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The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example - but is spacetime really continuous? Throughout the history of science, many have felt that the continuum model is an unphysical idealization, and that spacetime should be thought of as 'quantized' at the smallest of scales. Combining novel conceptual analysis, a fresh historical perspective, and concrete physical examples, this unique book tells the story of the search for the fundamental unit of length in modern physics, from early classical...

Novel conceptual analysis, fresh historical perspectives, and concrete physical examples illuminate one of the most thought-provoking topics in physics.

In quantum computing, where algorithms exist that can solve computational problems more efficiently than any known classical algorithms, the elimination of errors that result from external disturbances or from imperfect gates has become the "holy grail", and a worldwide quest for a large scale fault-tolerant, and computationally superior, quantum computer is currently taking place. Optimists rely on the premise that, under a certain threshold of errors, an arbitrary long fault-tolerant quantum computation can be achieved with only moderate (i.e., at most polynomial) overhead in computational...