Mario Livio

La proporción áurea es un viaje fascinante a través del arte y la arquitectura, la botánica y la biología, la física y las matemáticas, para descubrir la fascinante historia del número phi.A lo largo de la historia, desde pensadores hasta matematicos o teologos han meditado sobre la misteriosa relacion que se establece entre los numeros y la naturaleza de la realidad. En este libro fascinante, Mario Livio cuenta la historia del numero que se encuentra en el corazon de dicho misterio: phi o 1,6180339887. Esta curiosa relacion matematica, conocida popularmente como la proporcion aurea, fue definida por Euclides hace mas de dos mil años a raiz de su papel crucial en la construccion del pentagrama, al cual se le atribuyen propiedades magicas. Desde entonces, ha mostrado una propension a aparecer en una variedad de lugares de lo mas sorprendentes: en conchas de moluscos, en flosculos de girasoles, en cristales de algunos materiales o en la forma de galaxias que contienen billones de estrellas. ¡Incluso se ha sugerido que esta conectada con el comportamiento de los mercados de valores! Mario Livio nos presenta un mundo donde el orden, la belleza y el misterio eterno siempre coexistiran

En La ecuación jamás resuelta, de Mario Livio, autor de obras como La proporción aurea o Errores geniales que cambiaron el mundo, el autor narra cómo dos genios matemáticos descubrieron el lenguaje de la simetria. Mario Livio (Rumania, 1945) es director del instituto que gestiona el telescopio Hubble. Es autor de La proporcion aurea, un libro que, ademas de haber sido un exito en todo el mundo, le proporciono el premio Pitagoras y el Peano. La ecuacion jamas resuelta esta clasificado en la materia matematicas divulgativas.¿Que tienen en comun la musica de Bach, las fuerzas basicas de la naturaleza, el cubo de Rubik y la eleccion de pareja? Todos estan gobernados por las leyes de la simetria, que conectan la ciencia y el arte, entre el mundo de la fisica teorica y el mundo cotidiano en el que vivimos. Y sin embargo, el "lenguaje" de la simetria surgio de la fuente mas impensable: una ecuacion irresoluble. A lo largo de la historia, los matematicos fueron resolviendo progresivamente ecuaciones algebraicas cada vez mas complejas, hasta que toparon con la ecuacion de quinto grado. Durante varios siglos se resistio a ser resuelta, hasta que dos prodigios matematicos -el noruego Henrik Abel y el frances Evariste Galois- , que vivieron en pleno romanticismo y murieron jovenes y en circunstancias tragicas, descubrieron que no podia resolverse con los metodos al uso y debia ser afrontada con nuevos ojos... La ecuacion jamas resuelta es la apasionante narracion de como dos matematicos se enfrentaron a una ecuacion que se resistia a ser resuelta, como su gesta abrio nuevas perspectivas en las matematicas y ayudo a entender las "leyes" de la simetria cuya aplicacion desborda el mundo de las matematicas y la fisica y llega a la naturaleza y al arte.Fascinante.... Livio escribe apasionadamente sobre el papel de la simetria en la percepcion humana y en el arte The EconomistUna vasta indagacion en el fenomeno de la simetria... Hay en el libro matematicas, desde luego, pero tambien historias de amor, violencia, Historia... Y el resultado es mas apasionante que la mera suma de todos estos temas Newsweek

Un número enigmáticoA lo largo de la historia, desde pensadores hasta matemáticos o teólogos han meditado sobre la misteriosa relación que se establece entre los números y la naturaleza de la realidad. En este fascinante libro, Mario Livio cuenta la historia del numero que se encuentra en el corazon de dicho misterio: phi o 1,6180339887, un numero que no deja de sorprendernos.

¿Son las matemáticas una creación humana? ¿O lo que aparece a traves de ellas es el intrincado diseño del universo, que poco a poco vamos descubriendo? Desde la Antigüedad hasta el presente, científi

1ére éditioná: CNRS Éditions, 2017 / Qtés venduesá: 1700 ex. Une contre-histoire des sciences. Quand les erreurs de grands savants ont permis á la science de progresser. .

Charles Darwin, Lord William Kelvin, Linus Pauling, Fred Hoyle, Albert Einstein : cinq scientifiques hors du commun qui ont accompli des découvertes scientifiques considérables. Mais également cinq hommes qui se sont aussi, souvent en meme temps, parfois lourdement,Charles Darwin, Lord William Kelvin, Linus Pauling, Fred Hoyle, Albert Einstein : cinq scientifiques hors du commun qui ont accompli des découvertes scientifiques considérables. Mais également cinq hommes qui se sont aussi, souvent en meme temps, parfois lourdement, fourvoyes sur certains sujets. Charles Darwin na pas bien evalue les effets de " dilution " dans la transmission des caracteres genetiques ; Lord Kelvin a largement sous-evalue lage de la Terre ; Linus Pauling sest fait " coiffer au poteau " dans la decouverte de la structure de lADN par Jim Watson et Francis Crick ; Fred Hoyle fut un partisan irreductible de la theorie de lUnivers stationnaire ; enfin, Einstein crea une constante cosmologique pour une mauvaise raison. Il ne sagit pas denumerer les erreurs de ces grands hommes, mais bien plutot de constater et danalyser les consequences benefiques de ces errements : la theorie de levolution de Darwin fonde la genetique moderne ; Kelvin enseigne a ses successeurs comment utiliser la thermodynamique en astronomie et en geologie ; Linus Pauling introduit superbement les considerations chimiques en biologie ; Fred Hoyle demontre les bienfaits et les limites des approches scientifiques qui se demarquent des theories " a la mode " et, curieusement, au lieu detre une erreur, lintroduction de la constante cosmologique par Einstein savere extraordinairement benefique. Cest a une veritable enquete policiere, qui devoile de nombreux aspects jusque-la ignores de lhistoire des sciences, que sest consacre lastrophysicien Mario Livio, qui expose ici de façon originale et vivante les chemins parfois tortueux empruntes par la recherche scientifique.

Charles Darwin, Lord William Kelvin, Linus Pauling, Fred Hoyle, Albert Einstein : cinq scientifiques hors du commun qui ont accompli des découvertes scientifiques considérables. Mais également cinq hommes qui se sont aussi, souvent en meme temps, parfois lourdement,Charles Darwin, Lord William Kelvin, Linus Pauling, Fred Hoyle, Albert Einstein : cinq scientifiques hors du commun qui ont accompli des découvertes scientifiques considérables. Mais également cinq hommes qui se sont aussi, souvent en meme temps, parfois lourdement, fourvoyes sur certains sujets. Charles Darwin na pas bien evalue les effets de " dilution " dans la transmission des caracteres genetiques ; Lord Kelvin a largement sous-evalue lage de la Terre ; Linus Pauling sest fait " coiffer au poteau " dans la decouverte de la structure de lADN par Jim Watson et Francis Crick ; Fred Hoyle fut un partisan irreductible de la theorie de lUnivers stationnaire ; enfin, Einstein crea une constante cosmologique pour une mauvaise raison. Il ne sagit pas denumerer les erreurs de ces grands hommes, mais bien plutot de constater et danalyser les consequences benefiques de ces errements : la theorie de levolution de Darwin fonde la genetique moderne ; Kelvin enseigne a ses successeurs comment utiliser la thermodynamique en astronomie et en geologie ; Linus Pauling introduit superbement les considerations chimiques en biologie ; Fred Hoyle demontre les bienfaits et les limites des approches scientifiques qui se demarquent des theories " a la mode " et, curieusement, au lieu detre une erreur, lintroduction de la constante cosmologique par Einstein savere extraordinairement benefique. Cest a une veritable enquete policiere, qui devoile de nombreux aspects jusque-la ignores de lhistoire des sciences, que sest consacre lastrophysicien Mario Livio, qui expose ici de façon originale et vivante les chemins parfois tortueux empruntes par la recherche scientifique.

What do Bachs compositions, Rubiks Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldnt be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Evariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldnt Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

Drawing on the lives of five great scientists, this scholarly, insightful, and beautifully written book (Martin Rees, author of From Here to Infinity) illuminates the path to scientific discovery.Charles Darwin, William Thomson (Lord Kelvin), Linus Pauling, Fred Hoyle, and Albert Einstein all made groundbreaking contributions to their fieldsbut each also stumbled badly. Darwins theory of natural selection shouldnt have worked, according to the prevailing beliefs of his time. Lord Kelvin gravely miscalculated the age of the earth. Linus Pauling, the worlds premier chemist, constructed an erroneous model for DNA in his haste to beat the competition to publication. Astrophysicist Fred Hoyle dismissed the idea of a Big Bang origin to the universe (ironically, the caustic name he gave to this event endured long after his erroneous objections were disproven). And Albert Einstein speculated incorrectly about the forces of the universeand that speculation opened the door to brilliant conceptual leaps. As Mario Livio luminously explains in this thoughtful meditation on the course of science itself (The New York Times Book Review), these five scientists expanded our knowledge of life on earth, the evolution of the earth, and the evolution of the universe, despite and because of their errors.Thoughtful, well-researched, and beautifully written (The Washington Post), Brilliant Blunders is a wonderfully insightful examination of the psychology of five fascinating scientistsand the mistakes as well as the achievements that made them famous.

¿Qué tienen en común la música de Bach, las fuerzas básicas de la naturaleza, el cubo de Rubik y la elección de pareja? Todos están gobernados por las leyes de la simetría, que conectan la ciencia y el arte, el mundo de la fisica teorica y el mundo cotidiano en el que vivimos. Y, sin embargo, el "lenguaje" de la siemtria surgio de la fuente mas impensable: una ecuacion irresoluble.A lo largo de la historia, los matematicos fueron resolviendo progresivamente ecuaciones algebraicas cada vez mas complejas, hasta que toparon con la ecuacion de quinto grado. Durante varios siglos se resistio a ser resuelta, hasta que dos prodigios matematicos -el noruego Henrik Abel y el frances Evariste Galois-, que vivieron en pleno romanticismo y murieron jovenes y en circunstancias tragicas, descubrieron que no podia resolverse con los metodos al uso y debia ser afrontada con nuevos ojos...Este libro es la apasionante narracion de como dos matematicos se enfrentaron a una ecuacion que se resistia a ser resuelta, como su gesta abrio nuevas perspectivas matematicas y ayudo a entender las "leyes" de la simetria, cuya aplicacion desborda el mundo de las matematicas y de la fisica y llega a la naturaleza y al arte.

Astrophysicist and author Mario Livio investigates perhaps the most human of all our characteristicscuriosityin this lively, expert, and definitely not dumbed-down account (Kirkus Reviews) as he explores our innate desire to know why.Experiments demonstrate that people are more distracted when they overhear a phone conversationwhere they can know only one side of the dialoguethan when they overhear two people talking and know both sides. Why does half a conversation make us more curious than a whole conversation? Have you ever wondered why we wonder why? Mario Livio has, and he takes you on a fascinating quest to understand the origin and mechanisms of our curiosity. I thoroughly recommend it. (Adam Riess, Nobel Prize Winner in Physics, 2011). Curiosity is not only at the heart of mystery and suspense novels, it is also essential to other creative endeavors, from painting to sculpture to music. It is the principal driver of basic scientific research. Even so, there is still no definitive scientific consensus about why we humans are so curious, or about the mechanisms in our brain that are responsible for curiosity. In the ever-fascinating Why? Livio interviewed scientists in several fields to explore the nature of curiosity. He examined the lives of two of historys most curious geniuses, Leonardo da Vinci and Richard Feynman. He also talked to people with boundless curiosity: a superstar rock guitarist who is also an astrophysicist; an astronaut with degrees in computer science, biology, literature, and medicine. What drives these people to be curious about so many subjects?An astrophysicist who has written about mathematics, biology, and now psychology and neuroscience, Livio has firsthand knowledge of his subject which he explores in a lucid, entertaining way that will captivate anyone who is curious about curiosity.

As relações matemáticas representadas pelo número fi - 1,6180339887..., conhecida como razão áurea ou proporção divina - são encontradas na conformação das conchas, dos girassóis, dos cristais, das g

Em Galileu e os negadores da ciência, Mario Livio, astrofísico e autor best-seller, baseia-se em seu próprio conhecimento científico para conjecturar como Galileu chegou às suas conclusões revolucion

Em Deus é matemático?, o astrofísico e matemático Mario Livio, autor de A equação que ninguém conseguia resolver, investiga por que a matemática tem o poder que tem. O ganhador do Prêmio Nobel Eugene

Este livro é um exame fascinante daquela que talvez seja a nossa característica mais humana: o desejo profundo de conhecer e entender as coisas. A curiosidade é essencial para a criatividade, e também o principal agente motivador por tras da ciencia. Ainda assim, no existe um consenso cientifico sobre o motivo que torna os seres humanos curiosos, tampouco sobre que mecanismos especificos do nosso cerebro so responsaveis pela curiosidade. Seria essa caracteristica um produto direto da seleço natural? Por que ate questes aparentemente triviais as vezes nos deixam extremamente curiosos? Como nossa mente escolhe os objetos da nossa curiosidade? Essas e muitas outras questes intrigantes so exploradas por Mario Livio, cuja curiosidade insaciavel da origem a este livro irresistivel, que cativara qualquer um que esteja curioso em relaço a curiosidade.

Um passeio único pelo mundo da ciência e das realizações científicas. Charles Darwin, William Thomson (Lord Kelvin), Linus Pauling, Fred Hoyle e Albert Einstein eram cientistas incríveis e deram cont

En Errores geniales que cambiaron el mundo, de Mario Livio, autor de otros estudios generales como La proporción Áurea o La ecuación jamás resuelta, el autor bucea en la vida de cinco destacados cientificos y descubre como incluso los grandes genios cometen errores garrafales, y como esos errores son parte esencial de sus hallazgos. Mario Livio es uno de los divulgadores cientificos mas importantes del mundo y sus libros han sido grandes exitos de venta en todo el mundo.Todos nos equivocamos. Nadie es perfecto. Y eso incluye tambien a cinco de los mas grandes genios de la historia de la ciencia; Charles Darwin, William Thompson, Linus Pauling, Fred Hoyle y Albert Eisntein. Sin embargo, sus meteduras de pata fueron fundamentales en su investigacion cientifica y condujeron hacia algunos de los mas importantes hallazgos cientificos de la historia de la humanidad. Es mas, segun Mario Livio, la ciencia se basa en el error. Se avanza conforme se desmontan falsas ideas.Cuando era joven, Albert Einstein trato con insistencia de concebir una forma de describir la evolucion del universo basado en la teoria general de la relatividad. No obstante, fue victima de una nocion erronea de simplicidad estetica. Fred Hoyle era un eminente astrofisico que ridiculizo una teoria emergente sobre el origen del universo a la que peyorativamente catalogo de "Big Bang". Ambos, junto a Darwin y su teoria de la seleccion natural, Kelvin y su calculo erroneo de la edad dela Tierra y Pauling y su modelo fallido de la estructura del ADN, fueron todos ellos hombres geniales y fascinantes. Sus meteduras de pata fueron esenciales en el progreso cientifico y ayudaron a profundizar en el conocimiento de la evolucion de la Tierra, la vida y el universo.Gracias a su inmensa curiosidad, Livio convierte su libro no solo en un extraordinario viaje por la historia de la investigacion cientifica, sino en una reflexion profunda sobre la esencia misma de la ciencia. Carl Zimmer, New York TimesTiene la voluntad de desmentir el principio segun el cual la historia de la ciencia es una concatenacion de grandes hallazgos. El camino al exito cientifico esta trufado de grandes meteduras de pata. () Inteligente, riguroso y bellamente escrito, el libro nos ofrece una nueva perspectiva probablemente mas certera- sobre la travesia hacia el descubrimiento cienti...

An intriguing and accessible (Publishers Weekly) interpretation of the life of Galileo Galilei, one of historys greatest and most fascinating scientists, that sheds new light on his discoveries and how he was challenged by science deniers. We really need this story now, because were living through the next chapter of science denial (Bill McKibben).Galileos story may be more relevant today than ever before. At present, we face enormous crisessuch as minimizing the dangers of climate changebecause the science behind these threats is erroneously questioned or ignored. Galileo encountered this problem 400 years ago. His discoveries, based on careful observations and ingenious experiments, contradicted conventional wisdom and the teachings of the church at the time. Consequently, in a blatant assault on freedom of thought, his books were forbidden by church authorities.Astrophysicist and bestselling author Mario Livio draws on his own scientific expertise and uses his gifts as a great storyteller (The Washington Post) to provide a refreshing perspective (Booklist) into how Galileo reached his bold new conclusions about the cosmos and the laws of nature. A freethinker who followed the evidence wherever it led him, Galileo was one of the most significant figures behind the scientific revolution. He believed that every educated person should know science as well as literature, and insisted on reaching the widest audience possible, publishing his books in Italian rather than Latin.Galileo was put on trial with his life in the balance for refusing to renounce his scientific convictions. He remains a hero and inspiration to scientists and all of those who respect sciencewhich, as Livio reminds us in this admirably clear and concise (The Times, London) book, remains threatened everyday.

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vincis Mona Lisa to Salvador Dalis The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.

Bestselling author and astrophysicist Mario Livio examines the lives and theories of historys greatest mathematicians to ask howif mathematics is an abstract construction of the human mindit 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 thatmathematics 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.