The Book of Numbers

Dr Peter Bentley is one of the most creative thinkers working in computer science today. He is Senior Research Fellow and College Teacher at the Department of Computer Science, University College London. He is known for his prolific research covering all aspects of Evolutionary Computation and Digital Biology. He is the author of the popular science book Digital Biology (Simon and Schuster USA), and editor of the books Evolutionary Design by Computers, Creative Evolutionary Systems and On Growth, Form and Computers. He is a regular contributor to programming on BBC Radio 4.

Chapter 0 - Much Ado About Nothing. The beginnings of counting and recognising number. Trade, warfare and reparation. Spoken numbers. Sticks and stones - early tally sticks. On the fingers of one hand - why we count in fives. Roman numerals and the invention of nothing. The Year Zero. Chapter 0.000000001 - Small is Beautiful. Rational numbers and Pythagoras. Fractions and trading. The decimal point. Buddha, tiny numbers, string theory and nanotechnology . Chapter 1 - All is One. The first number. The Philosopher's Stone and Feng Shui. Natural Numbers. Perfect Numbers. Amicable Numbers. Prime Numbers and the "Sieve of Eratosthenes". Euclid. Secure Primes. Fractionally One. Chapter v2 - Murdering Irrationals. Pythagoras and the murder of Hippasus. Greek geometry. The principles of formal mathematical proof. Religion and revolution. The development of Algebra. Fermat's last theorem. Euclidean geometry to non-Euclidean. Chapter ? - Golden Phi. The Fibonacci Series and the ratio between pairs. The application of Fibonacci to growth. The Strong Law of Small Numbers. The 'Golden Rectangle'. 'Surds' their convenient . Chapter 2 - Good and Even. Odd and Even numbers. The basis of the Binary arithmetic. How computers came into being,. Godel, Russell and Turing. Computability and inexpressible numbers. The breaking of the Enigma code. Chapter e - The Greatest Invention. The work of Isaac Newton on 'flux'. The invention of Calculus. The arguments. Archimedes: Differentiation and Integration. Mathematical functions. ex is the 'identity'. e. The logarithm. Napier and of the slide rule. Logarithmic spiral and Jacques Bernoull's gravestone. Chapter 3 - The Eternal Triangle. The importance of the triangle. The symbolism of the trinity. Tiling planes . Topology. Cubit equations and Omar Khayam. Polynomial equations. Graph theory and 'proof by computer'. The Mobius strip. Geometric solids . Chapter p - A Slice of Pi. Archimedes and his grave. The fundamental constant of geometry. Measuring the circle. Trigonometry, squaring the circle, and the helix. Galileo's pendulums. The Pisa experiment. Sine waves; frequencies, amplitudes, sound and music. Probability and Game theory. Quantum mechanics. Geometric solids of higher numbers of sides. Chapter 10 - Decimalisation. Before decimalisation. The Shephard shell story. The decimal system. Numbers versus numerals. Mathematical notation and Euler. Proof by induction. Sacred Tetractys. Ten - the very best number. Chapter 12a - Triskaidekaphobia. Numbers in society and in our minds. The unlucky number. Numerology and the power of numbers. Lucky and unlucky numbers. The Bible Code. Numerology and the growth of maths. Chapter 60. Now is the Hour. The Babylonian number system. Telling the time. Number theory. Prime factors and frequencies. Chapter 8 - The End of the Road? The origin of infinity. The fear of infinity. Cantor and the transfinite numbers. The 'Diagonalisation' argument . A reprise of Galileo's arguments and the 'countable infinite'. Infinite solutions in physics - black holes and the big bang. Chapter i - Imagine Something Complex. v-1 - 'i' the base of the Complex numbers. Taking numbers away from reality. From the number line to the number plane. Cartesian geometry. fractals and fractal dimensions. Euler's magical, impossible result, combining arithmetic, calculus, trigonometry, complex analysis and number - God's final word on the subject: eip + 1 = 0. Chaos theory, complexity and new forms of number behaviour.