Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Atoms and the void
- 2 Sets
- 3 Gödel, Turing, and friends
- 4 Minds and machines
- 5 Paleocomplexity
- 6 P, NP, and friends
- 7 Randomness
- 8 Crypto
- 9 Quantum
- 10 Quantum computing
- 11 Penrose
- 12 Decoherence and hidden variables
- 13 Proofs
- 14 How big are quantum states?
- 15 Skepticism of quantum computing
- 16 Learning
- 17 Interactive proofs, circuit lower bounds, and more
- 18 Fun with the Anthropic Principle1
- 19 Free will
- 20 Time travel
- 21 Cosmology and complexity
- 22 Ask me anything
- Index
- References
5 - Paleocomplexity
Published online by Cambridge University Press: 05 April 2013
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Atoms and the void
- 2 Sets
- 3 Gödel, Turing, and friends
- 4 Minds and machines
- 5 Paleocomplexity
- 6 P, NP, and friends
- 7 Randomness
- 8 Crypto
- 9 Quantum
- 10 Quantum computing
- 11 Penrose
- 12 Decoherence and hidden variables
- 13 Proofs
- 14 How big are quantum states?
- 15 Skepticism of quantum computing
- 16 Learning
- 17 Interactive proofs, circuit lower bounds, and more
- 18 Fun with the Anthropic Principle1
- 19 Free will
- 20 Time travel
- 21 Cosmology and complexity
- 22 Ask me anything
- Index
- References
Summary
By any objective standard, the theory of computational complexity ranks as one of the greatest intellectual achievements of humankind – along with fire, the wheel, and computability theory. That it isn't taught in high schools is really just an accident of history. In any case, we'll certainly need complexity theory for everything else we're going to do in this book, which is why the next five or six chapters will be devoted to it. So before we dive in, let's step back and pontificate about where we're going.
What I’ve been trying to do is show you the conceptual underpinnings of the universe, before quantum mechanics comes on the scene. The amazing thing about quantum mechanics is that, despite being a grubby empirical discovery, it changes some of the underpinnings! Others it doesn't change, and others it's not so clear whether it changes them or not. But if we want to debate how things are changed by quantum mechanics, then we'd better understand what they looked like before quantum mechanics.
1950s: Late Turingzoic
1960s: Dawn of the Asymptotic Age
1971: The Cook–Levin Asteroid; extinction of the Diagonalosaurs
Early 1970s: The Karpian Explosion
1978: Early Cryptozoic
1980s: Randomaceous Era
1993: Eruption of Mt Razborudich; extinction of the Combinataurs
1994: Invasion of the Quantodactyls
Mid-1990s to present: Derandomaceous Era
- Type
- Chapter
- Information
- Quantum Computing since Democritus , pp. 44 - 53Publisher: Cambridge University PressPrint publication year: 2013