Book Outline Topics

• Chapter 1: Flight of the Swallows
  • Introduction to motion and trajectories
• Chapter 2: A New Scientist
  • Galileo’s Biography
• Chapter 3: Galileo’s Trajectory
  • His study of the science of motion
  • Publication of Two New Sciences
• Chapter 4: On the Shoulders of Giants
  • Newton’s Principia
  • The Principle of Least Action: Maupertuis, Euler, and Voltaire
  • Lagrange and his new dynamics
• Chapter 5: Geometry on my Mind
  • Differential geometry of Gauss and Riemann
  • Vector spaces rom Grassmann to Hilbert
  • Fractals: Cantor, Weierstrass, Hausdorff
• Chapter 6: The Tangled Tale of Phase Space
  • Liouville and Jacobi
  • Entropy and Chaos: Clausius, Boltzmann and Poincare
  • Phase Space: Gibbs and Ehrenfest
• Chapter 7: The Lens of Gravity
  • Einstein and the warping of light
  • Black Holes: Schwarzschild’s radius
  • Oppenheimer versus Wheeler
  • The Golden Age of General Relativity
• Chapter 8: On the Quantum Footpath
  • Heisenberg’s matrix mechanics
  • Schrödinger’s wave mechanics
  • Bohr’s complementarity
  • Einstein and entanglement
  • Feynman and the path-integral formulation of quantum
• Chapter 9: From Butterflies to Hurricanes
  • KAM theory of stability of the solar system
  • Steven Smale’s horseshoe
  • Lorenz’ butterfly: strange attractor
  • Feigenbaum and chaos
• Chapter 10: Darwin in the Clockworks
  • Charles Darwin and the origin of species
  • Fibonnacci’s bees
  • Economic dynamics
  • Mendel and the landscapes of life
  • Evolutionary dynamics
  • Linus Pauling’s molecular clock and Dawkins meme
• Chapter 11: The Measure of Life
  • Huygens, von Helmholtz and Rayleigh oscillators
  • Neurodynamics
  • Euler and the Seven Bridges of Königsberg
  • Network theory: Strogatz and Barabasi

In June of 1633 Galileo was found guilty of heresy and sentenced to house arrest for what remained of his life. He was a renaissance Prometheus, bound for giving knowledge to humanity. With little to do, and allowed few visitors, he at last had the uninterrupted time to finish his life’s labor. When Two New Sciences was published in 1638, it contained the seeds of the science of motion that would mature into a grand and abstract vision that permeates all science today. In this way, Galileo was unbound, not by Hercules, but by his own hand as he penned the introduction to his work:

. . . what I consider more important, there have been opened up to this vast and most excellent science, of which my work is merely the beginning, ways and means by which other minds more acute than mine will explore its remote corners.

            Galileo Galilei (1638) Two New Sciences

Galileo Unbound (Oxford University Press, 2018) explores the continuous thread from Galileo’s discovery of the parabolic trajectory to modern dynamics and complex systems. It is a history of expanding dimension and increasing abstraction, until today we speak of entangled quantum particles moving among many worlds, and we envision our lives as trajectories through spaces of thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets. Galileo laid the foundation upon which Newton built a theory of dynamics that could capture the trajectory of the moon through space using the same physics that controlled the flight of a cannon ball. Late in the nineteenth-century, concepts of motion expanded into multiple dimensions, and in the 20th century geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, causing light rays to bend past the Sun. Possibly more radical was Feynman’s dilemma of quantum particles taking all paths at once—setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant—the need to track ever more complex changes and to capture their essence—to find patterns in the chaos as we try to predict and control our world. Today’s ideas of motion go far beyond the parabolic trajectory, but even Galileo might recognize the common thread that winds through all these motions, drawing them together into a unified view that gives us the power to see, at least a little, through the mists shrouding the future.