Timelines in the History and Physics of Dynamics (with links to primary texts)

These timelines in the History of Dynamics are organized along the Chapters in Galileo Unbound (Oxford, 2018). The book is about the physics and history of dynamics including classical and quantum mechanics as well as general relativity and nonlinear dynamics (with a detour down evolutionary dynamics and game theory along the way). The first few chapters focus on Galileo, while the following chapters follow his legacy, as theories of motion became more abstract, eventually to encompass the evolution of species within the same theoretical framework as the orbit of photons around black holes.

Galileo: A New Scientist

Galileo Galilei was the first modern scientist, launching a new scientific method that superseded, after one and a half millennia, Aristotle’s physics.  Galileo’s career began with his studies of motion at the University of Pisa that were interrupted by his move to the University of Padua and his telescopic discoveries of mountains on the moon and the moons of Jupiter.  Galileo became the first rock star of science, and he used his fame to promote the ideas of Copernicus and the Sun-centered model of the solar system.  But he pushed too far when he lampooned the Pope.  Ironically, Galileo’s conviction for heresy and his sentence to house arrest for the remainder of his life gave him the free time to finally finish his work on the physics of motion, which he published in Two New Sciences in 1638.

1543 Copernicus dies, publishes posthumously De Revolutionibus

1564    Galileo born

1581    Enters University of Pisa

1585    Leaves Pisa without a degree

1586    Invents hydrostatic balance

1588    Receives lecturship in mathematics at Pisa

1592    Chair of mathematics at Univeristy of Padua

1595    Theory of the tides

1595    Invents military and geometric compass

1596    Le Meccaniche and the principle of horizontal inertia

1600    Bruno Giordano burned at the stake

1601    Death of Tycho Brahe

1609    Galileo constructs his first telescope, makes observations of the moon

1610    Galileo discovers 4 moons of Jupiter, Starry Messenger (Sidereus Nuncius), appointed chief philosopher and mathematician of the Duke of Tuscany, moves to Florence, observes Saturn, Venus goes through phases like the moon

1611    Galileo travels to Rome, inducted into the Lyncean Academy, name “telescope” is first used

1611    Scheiner discovers sunspots

1611    Galileo meets Barberini, a cardinal

1611 Johannes Kepler, Dioptrice

1613    Letters on sunspots published by Lincean Academy in Rome

1614    Galileo denounced from the pulpit

1615    (April) Bellarmine writes an essay against Coperinicus

1615    Galileo investigated by the Inquisition

1615    Writes Letter to Christina, but does not publish it

1615    (December) travels to Rome and stays at Tuscan embassy

1616    (January) Francesco Ingoli publishes essay against Copernicus

1616    (March) Decree against copernicanism

1616    Galileo publishes theory of tides, Galileo meets with Pope Paul V, Copernicus’ book is banned, Galileo warned not to support the Coperinican system, Galileo decides not to reply to Ingoli, Galileo proposes eclipses of Jupter’s moons to determine longitude at sea

1618    Three comets appear, Grassi gives a lecture not hostile to Galileo

1618    Galileo, through Mario Guiducci, publishes scathing attack on Grassi

1619    Jesuit Grassi (Sarsi) publishes attack on Galileo concerning 3 comets

1619    Marina Gamba dies, Galileo legitimizes his son Vinczenzio

1619 Kepler’s Laws, Epitome astronomiae Copernicanae.

1623    Barberini becomes Urban VIII, The Assayer published (response to Grassi)

1624    Galileo visits Rome and Urban VIII

1629    Birth of his grandson Galileo

1630    Death of Johanes Kepler

1632    Publication of the Dialogue Concerning the Two Chief World Systems, Galileo is indicted by the Inquisition (68 years old)

1633    (February) Travels to Rome

1633    Convicted, abjurs, house arrest in Rome, then Siena, then home to Arcetri

1638    Blind, publication of Two New Sciences

1642    Galileo dies (77 years old)

Galileo’s Trajectory

Galileo’s discovery of the law of fall and the parabolic trajectory began with early work on the physics of motion by predecessors like the Oxford Scholars, Tartaglia and the polymath Simon Stevin who dropped lead weights from the leaning tower of Delft three years before Galileo (may have) dropped lead weights from the leaning tower of Pisa.  The story of how Galileo developed his ideas of motion is described in the context of his studies of balls rolling on inclined plane and the surprising accuracy he achieved without access to modern timekeeping.

1583    Galileo Notices isochronism of the pendulum

1588    Receives lecturship in mathematics at Pisa

1589 – 1592  Work on projectile motion in Pisa

1592    Chair of mathematics at Univeristy of Padua

1596    Le Meccaniche and the principle of horizontal inertia

1600    Guidobaldo shares technique of colored ball

1602    Proves isochronism of the pendulum (experimentally)

1604    First experiments on uniformly accelerated motion

1604    Wrote to Scarpi about the law of fall (s ≈ t2)

1607-1608  Identified trajectory as parabolic

1609    Velocity proportional to time

1632    Publication of the Dialogue Concerning the Two Chief World Systems, Galileo is indicted by the Inquisition (68 years old)

1636    Letter to Christina published in Augsburg in Latin and Italian

1638    Blind, publication of Two New Sciences

1641    Invented pendulum clock (in theory)

1642    Dies (77 years old)

On the Shoulders of Giants

Galileo’s parabolic trajectory launched a new approach to physics that was taken up by a new generation of scientists like Isaac Newton, Robert Hooke and Edmund Halley.  The English Newtonian tradition was adopted by ambitious French iconoclasts who championed Newton over their own Descartes.  Chief among these was Pierre Maupertuis, whose principle of least action was developed by Leonhard Euler and Joseph Lagrange into a rigorous new science of dynamics.  Along the way, Maupertuis became embroiled in a famous dispute that entangled the King of Prussia as well as the volatile Voltaire who was mourning the death of his mistress Emilie du Chatelet, the lone female French physicist of the eighteenth century.

1644    Descartes’ vortex theory of gravitation

1662    Fermat’s principle

1669 – 1690    Huygens expands on Descartes’ vortex theory

1687 Newton’s Principia

1698    Maupertuis born

1729    Maupertuis entered University in Basel.  Studied under Johann Bernoulli

1736    Euler publishes Mechanica sive motus scientia analytice exposita

1737   Maupertuis report on expedition to Lapland.  Earth is oblate.  Attacks Cassini.

1744    Maupertuis Principle of Least Action.  Euler Principle of Least Action.

1745    Maupertuis becomes president of Berlin Academy.  Paris Academy cancels his membership after a campaign against him by Cassini.

1746    Maupertuis principle of Least Action for mass

1751    Samuel König disputes Maupertuis’ priority

1756    Cassini dies.  Maupertuis reinstated in the French Academy

1759    Maupertuis dies

1759    du Chatelet’s French translation of Newton’s Principia published posthumously

1760    Euler 3-body problem (two fixed centers and coplanar third body)

1760-1761 Lagrange, Variational calculus (J. L. Lagrange, “Essai d’une nouvelle méthod pour dEeterminer les maxima et lest minima des formules intégrales indéfinies,” Miscellanea Teurinensia, (1760-1761))

1762    Beginning of the reign of Catherine the Great of Russia

1763    Euler colinear 3-body problem

1765    Euler publishes Theoria motus corporum solidorum on rotational mechanics

1766    Euler returns to St. Petersburg

1766    Lagrange arrives in Berlin

1772    Lagrange equilateral 3-body problem, Essai sur le problème des trois corps, 1772, Oeuvres tome 6

1775    Beginning of the American War of Independence

1776    Adam Smith Wealth of Nations

1781    William Herschel discovers Uranus

1783    Euler dies in St. Petersburg

1787    United States Constitution written

1787    Lagrange moves from Berlin to Paris

1788    Lagrange, Méchanique analytique

1789    Beginning of the French Revolution

1799    Pierre-Simon Laplace Mécanique Céleste (1799-1825)

Geometry on My Mind

This history of modern geometry focuses on the topics that provided the foundation for the new visualization of physics.  It begins with Carl Gauss and Bernhard Riemann, who redefined geometry and identified the importance of curvature for physics.  Vector spaces, developed by Hermann Grassmann, Giuseppe Peano and David Hilbert, are examples of the kinds of abstract new spaces that are so important for modern physics, such as Hilbert space for quantum mechanics.  Fractal geometry developed by Felix Hausdorff later provided the geometric language needed to solve problems in chaos theory.

1629    Fermat described higher-dim loci

1637    Descarte’s Geometry

1649    van Schooten’s commentary on Descartes Geometry

1694    Leibniz uses word “coordinate” in its modern usage

1697    Johann Bernoulli shortest distance between two points on convex surface

1732    Euler geodesic equations for implicit surfaces

1748    Euler defines modern usage of function

1801    Gauss calculates orbit of Ceres

1807    Fourier analysis (published in 1822(

1807    Gauss arrives in Göttingen

1827    Karl Gauss establishes differential geometry of curved surfaces, Disquisitiones generales circa superficies curvas

1830    Bolyai and Lobachevsky publish on hyperbolic geometry

1834    Jacobi n-fold integrals and volumes of n-dim spheres

1836    Liouville-Sturm theorem

1838    Liouville’s theorem

1841    Jacobi determinants

1843    Arthur Cayley systems of n-variables

1843    Hamilton discovers quaternions

1844    Hermann Grassman n-dim vector spaces, Die Lineale Ausdehnungslehr

1846    Julius Plücker System der Geometrie des Raumes in neuer analytischer Behandlungsweise

1848 Jacobi Vorlesungen über Dynamik

1848    “Vector” coined by Hamilton

1854    Riemann’s habilitation lecture

1861    Riemann n-dim solution of heat conduction

1868    Publication of Riemann’s Habilitation

1869    Christoffel and Lipschitz work on multiple dimensional analysis

1871    Betti refers to the n-ply of numbers as a “space”.

1871    Klein publishes on non-euclidean geometry

1872 Boltzmann distribution

1872    Jordan Essay on the geometry of n-dimensions

1872    Felix Klein’s “Erlangen Programme”

1872    Weierstrass’ Monster

1872    Dedekind cut

1872    Cantor paper on irrational numbers

1872    Cantor meets Dedekind

1872 Lipschitz derives mechanical motion as a geodesic on a manifold

1874    Cantor beginning of set theory

1877    Cantor one-to-one correspondence between the line and n-dimensional space

1881    Gibbs codifies vector analysis

1883    Cantor set and staircase Grundlagen einer allgemeinen Mannigfaltigkeitslehre

1884    Abbott publishes Flatland

1887    Peano vector methods in differential geometry

1890    Peano space filling curve

1891    Hilbert space filling curve

1887    Darboux vol. 2 treats dynamics as a point in d-dimensional space.  Applies concepts of geodesics for trajectories.

1898    Ricci-Curbastro Lesons on the Theory of Surfaces

1902    Lebesgue integral

1904    Hilbert studies integral equations

1904    von Koch snowflake

1906    Frechet thesis on square summable sequences as infinite dimensional space

1908    Schmidt Geometry in a Function Space

1910    Brouwer proof of dimensional invariance

1913    Hilbert space named by Riesz

1914    Hilbert space used by Hausdorff

1915    Sierpinski fractal triangle

1918    Hausdorff non-integer dimensions

1918    Weyl’s book Space, Time, Matter

1918    Fatou and Julia fractals

1920    Banach space

1927    von Neumann axiomatic form of Hilbert Space

1935    Frechet full form of Hilbert Space

1967    Mandelbrot coast of Britain

1982    Mandelbrot’s book The Fractal Geometry of Nature

The Tangled Tale of Phase Space

Phase space is the central visualization tool used today to study complex systems.  The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy.  The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system.  Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.

1804    Jacobi born (1904 – 1851) in Potsdam

1804    Napoleon I Emperor of France

1806    William Rowan Hamilton born (1805 – 1865)

1807    Thomas Young describes “Energy” in his Course on Natural Philosophy (Vol. 1 and Vol. 2)

1808    Bethoven performs his Fifth Symphony

1809    Joseph Liouville born (1809 – 1882)

1821    Hermann Ludwig Ferdinand von Helmholtz born (1821 – 1894)

1824    Carnot published Reflections on the Motive Power of Fire

1834    Jacobi n-fold integrals and volumes of n-dim spheres

1834-1835       Hamilton publishes his principle (1834, 1835).

1836    Liouville-Sturm theorem

1837    Queen Victoria begins her reign as Queen of England

1838    Liouville develops his theorem on products of n differentials satisfying certain first-order differential equations.  This becomes the classic reference to Liouville’s Theorem.

1847    Helmholtz  Conservation of Energy (force)

1849    Thomson makes first use of “Energy” (From reading Thomas Young’s lecture notes)

1850    Clausius establishes First law of Thermodynamics: Internal energy. Second law:  Heat cannot flow unaided from cold to hot.  Not explicitly stated as first and second laws

1851    Thomson names Clausius’ First and Second laws of Thermodynamics

1852    Thomson describes general dissipation of the universe (“energy” used in title)

1854    Thomson defined absolute temperature.  First mathematical statement of 2nd law.  Restricted to reversible processes

1854    Clausius stated Second Law of Thermodynamics as inequality

1857    Clausius constructs kinetic theory, Mean molecular speeds

1858    Clausius defines mean free path, Molecules have finite size. Clausius assumed that all molecules had the same speed

1860    Maxwell publishes first paper on kinetic theory. Distribution of speeds. Derivation of gas transport properties

1865    Loschmidt size of molecules

1865    Clausius names entropy

1868    Boltzmann adds (Boltzmann) factor to Maxwell distribution

1872    Boltzmann transport equation and H-theorem

1876    Loschmidt reversibility paradox

1877    Boltzmann  S = k logW

1890    Poincare: Recurrence Theorem. Recurrence paradox with Second Law (1893)

1896    Zermelo criticizes Boltzmann

1896    Boltzmann posits direction of time to save his H-theorem

1898    Boltzmann Vorlesungen über Gas Theorie

1905    Boltzmann kinetic theory of matter in Encyklopädie der mathematischen Wissenschaften

1906    Boltzmann dies

1910    Paul Hertz uses “Phase Space” (Phasenraum)

1911    Ehrenfest’s article in Encyklopädie der mathematischen Wissenschaften

1913    A. Rosenthal writes the first paper using the phrase “phasenraum”, combining the work of Boltzmann and Poincaré. “Beweis der Unmöglichkeit ergodischer Gassysteme” (Ann. D. Physik, 42, 796 (1913)

1913    Plancheral, “Beweis der Unmöglichkeit ergodischer mechanischer Systeme” (Ann. D. Physik, 42, 1061 (1913).  Also uses “Phasenraum”.

The Lens of Gravity

Gravity provided the backdrop for one of the most important paradigm shifts in the history of physics.  Prior to Albert Einstein’s general theory of relativity, trajectories were paths described by geometry.  After the theory of general relativity, trajectories are paths caused by geometry.  This chapter explains how Einstein arrived at his theory of gravity, relying on the space-time geometry of Hermann Minkowski, whose work he had originally harshly criticized.  The confirmation of Einstein’s theory was one of the dramatic high points in 20th century history of physics when Arthur Eddington journeyed to an island off the coast of Africa to observe stellar deflections during a solar eclipse.  If Galileo was the first rock star of physics, then Einstein was the first worldwide rock star of science.

1697    Johann Bernoulli was first to find solution to shortest path between two points on a curved surface (1697).

1728    Euler found the geodesic equation.

1783    The pair 40 Eridani B/C was discovered by William Herschel on 31 January

1783    John Michell explains infalling object would travel faster than speed of light

1796    Laplace describes “dark stars” in Exposition du system du Monde

1827    The first orbit of a binary star computed by Félix Savary for the orbit of Xi Ursae Majoris.

1827    Gauss curvature Theoriem Egregum

1844    Bessel notices periodic displacement of Sirius with period of half a century

1844    The name “geodesic line” is attributed to Liouville.

1845    Buys Ballot used musicians with absolute pitch for the first experimental verification of the Doppler effect

1854    Riemann’s habilitationsschrift

1862    Discovery of Sirius B (a white dwarf)

1868    Darboux suggested motions in n-dimensions

1872    Lipshitz first to apply Riemannian geometry to the principle of least action.

1895    Hilbert arrives in Göttingen

1902    Minkowski arrives in Göttingen

1905    Einstein’s miracle year

1906    Poincaré describes Lorentz transformations as rotations in 4D

1907    Einstein has “happiest thought” in November

1907    Einstein’s relativity review in Jahrbuch

1908    Minkowski’s Space and Time lecture

1908    Einstein appointed to unpaid position at University of Bern

1909    Minkowski dies

1909    Einstein appointed associate professor of theoretical physics at U of Zürich

1910    40 Eridani B was discobered to be of spectral type A (white dwarf)

1910    Size and mass of Sirius B determined (heavy and small)

1911    Laue publishes first textbook on relativity theory

1911    Einstein accepts position at Prague

1911    Einstein goes to the limits of special relativity applied to gravitational fields

1912    Einstein’s two papers establish a scalar field theory of gravitation

1912    Einstein moves from Prague to ETH in Zürich in fall.  Begins collaboration with Grossmann.

1913    Einstein EG paper

1914    Adams publishes spectrum of 40 Eridani B

1915    Sirius B determined to be also a low-luminosity type A white dwarf

1915    Einstein Completes paper

1916    Density of 40 Eridani B by Ernst Öpik

1916    Schwarzschild paper

1916 Einstein’s publishes theory of gravitational waves

1919    Eddington expedition to Principe

1920    Eddington paper on deflection of light by the sun

1922    Willem Luyten coins phrase “white dwarf”

1924    Eddington found a set of coordinates that eliminated the singularity at the Schwarzschild radius

1926    R. H. Fowler publishes paper on degenerate matter and composition of white dwarfs

1931    Chandrasekhar calculated the limit for collapse to white dwarf stars at 1.4MS

1933    Georges Lemaitre states the coordinate singularity was an artefact

1934    Walter Baade and Fritz Zwicky proposed the existence of the neutron star only a year after the discovery of the neutron by Sir James Chadwick.

1939    Oppenheimer and Snyder showed ultimate collapse of a 3MS  “frozen star”

1958    David Finkelstein paper

1965    Antony Hewish and Samuel Okoye discovered “an unusual source of high radio brightness temperature in the Crab Nebula”. This source turned out to be the Crab Nebula neutron star that resulted from the great supernova of 1054.

1967    Jocelyn Bell and Antony Hewish discovered regular radio pulses from CP 1919. This pulsar was later interpreted as an isolated, rotating neutron star.

1967    Wheeler’s “black hole” talk

1974    Joseph Taylor and Russell Hulse discovered the first binary pulsar, PSR B1913+16, which consists of two neutron stars (one seen as a pulsar) orbiting around their center of mass.

2015    LIGO detects gravitational waves on Sept. 14 from the merger of two black holes

2017    LIGO detects the merger of two neutron stars

On the Quantum Footpath

The concept of the trajectory of a quantum particle almost vanished in the battle between Werner Heisenberg’s matrix mechanics and Erwin Schrödinger’s wave mechanics.  It took Niels Bohr and his complementarity principle of wave-particle duality to cede back some reality to quantum trajectories.  However, Schrödinger and Einstein were not convinced and conceived of quantum entanglement to refute the growing acceptance of the Copenhagen Interpretation of quantum physics.  Schrödinger’s cat was meant to be an absurdity, but ironically it has become a central paradigm of practical quantum computers.  Quantum trajectories took on new meaning when Richard Feynman constructed quantum theory based on the principle of least action, inventing his famous Feynman Diagrams to help explain quantum electrodynamics.

1885    Balmer Theory: 

1897    J. J. Thomson discovered the electron

1904    Thomson plum pudding model of the atom

1911    Bohr PhD thesis filed. Studies on the electron theory of metals.  Visited England.

1911    Rutherford nuclear model

1911    First Solvay conference

1911    “ultraviolet catastrophe” coined by Ehrenfest

1913    Bohr combined Rutherford’s nuclear atom with Planck’s quantum hypothesis: 1913 Bohr model

1913    Ehrenfest adiabatic hypothesis

1914-1916       Bohr at Manchester with Rutherford

1916    Bohr appointed Chair of Theoretical Physics at University of Copenhagen: a position that was made just for him

1916    Schwarzschild and Epstein introduce action-angle coordinates into quantum theory

1920    Heisenberg enters University of Munich to obtain his doctorate

1920    Bohr’s Correspondence principle: Classical physics for large quantum numbers

1921    Bohr Founded Institute of Theoretical Physics (Copenhagen)

1922-1923       Heisenberg studies with Born, Franck and Hilbert at Göttingen while Sommerfeld is in the US on sabbatical.

1923    Heisenberg Doctorate.  The exam does not go well.  Unable to derive the resolving power of a microscope in response to question by Wien.  Becomes Born’s assistant at Göttingen.

1924    Heisenberg visits Niels Bohr in Copenhagen (and met Einstein?)

1924    Heisenberg Habilitation at Göttingen on anomalous Zeeman

1924 – 1925    Heisenberg worked with Bohr in Copenhagen, returned summer of 1925 to Göttiingen

1924    Pauli exclusion principle and state occupancy

1924    de Broglie hypothesis extended wave-particle duality to matter

1924    Bohr Predicted Halfnium (72)

1924    Kronig’s proposal for electron self spin

1924    Bose (Einstein)

1925    Heisenberg paper on quantum mechanics

1925    Dirac, reading proof from Heisenberg, recognized the analogy of noncommutativity with Poisson brackets and the correspondence with Hamiltonian mechanics.

1925    Uhlenbeck and Goudschmidt: spin

1926    Born, Heisenberg, Kramers: virtual oscillators at transition frequencies: Matrix mechanics (alternative to Bohr-Kramers-Slater 1924 model of orbits).  Heisenberg was Born’s student at Göttingen.

1926    Schrödinger wave mechanics

1927    de Broglie hypotehsis confirmed by Davisson and Germer

1927    Complementarity by Bohr: wave-particle duality “Evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects.

1927    Heisenberg uncertainty principle (Heisenberg was in Copenhagen 1926 – 1927)

1927    Solvay Conference in Brussels

1928    Heisenberg to University of Leipzig

1928    Dirac relativistic QM equation

1929    de Broglie Nobel Prize

1930    Solvay Conference

1932    Heisenberg Nobel Prize

1932    von Neumann operator algebra

1933    Dirac Lagrangian form of QM (basis of Feynman path integral)

1933    Schrödinger and Dirac Nobel Prize

1935    Einstein, Poldolsky and Rosen EPR paper

1935 Bohr’s response to Einsteins “EPR” paradox

1935    Schrodinger’s cat

1939    Feynman graduates from MIT

1941    Heisenberg (head of German atomic project) visits Bohr in Copenhagen

1942    Feynman PhD at Princeton, “The Principle of Least Action in Quantum Mechanics

1942 – 1945    Manhattan Project, Bethe-Feynman equation for fission yield

1943    Bohr escapes to Sweden in a fishing boat.  Went on to England secretly.

1945    Pauli Nobel Prize

1945    Death of Feynman’s wife Arline (married 4 years)

1945    Fall, Feynman arrives at Cornell ahead of Hans Bethe

1947    Shelter Island conference: Lamb Shift, did Kramer’s give a talk suggesting that infinities could be subtracted?

1947    Fall, Dyson arrives at Cornell

1948    Pocono Manor, Pennsylvania, troubled unveiling of path integral formulation and Feynman diagrams, Schwinger’s master presentation

1948    Feynman and Dirac. Summer drive across the US with Dyson

1949    Dyson joins IAS as a postdoc, trains a cohort of theorists in Feynman’s technique

1949    Karplus and Kroll first g-factor calculation

1950    Feynman moves to Cal Tech

1965    Schwinger, Tomonaga and Feynman Nobel Prize

1967    Hans Bethe Nobel Prize

From Butterflies to Hurricanes

Half a century after Poincaré first glimpsed chaos in the three-body problem, the great Russian mathematician Andrey Kolmogorov presented a sketch of a theorem that could prove that orbits are stable.  In the hands of Vladimir Arnold and Jürgen Moser, this became the KAM theory of Hamiltonian chaos.  This chapter shows how KAM theory fed into topology in the hands of Stephen Smale and helped launch the new field of chaos theory.  Edward Lorenz discovered chaos in numerical models of atmospheric weather and discovered the eponymous strange attractor.  Mathematical aspects of chaos were further developed by Mitchell Feigenbaum studying bifurcations in the logistic map that describes population dynamics.

1760    Euler 3-body problem (two fixed centers and coplanar third body)

1763    Euler colinear 3-body problem

1772    Lagrange equilateral 3-body problem

1881-1886       Poincare memoires “Sur les courbes de ́finies par une equation differentielle”

1890    Poincare “Sur le probleme des trois corps et les equations de la dynamique”. First-return map, Poincare recurrence theorem, stable and unstable manifolds

1892 – 1899    Poincare New Methods in Celestial Mechanics

1892    Lyapunov The General Problem of the Stability of Motion

1899    Poincare homoclinic trajectory

1913    Birkhoff proves Poincaré’s last geometric theorem, a special case of the three-body problem.

1927    van der Pol and van der Mark

1937    Coarse systems, Andronov and Pontryagin

1938    Morse theory

1942    Hopf bifurcation

1945    Cartwright and Littlewood study the van der Pol equation (Radar during WWII)

1954    Kolmogorov A. N., On conservation of conditionally periodic motions for a small change in Hamilton’s function.

1960    Lorenz: 12 equations

1962    Moser On Invariant Curves of Area-Preserving Mappings of an Annulus.

1963    Arnold Small denominators and problems of the stability of motion in classical and celestial mechanics

1963    Lorenz: 3 equations

1964    Arnold diffusion

1965    Smale’s horseshoe

1969    Chirikov standard map

1971    Ruelle-Takens (Ruelle coins phrase “strange attractor”)

1972    “Butterfly Effect” given for Lorenz’ talk (by Philip Merilees)

1975    Gollub-Swinney observe route to turbulence along lines of Ruelle

1975    Yorke coins “chaos theory”

1976    Robert May writes review article of the logistic map

1977    New York conference on bifurcation theory

1987    James Gleick Chaos: Making a New Science

Darwin in the Clockworks

The preceding timelines related to the central role played by families of trajectories phase space to explain the time evolution of complex systems.  These ideas are extended to explore the history and development of the theory of natural evolution by Charles Darwin.  Darwin had many influences, including ideas from Thomas Malthus in the context of economic dynamics.  After Darwin, the ideas of evolution matured to encompass broad topics in evolutionary dynamics and the emergence of the idea of fitness landscapes and game theory driving the origin of new species.  The rise of genetics with Gregor Mendel supplied a firm foundation for molecular evolution, leading to the moleculer clock of Linus Pauling and the replicator dynamics of Richard Dawkins.

1202    Fibonacci

1766    Thomas Robert Malthus born

1776    Adam Smith The Wealth of Nations

1798    Malthus “An Essay on the Principle of Population

1817    Ricardo Principles of Political Economy and Taxation

1838    Cournot early equilibrium theory in duopoly

1848    John Stuart Mill

1848    Karl Marx Communist Manifesto

1859    Darwin Origin of Species

1867    Karl Marx Das Kapital

1871    Darwin Descent of Man, and Selection in Relation to Sex

1871    Jevons Theory of Political Economy

1871    Menger Principles of Economics

1874    Walrus Éléments d’économie politique pure, or Elements of Pure Economics (1954)

1890    Marshall Principles of Economics

1908    Hardy constant genetic variance

1910    Brouwer fixed point theorem

1910    Alfred J. Lotka autocatylitic chemical reactions

1913    Zermelo determinancy in chess

1922    Fisher dominance ratio

1922    Fisher mutations

1925    Lotka predator-prey in biomathematics

1926    Vita Volterra published same equations independently

1927    JBS Haldane (1892—1964) mutations

1928    von Neumann proves the minimax theorem

1930    Fisher ratio of sexes

1932    Wright Adaptive Landscape

1932    Haldane The Causes of Evolution

1933    Kolmogorov Foundations of the Theory of Probability

1934    Rudolph Carnap The Logical Syntax of Language

1936    John Maynard Keynes, The General Theory of Employment, Interest and Money

1936    Kolmogorov generalized predator-prey systems

1938    Borel symmetric payoff matrix

1942    Sewall Wright    Statistical Genetics and Evolution

1943    McCulloch and Pitts A Logical Calculus of Ideas Immanent in Nervous Activity

1944    von Neumann and Morgenstern Theory of Games and Economic Behavior

1950    Prisoner’s Dilemma simulated at Rand Corportation

1950    John Nash Equilibrium points in n-person games and The Bargaining Problem

1951    John Nash Non-cooperative Games

1952    McKinsey Introduction to the Theory of Games (first textbook)

1953    John Nash Two-Person Cooperative Games

1953    Watson and Crick DNA

1955    Braithwaite’s Theory of Games as a Tool for the Moral Philosopher

1961    Lewontin Evolution and the Theory of Games

1962    Patrick Moran The Statistical Processes of Evolutionary Theory

1962    Linus Pauling molecular clock

1968    Motoo Kimura  neutral theory of molecular evolution

1972    Maynard Smith introduces the evolutionary stable solution (ESS)

1972    Gould and Eldridge Punctuated equilibrium

1973    Maynard Smith and Price The Logic of Animal Conflict

1973    Black Scholes

1977    Eigen and Schuster The Hypercycle

1978    Replicator equation (Taylor and Jonker)

1982    Hopfield network

1982    John Maynard Smith Evolution and the Theory of Games

1984    R. Axelrod The Evolution of Cooperation

The Measure of Life

This final topic extends the ideas of dynamics into abstract spaces of high dimension to encompass the idea of a trajectory of life.  Health and disease become dynamical systems defined by all the proteins and nucleic acids that comprise the physical self.  Concepts from network theory, autonomous oscillators and synchronization contribute to this viewpoint.  Healthy trajectories are like stable limit cycles in phase space, but disease can knock the system trajectory into dangerous regions of health space, as doctors turn to new developments in personalized medicine try to return the individual to a healthy path.  This is the ultimate generalization of Galileo’s simple parabolic trajectory.

1642    Galileo dies

1656    Huygens invents pendulum clock

1665    Huygens observes “odd kind of sympathy” in synchronized clocks

1673    Huygens publishes Horologium Oscillatorium sive de motu pendulorum

1736    Euler Seven Bridges of Königsberg

1845    Kirchhoff’s circuit laws

1852    Guthrie four color problem

1857    Cayley trees

1858    Hamiltonian cycles

1887    Cajal neural staining microscopy

1913    Michaelis Menten dynamics of enzymes

1924    Berger, Hans: neural oscillations (Berger invented the EEG)

1926    van der Pol dimensioness form of equation

1927    van der Pol periodic forcing

1943    McCulloch and Pits mathematical model of neural nets

1948    Wiener cybernetics

1952    Hodgkin and Huxley action potential model

1952    Turing instability model

1956    Sutherland cyclic AMP

1957    Broadbent and Hammersley bond percolation

1958    Rosenblatt perceptron

1959    Erdös and Renyi random graphs

1962    Cohen EGF discovered

1965    Sebeok coined zoosemiotics

1966    Mesarovich systems biology

1967    Winfree biological rythms and coupled oscillators

1969    Glass Moire patterns in perception

1970    Rodbell G-protein

1971    phrase “strange attractor” coined (Ruelle)

1972    phrase “signal transduction” coined (Rensing)

1975    phrase “chaos theory” coined (Yorke)

1975    Werbos backpropagation

1975    Kuramoto transition

1976    Robert May logistic map

1977    Mackey-Glass equation and dynamical disease

1982    Hopfield network

1990    Strogatz and Murillo pulse-coupled oscillators

1997    Tomita systems biology of a cell

1998    Strogatz and Watts Small World network

1999    Barabasi Scale Free networks

2000    Sequencing of the human genome

Physics and the Zen of Motorcycle Maintenance

When I arrived at Berkeley in 1981 to start graduate school in physics, the single action I took that secured my future as a physicist, more than spending scores of sleepless nights studying quantum mechanics by Schiff or electromagnetism by Jackson —was buying a motorcycle!  Why motorcycle maintenance should be the Tao of Physics was beyond me at the time—but Zen is transcendent.


The Quantum Sadistics

In my first semester of grad school I made two close friends, Keith Swenson and Kent Owen, as we stayed up all night working on impossible problem sets and hand-grading a thousand midterms for an introductory physics class that we were TAs for.  The camaraderie was made tighter when Keith and Kent bought motorcycles and I quickly followed suit, buying my first wheels –– a 1972 Suzuki GT550.    It was an old bike, but in good shape and ready to ride, so the three of us began touring around the San Francisco Bay Area together on weekend rides.  We went out to Mt. Tam, or up to Vallejo, or around the North and South Bay.  Kent thought this was a very cool way for physics grads to spend their time and he came up with a name for our gang –– the “Quantum Sadistics”!  He even made a logo for our “colors” that was an eye shedding a tear drop shaped like the dagger of a quantum raising operator.

At the end of the first year, Keith left the program, not sure he was the right material for a physics degree, and moved to San Diego to head up the software arm of a start-up company that he had founder’s shares in.  Kent and I continued at Berkeley, but soon got too busy to keep up the weekend rides.  My Suzuki was my only set of wheels, so I tooled around with it, keeping it running when it really didn’t want to go any further.  I had to pull its head and dive deep into it to adjust the rockers.  It stayed together enough for a trip all the way down Highway 1 to San Diego to visit Keith and back, and a trip all the way up Highway 1 to Seattle to visit my grandparents and back, having ridden the full length of the Pacific Coast from Tijuana to Vancouver.  Motorcycle maintenance was always part of the process.

Andrew Lange

After a few semesters as a TA for the large lecture courses in physics, it was time to try something real and I noticed a job opening posted on a bulletin board.  It was for a temporary research position in Prof. Paul Richard’s group.  I had TA-ed for him once, but knew nothing of his research, and the interview wasn’t even with him, but with a graduate student named Andrew Lange.  I met with Andrew in a ground-floor lab on the south side of Birge Hall.  He was soft-spoken and congenial, with round architect glasses, fine sandy hair and had about him a hint of something exotic.  He was encouraging in his reactions to my answers.  Then he asked if I had a motorcycle.  I wasn’t sure if he already knew, or whether it was a test of some kind, so I said that I did.  “Do you work on it?”, he asked.  I remember my response.  “Not really,” I said.  In my mind I was no mechanic.  Adjusting the overhead rockers was nothing too difficult.  It wasn’t like I had pulled the pistons.

“It’s important to work on your motorcycle.”

For some reason, he didn’t seem to like my answer.  He probed further.  “Do you change the tires or the oil?”.  I admitted that I did, and on further questioning, he slowly dragged out my story of pulling the head and adjusting the cams.  He seemed to relax, like he had gotten to the bottom of something.  He then gave me some advice, focusing on me with a strange intensity and stressing very carefully, “It’s important to work on your motorcycle.”

I got the job and joined Paul Richards research group.  It was a heady time.  Andrew was designing a rocket-borne far-infrared spectrometer that would launch on a sounding rocket from Nagoya, Japan.  The spectrometer was to make the most detailed measurements ever of the cosmic microwave background (CMB) radiation during a five-minute free fall at the edge of space, before plunging into the Pacific Ocean.  But the spectrometer was missing a set of key optical elements known as far-infrared dichroic beam splitters.  Without these beam splitters, the spectrometer was just a small chunk of machined aluminum.  It became my job to create these beam splitters.  The problem was that no one knew how to do it.  So with Andrew’s help, I scanned the literature, and we settled on a design related to results from the Ulrich group in Germany.

Our spectral range was different than previous cases, so I created a new methodology using small mylar sheets, patterned with photolithography, evaporating thin films of aluminum on both sides of the mylar.  My first photomasks were made using an amazingly archaic technology known as rubylith that had been used in the 70’s to fabricate low-level integrated circuits.  Andrew showed me how to cut the fine strips of red plastic tape at a large scale that was then photo-reduced for contract printing.  I modeled the beam splitters with equivalent circuits to predict the bandpass spectra, and learned about Kramers-Kronig transforms to explain an additional phase shift that appeared in the interferometric tests of the devices.  These were among the first metamaterials ever created (although this was before that word existed), with an engineered magnetic response for millimeter waves.  I fabricated the devices in the silicon fab on the top floor of the electrical engineering building on the Berkeley campus.  It was one of the first university-based VLSI fabs in the country, with high-class clean rooms and us in bunny suits.  But I was doing everything but silicon, modifying all their carefully controlled processes in the photolithography bay.  I made and characterized a full set of 5 of these high-tech beam splitters–right before I was ejected from the lab and banned.  My processes were incompatible with the VLSI activities of the rest of the students.  Fortunately, I had completed the devices, with a little extra material to spare.

I rode my motorcycle with Andrew and his friends around the Bay Area and up to Napa and the wine country.  One memorable weekend Paul had all his grad students come up to his property in Mendocino County to log trees.  Of course, we rode up on our bikes.  Paul’s land was high on a coastal mountain next to the small winery owned by Charles Kittel (the famous Kittel of “Solid State Physics”).  The weekend was rustic.  The long-abandoned hippie-shack on the property was uninhabitable so we roughed it.  After two days of hauling and stacking logs, I took a long way home riding along dark roads under tall redwoods.

Andrew moved his operation to the University of Nagoya, Japan, six months before the launch date.  The spectrometer checked out perfectly.  As launch day approached, it was mounted into the nose cone of the sounding rocket, continuing to pass all calibration tests.  On the day of launch, we held our breath back in Berkeley.  There was a 12 hour time difference, then we received the report.  The launch was textbook perfect, but at the critical moment when the explosive nose-cone bolts were supposed to blow, they failed.  The cone stayed firmly in place, and the spectrometer telemetered back perfect measurements of the inside of the rocket all the way down until it crashed into the Pacific, and the last 9 months of my life sank into the depths of the Marianas Trench.  I read the writing on the thin aluminum wall, and the following week I was interviewing for a new job up at Lawrence Berkeley Laboratory, the DOE national lab high on the hill overlooking the Berkeley campus.

Eugene Haller

The  instrument I used in Paul Richard’s lab to characterize my state-of-the-art dichroic beamsplitters was a far-infrared Fourier-transform spectrometer that Paul had built using a section of 1-foot-diameter glass sewer pipe.  Bob McMurray, a graduate student working with Prof. Eugene Haller on the hill, was a routine user of this makeshift spectrometer, and I had been looking over Bob’s shoulder at the interesting data he was taking on shallow defect centers in semiconductors.   The work sounded fascinating, and as Andrew’s Japanese sounding rocket settled deeper into the ocean floor, I arranged to meet with Eugene Haller in his office at LBL.

I was always clueless about interviews.  I never thought about them ahead of time, and never knew what I needed to say.  On the other hand, I always had a clear idea of what I wanted to accomplish.  I think this gave me a certain solid confidence that may have come through.  So I had no idea what Eugene was getting at as we began the discussion.  He asked me some questions about my project with Paul, which I am sure I answered with lots of details about Kramers-Kronig and the like.  Then came the question strangely reminiscent of when I first met Andrew Lange:  Did I work on my car?  Actually, I didn’t have a car, I had a motorcycle, and said so.  Well then, did I work on my motorcycle?  He had that same strange intensity that Andrew had when he asked me roughly the same question.  He looked like a prosecuting attorney waiting for the suspect to incriminate himself.  Once again, I described pulling the head and adjusting the rockers and cams.

Eugene leaned back in his chair and relaxed.  He began talking in the future tense about the project I would be working on.  It was a new project for the new Center for Advanced Materials at LBL, for which he was the new director.  The science revolved around semiconductors and especially a promising new material known as GaAs.  He never actually said I had the job … all of a sudden it just seemed to be assumed.  When the interview was over, he simply asked me to give him an answer in a few days if I would come up and join his group.

I didn’t know it at the time, by Eugene had a beautiful vintage Talbot roadster that was his baby.  One of his loves was working on his car.  He was a real motor head and knew everything about the mechanics.  He was also an avid short-wave radio enthusiast and knew as much about vacuum tubes as he did about transistors.  Working on cars (or motorcycles) was a guaranteed ticket into his group.  At a recent gathering of his former students and colleagues for his memorial, similar stories circulated about that question:  Did you work on your car?  The answer to this one question mattered more than any answer you gave about physics.

I joined Eugene Haller’s research group at LBL in March of 1984 and received my PhD on topics of semiconductor physics in 1988.  My association with his group opened the door to a post-doc position at AT&T Bell Labs and then to a faculty position at Purdue University where I currently work on the physics of oncology in medicine and have launched two biotech companies—all triggered by the simple purchase of a motorcycle.

Andrew Lange’s career was particularly stellar.  He joined the faculty of Cal Tech, and I was amazed to read in Science magazine in 2004 or 2005, in a section called “Nobel Watch”, that he was a candidate for the Nobel Prize for his work on BoomerAng that had launched and monitored a high-altitude balloon as it circled the South Pole taking unprecedented data on the CMB that constrained the amount of dark matter in the universe.  Around that same time I invited Paul Richards to Purdue to give our weekly physics colloquium to talk about his own work on MAXIMA. There was definitely a buzz going around that the BoomerAng and MAXIMA collaborations were being talked about in Nobel circles. The next year, the Nobel Prize of 2006 was indeed awarded for work on the Cosmic Microwave Background, but to Mather and Smoot for their earlier work on the COBE satellite.

Then, in January 2010, I was shocked to read in the New York Times that Andrew, that vibrant sharp-eyed brilliant physicist, was found lifeless in a hotel room, dead from asphyxiation.  The police ruled it a suicide.  Apparently few had known of his life-long struggle with depression, and it had finally overwhelmed him.  Perhaps he had sold his motorcycle by then.  But I wonder—if he had pulled out his wrenches and gotten to work on its engine, whether he might have been enveloped by the zen of motorcycle maintenance and the crisis would have passed him by.  As Andrew had told me so many years ago, and I wish I could have reminded him, “It’s important to work on your motorcycle.”

2018 Nobel Prize in Laser Physics

When I arrived at Bell Labs in 1988 on a postdoctoral appointment to work with Alastair Glass in the Department of Optical materials, the office I shared with Don Olsen was next door to the mysterious office of Art Ashkin.  Art was a legend in the corridors in a place of many legends.  Bell Labs in the late 80’s, even after the famous divestiture of AT&T into the Baby Bells, was a place of mythic proportions.  At the Holmdel site in New Jersey, the home of the laser physics branch of Bell Labs, the lunch table was a who’s who of laser science.  Chuck Shank, Daniel Chemla, Wayne Knox, Linn Mollenauer.  A new idea would be floated at lunchtime, and the resulting Phys Rev Letter would be submitted within the month…that was the speed of research at Bell Labs.  If you needed expertise, or hit a snag in an experiment, the World’s expert on almost anything was just down a hallway to help solve it.

Bell Labs in the late 80’s, even after the famous divestiture of AT&T into the Baby Bells, was a place of mythic proportions.

One of the key differences I have noted about the Bell Labs at that time, that set it apart from any other research organization I have experienced, whether at national labs like Lawrence Berkeley Laboratory, or at universities, was the genuine awe in people’s voices as they spoke about the work of their colleagues.  This was the tone as people talked about Steven Chu, recently departed from Bell Labs for Stanford, and especially Art Ashkin.

Art Ashkin had been at Bell Labs for nearly 40 years when I arrived.  He was a man of many talents, delving into topics as diverse as the photorefractive effect (which I had been hired to pursue in new directions), nonlinear optics in fibers (one of the chief interests of Holmdel in those days of exponential growth of fiber telecom) and second harmonic generation.  But his main scientific impact had been in the field of optical trapping.

Optical trapping uses focused laser fields to generate minute forces on minute targets.  If multiple lasers are directed in opposing directions, a small optical trap is formed.  This could be applied to atoms, which was used by Chu for atom trapping and cooling, and even to small particles like individual biological cells.  In this context, the trapping phenomenon was known as “optical tweezers”, because by moving the laser beams, the small targets could be moved about just as if they were being held by small tweezers.

In the late 80’s Steven Chu was on the rise as one of the leaders in the field of optical physics, receiving many prestigious awards for his applications of optical traps, while many felt that Art was being passed over.  This feeling intensified when Chu received the Nobel Prize in 1997 for optical trapping (shared with Cohen-Tannoudji and Phillips) but Art did not.  Several Nobel Prizes in laser physics later, and most felt that Art’s chances were over … until this morning, Oct. 2, 2018, when it was announced that Art, now age 96, was finally receiving the Nobel Prize.

Around the same time that Art and Steve were developing optical traps at Bell Labs using optical gradients to generate forces on atoms and particles, Gerard Mourou and Donna Strickland in the optics department at the University of Rochester discovered that optical gradients in nonlinear crystals could trap focused beams of light inside a laser cavity, causing a stable pulsing effect called Kerr-lens modelocking.  The optical pulses in lasers like the Ti:Sapphire laser had ultrafast durations around 100 femtoseconds with extremely stable repetition rates.  These pulse trains were the time-domain equivalent of optical combs in the frequency domain (for which Hall and Hansch  received the Nobel Prize for physics in 2005).  Before Kerr-lens modelocking, it took great skill with very nasty dye lasers to get femtosecond pulses in a laboratory.  But by the early 90’s, anyone who wanted femtosecond pulses could get them easily just by buying a femtosecond modelocked laser kit from Mourou’s company, Clark-MXR.  These types of lasers moved into ophthalmology and laser eye surgery, becoming one of the most common and most valuable commercial lasers.

Donna Strickland and Gerard Mourou shared the 2018 Nobel Prize with Art Ashkin on laser trapping, complementing the trapping of material particles by light gradients with the trapping of light beams themselves.

Galileo Unbound

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

Welcome to my blog site Galileo Unbound: The History and Physics of Dynamics. This is the Blog where you can find the historical background and the physical concepts behind many of the current trends in the physics of complex systems.

Galileo Unbound Posts

The topics will fall under two headings that mirror my two recent books:  Introduction to Modern Dynamics (Oxford University Press, 2015), a college junior-level physics textbook describing the mathematical details of modern dynamics, and Galileo Unbound (Oxford University Press, 2018), a general-interest book on the historical development of the same ideas.

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.

Second Edition of Introduction to Modern Dynamics (IMD). Publication date: Fall 2019.

Top 10 Books to Read on the History of Dynamics

Here are my picks for the top 10 books on the history of dynamics. These books have captivated me for years and have been an unending source of inspiration and information as I have pursued my own interests in the history of physics. The emphasis is on dynamics, rather than quantum and particle physics, although these traditional topics of “modern physics” have inherited many of the approaches of classical mechanics.

(1) Diacu, F. and P. Holmes (1996). Celestial encounters: The origins of chaos and stability. Princeton, N.J., Princeton Univ. Press.

Diacu and Holmes have written a clear, accessible and information-rich general history of the role that the solar system played in the development of dynamical theory, especially issues of the stability of the solar system.

(2) Pais, A. (2005) Subtle is the Lord: The Science and the Life of Albert Einstein: Oxford.

Pais has produced a masterpiece with his inside view of the historical development of Einstein’s ideas, for both special and general relativity. Through Pais’ story telling, it is possible to follow each turn in Einstein’s thinking as he proposed some of the most mind-bending ideas of physics.

(3) Thorne, K. S. (1994). Black holes and time warps : Einstein’s outrageous legacy. New York, W.W. Norton.

This book is an exuberant journey through the history of general relativity seen through the eyes of the recent Nobel Prize winner Kip Thorne. The book is full of details, many of them personal recollections as GR went from its early days through the “golden age” with John Wheeler located at the center of the motion.

(4) Schweber, S. S. (1994). QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga. Princeton, Princeton University Press.

Schweber has produced a master work in the same genre as Pais, describing the development of QED in such moment-by-moment detail that you feel you are living the history itself. The description of Feynman’s stumble into the world of the “grown ups” at the Shelter Island and Pocono Conferences is priceless.

(5) Bacaer, N. (2011). A Short History of Mathematical Population Dynamics, Springer.

This compact little book is one of my favorites in terms of conciseness and completeness. It tracks a history that is little known inside physics, but which has taken on out-sized importance in the new era of complex systems where evolutionary dynamics describes diverse systems from neural networks to genetic algorithms.

(6) Gleick, J. (1987). Chaos: Making a New Science, Viking.

Gleick’s book is an absolute classic. This was one of my first introductions into the history of modern physics when I read it at the end of my post-doc position at Bell Labs in 1989. It has been a role model for my own dive into the history of physics.

(7) Cassidy, David C. (2010). Beyond Uncertainty : Heisenberg, Quantum Physics, and The Bomb. New York, NY, Bellevue Literary Press.

Cassidy’s sequel to his first book on Heisenberg (Uncertainty) is in the same master genre as Pais and Schweber. Reading page by page allows you to live the history yourself as Heisenberg struggled to escape from an overbearing father (and a disastrous doctoral defense) to make his mark on the world of physics.

(8) Jammer, M. (1989), The conceptual development of quantum mechanics. Tomash Publishers Woodbury, N.Y., American Institute of Physics.

Although dry and a dense read, this book is definitive. If you ever want to understand step-by-step how quantum mechanics evolved from the early thinking of Bohr to the advanced transformations of Dirac and Jordan, this is the book you want as a reference. It is endlessly deep and detailed.

(9) Crowe, M. J. (2007), Mechanics from Aristotle to Einstein: Green Lion Press.

This book is filled with lots of myth-busting about the early days of physics. It’s amazing that what we call “Newtonian Physics” was mostly not invented by Newton himself, but by others … even by his nemesis Leibniz!

(10) Coopersmith, J. (2010), Energy, the Subtle Concept: The Discovery of Feynman’s Blocks from Leibniz to Einstein: Oxford, Oxford University Press.

Coopersmith shows how the history of concepts of work and energy is surprisingly obscure. Newton himself made no mention of energy, and it took nearly 100 years for a clear picture of energy to emerge, despite its central role in dynamical systems.


There are many wonderful review articles in review journals. A few of my favorites are:

Aubin A. and Dahan Dalmedico, D. (2002). “Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures”. Historia Mathematica, 29, 273-339.

Ginoux, J. M. and C. Letellier (2012). “Van der Pol and the history of relaxation oscillations: Toward the emergence of a concept.” Chaos 22(2).

Gutzwiller, M. (1998), Moon-Earth-Sun: The oldest three-body problem, Reviews of Modern Physics, vol. 70, No. 2

Jenkins, A. (2013). “Self-oscillation.” Physics Reports-Review Section of Physics Letters 525(2): 167-222.

Morgan, G. J. (1998). “Emile Zuckerkandl, Linus Pauling, and the molecular evolutionary clock, 1959-1965.” Journal of the History of Biology 31(2): 155-178.