The Outer Limits of Reason

The Outer Limits of Reason
Author: Noson S. Yanofsky
Publisher: MIT Press
Total Pages: 419
Release: 2016-11-04
Genre: Science
ISBN: 026252984X

This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

Beyond Pluto

Beyond Pluto
Author: John Davies
Publisher: Cambridge University Press
Total Pages: 260
Release: 2001-07-19
Genre: Science
ISBN: 9781139428774

In the ten years preceding publication, the known solar system more than doubled in size. For the first time in almost two centuries an entirely new population of planetary objects was found. This 'Kuiper Belt' of minor planets beyond Neptune revolutionised our understanding of the solar system's formation and finally explained the origin of the enigmatic outer planet Pluto. This is the fascinating story of how theoretical physicists decided that there must be a population of unknown bodies beyond Neptune and how a small band of astronomers set out to find them. What they discovered was a family of ancient planetesimals whose orbits and physical properties were far more complicated than anyone expected. We follow the story of this discovery, and see how astronomers, theoretical physicists and one incredibly dedicated amateur observer came together to explore the frozen boundary of the solar system.

Why Beliefs Matter

Why Beliefs Matter
Author: E. Brian Davies
Publisher: OUP Oxford
Total Pages: 272
Release: 2010-07-09
Genre: Science
ISBN: 0191591564

In the follow-up to his acclaimed Science in the Looking Glass, Brian Davies discusses deep problems about our place in the world, using a minimum of technical jargon. The book argues that 'absolutist' ideas of the objectivity of science, dating back to Plato, continue to mislead generations of both theoretical physicists and theologians. It explains that the multi-layered nature of our present descriptions of the world is unavoidable, not because of anything about the world, but because of our own human natures. It tries to rescue mathematics from the singular and exceptional status that it has been assigned, as much by those who understand it as by those who do not. Working throughout from direct quotations from many of the important contributors to its subject, it concludes with a penetrating criticism of many of the recent contributions to the often acrimonious debates about science and religions.

History of Topology

History of Topology
Author: I.M. James
Publisher: Elsevier
Total Pages: 1067
Release: 1999-08-24
Genre: Mathematics
ISBN: 0080534074

Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

The Déjà Vu Experiment

The Déjà Vu Experiment
Author: J. G. Renato
Publisher: Veritas Shield
Total Pages: 71
Release: 2015-02-27
Genre: Body, Mind & Spirit
ISBN: 0989718603

They're everywhere around us, but usually we choose to ignore them. They happen in space. They happen in time. They’re little moments of discontinuity in our experience, but they can become portals to the greater experience of our world as illusion, as the veil, as maya, as the collective dream – and the experience of ourselves as the dreamers. If we choose not to ignore them, but to follow them, like Alice down a cosmic rabbit hole, we might just begin to understand how it was that we got here in the first place. Offering unique ways to look at light, quantum physics, string theory, the universe existing as a single unified melody, the power of imagination, free will, the language of mathematics, death, and more, Renato successfully challenged me to consider not just “Who am I?” but “What am I?” — Patricia Reding, Readers’ Favorite J. G. Renato attempts to uncover the deeper meaning behind that often disconcerting déjà vu we’ve all experienced at some time or other. He skillfully uses this sense of stepping out of one plane of reality and seeing things from a different perspective to explore the whole nature of being, presence, and existence. Most crucially, he poses the thorny question of how spiritual phenomena can fit within a world obsessed by rationality and tangible productivity. … The key achievement of this slight volume is managing to be metaphysical while remaining lighthearted and fun. — Seamus Mullarkey, ForeWord Reviews

Foolproof, and Other Mathematical Meditations

Foolproof, and Other Mathematical Meditations
Author: Brian Hayes
Publisher: MIT Press
Total Pages: 245
Release: 2018-10-30
Genre: Mathematics
ISBN: 0262536072

A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability. Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung and nearby, bringing readers tidings of mathematical topics from Markov chains to Sudoku. Hayes, a non-mathematician, argues that mathematics is not only an essential tool for understanding the world but also a world unto itself, filled with objects and patterns that transcend earthly reality. In a series of essays, Hayes sets off to explore this exotic terrain, and takes the reader with him. Math has a bad reputation: dull, difficult, detached from daily life. As a talking Barbie doll opined, “Math class is tough.” But Hayes makes math seem fun. Whether he's tracing the genealogy of a well-worn anecdote about a famous mathematical prodigy, or speculating about what would happen to a lost ball in the nth dimension, or explaining that there are such things as quasirandom numbers, Hayes wants readers to share his enthusiasm. That's why he imagines a cinematic treatment of the discovery of the Riemann zeta function (“The year: 1972. The scene: Afternoon tea in Fuld Hall at the Institute for Advanced Study in Princeton, New Jersey”), explains that there is math in Sudoku after all, and describes better-than-average averages. Even when some of these essays involve a hike up the learning curve, the view from the top is worth it.

The Zanti Misfits

The Zanti Misfits
Author: John Peel
Publisher: Tor Books
Total Pages: 130
Release: 1997
Genre: Children's stories
ISBN: 9780812590630

An exciting series of six original digest-sized novels based on the hit-TV series "The Outer Limits". The rulers of the planet Zanti have found a solution to the problem of what to do with undesirable misfits and dangerous malcontents who threaten their society--exile them to Earth! The leaders of Earth are powerless to object. Teenagers Ben Garth and Lisa Lawrence are outcasts, too. Now they're on the run and headed towards a terrifying showdown with the Zanti misfits.

The Pea and the Sun

The Pea and the Sun
Author: Leonard M. Wapner
Publisher: CRC Press
Total Pages: 233
Release: 2005-04-29
Genre: Mathematics
ISBN: 1439864845

Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

Discrete Mathematics

Discrete Mathematics
Author: Norman Biggs
Publisher: Oxford University Press
Total Pages: 444
Release: 2002-12-19
Genre: Computers
ISBN: 9780198507178

Discrete mathematics is a compulsory subject for undergraduate computer scientists. This new edition includes new chapters on statements and proof, logical framework, natural numbers and the integers and updated exercises from the previous edition.