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1Sautoy, M. du: What we cannot know.
London : 4th Estate, 2016. 440 S.
Abstract: Britain's most famous mathematician takes us to the edge of knowledge to show us what we cannot know. Science is king. Every week, headlines announce new breakthroughs in our understanding of the universe, new technologies that will transform our environment, new medical advances that will extend our lives. Science is giving us unprecedented insight into some of the big questions that have challenged humanity ever since we've been able to formulate those questions. Where did we come from? What is the ultimate destiny of the universe? What are the building blocks of the physical world? What is consciousness? This book asks us to rein in this unbridled enthusiasm for the power of science. Marcus du Sautoy explores the limits of human knowledge, to probe whether there is anything we truly cannot know
Inhalt: To be published in America by Viking Penguin in April 2017.
Anmerkung: Rez. in: Economist vom Jun 18.06.2016 [http://www.economist.com/news/books-and-arts/21700611-circle-circle]: "Everyone by nature desires to know," wrote Aristotle more than 2,000 years ago. But are there limits to what human beings can know? This is the question that Marcus du Sautoy, the British mathematician who succeeeded Richard Dawkins as the Simonyi professor for the public understanding of science at Oxford University, explores in "What We Cannot Know", his fascinating book on the limits of scientific knowledge. As Mr du Sautoy argues, this is a golden age of scientific knowledge. Remarkable achievements stretch across the sciences, from the Large Hadron Collider and the sequencing of the human genome to the proof of Fermat's Last Theorem. And the rate of progress is accelerating: the number of scientific publications has doubled every nine years since the second world war. But even bigger challenges await. Can cancer be cured? Ageing beaten? Is there a "Theory of Everything" that will include all of physics? Can we know it all? One limit to people's knowledge is practical. In theory, if you throw a die, Newton's laws of motion make it possible to predict what number will come up. But the calculations are too long to be practicable. What is more, many natural systems, such as the weather, are "chaotic" or sensitive to small changes: a tiny nudge now can lead to vastly different behaviour later. Since people cannot measure with complete accuracy, they can't forecast far into the future. The problem was memorably articulated by Edward Lorenz, an American scientist, in 1972 in a famous paper called "Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" ; Even if the future cannot be predicted, people can still hope to uncover the laws of physics. As Stephen Hawking wrote in his 1988 bestseller "A Brief History of Time", "I still believe there are grounds for cautious optimism that we may be near the end of the search for the ultimate laws of nature." But how can people know when they have got there? They have been wrong before: Lord Kelvin, a great physicist, confidently announced in 1900: "There is nothing new to be discovered in physics now." Just a few years later, physics was upended by the new theories of relativity and quantum physics. Quantum physics presents particular limits on human knowledge, as it suggests that there is a basic randomness or uncertainty in the universe. For example, electrons exist as a "wave function", smeared out across space, and do not have a definite position until you observe them (which "collapses" the wave function). At the same time there seems to be an absolute limit on how much people can know. This is quantified by Heisenberg's Uncertainty Principle, which says that there is a trade-off between knowing the position and momentum of a particle. So the more you know about where an electron is, the less you know about which way it is going. Even scientists find this weird. As Niels Bohr, a Danish physicist, said: "If quantum physics hasn't profoundly shocked you, you haven't understood it yet." ; Mr du Sautoy probes these limits throughout his book. He talks about the origins of the universe in the Big Bang, the discovery of subatomic particles (starting with the positron in the 1930s) and the disappearance of matter and information into black holes. There are also fascinating details about the human brain, where his discussion ranges from the structure of neurons to the problem of consciousness. Eventually, he turns to his own field of mathematics. If people cannot know everything about the physical world, then perhaps they can at least rely on mathematical truth? But even here there are limits. Mathematicians have shown that some theorems have proofs so long that it would take the lifetime of the universe to finish them. And no mathematical system is complete: as Kurt Gödel, an Austrian logician, showed in the 1930s, there are always true statements that the system is not strong enough to prove. Where does this leave us? In the end, Mr du Sautoy has an optimistic message. There may be things people will never know, but they don't know what they are. And ultimately, it is the desire to know the unknown that inspires humankind's search for knowledge in the first place."
Wissenschaftsfach: Naturwissenschaften ; Wissenschaftstheorie
2Sautoy, M. du: Alle Symmetrien der Welt.
In: Spektrum der Wissenschaft. 2008, H.5, S.17-20.
Abstract: In diesem Jahr erhalten John G. Thompson und Jacques Tits den Abel-Preis für grundlegende Arbeiten zur Gruppentheorie, die in einem Mammutwerk gipfelten: der Klassifikation der endlichen einfachen Gruppen.
Inhalt: Ein Beitrag mit Beispielen zur Vorhersage von neuen Strukturen aus Ordnungsprinzipien (hier die Klassifikation der endlichen einfachen Gruppen, Feit-Thompson; Abel-Preis 2008 für Thompson und Tits)