The Man Who Knew Too Much
Alan Turing and the Invention of the Computer
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The Man Who Knew Too Much
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Narrado por:
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Richard Powers
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De:
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David Leavitt
Acerca de esta escucha
A '"skillful, literate'" (New York Times Book Review) biography of the persecuted genius who helped create the modern computer.
To solve one of the great mathematical problems of his day, Alan Turing proposed an imaginary computer. Then, attempting to break a Nazi code during World War II, he successfully designed and built one, thus ensuring the Allied victory. Turing became a champion of artificial intelligence, but his work was cut short. As an openly gay man at a time when homosexuality was illegal in England, he was convicted and forced to undergo a humiliating "treatment" that may have led to his suicide.
With a novelist's sensitivity, David Leavitt portrays Turing in all his humanity - his eccentricities, his brilliance, his fatal candor - and elegantly explains his work and its implications.
©2012 David Leavitt (P)2014 Blackstone Audio, Inc.Los oyentes también disfrutaron...
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Historia4.5 out of 5 stars 545
Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot.
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5 out of 5 stars
-
A good overview of scientific theory
- De MJ Walters en 09-11-18
De: Jim Holt
-
Alan Turing
- Unlocking The Enigma
- De: David Boyle
- Narrado por: Barnaby Edwards
- Duración: 2 h y 3 m
- Versión completa
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General4 out of 5 stars 408
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Narración:4.5 out of 5 stars 338
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Historia4.5 out of 5 stars 334
Alan Mathison Turing. Mathematician, philosopher, codebreaker, a founder of computer science, and the father of Artificial Intelligence, Turing was one of the most original thinkers of the last century - and the man whose work helped create the computer-driven world we now inhabit. But he was also an enigmatic figure, deeply reticent yet also strikingly naive. Turing's openness about his homosexuality at a time when it was an imprisonable offense ultimately led to his untimely death at the age of only 41.
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5 out of 5 stars
-
Fascinating look at a fascinating man
- De kwestrope en 10-16-18
De: David Boyle
-
A Most Elegant Equation
- Euler’s Formula and the Beauty of Mathematics
- De: David Stipp
- Narrado por: Sean Pratt
- Duración: 5 h y 2 m
- Versión completa
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General4 out of 5 stars 312
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Narración:4.5 out of 5 stars 279
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Historia4 out of 5 stars 276
Bertrand Russell wrote that mathematics can exalt "as surely as poetry". This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity, or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections.
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3 out of 5 stars
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Good treatment of the subject
- De Kindle Customer en 04-09-18
De: David Stipp
-
The Equation That Couldn't Be Solved
- How Mathematical Genius Discovered the Language of Symmetry
- De: Mario Livio
- Narrado por: Tom Parks
- Duración: 11 h y 45 m
- Versión completa
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General4.5 out of 5 stars 67
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Narración:4.5 out of 5 stars 58
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Historia4.5 out of 5 stars 58
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 prodigies ultimately proved that the quintic cannot be solved by a simple formula. The first popular account of the mathematics of symmetry and order, The Equation That Couldn't 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.
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5 out of 5 stars
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Historical Perspective Appreciated
- De Michael Hanrahan en 01-22-20
De: Mario Livio
-
A Brief History of Infinity: The Quest to Think the Unthinkable
- Brief Histories
- De: Brian Clegg
- Narrado por: Gordon Griffin
- Duración: 9 h y 3 m
- Versión completa
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General4.5 out of 5 stars 41
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Narración:4.5 out of 5 stars 35
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Historia4.5 out of 5 stars 35
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
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3 out of 5 stars
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Really not great in Audio, not great otherwise
- De Michael en 03-29-13
De: Brian Clegg
-
Intuition Pumps and Other Tools for Thinking
- De: Daniel C. Dennett
- Narrado por: Jeff Crawford
- Duración: 13 h y 22 m
- Versión completa
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General4 out of 5 stars 427
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Narración:4 out of 5 stars 363
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Historia4 out of 5 stars 357
Over a storied career, Daniel C. Dennett has engaged questions about science and the workings of the mind. His answers have combined rigorous argument with strong empirical grounding. And a lot of fun. Intuition Pumps and Other Tools for Thinking offers seventy-seven of Dennett’s most successful “imagination-extenders and focus-holders” meant to guide you through some of life’s most treacherous subject matter: evolution, meaning, mind, and free will.
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4 out of 5 stars
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Loved it, but some philosophy background needed.
- De LongerILiveLessIKnow en 11-14-13
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The Riddle of the Labyrinth
- The Quest to Crack an Ancient Code
- De: Margalit Fox
- Narrado por: Pam Ward
- Duración: 7 h y 44 m
- Versión completa
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General4 out of 5 stars 147
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Narración:4.5 out of 5 stars 133
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Historia4 out of 5 stars 132
In the tradition of Simon Winchester and Dava Sobel, The Riddle of the Labyrinth: The Quest to Crack an Ancient Code tells one of the most intriguing stories in the history of language, masterfully blending history, linguistics, and cryptology with an elegantly wrought narrative. When famed archaeologist Arthur Evans unearthed the ruins of a sophisticated Bronze Age civilization that flowered on Crete 1,000 years before Greece's Classical Age, he discovered a cache of ancient tablets, Europe's earliest written records.
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4 out of 5 stars
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Discovery and Translation of Linear B Script
- De Sires en 01-11-14
De: Margalit Fox
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Is God a Mathematician?
- De: Mario Livio
- Narrado por: Tom Parks
- Duración: 9 h y 4 m
- Versión completa
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General4.5 out of 5 stars 71
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Narración:4.5 out of 5 stars 62
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Historia4.5 out of 5 stars 62
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.
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5 out of 5 stars
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Origins of Mathematics
- De Rick B en 07-08-21
De: Mario Livio
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Uncertainty
- Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science
- De: David Lindley
- Narrado por: Robert Blumenfeld
- Duración: 7 h y 2 m
- Versión completa
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General4 out of 5 stars 370
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Narración:4 out of 5 stars 209
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Historia4.5 out of 5 stars 210
Werner Heisenberg's "uncertainty principle" challenged centuries of scientific understanding, placed him in direct opposition to Albert Einstein, and put Niels Bohr in the middle of one of the most heated debates in scientific history. Heisenberg's theorem stated that there were physical limits to what we could know about sub-atomic particles; this "uncertainty" would have shocking implications.
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4 out of 5 stars
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fascinating insight into the real drama of physics
- De Ryan en 09-07-10
De: David Lindley
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Undeniable
- How Biology Confirms Our Intuition That Life Is Designed
- De: Douglas Axe
- Narrado por: Neil Hellegers
- Duración: 7 h y 14 m
- Versión completa
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General4.5 out of 5 stars 311
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Narración:4.5 out of 5 stars 273
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Historia4.5 out of 5 stars 272
Throughout his distinguished and unconventional career, engineer-turned-molecular-biologist Douglas Axe has been asking the questions that much of the scientific community would rather silence. Now, he presents his conclusions in this brave and pioneering book. Axe argues that the key to understanding our origin is the "design intuition" - the innate belief held by all humans that tasks we would need knowledge to accomplish can be accomplished only by someone who has that knowledge.
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5 out of 5 stars
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Seductively Challenge what are consider facts
- De Rafael Vila en 10-08-16
De: Douglas Axe
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The Metaphysical Club
- De: Louis Menand
- Narrado por: Henry Leyva
- Duración: 6 h y 53 m
- Versión resumida
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General4 out of 5 stars 304
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Narración:4 out of 5 stars 167
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Historia4 out of 5 stars 163
Hardly a club in the conventional sense, the organization referred to in the title of this superb literary hybrid (part history, part biography, part philosophy) consisted of four members and probably existed for less than nine months.
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5 out of 5 stars
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The Great American Experiment
- De Victoria en 12-08-03
De: Louis Menand
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What Is Real?
- The Unfinished Quest for the Meaning of Quantum Physics
- De: Adam Becker
- Narrado por: Greg Tremblay
- Duración: 11 h y 45 m
- Versión completa
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General4.5 out of 5 stars 717
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Narración:4.5 out of 5 stars 623
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Historia4.5 out of 5 stars 616
Every physicist agrees quantum mechanics is among humanity's finest scientific achievements. But ask what it means, and the result will be a brawl. For a century, most physicists have followed Niels Bohr's Copenhagen interpretation and dismissed questions about the reality underlying quantum physics as meaningless. A mishmash of solipsism and poor reasoning, Copenhagen endured, as Bohr's students vigorously protected his legacy, and the physics community favored practical experiments over philosophical arguments.
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5 out of 5 stars
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Good, "light" "read"... potential caveat below...
- De James S. en 03-31-18
De: Adam Becker
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The Pleasure of Finding Things Out
- The Best Short Works of Richard P. Feynman
- De: Richard P. Feynman
- Narrado por: Sean Runnette
- Duración: 8 h y 23 m
- Versión completa
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General4.5 out of 5 stars 1,823
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Narración:4.5 out of 5 stars 1,569
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Historia4.5 out of 5 stars 1,561
The Pleasure of Finding Things Out is a magnificent treasury of the best short works of Richard P. Feynman, from interviews and speeches to lectures and printed articles. A sweeping, wide-ranging collection, it presents an intimate and fascinating view of a life in science - a life like no other. From his ruminations on science in our culture to his Nobel Prize acceptance speech, this book will delight anyone interested in the world of ideas.
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4 out of 5 stars
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Interesting, but material is covered in better book.
- De Erlend en 04-06-16
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The Invention of Science
- A New History of the Scientific Revolution
- De: David Wootton
- Narrado por: James Langton
- Duración: 22 h y 5 m
- Versión completa
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General4 out of 5 stars 136
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Narración:4.5 out of 5 stars 120
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Historia4.5 out of 5 stars 121
In this fascinating history spanning continents and centuries, historian David Wootton offers a lively defense of science, revealing why the Scientific Revolution was truly the greatest event in our history. The Invention of Science goes back 500 years in time to chronicle this crucial transformation, exploring the factors that led to its birth and the people who made it happen. Wootton argues that the Scientific Revolution was actually five separate yet concurrent events that developed independently.
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2 out of 5 stars
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A Good Read Spoiled
- De David A. Donnelly en 12-23-16
De: David Wootton
-
The Book of Why
- The New Science of Cause and Effect
- De: Judea Pearl, Dana Mackenzie
- Narrado por: Mel Foster
- Duración: 15 h y 14 m
- Versión completa
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General4.5 out of 5 stars 837
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Narración:4.5 out of 5 stars 691
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Historia4.5 out of 5 stars 689
"Correlation does not imply causation". This mantra has been invoked by scientists for decades and has led to a virtual prohibition on causal talk. But today, that taboo is dead. The causal revolution, sparked by Judea Pearl and his colleagues, has cut through a century of confusion and placed causality - the study of cause and effect - on a firm scientific basis.
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5 out of 5 stars
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Great book! Not a great audiobook.
- De rrwright en 05-30-18
De: Judea Pearl, y otros
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The Landscape of History
- How Historians Map the Past
- De: John Lewis Gaddis
- Narrado por: Jack Chekijian
- Duración: 6 h y 16 m
- Versión completa
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General4 out of 5 stars 107
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Narración:4 out of 5 stars 96
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Historia4.5 out of 5 stars 92
What is history, and why should we study it? Is there such a thing as historical truth? Is history a science? One of the most accomplished historians at work today, John Lewis Gaddis, answers these and other questions in this short, witty, and humane book. The Landscape of History provides a searching look at the historian's craft as well as a strong argument for why a historical consciousness should matter to us today.
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5 out of 5 stars
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Excellent Book!
- De Billy en 09-15-18
Las personas que vieron esto también vieron...
-
Alan Turing
- Unlocking The Enigma
- De: David Boyle
- Narrado por: Barnaby Edwards
- Duración: 2 h y 3 m
- Versión completa
-
General4 out of 5 stars 408
-
Narración:4.5 out of 5 stars 338
-
Historia4.5 out of 5 stars 334
Alan Mathison Turing. Mathematician, philosopher, codebreaker, a founder of computer science, and the father of Artificial Intelligence, Turing was one of the most original thinkers of the last century - and the man whose work helped create the computer-driven world we now inhabit. But he was also an enigmatic figure, deeply reticent yet also strikingly naive. Turing's openness about his homosexuality at a time when it was an imprisonable offense ultimately led to his untimely death at the age of only 41.
-
5 out of 5 stars
-
Fascinating look at a fascinating man
- De kwestrope en 10-16-18
De: David Boyle
-
Prof
- Alan Turing Decoded
- De: Dermot Turing
- Narrado por: Chris Courtenay
- Duración: 10 h y 23 m
- Versión completa
-
General4.5 out of 5 stars 15
-
Narración:5 out of 5 stars 14
-
Historia5 out of 5 stars 14
Alan Turing was an extraordinary man who crammed into a life of only 42 years the careers of mathematician, codebreaker, computer scientist and biologist. He is widely regarded as a war hero grossly mistreated by his unappreciative country, and it has become hard to disentangle the real man from the story. It is easy to cast him as a misfit, the stereotypical professor.
-
5 out of 5 stars
-
Alan Turing Bio
- De G. Elliot en 01-08-19
De: Dermot Turing
-
On the Trail of the JFK Assassins
- A Groundbreaking Look at America's Most Infamous Conspiracy
- De: Dick Russell
- Narrado por: Sean Runnette
- Duración: 15 h y 31 m
- Versión completa
-
General4.5 out of 5 stars 89
-
Narración:4.5 out of 5 stars 78
-
Historia4.5 out of 5 stars 79
Using newly declassified information, Dick Russell builds on three decades of painstaking research in On the Trail of the JFK Assassins, offering one of the most comprehensive and authoritative examinations of the assassination of our 35th president. Included are new revelations, such as the theory that Lee Harvey Oswald was subjected to “mind control,” Russell’s personal encounters inside the KGB headquarters, and new information gleaned from an interview with Oswald’s widow.
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4 out of 5 stars
-
noooooooooooooooo!
- De JSR1972 en 10-03-18
De: Dick Russell
-
The Codebreakers of Bletchley Park
- The Secret Intelligence Station That Helped Defeat the Nazis
- De: Dermot Turing
- Narrado por: Richard Trinder
- Duración: 7 h y 47 m
- Versión completa
-
General4.5 out of 5 stars 12
-
Narración:4.5 out of 5 stars 7
-
Historia5 out of 5 stars 7
At Bletchley Park, some of Britain's most talented mathematicians, linguists, and intellectuals were assembled to break Nazi codes. It was kept secret for nearly 30 years, but we have now come to realize the crucial role that these codebreakers played in the Allied victory in World War II. Written by Dermot Turing - the nephew of famous codebreaker Alan Turing - this account provides unique insight into the behind-the-scenes action at Bletchley Park. This book brings to life the stories of the men and women who toiled day and night to crack the seemingly unbreakable enigma code.
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4 out of 5 stars
-
concise and useful
- De Amazon Customer en 11-30-24
De: Dermot Turing
-
Alan Turing
- A Life From Beginning to End (World War 2 Biographies, Book 7)
- De: Hourly History
- Narrado por: Matthew J. Chandler-Smith
- Duración: 56 m
- Versión completa
-
General4.5 out of 5 stars 12
-
Narración:4.5 out of 5 stars 10
-
Historia4.5 out of 5 stars 10
Alan Turing had a radical and ingenious mind. He is considered one of the fathers of artificial intelligence, and his theories on this matter range from purely mechanical to almost spiritual. During World War II, his decryption of the Nazis’ Enigma codes proved vital for the Allied victory over the Axis powers. Turing’s fingerprints are everywhere, and yet his own country for quite some time failed to acknowledge it.
De: Hourly History
-
When Einstein Walked with Gödel
- Excursions to the Edge of Thought
- De: Jim Holt
- Narrado por: David Stifel
- Duración: 15 h y 19 m
- Versión completa
-
General4.5 out of 5 stars 641
-
Narración:4.5 out of 5 stars 543
-
Historia4.5 out of 5 stars 545
Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot.
-
5 out of 5 stars
-
A good overview of scientific theory
- De MJ Walters en 09-11-18
De: Jim Holt
-
Alan Turing
- Unlocking The Enigma
- De: David Boyle
- Narrado por: Barnaby Edwards
- Duración: 2 h y 3 m
- Versión completa
-
General4 out of 5 stars 408
-
Narración:4.5 out of 5 stars 338
-
Historia4.5 out of 5 stars 334
Alan Mathison Turing. Mathematician, philosopher, codebreaker, a founder of computer science, and the father of Artificial Intelligence, Turing was one of the most original thinkers of the last century - and the man whose work helped create the computer-driven world we now inhabit. But he was also an enigmatic figure, deeply reticent yet also strikingly naive. Turing's openness about his homosexuality at a time when it was an imprisonable offense ultimately led to his untimely death at the age of only 41.
-
5 out of 5 stars
-
Fascinating look at a fascinating man
- De kwestrope en 10-16-18
De: David Boyle
-
Prof
- Alan Turing Decoded
- De: Dermot Turing
- Narrado por: Chris Courtenay
- Duración: 10 h y 23 m
- Versión completa
-
General4.5 out of 5 stars 15
-
Narración:5 out of 5 stars 14
-
Historia5 out of 5 stars 14
Alan Turing was an extraordinary man who crammed into a life of only 42 years the careers of mathematician, codebreaker, computer scientist and biologist. He is widely regarded as a war hero grossly mistreated by his unappreciative country, and it has become hard to disentangle the real man from the story. It is easy to cast him as a misfit, the stereotypical professor.
-
5 out of 5 stars
-
Alan Turing Bio
- De G. Elliot en 01-08-19
De: Dermot Turing
-
On the Trail of the JFK Assassins
- A Groundbreaking Look at America's Most Infamous Conspiracy
- De: Dick Russell
- Narrado por: Sean Runnette
- Duración: 15 h y 31 m
- Versión completa
-
General4.5 out of 5 stars 89
-
Narración:4.5 out of 5 stars 78
-
Historia4.5 out of 5 stars 79
Using newly declassified information, Dick Russell builds on three decades of painstaking research in On the Trail of the JFK Assassins, offering one of the most comprehensive and authoritative examinations of the assassination of our 35th president. Included are new revelations, such as the theory that Lee Harvey Oswald was subjected to “mind control,” Russell’s personal encounters inside the KGB headquarters, and new information gleaned from an interview with Oswald’s widow.
-
4 out of 5 stars
-
noooooooooooooooo!
- De JSR1972 en 10-03-18
De: Dick Russell
-
The Codebreakers of Bletchley Park
- The Secret Intelligence Station That Helped Defeat the Nazis
- De: Dermot Turing
- Narrado por: Richard Trinder
- Duración: 7 h y 47 m
- Versión completa
-
General4.5 out of 5 stars 12
-
Narración:4.5 out of 5 stars 7
-
Historia5 out of 5 stars 7
At Bletchley Park, some of Britain's most talented mathematicians, linguists, and intellectuals were assembled to break Nazi codes. It was kept secret for nearly 30 years, but we have now come to realize the crucial role that these codebreakers played in the Allied victory in World War II. Written by Dermot Turing - the nephew of famous codebreaker Alan Turing - this account provides unique insight into the behind-the-scenes action at Bletchley Park. This book brings to life the stories of the men and women who toiled day and night to crack the seemingly unbreakable enigma code.
-
4 out of 5 stars
-
concise and useful
- De Amazon Customer en 11-30-24
De: Dermot Turing
-
Alan Turing
- A Life From Beginning to End (World War 2 Biographies, Book 7)
- De: Hourly History
- Narrado por: Matthew J. Chandler-Smith
- Duración: 56 m
- Versión completa
-
General4.5 out of 5 stars 12
-
Narración:4.5 out of 5 stars 10
-
Historia4.5 out of 5 stars 10
Alan Turing had a radical and ingenious mind. He is considered one of the fathers of artificial intelligence, and his theories on this matter range from purely mechanical to almost spiritual. During World War II, his decryption of the Nazis’ Enigma codes proved vital for the Allied victory over the Axis powers. Turing’s fingerprints are everywhere, and yet his own country for quite some time failed to acknowledge it.
De: Hourly History
-
When Einstein Walked with Gödel
- Excursions to the Edge of Thought
- De: Jim Holt
- Narrado por: David Stifel
- Duración: 15 h y 19 m
- Versión completa
-
General4.5 out of 5 stars 641
-
Narración:4.5 out of 5 stars 543
-
Historia4.5 out of 5 stars 545
Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot.
-
5 out of 5 stars
-
A good overview of scientific theory
- De MJ Walters en 09-11-18
De: Jim Holt
Lo que los oyentes dicen sobre The Man Who Knew Too Much
Calificaciones medias de los clientesReseñas - Selecciona las pestañas a continuación para cambiar el origen de las reseñas.
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Total5 out of 5 stars
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Ejecución5 out of 5 stars
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Historia5 out of 5 stars
- Ryan Brooks
- 06-16-23
Coming to age in Mathematics and being gay
If you know anyone into mathematics or computers and is homosexual, you might say your nerdy friend but it goes deeper than just this concept... I highly suggest they learn about Alan Turing and his actual story. I feel if I read this book when I was in high school or early college, I would have learned so much about myself earlier. David Leavitt is an amazing author and Richard Powers narration has just enough flair to keep all the 1s and 0s from putting me asleep.
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Total4 out of 5 stars
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Ejecución5 out of 5 stars
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Historia3 out of 5 stars
- CP
- 09-11-15
good book
very educational. Glossed through a lot at end if his life, but his contribution was interesting
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Total1 out of 5 stars
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Ejecución1 out of 5 stars
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Historia1 out of 5 stars
- Dan Fritze
- 04-01-22
terrible book I'd like to return it
Gobaly goop. I couldn't finish it. if you like listening to incomprehensible streams of numbers...
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esto le resultó útil a 1 persona
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Total1 out of 5 stars
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Ejecución1 out of 5 stars
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Historia1 out of 5 stars
- Rush D. Austin
- 07-17-14
First Audible Book I Returned
Any additional comments?
Professional programmer since 1999 and I had very high hopes for this book. Could not abide the long passages where the narrator was saying, "..zero, zero, zero, zero, zero, zero, zero, zero, zero, zero, zero, zero, zero, nine, nine, nine, nine, nine, nine, nine, nine, nine, nine, nine, nine, nine, nine, nine.." to describe the mathematical logic.
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esto le resultó útil a 10 personas