Infinity and the Mind

Author: Rudy Rucker
Publisher: Princeton University Press
ISBN: 9781400849048
Release Date: 2013-07-14
Genre: Mathematics

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

Ist Gott ein Mathematiker

Author: Mario Livio
Publisher: C.H.Beck
ISBN: 9783406616600
Release Date: 2012-03-01
Genre: Mathematics

Von der Antike bis in unsere Tage haben sich Wissenschaftler und Philosophen darüber gewundert, dass eine so abstrakte Disziplin wie die Mathematik die Natur derart perfekt erklären kann. Sogar mehr als das: Mathematiker haben oft Voraussagen gemacht, etwa über die Existenz bestimmter Teilchen, die sich später als richtig erwiesen haben. Was ist es, das der Mathematik solch unglaubliche Macht verleiht? Oder, wie Einstein sich einst fragte: „Wie ist es möglich, dass die Mathematik, die doch ein von aller Erfahrung unabhängiges Produkt des menschlichen Denkens ist, auf die Gegenstände der Welt so vortrefflich passt?“ Werden mathematische Erkenntnisse also nicht erfunden, sondern entdeckt? Diese Fragestellung bildet den roten Faden, an dem der Astrophysiker Mario Livio mit großer Lebendigkeit durch die Geistesgeschichte des mathematischen und naturwissenschaftlichen Denkens führt. Zugleich wirft sein Buch einen frischen und unterhaltsamen Blick auf die Lebensgeschichte und die Erkenntnisse großer Denker wie Pythagoras, Platon, Newton und Einstein. „Eine lebendige und faszinierende Lektüre für ein breites Publikum“ – Nature

The End of Theory

Author: Richard Bookstaber
Publisher: Princeton University Press
ISBN: 9781400884964
Release Date: 2017-04-17
Genre: Business & Economics

An in-depth look at how to account for the human complexities at the heart of today's financial system Our economy may have recovered from the Great Recession—but not our economics. In The End of Theory, Richard Bookstaber discusses why the human condition and the radical uncertainty of our world renders the standard economic model—and the theory behind it—useless for dealing with financial crises. What model should replace it? None. At least not any version we've been using for the past two hundred years. Instead, Bookstaber argues for a new approach called agent-based economics, one that takes as a starting point the fact that we are humans, not the optimizing automatons that standard economics assumes we are. Bookstaber's groundbreaking paradigm promises to do a far better job at preventing crises and managing those that break out. As he explains, our varied memories and imaginations color our economic behavior in unexpected hues. Agent-based modeling embraces these nuances by avoiding the mechanistic, unrealistic structure of our current economic approach. Bookstaber tackles issues such as radical uncertainty, when circumstances take place beyond our anticipation, and emergence, when innocent, everyday interactions combine to create sudden chaos. Starting with the realization that future crises cannot be predicted by the past, he proposes an approach that recognizes the human narrative while addressing market realities. Sweeping aside the historic failure of twentieth-century economics, The End of Theory offers a novel and innovative perspective, along with a more realistic and human framework, to help prevent today's financial system from blowing up again.

Is God a Mathematician

Author: Mario Livio
Publisher: Simon and Schuster
ISBN: 1416594434
Release Date: 2011-02-22
Genre: Mathematics

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

Principia Mathematica

Author: Alfred North Whitehead
ISBN: STANFORD:36105039675058
Release Date: 1984-01
Genre: Logic, Symbolic and mathematical

Wei es Licht

Author: Rudy Rucker
Publisher: Heyne Verlag
ISBN: 9783641151751
Release Date: 2014-12-18
Genre: Fiction

Am Ende der Unendlichkeit Felix Rayman lebt im Staat New York und hat den langweiligsten Beruf der Welt: Er ist Mathematiklehrer in einer Provinzstadt. Seine Familie ist zerrüttet, seine Karriere stritt schon seit Jahren auf der Stelle – Was hat Felix also zu verlieren? Er bringt sich selbst das luzide Träumen bei, um komplexe mathematische Probleme zu lösen, und macht so außerkörperliche Erfahrungen. Bei einer davon trifft er auf den Teufel, dem er mit knapper Not entkommt. Sein Retter ist niemand geringeres als Jesus, der ihn um einen Gefallen bittet: Rayman soll Kathy, einer jungen Frau, die im Wochenbett gestorben ist, nach Cimön bringen. Doch wie gelangt man in ein Land, das unendlich weit entfernt ist? Wie besteigt man dort einen Berg, der unendlich hoch ist? Und gibt es das absolut Unendliche eigentlich?

To Infinity and Beyond

Author: Eli Maor
Publisher: Princeton University Press
ISBN: 0691025118
Release Date: 1991
Genre: Mathematics

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


Author: Julian Havil
Publisher: Springer-Verlag
ISBN: 9783540484967
Release Date: 2007-04-21
Genre: Mathematics

Jeder kennt p = 3,14159..., viele kennen e = 2,71828..., einige i. Und dann? Die "viertwichtigste" Konstante ist die Eulersche Zahl g = 0,5772156... - benannt nach dem genialen Leonhard Euler (1707-1783). Bis heute ist unbekannt, ob g eine rationale Zahl ist. Das Buch lotet die "obskure" Konstante aus. Die Reise beginnt mit Logarithmen und der harmonischen Reihe. Es folgen Zeta-Funktionen und Eulers wunderbare Identität, Bernoulli-Zahlen, Madelungsche Konstanten, Fettfinger in Wörterbüchern, elende mathematische Würmer und Jeeps in der Wüste. Besser kann man nicht über Mathematik schreiben. Was Julian Havil dazu zu sagen hat, ist spektakulär.


ISBN: STANFORD:36105117254784
Release Date: 1997
Genre: American literature