby University books like Quantum Physics for Babies. Defining infinity is difficult. But there is one thing people do every day that leads to infinity—counting. No matter what large number you name, there is always a larger number. By reading this book, kids can begin to think about this and other powerful ideas involving infinity, including how infinity relates to rocket science. Featuring clear text and beautiful photographs, this is an excellent choice for kids who want to delve deeper into math and science and for those ready to look at the world in a new way.
| Author | : Loren Graham |
| Publisher | : Harvard University Press |
| Total Pages | : 252 |
| Release | : 2009-03-31 |
| Genre | : History |
| ISBN | : 0674032934 |
In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.
| Author | : David Deutsch |
| Publisher | : Penguin UK |
| Total Pages | : 571 |
| Release | : 2011-03-31 |
| Genre | : Science |
| ISBN | : 0141969695 |
'Science has never had an advocate quite like David Deutsch ... A computational physicist on a par with his touchstones Alan Turing and Richard Feynman, and a philosopher in the line of his greatest hero, Karl Popper. His arguments are so clear that to read him is to experience the thrill of the highest level of discourse available on this planet and to understand it' Peter Forbes, Independent In our search for truth, how far have we advanced? This uniquely human quest for good explanations has driven amazing improvements in everything from scientific understanding and technology to politics, moral values and human welfare. But will progress end, either in catastrophe or completion - or will it continue infinitely? In this profound and seminal book, David Deutsch explores the furthest reaches of our current understanding, taking in the Infinity Hotel, supernovae and the nature of optimism, to instill in all of us a wonder at what we have achieved - and the fact that this is only the beginning of humanity's infinite possibility. 'This is Deutsch at his most ambitious, seeking to understand the implications of our scientific explanations of the world ... I enthusiastically recommend this rich, wide-ranging and elegantly written exposition of the unique insights of one of our most original intellectuals' Michael Berry, Times Higher Education Supplement 'Bold ... profound ... provocative and persuasive' Economist 'David Deutsch may well go down in history as one of the great scientists of our age' Scotsman
| Author | : Ian Stewart |
| Publisher | : Profile Books |
| Total Pages | : 468 |
| Release | : 2013-03-07 |
| Genre | : Mathematics |
| ISBN | : 1847653510 |
There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincaré Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.
| Author | : Gordon Fraser |
| Publisher | : Checkmark Books |
| Total Pages | : 144 |
| Release | : 1995 |
| Genre | : Science |
| ISBN | : 9780816032501 |
Explores the scientific discoveries in particle physics and astronomy concerning the origin of the universe
| Author | : Robert Kanigel |
| Publisher | : Simon and Schuster |
| Total Pages | : 464 |
| Release | : 2016-04-26 |
| Genre | : Biography & Autobiography |
| ISBN | : 1476763496 |
A biography of the Indian mathematician Srinivasa Ramanujan. The book gives a detailed account of his upbringing in India, his mathematical achievements, and his mathematical collaboration with English mathematician G. H. Hardy. The book also reviews the life of Hardy and the academic culture of Cambridge University during the early twentieth century.
| Author | : Amir D. Aczel |
| Publisher | : Simon and Schuster |
| Total Pages | : 278 |
| Release | : 2001-08-28 |
| Genre | : Mathematics |
| ISBN | : 0743422996 |
A compelling narrative that blends the story of infinity with the tragic tale of a tormented and brilliant mathematician.
| Author | : Antonio Padilla |
| Publisher | : Farrar, Straus and Giroux |
| Total Pages | : 211 |
| Release | : 2022-07-26 |
| Genre | : Science |
| ISBN | : 0374600570 |
A fun, dazzling exploration of the strange numbers that illuminate the ultimate nature of reality. For particularly brilliant theoretical physicists like James Clerk Maxwell, Paul Dirac, or Albert Einstein, the search for mathematical truths led to strange new understandings of the ultimate nature of reality. But what are these truths? What are the mysterious numbers that explain the universe? In Fantastic Numbers and Where to Find Them, the leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics, offering a startling picture of how the universe works. These strange numbers include Graham’s number, which is so large that if you thought about it in the wrong way, your head would collapse into a singularity; TREE(3), whose finite nature can never be definitively proved, because to do so would take so much time that the universe would experience a Poincaré Recurrence—resetting to precisely the state it currently holds, down to the arrangement of individual atoms; and 10^{-120}, measuring the desperately unlikely balance of energy needed to allow the universe to exist for more than just a moment, to extend beyond the size of a single atom—in other words, the mystery of our unexpected universe. Leading us down the rabbit hole to a deeper understanding of reality, Padilla explains how these unusual numbers are the key to understanding such mind-boggling phenomena as black holes, relativity, and the problem of the cosmological constant—that the two best and most rigorously tested ways of understanding the universe contradict one another. Fantastic Numbers and Where to Find Them is a combination of popular and cutting-edge science—and a lively, entertaining, and even funny exploration of the most fundamental truths about the universe.
