In 1936, when he was just twenty-four years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing's Vision, Chris Bernhardt explains the theory, Turing's most important contribution, for the general reader. Bernhardt argues that the strength of Turing's theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, “The sheer simplicity of the theory's foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory.” Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turing's theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing's later work, and the birth of the modern computer.
In the paper, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computer's ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing's ideas, Bernhardt examines three well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing's problem concerning computable numbers.
"UltraMarathon Man: 50 Marathons - 50 States - 50 Days", a Journeyfilm documentary, follows Dean’s incredible step-by-step journey across the country.
Ultrarunning legend Dean Karnazes has run 262 miles-the equivalent of ten marathons-without rest. He has run over mountains, across Death Valley, and to the South Pole-and is probably the first person to eat an entire pizza while running. With an insight, candor, and humor rarely seen in sports memoirs (and written without the aid of a ghostwriter or cowriter), Ultramarathon Man has inspired tens of thousands of people-nonrunners and runners alike-to push themselves beyond their comfort zones and be reminded of "what it feels like to be truly alive," says Sam Fussell, author of Muscle.
Ultramarathon Man answers the questions Karnazes is continually asked:
- Why do you do it?
- How do you do it?
- Are you insane?
And in the new paperback edition, Karnazes answers the two questions he was most asked on his book tour:
- What, exactly, do you eat?
- How do you train to stay in such good shape?
On June 3rd, 2017, Alex Honnold became the first person to free solo Yosemite's El Capitan—to scale the wall without rope, a partner, or any protective gear—completing what was described as "the greatest feat of pure rock climbing in the history of the sport" (National Geographic) and "one of the great athletic feats of any kind, ever" (New York Times). Already one of the most famous adventure athletes in the world, Honnold has now been hailed as "the greatest climber of all time" (Vertical magazine).
Alone on the Wall recounts the most astonishing achievements of Honnold’s extraordinary life and career, brimming with lessons on living fearlessly, taking risks, and maintaining focus even in the face of extreme danger. Now Honnold tells, for the first time and in his own words, the story of his 3 hours and 56 minutes on the sheer face of El Cap, which Outside called "the moon landing of free soloing…a generation-defining climb. Bad ass and beyond words…one of the pinnacle sporting moments of all time."