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Galileo:

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 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.

Book Outline Topics

• Chapter 1: Flight of the Swallows
  • Introduction to motion and trajectories
• Chapter 2: A New Scientist
  • Galileo’s life
• 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

What “Galileo Unbound” is about:

This book isn’t a traditional biography of Galileo, nor is it strictly a history of classical dynamics. Instead, I have used Galileo’s foundational work on the law of free fall and the parabolic trajectory as a starting point to trace the evolution of the concept of trajectories and dynamical systems through many branches of science, leading to modern-day applications in fields far beyond classical physics.

Main Arguments and Themes:

1. The Enduring Power of Trajectories: In this book, I argue that the concept of a “trajectory” – a path through space and time – is a remarkably persistent and powerful idea that has evolved and expanded in scope since Galileo. From the simple parabolic path of a projectile, this concept has been generalized to describe complex phenomena.
2. Expanding Dimensions and Abstraction: A central theme is how the “space” in which these trajectories are described has continually expanded in dimension and abstraction.
   • Galileo/Newton: Beginning with simple 2D or 3D physical space.
   • Lagrange/Hamilton/Poincaré: Phase space, where position and momentum (or other generalized coordinates) define a point in a higher-dimensional space, providing a complete description of the system’s state. This is crucial for understanding modern dynamics and chaos.
   • Einstein: Spacetime, where geometry itself becomes the “cause” of motion.
   • Quantum Mechanics: Paths become probabilistic and can even be “many-worlds” trajectories.
   • Modern Applications: The book extends the idea of trajectories to highly abstract, multi-dimensional “spaces” in fields like:
     • Genetics/Evolutionary Biology: Tracing “evolutionary drift” through a genetic landscape.
     • Big Data/Complex Systems: Describing the “trajectory” of a system through a high-dimensional state space, like a person’s health state defined by thousands of biological markers.
     • Quantum Computing: Where quantum particles can explore “many worlds” or paths simultaneously.
3. The Quest for Patterns in Chaos: Despite the increasing complexity and sometimes chaotic nature of these systems, Nolte highlights the continuous human endeavor to find patterns, predict behavior, and “tame” these dynamics. He shows how the drive to understand and predict motion, which started with Galileo, remains a fundamental impulse in science today.
4. Connecting Seemingly Disparate Fields: I believe the book’s most compelling aspect is how it draws common threads between seemingly unrelated scientific disciplines. I show how the underlying mathematical and conceptual frameworks of dynamics, rooted in Galileo’s initial insights, unite fields as diverse as celestial mechanics, quantum physics, biology, and data science.

(Buy Galileo Unbound at Amazon Books)

Why Galileo Unbound?

• Unique Perspective: It offers a fresh and broad perspective on the history of dynamics, connecting classical mechanics to cutting-edge research in complex systems.
• Narrative Style: I try to adopt an engaging and accessible writing style, making complex scientific and historical concepts understandable to a broad audience without sacrificing technical depth where needed.
• Author’s Expertise: As a physicist with a background in interferometry and optics, I bring a strong scientific foundation to this historical narrative.
• Modern Relevance: It explicitly links the historical development of dynamics to contemporary challenges and fields, demonstrating the ongoing utility and evolution of these fundamental ideas.

“Galileo Unbound” offers a “path across life, the universe and everything” by tracing the profound and evolving concept of a “trajectory” from its simple beginnings with Galileo to its highly abstract and multi-dimensional manifestations in modern science. If you’re interested in how foundational ideas in physics continue to shape our understanding of the world in unexpected ways, then this is the read you want.