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History of science and civilization
Dr. Jay Maron




Stone age
Copper age
Bronze age
Iron age
Carbon age

      Discovery   Yield    Density
       (year)    Strength  (g/cm3)

Gold     Ancient   .20     19.3
Silver   Ancient   .10     10.5
Copper   -5000     .12      9.0
Bronze   -3200     .20      9      Copper + Tin.   Stronger than copper
Brass    -2000     .20      9      Copper + Zinc.  Stronger than copper
Iron     -1200     .25      7.9    Stronger than bronze and brass
Carbon    1987    1.4       1.75
The "yield strength" is the maximum stress a material can sustain before breaking.
The carbon age began in 1987 when Jimmy Connors switched from a steel to a carbon racquet.
History of physics




-2650 -2600  Imhotep      1627 1691  Boyle         1862 1943  Hilbert
-570 -495  Pythagoras     1629 1695  Huygens       1858 1947  Planck
-310 -230  Aristarchus    1632 1723  Wren          1871 1937  Rutherford
-276 -194  Eratosthenes   1635 1703  Hooke         1879 1955  Einstein
-287 -212  Archimedes     1643 1727  Newton        1885 1962  Bohr
  90  168  Ptolemy        1646 1716  Leibniz       1887 1961  Schroedinger
 476  550  Aryabhata      1656 1742  Halley        1898 1964  Szilard
1452 1519  da Vinci       1700 1782  Bernoulli     1900 1958  Pauli
1473 1543  Copernicus     1707 1783  Euler         1901 1954  Fermi
1501 1576  Cardano        1731 1810  Cavendish     1901 1976  Heisenberg
1546 1601  Brahe          1777 1855  Gauss         1902 1984  Dirac
1548 1600  Bruno          1791 1867  Faraday       1903 1957  von Neumann
1548 1620  Stevin         1811 1832  Galois        1906 1978  Godel
1550 1617  Napier         1821 1894  Helmholtz     1906 1998  Weil
1561 1626  Bacon          1831 1879  Maxwell       1908 1968  Landau
1564 1642  Galileo        1844 1906  Boltzmann     1913 1996  Erdos
1571 1630  Kepler         1845 1918  Cantor        1918 1988  Feynman
1580 1626  Snellius       1850 1925  Heaviside     1928 2014  Grothendieck
1596 1650  Descartes      1853 1925  Ricci         1951       Witten
1601 1665  Fermat         1853 1928  Lorentz
1623 1662  Pascal         1854 1912  Poincare


Galileo's telescope
Replica of Newton's telescope
Herschel 1.2 meter reflector
Herschel 1.2 meter reflector
Yerkes 1 meter refractor

Hale 1.5 meter
Hooker 2.5 meter
Palomar 5 meter
Keck 10 meter

Keck 10 meter
Hubble 2.4 meter
Webb 5 meter
30 Meter Telescope

Telescope            Diameter  Resolution  Year
                     (meters)  (microrad)

Human eye                .005    291
Lippershey's telescope    ?        ?       1608   First telescope.  Refractor
Galileo's telescope #1   .015     34       1609   Refractor
Galileo's telescope #2   .038     10       1620   Refractor
Newton's telescope       .033     12       1668   First reflecting telescope
Herschel telescope      1.20       2.5     1789   Reflector
Yerkes refractor        1.02       2.5     1897   Refractor.  End of refractor age
Hale 60-inch            1.52       2.5     1908   Mount Wilson observatory
Hooker 100-inch         2.54       2.5     1917   Mount Wilson observatory
Hale 200-inch           5.08       2.5     1948   Palomar Observatory
Keck                   10          2.5     1993   Mauna Kea Observatory
Hubble                  2.4         .20    1990   Earth orbit
Webb Space Telescope    6.5         .10       ?   L2 Lagrange point
Thirty Meter Telescope 30           .20       ?   Mauna Kea Observatory

-240     Eratosthenes measures the Earth's circumference to 20% error.
-240     Aristarchus proves that the sun is at least 10 times larger than the Earth
         using lunar eclipses.
 150     Ptolemy publishes The Almagest with the geocentric model
 550     Aryabhata publishes accurate measurements of size of the sun and moon
1543     Copernicus publishes a heliocentric model.
1600     Brahe measures accurate planet positions
1608     Lippershey invents the telescope
1609     Galileo builds a telescope and begins observing
1609     Kepler proves that planets orbit as ellipses using Brahe's data
1613     Galileo publishes observations of the phases of Venus, which support
         the heliocentric model
1632     Galileo publishes the "Dialogue Concerning the Two Chief World Systems",
         which contained a comparison of the systems of Ptolemy and Copernicus
1672     Richter and Cassini measure the parallax of Mars, producing a precise
         value for the size of the sun
1687     Newton publishes the Principia Mathematica, which contained the calculus,
         the laws of motion (F=MA), and a proof that planets orbit as ellipses.
1718     Halley finds that the stars move.  He found that Sirius, Arcturus and
         Aldebaran were 1/2 of a degree from the positions charted by the Ancient
         Greek astronomer Hipparchus
1783     Herschel finds that the solar system is moving with respect to the stars
1826     Olbers' paradox.  If the stars in the universe are uniformly distributed
         and if the universe is infinite, then the sky would appear infinitely bright
         with stars.
1863     Bessel measures the first stellar parallax, showing that the
         stars are more than 4 light years away.  This also implies that stars
         are as luminous as the sun.
         The parallax of stars is too small to see without a telescope.
1905     Einstein publishes special relativity
1915     Einstein publishes the general theory of relativity.
         Einstein shows that general relativity is consistent with the existence
         of a cosmological constant.  At the time the cosmological constant was a
         proposed explanation for why the universe hasn't collapsed gravitationally.
1920     Shapley finds that the sun is not at the center of the galaxy.
         Because starlight is absorbed by interstellar gas, we only see the nearby
         stars and it appears as though we live at the center of a disk of stars.
         Shapley measured the distances to globular clusters and found that they
         are centered on a point (the galactic center) that is far from the sun.
1922     Friedmann finds a solution to the equations of general relativity that
         are consistent with an expanding universe.
1923     Hubble measures the distances to Andromeda and Triangulum and finds that
         they are outside the Milky Way.  These were the first objects to be shown
         to be outside the Milky Way.
1929     Hubble's law published.  For distant galaxies, the recession velocity is
         proportional to distance.
1933     Zwicky's analysis of the Coma cluster of galaxies shows that they contain
         unseen matter that is not due to stars.
1965     Penzias and Wilson discover the cosmic microwave background radiation.
1970     Rubin and Ford measure galactic rotation and show that galaxies contain
         matter that is not due to stars.
1980     Guth and Starobinsky propose the theory of inflation to explain why the
         universe is flat
1998     Observations of supernovae show that the expansion of the universe is
         accelerating and the the cosmological constant is positive.
         Previous to this it was not known if the universe was destined for
         collapse (big crunch) or for infinite expansion (big chill).
2003     WMAP mission measures the Hubble constant to 5% precision, as well as
         other cosmological parameters.
         Previous to this, the Hubble constant had an error of ~ 20%.
         This settled once and for all the question of the overall structure of the

Measurement of the distance to the sun

-260 Aristarchus established that the distance to the sun is at least 20 times the distance to the moon.

In 499, Aryabhata publishes a measurement of the distance to the sun.

Brahe's data consisted of measurements of angles between different objects. This data could be used to establish the shape of orbits but not their size. For example, if the size of the solar system were doubled along with the speeds of the planets, the angles would stay the same and you wouldn't be able to tell the difference.

In 1639, Horrocks used a transit of Venus to measure the distance to the sun, but this method is incapable of giving an accurate value, and it can only be done once per century.

In 1672, Richter and Cassini measured the parallax of Mars which gives a result for the distance to the sun that is more accurate than the Venus method. The Mars method has an advantage over the Venus method in that it can be done once every 26 months, when Mars is at closest approach.

In 1676, Romer used the moons of Jupiter to measure the time it takes for light to cross the Earth's orbit. This gives a value for R/C.

In 1729, Bradley measured the deflection of starlight due to the Earth's motion, which gives a measurement of V/C, or equivalently, a measurement of R/C.

In 1849, Fizeau produced the first measurement for the speed of light that was independent of the Earth-sun distance R.

Speed of light                           =  C
Earth-sun distance                       =  R
Earth orbital velocity                   =  V
Earth orbital time (1 year)              =  T  =  2 π R / V
Time for light to cross the Earth's orbit=  t  =  2 R / C

~808    Qing Xuzi publishes a formula resembling gunpower, consisting of
        6 parts sulfur, 6 parts saltpeter, and 1 part birthwort herb (for carbon).
~850    Incendiary property of gunpower discovered
1540    Biringuccio publishes "De la pirotechnia", giving recipes for gunpowder
1661    Boyle publishes "The Sceptical Chymist", a treatise on the
        distinction between chemistry and alchemy.  It contains some of the
        earliest modern ideas of atoms, molecules, and chemical reaction,
        and marks the beginning of the history of modern chemistry.
1662    Boyle discovers that for air at fixed temperature,
        Pressure * Volume = Constant
1663    Guericke invents the first electrostatic generator, which uses
        mechanical work to separate charge.  Generators were refined until
        they were superceded by the battery.
1671    Boyle discovers that combining iron filings and acid produces hydrogen gas.
1754    Black isolates CO2
1758    Black formulates the concept of latent heat to explain phase transitions
1766    Cavendish identifies hydrogen as a colorless, odourless gas that burns
        in air.
1772    Scheele produces pure oxygen gas by heating HgO.
1774    Priestly produces pure oxygen gas by focusing sunlight on HgO.
        He noted that it is combustible and that it gives energy when breathed.
1745    von Kleist invents the capacitor, a device for storing charge generated
        by an electrostatic generator.
1746    van Musschenbroek refines the capacitor, which comes to be known as a
        "Leyden jar".
1777    Lavoisier finds that in the reaction tin+oxygen, mass is conserved.
        He also finds that oxygen is not the only component of air, that air also
        consists of something else.
1780    Galvani observes that when a frog leg is touched by an iron scalpel,
        it twitches.  This was the inspiration for Volta to invent the battery.
1781    Cavendish finds that buring hydrogen + oxygen produces water.
1787    Charles finds that for air at constant pressure,
        Volume = Constant * Temperature
        He also finds that this applies for O2, N2, H2, and CO2.
1789    Lavoisier publishes "Traite Elementaire de Chimie", the first modern
        chemistry textbook.  It is a complete survey of (at that time) modern
        chemistry, the law of conservation of mass.
1791    Volta develops the first electrochemical cell, consisting of two different
        metals separated by a moist intermediary.
1797    Proust proposes the law of definite proportions, that elements
        combine in small whole number ratios to form compounds.
1800    Volta constructs the first "battery" by connecting multiple electrochemical
        cells in parallel, increasing the output power and voltage.
1800    Volta constructs the first battery, a set of electrochemical cells wired
        in serial to increase the voltage.
1801    Dalton publishes the law of partial pressures.
        The pressure of a mix of gases is equal to the sum of the pressures
        of the components.  He also finds that when a light and heavy gas are mixed,
        the heavy gas does not drift to the bottom but rather fills the space
1805    Gay-Lussac and Humboldt find that water is formed of two volumes of
        hydrogen gas and one volume of oxygen gas.
1809    Gay-Lussac finds that for an ideal gas at constant volume,
        Pressure = Constant * Temperature
1811    Avogadro finds that equal volumes of different gases have the same number
        of particles.  At constant temperature and pressure,
        Volume = Constant * NumberOfParticles
1811    Avogadro arrives at the correct interpretation of water's composition,
        based on what is now called Avogadro's law and the assumption of diatomic
        elemental molecules
1840    Hess finds that energy is conserved in chemical reactions
1848    Lord Kelvin establishes concept of absolute zero, the temperature at
        which all molecular motion ceases.
1860    Cannizzaro publishes a table of atomic weights of the known elements
1864    Gulberg and Waage propose the law of mass action
1869    Mendeleev publishes a periodic table containing the 66 known elements
1876    Gibbs publishes the concept of "Gibbs free energy"
1877    Boltzmann defines entropy and develops thermodynamics
1877    Pictet freezes CO2 and liquefies oxygen.
        Liquification enables the purification of gases.
1894    Ramsay discovers the noble gases, filling a large and unexpected gap in
        the periodic table

1635   Gassendi measures the speed of sound to be 478 m/s with 25% error.
1660   Viviani and Borelli produce the first accurate measurement of the speed of
       sound, giving a value of 350 m/s.
1660   Hooke's law published.  The force on a spring is proportional to the change
       in length.
1662   Boyle discovers that for air at fixed temperature,
       Pressure * Volume = Constant
       Hence, air obey's Hooke's law
1687   Newton publishes the Principia Mathematica, which contains the first analytic
       calculation of the speed of sound.  The calculated value was 290 m/s
       and the true value is 342 m/s (at 20 Celsius).
Newton's result was the first solid evidence for the existence of atoms. His result differed from the correct value because it had not yet been discovered that air heats when compressed. If you add this effect you get the right value.

The reason air heats when compressed is because it is composed of atoms. You can see this in action with the "Gas" simulation at You can also see how atoms in a gas can carry a sound wave, and why the sound speed has the same order-of-magnitude as the thermal velocity of the atoms.

1789  Lavoisier publishes "Traite Elementaire de Chimie", the first modern
      chemistry textbook.  It is a complete survey of (at that time) modern
      chemistry, the law of conservation of mass.
1797  Proust proposes the law of definite proportions, that elements
      combine in small whole number ratios to form compounds.
1801  Dalton publishes the law of partial pressures.
      The pressure of a mix of gases is equal to the sum of the pressures
      of the components.  He also finds that when a light and heavy gas are mixed,
      the heavy gas does not drift to the bottom but rather fills the space
1805  Gay-Lussac and Humboldt find that water is formed of two volumes of
      hydrogen gas and one volume of oxygen gas.
1809  Gay-Lussac finds that for an ideal gas at constant volume,
      Pressure = Constant * Temperature
1811  Avogadro finds that equal volumes of different gases have the same number
      of particles.  At constant temperature and pressure,
      Volume = Constant * NumberOfParticles
1811  Avogadro arrives at the correct interpretation of water's composition,
      based on what is now called Avogadro's law and the assumption of diatomic
      elemental molecules
1860  Cannizzaro publishes a table of atomic weights of the known elements
1869  Mendeleev publishes a periodic table containing the 66 known elements
1877  Boltzmann defines entropy and develops thermodynamics
All of these results support the hypothesis that matter is composed of atoms, but there was no known experiment sensitive enough to measure the size and mass of an individual atom.
Wavelength of violet light = 4e-7 meters
Diameter of an iron atom   = 2e-10 meters
Violet photons are much larger than atoms and so you can't see atoms in an optical microscope.
1905  Einstein publishes a method for measuring the mass of an atom using
      Brownian motion
1908  Perrin uses Einstein's method to produce the first measurement of the mass of
      an atom.  This is equivalent to measuring the value of Avogadro's number.
Minutephysics atoms

Discovery of elements

The ancient metals such as iron, copper, tin, and zinc are obtained by carbon smelting minerals. Cobalt was the first metal discovered since iron and it's discovery inspired people to smelt every known mineral in the hope of yielding a new metal. By 1800 nearly all of the carbon smeltable metals had been discovered.

Some elements can't be carbon smelted and require electrolysis to isolate. Electrochemistry began in 1800 with the invention of the battery and most of the remaining metals were discovered soon after. Sodium and potassium were isolated by electrolysis in 1807 and these were used to smelt metals that couldn't be smelted with carbon.

         Discovery   Method of
          (year)     discovery

Carbon     Ancient   Naturally occuring     Coal, diamond
Gold       Ancient   Naturally occuring
Silver     Ancient   Naturally occuring
Sulfur     Ancient   Naturally occuring
Lead         -6500   Smelt with carbon
Copper       -5000   Smelt with carbon
Bronze (As)  -4200                          Copper + Arsenic
Bronze (Sn)  -3200                          Copper + Tin
Tin          -3200   Smelt with carbon
Brass        -2000                          Copper + Zinc
Mercury      -2000   Heat the oxide
Iron         -1200   Smelt with carbon      In the form of steel
Zinc          1300   Smelt with carbon      Date first produced in pure form
Antimony      1540   Smelt with iron
Arsenic       1649   Heat the oxide
Phosphorus    1669   Heat the oxide
Cobalt        1735   Smelt with carbon      First metal discovered since iron
Platinum      1735   Naturally occuring
Nickel        1751   Smelt with carbon
Hydrogen      1766   Hot iron + steam
Oxygen        1771   Heat HgO
Nitrogen      1772   From air
Manganese     1774   Smelt with carbon
Molybdenum    1781   Smelt with carbon
Tungsten      1783   Smelt with carbon
Chromium      1797   Smelt with carbon
Palladium     1802   Chemistry
Osmium        1803
Iridium       1803
Rhodium       1804   Smelt with zinc        Smelt Na3RhCl6 with zinc
Sodium        1807   Electrolysis
Potassium     1807   Electrolysis
Magnesium     1808   Electrolysis
Cadmium       1817   Smelt with carbon
Lithium       1821   Electrolysis
Zirconium     1824   Smelt with potassium
Aluminum      1827   Smelt with potassium
Silicon       1823   Smelt with potassium
Beryllium     1828   Smelt with potassium
Thorium       1929   Smelt with potassium
Vanadium      1831
Uranium       1841   Smelt with potassium
Ruthenium     1844   Smelt with carbon
Tantalum      1864   Smelt with hydrogen
Niobium       1864   Smelt with hydrogen
Fluorine      1886   Electrolysis
Helium        1895   From uranium ore
Titanium      1910   Smelt with sodium
Hafnium       1924
Rhenium       1928   From molybdenite
Scandium      1937

Gold was the densest element known until the discovery of platinun in 1735. It was useful as an uncounterfeitable currency until the discovery of tungsten in 1783, which has the same density as gold.

Wood fires are 200 Celsius short of the copper smelting temperature. Coal has to be used.

Titanium can't be smelted with carbon because it produces titanium carbide (TiC).

Discovery of the strong metals

The usefulness of a metal as a sword depends on its strength/density ratio. The table below shows all the metals with a ratio of at least 5 MJoules/kg. For these metals, strength tends to be proportional to density and the strength/density ratio has a characteristic value of 10 MJoules/kg. Beryllium is the sole outlier with a superlatively large value of 71 MJoules/kg.

The low density metals are ones up to vanadium on the periodic table. None are carbon smeltable and all require electrochemistry to isolate. The first low density metal to be produced was magnesium in 1808.

        Protons  Strength  Density  Strength/Density   Carbon    Discovery
                  (GPa)    (g/cm3)   (MJoule/kg)      smeltable    year

Beryllium    4      132      1.85      71.4          no      1828
Magnesium   12       17      1.74       9.8          no      1808
Aluminum    13       26      2.70       9.6          no      1827
Scandium    21       29      3.0        9.7          no      1937
Titanium    22       44      4.5        9.8          no      1910
Vanadium    23       47      6.0        7.8          no      1831
Chromium    24      115      7.2       16.0          yes     1797
Manganese   25       75      7.2       10.4          yes     1774
Iron        26       82      7.9       10.4          yes    -1200
Cobalt      27       75      8.9        8.4          yes     1735
Nickel      28       76      8.9        8.5          yes     1751
Copper      29       48      9.0        5.3          yes    -5000
Zinc        30       43      7.1        6.0          yes     1746
Molybdenum  42      120     10.3       11.7          yes     1781
Ruthenium   44      173     12.4       14.0          yes     1844
Rhodium     45      150     12.4       12.1          yes     1804
Tungsten    74      161     19.2        8.4          yes     1783
Rhenium     75      178     21.0        8.5          yes     1928
Osmium      76      222     22.6        9.8          yes     1803
Iridium     77      210     22.6        9.3          yes     1803
Uranium     92      111     19.1        5.8          no      1841

Strength:          Shear modulus            (GPascals)
Density:           Density                  (grams/cm3)
Strength/Density:  Shear modulus / Density  (MJoules/kg)

Metals known since antiquity

For a metal, the stiffness is characterized by the "shear strength" and the sword worthiness is characterized by the shear strength over the density (the "strength to weight ratio"). For example for iron,

Shear modulus    =  S         =   82 GJoules/meter3
Density          =  D         = 7900 kg/meter3
Sword worthiness =  Q  = S/D  = 10.4 MJoules/kg


This plot includes all metals with a strength/density at least as large as lead, plus mercury. Beryllium is beyond the top of the plot.

Wootz steel

-600  Wootz steel developed in India and is renowned as the finest steel in the world.
1700  The technique for making Wootz steel is lost.
1790  Wootz steel begins to be studied by the British Royal Society.
1838  Anosov replicates Wootz steel.
Wootz steel is a mix of two phases: martensite (crystalline iron with .5% carbon), and cementite (iron carbide, Fe, 6.7% carbon).

Iron meteorites

In prehistoric times iron meteorites were the only source of metallic iron. They consist of 90% iron and 10% nickel.


Spodumene: LiAl(SiO3)2
Beryl: Be3Al2(SiO3)6
Magnesite: MgCO3
Bauxite: Al(OH)3 and AlO(OH)
Rutile: TiO2
Vanadinite: Pb5(VO4)3Cl

Chromite: FeCr2O4
Pyrolusite: MnO2
Hematite: Fe2O3
Iron meteorite
Cobaltite: CoAsS
Millerite: NiS

Chalcopyrite: CuFeS2
Sphalerite: ZnS
Molybdenite: MoS2
Acanthite: Ag2S
Cassiterite: SnO2
Wolframite: FeWO4
Cinnabar: HgS
Platinum nugget
Gold nugget
Galena: PbS

The Calculus
1585  Simon Stevin introduces decimal numbers to Europe. (for example, writing 1/4 as .25)

1586  Simon Stevin drops objects of varying mass from a church tower to demonstrate that
      acceleration is independent of mass.

1604  Galileo publishes the mathematical description of acceleration.

1614  Logarithms invented by John Napier, making possible precise calculations
      of equal tuning ratios.  Stevin's calculations were mathematically sound but
      the frequencies couldn't be calculated with precision until logarithms were

1637  Cartesian geometry published by Fermat and Descartes.
      This was the crucial development that triggered an explosion of mathematics
      and opened the way for the calculus.

1684  Leibniz publishes the calculus

1687  Newton publishes the Principia Mathematica, which contained the calculus,
      the laws of motion (F=MA), and a proof that planets orbit as ellipses.

1733  Euler develops the calculus of variations

1762  Lagrange discovers the divergence theorem, the 2D generalization of the fundamental
      theorem of calculus. The surface flux integral equals the volume divergence integral.

1788  Lagrangian mechanics published

1821  Cauchy publishes the "epsilon-delta" definition of a limit, raising the
      level of rigor in mathematics.

1822  Fourier transform published

1828  Green's theorem.  In 2D, the circulation line integral equals the curl area integral

1833  Hamiltonian mechanics published

1834  Eikonal approximation developed by Hamilton

1850  Kelvin-Stokes theorem.  3D generalization of Green's theorem

1854  Stokes theorem.  Generalization of the Kelvin-Stokes theorem

1854  Riemann Integral published, the first rigorous definition of an integral

1854  Chebyshev polynomials published

1863  Helmholtz publishes "On the Sensations of Tone"

1870  Heine defines "uniform continuity"

1872  Heine proves that a continuous function on an open interval need not be
      uniformly continuous.

1872  Weierstrass publishes the "Weierstrass function", the first example of
      a function that is continuous everywhere and differentiable nowhere.

1877  Lord Rayleigh publishes "Theory of Sound"

1887  Poincare discovers the phenomenon of chaos while studying celestial mechanics

1926  WKB theory published

1978  "Bender & Orszag" textbook published.  Art of blending special functions
      like Scotch.


Foucault pendulum

-2000 System of hours, minutes, and seconds developed in Sumer
-300  Water clock developed in Ancient Greece
 100  Zhang Heng constructs a seismometer using pendulums that was capable of
      detecting the direction of the Earthquake.
1300  First mechanical clock developed.
1400  Spring-based clocks developed.
1500  Pendulums are used for power, for machines such as saws, bellows, and pumps.
1582  Galileo finds that the period of a pendulum is independent of mass
      and oscillation angle, if the angle is small.
1636  Mersenne and Descartes find that the pendulum was not quite isochronous.
        Its period increased somewhat with its amplitude.
1656  Huygens builds the first pendulum clock, delivering a precision of
      15 seconds per day.  Previous devices had a precision of 15 minutes per day.
      Fron this point on pendulum clocks were the most accurate timekeeping devices
      until the development of the quartz oscillator was developed in 1921.
1657  Balance spring developed by Hooke and Huygens, making possible portable
1658  Huygens publishes the result that pendulum rods expand when heated.
      This was the principal error in pendulum clocks.
1670  Previous to 1670 the verge escapement was used, which requires a large angle.
      The anchor escapement mechanism is developed in 1670, which allows for a smaller
      angle.  This increased the precision because the oscillation period is
      independent of angle for small angles.
1673  Huygens publishes a treatise on pendulums.
1714  The British Parliament establishes the "Longitude Prize" for anyne
      who could find an accurate method to determine longitude at sea.
      At the time there was no clock that could measure time on a moving ship
      accurately enough to determine longitude.
1721  Methods are developed for compensating for thermal expansion error of a pendulum.
1726  Gridiron pendulum developed, improving precision to 1 second per day.
1772  Harrison builds a clock which James Cook used in his exploration of the Pacific.
      Cook's log is full of praise for the watch and the charts of the Pacific
      Ocean were remarkably accurate.
1772  Harrison gives one of his clocks to King George III, who personally tested it and
      found it to be accurate to 1/3 of one second per day.  King George III advised
      Harrison to petition Parliament for the full Longitude Prize after threatening
      to appear in person to dress them down.
1851  Foucault shows that a pendulum can be used to measure the rotation period of
      the Earth.  The penulum swings in a fixed frame and the Earth rotates with
      respect to this frame.  In the Earth frame the pendulum appears to precess.
1921  Quartz electronic oscillator developed
1927  First quartz clocks developed, which were more precise than pendulum clocks.

Length of the pendulum  =  L
Gravity constant        =  g  =  9.8 meters/second2
Angle of oscillation    =  Z     (radians)
Period of the pendulum  =  T  =  2 π (L/g)½     For small angles (Z << 1)
As the angle increases the period of oscillation increases.
-600       Thales discovers static electricity
-600       Thales discovers natural magnets, which are magnetized magnetite (Fe3O4)
-250       Magnetic compass invented
1600       Gilbert publishes a treatise on electromagnetism
1663       Guericke invents the first electrostatic generator, which uses
           mechanical work to separate charge.  Generators were refined until
           they were superceded by the battery.
1745       von Kleist invents the capacitor, a device for storing charge generated
           by an electrostatic generator.
1746       van Musschenbroek refines the capacitor, which comes to be known as a
           "Leyden jar".
1748       Franklin determines that there are two types of charge, positive and
           negative, and that charge is conserved.
1752       Franklin discovers the link between lightning and electricity by using a
           kite to transfer charge from lightning to a Leyden jar.
1780       Galvani observes that when a frog leg is touched by an iron scalpel,
           it twitches.  This was the inspiration for Volta to invent the battery.
1785       Coulomb discovers the electric force law
1791       Volta develops the first electrochemical cell, consisting of two different
           metals separated by a moist intermediary.
1800       Volta constructs the first "battery" by connecting multiple electrochemical
           cells in parallel, increasing the output power and voltage.
           In 1836 Daniell refined the battery, making it suitable for industrial use
1820       Oersted finds that an electric current produces a magnetic field
1826       Ampere finds that electric currents attract each other
1831       Faraday finds that a changing magnetic field produces an electric field
1861       Maxwell finds that a changing electric field produces a magnetic field
1862       Maxwell unifies the previous discoveries about currents and magnetic
           fields with "Maxwell's equations"
1864       Maxwell finds that light is an electromagnetic wave
           This theory predicts a paradox, that the speed of light is invariant
1883       Wimshurst machine invented for using induction to separate charge
1884       Heaviside invents the vector calculus and uses it to simplify Maxwell's
1887       Hertz achieves the first detection of electromagnetic waves
1887       Michelson-Morley experiment finds that the speed of light is invariant
1889       Heaviside publishes the force law for a charge moving in a magnetic field
1892       Lorentz discovers the "Lorentz transform" for special relativity
           This offered an explanation for the Michelson-Morley experiment
1904       Lorentz finds that the Lorentz transform resolves the paradoxes of
           Maxwell's equations
1905       Einstein and Poincare each publish a complete formulation of the
           theory of special relativity

1650  Guericke builds the first vacuum pump
1660  Boyle's law for a gas at constant temperature:  Pressure * Volume = Constant
1676  Leibniz defines kinetic energy and notes that it is conserved in many
      mechanical processes
1698  Savery develops a steam engine
1702  Amontons introduces the concept of absolute zero, based on observations of gases
1761  Black discovers that ice absorbs heat without changing its temperature when
1776  Smeaton publishes a paper on experiments related to power, work, momentum,
      and kinetic energy, supporting the conservation of energy
1777  Scheele distinguishes heat transfer by thermal radiation from that by
      convection and conduction
1791  Prevost shows that all bodies radiate heat, no matter how hot or cold they are
1798  Thompson performs measurements of the frictional heat generated in
      boring cannons and develops the idea that heat is a form of kinetic energy
1802  Gay-Lussac publishes Charles's law.
      For a gas at constant pressure, Temperature * Volume = Constant
1802  Gay-Lussac publishes Gay-Lussac's law.
      For a gas at constant volume, Temperature * Pressure = Constant
1804  Leslie observes that dark surfaces radiate heat more effectively than
      light-colored surfaces.
1810  Leslie freezes water to ice artificially
1819  Dulong and Petit find that the heat capacity of a crystal is proportional to the
      number of atoms
1824  Carnot analyzes the efficiency of steam engines; he develops the notion of a
      reversible process and, in postulating that no such thing exists in nature,
      lays the foundation for the second law of thermodynamics, and initiating the
      science of thermodynamics
1827  Brown discovers the Brownian motion of pollen and dye particles in water
1831  Melloni demonstrates that infrared radiation can be  reflected, refracted,
      and polarized in the same way as light
1834  Clapeyron combines Boyle's Law, Charles's Law, and Gay-Lussac's Law to
      produce a Combined Gas Law.
      Pressure * Volume  =  Constant * Temperature
1842  Mayer calculates the equivalence between heat and kinetic energy
1847  Helmholtz publishes "On the Conservation of Force", where energy is used to
        connect mechanics, heat, light, electricity and magnetism.

1752  Dalibard uses a lightening rod to validate Franklin's hypothesis.
1909  Millikan and Fletcher use the "Oil drop" experiment to obtain the first
      measurement of the electron mass and charge.  They find that the electron
      mass is 2000 times smaller than a hydrogen atom.
1947  Franklin finds that electricity is composed of positive and
      negative charge and that charge is conserved.
1750  Franklin proposes an experiment to prove that lightening is electricity
      by flying a kite in a lightening storm.

1909  Rutherford, Geiger, and Marsden use the "Rutherford scattering" experiment
      to show that the nucleus is much smaller than the atom.

Size of atom     ~  2e-10 meters
Size of nucleus  ~  2e-15 meters
Phet simulation on Rutherford scattering
Quantum mechanics
1635  Gassendi measures the speed of sound to be 478 m/s with 25% error.
1660  Viviani and Borelli produce the first accurate measurement of the speed of
      sound, giving a value of 350 m/s.
1660  Hooke's law published.  The force on a spring is proportional to the change
      in length.
1662  Boyle discovers that for air at fixed temperature,
      Pressure * Volume = Constant
1687  Newton publishes the Principia Mathematica, which contains the first analytic
      calculation of the speed of sound.  The calculated value was 290 m/s.
      The fact that Newton's calculation differed from the measured speed was the first
      solid clue for the existence of atoms, and it also contained a clue for quantum
      In Newton's age it was not known that a gas heats if compressed.  If you include
      this effect you get the correct value for the speed of sound.  The fact that
      a gas heats when compressed is due to the fact that a gas is composed of atoms.
1859  Kirchhoff finds that the blackbody spectrum depends only on temperature
1877  Boltzmann suggests that the energy levels of a physical system could be
      discrete based on statistical mechanics and mathematical arguments
1887  Hertz discovers the photoelectric effect, that light can eject electrons
      from a material
1888  Rydberg measures the emission frequencies of the hydrogen atom
1900  Planck finds if you assume photon energy is quantized, the correct blackbody
      spectrum emerges
1905  Einstein interprets the photoelectric effect as being caused by discrete
      packets of light (photons)
1907  Rutherford discovers the nucleus with the "Rutherford scattering" experiment
1909  Taylor demonstrates that the diffraction pattern of light through a double
      slit is preserved even if the photons are emitted one at a time
1909  Einstein shows that the Planck law implies that photons carry momentum

Matter waves
1803  Young discovers the diffraction of light, suggesting that light is a wave
1861  Maxwell develops the "Maxwell's equations", unifying electricity and magnetism
1864  Maxwell finds that light is an electromagnetic wave
1900  Planck solves the blackbody problem by assuming that photon energy is quantized as
      E = h F
1905  Einstein publishes the "photoelectric effect" experiment, providing the first
      direct measurement of photon energy and momentum.
1905  Theory of special relativity completed.
1913  Bohr model of the atom published
1924  de Broglie postulates that for particles with mass,
      Momentum * Wavelength = PlanckConstant
1927  Davisson and Germer experimentally verify the de Broglie relation for electrons.


The Cray-1, developed in 1976
The Kraken Supercomputer, built in 2009

c. -2400  Abacus invented by the Babylonians
c.  -500  First known use of the number "0" in Ancient India
c.  -300  Pingala develops binary numbers
c.  -100  Negative numbers used in Ancient China
c.   200  Logarithms developed in Ancient India
c.   600  Brahmagupta develops a place-value number system
c.  1400  Kerala school of astronomy and mathematics in South India invents the
          floating point number system.
    1585  Stevin popularizes decimal numbers in Europe
    1614  Napier develops logarithm tables
    1622  Oughtred develops the slide rule
    1642  Pascal builds a mechanical calculator
    1671  Leibniz builds a mechanical calculator
    1910  Vacuum tube invented
    1646  ENIAC built.  17468 vacuum tubes.  5000 additions per second.
    1947  Transistor invented
    1957  Fortran compiler developed.  This was the first high-level programming language
    1967  Dijkstra declares that the "goto" statement is harmful and advocates
          structured programming
Fastest supercomputer as a function of time

The world's fastest supercomputer is the Tianhe-2, built in 2013. It has the following properties:

Speed                  34 Petaflops
Processor cores    384000
Memory               1357 Terabytes
Disk drives          12.4 Petabytes
Power                  24 MWatts
Footprint             700 meters^2

Slide rule

1624  Slide rule age begins when Wingate publishes a table of logarithms
1630  Oughtred builds a circular slide rule
1632  Oughtred develops the modern design for the slide rule
1677  First commercial slide rule
1976  Slide rule era ends when Texas Instruments creates the
      electronic calculator, available for $104 in 2015 dollars.


History of Science and Western Civilization

 3200       Mesopotamians develop the first known written language
 2900       Bronze age begins in Mesopotamia, replaces stone age
 2700  1450 Minoan civilization in Crete
~2600       Imhotep, an Egyptian engineer, constructs the first pyramid.
 1600  1100 Mycenaean civilization in Crete
~1600       Thera volcano explodes in the Aegean Sea.
~1250       Hercules
~1188       Trojan war, sometime between 1194 and 1184 BC.
 1100  800  Greek dark age
  776       First Olympic games. Reemergence of Greek civilization. Iron age replaces bronze age
  624  546  Thales of Miletus. Philosopher
  570  495  Pythagoras of Croton
  563  483  Gautama Buddha
  534       First theatre competition in Athens, won by Thespis
  490       Battle of Marathon. Athenians defeat the Persians
  508       Roman Republic founded, replacing monarchy rule
  490       First Persian invasion.  Battle of Marathon.  Athenians defeat the Persians
  480       Second Persian invasion.
  480       Battle of Thermopylae.  300 Spartans humble the Persian army.
  480       Battle of Salamis.  Greeks defeat the Persian fleet
  479       Battle of Plataea.  Pan-Greek force defeats the Persians.
  469  399  Socrates
  460       War commences between Sparta and Athens and continues off and on until 405.
  430       Plague of Athens
  428  348  Plato
  405       Sparta defeats Athens at the battle of Aegospotami.  Athens declines hereafter.
  395  387  Corinthian war.  Hereafter Sparta dominates Greece until the battle of Leuctra
  384  322  Aristotle
  371       Battle of Leuctra. Thebes and allies defeat Sparta.
  362       Battle of Mantinea. Thebes & allies defeat Sparta.  Thebes and Sparta decline hereafter and Macedonia rises in power.
  356  323  Alexander
  331       Battle of Gaugamela. Alexander's Macedonian and Greek army defeats the Persians
  350  280  Demetrius.       Student of Aristotle. Founded Library of Alexandria
  310  230  Aristarchus. Measured the size and distance of the moon and the sun.
  287  212  Archimedes
  275  195  Eratosthenes.  Chief of the Alexandrian Library.
  202       Battle of Zama. Rome defeats Carthage.
  197       Rome defeats Macedon at the Battle of Cynoscephalae. Rome dominates Greece hereafter.
  190  120  Hipparchus, astronomer
  100   44  Julius Caesar
   73       Revolt of Roman slaves led by Spartacus and Crixus
   60   53  First Triumvirate (Caesar, Pompey, Crassus)
   53       Battle of Carrhae. Crassus defeated by the Persians.
   48       Battle of Pharsalus. Julius Caesar and Mark Antony defeat Pompei.
   44       Assassination of Julius Caesar
   43   33  Second Triumvirate (Octavian, Antony, Lepidus). End of Roman Republic
   42       Battle of Philippi. Octavian and Antony defeat Brutus and Cassius.
   31  -14  Reign of Octavian, Roman emperor
   30       Octavian defeats Antony and Cleopatra at Alexandria
   27       Pax Romana begins and lasts until 180 CE

   90  168  Ptolemy.          Library of Alexandria.
  476  550  Aryabhata, Indian mathematician.  Refines Aristarchus' measurements of the size of the sun.
  780  850  Muhammad al Khwarizmi. Mathematician in Baghdad.
  872  950  Al-Farabi, mathematician
 1206       Ghenghis Khan becomes leader of the Mongolians.  Mongolian empire begins
 1258       Baghdad, a city of scholars, is destroyed by Mongolian invaders.
 1473 1543  Nicolaus Copernicus
 1492       New World discovered
 1543       Copernicus publishes the heliocentric model of the solar system.
 1546 1601  Tycho Brahe does precision measurements of the orbits of the planets.
 1561 1626  Francis Bacon.  Introduces empiricism in science. Influential in the founding of the Royal Society
 1571 1630  Johannes Kepler. Discovers that planets orbit in ellipses.
 1564 1642  Galileo. Develops the concept of acceleration.
 1632 1723  Christopher Wren. Builder of cathedrals and founder of the Royal Society
 1643 1727  Isaac Newton. Develops laws of inertia, gravity, and The Calculus.
 1660       Royal Society founded
 1666       French Academy of Sciences founded
 1707 1783  Leonhard Euler
 1776       American revolution
 1777 1855  Carl Friedrich Gauss
 1789       French revolution
 1800       Volta invents the battery, launching modern electromagnetism and chemistry
 1864       Maxwell completes the theory of classical electromagnetism with the "Maxwell equations"
 1905       Einstein develops the theory of special relativity for relativistic motion
 1909       Rutherford discovers the nucleus
 1914       World War 1
 1915       Einstein develops the theory of general relativity for gravitation
 1926       Schroedinger discovers the "Schroedinger formula" for quantum mechanics
 1927       Quantum mechanics developed.
 1940 1945  World War 2
 1947       Transistor invented. Silicon age begins
 1987       Jimmy Connors switches from a steel to a graphite racket. Carbon age begins


Voyages of James Cook.     Red: 1768-71     Green: 1772-75     Blue: 1776-79

1312  Europeans arrive at The Canary Islands  Unknown
1351  Azores. First appearance on a map.      Unknown
1427  Azores Islands, Portugal                de Silves
1419  Madeira Islands, Portugal               Zarco & Teixeira
1456  Cape Verde                              de Noli
1487  Southern tip of Africa                  Dias
1492  West Indies                             Columbus
1494  Treaty of Tordesillas
1497  Newfundland                             Caboto
1498  India                                   Da Gama
1500  Brazil                                  Cabral
1501  Greenland (first modern mapping)        Corte-Real
1501  Newfoundland                            Corte-Real
1505  Bermuda                                 de Bermudez
1512  Spice Islands                           de Abreu
1520  Strait of Magellan                      Magellan
1520  Conquest of the Aztec Empire            Cortez
1522  Westward circumnavigation of the world  Magellan
1526  Marshall Islands                        de Salazar
1533  Conquest of the Incan Empire            Pizarro
1565  Eastward crossing of the Pacific        de Legazpi     Passed north of Hawaii
1574  Archipellago Juan Fernandez Islands
1574  Desventuradas Islands
1606  Australia                               Janszoon
1606  Pitcairn Islands
1642  New Zealand and Tasmania                Tasman
1722  Easter Island                           Roggeveen
1750  Cumberland gap                          Walker
1793  Isla Salas y Gomez
1778  Hawaii                                  Cook
1820  Antarctica                              Bransfield
1859  Midway                                  Middlebrooks

History of democracy

Acropolis of Athens
Palace of Westminster
United States Capitol

 -510       Cleisthenes establishes democracy in Athens upon the overthrow of King Hippias
 -508       Roman Republic founded, replacing monarchy rule
 1215       English Magna Carta
 1660       Royal Society founded by Christopher Wren
 1666       French Academy of Sciences founded
 1688       England, Revolutionary Settlement.  Parliament enacts laws limiting
            the power of the king.
 1689       England, Bill of Rights and Mutiny Bill
 1694       England, Triennial Bill
 1696       England, Treason Act
 1701       England, Act of Settlement
 1769       Golden age of the American Philosophical Society begins as Benjamin
               Franklin becomes president.  Members included Jefferson, Washington,
               Hamilton, Adams, Madison, Paine, and McHenry.
 1775       American patriots form Provisional Congresses in each of the 13 colonies that are
               independent of Great Britain, and they form a unified Continental Congress
 1776       American Declaration of Independence, July 4
 1781       American Articles of Confederation
 1787       Federalist Papers published by Hamilton, Madison, & Jay
 1788       American Constitution established
 1791       American Bill of Rights
 1810       Modern era of British Prime Ministers begins when King George III goes insane
 1830       England, Westminster system of government established (Parliament)
 1911       England, Parliament Act, lessening the power of the House of Lords
 1949       British Parliaments acts of 1949
 2014       British House of Lords Reform Act of 2014

Founding Fathers of America


Boston tea party
Battle of Yorktown
Gaspee affair
Franklin's meme

British colonies of 1750

1743   American Philosophical Society founded by Franklin, located in Philadelphia.
       Members included Washington, Adams, Jefferson, Madison, Hamilton, McHenry, & Paine
1773   Boston Tea party
1774   First Continental Cngress held, consisting of delegates from 12 of the 13 colonies
1774   Patriots of Boston form an informal government independent of Great Britain
1775   Battles of Lexington and Concord
1775   Patriots form Provisional Congresses in each of the 13 colonies that are
       independent of Great Britain, and they form a unified Continental Congress
1775   Patriots form the Continental Army, commanded by Washington
1775   Global war erupts. American Patriots, France, Spain, & The Dutch vs.
       American Loyalists and Great Britain
1776   Declaration of Independence, July 4
1776   British expelled from Boston
1776   British capture New York and hold it for the duration of the War
1776   Patriot invasion of Canada fails
1777   Patriots win the Battle of Saratoga and capture a British army
1777   France enters the war on the side of the Patriots
1781   Patriots and French win the Battle of Yorktown and capture a British army
1781   Articles of Confederation
1783   Treaty of Paris ends the war with America as an independent nation
       America holds all territory east of the Mississippi and south of the Great Lakes
       Britain holds Canada
       Spain holds Florida
1787   Federalist Papers published by Hamilton, Madison, & Jay
1788   Constitution
1789   Washington's term as President begins
1791   Bill of Rights
Declaration of Independence

Declaration of Independence
Articles of Confederation
Bill of Rights


                                           Friends                  Foes

1775  1783   War of Independence           France                   England
1789         Washington become President
1801  1805   First Barbary War             Sweden, Sicily           Barbary States
1803         Louisiana Purchase
1812  1815   War of 1812                   France                   Great Britain
1815  1816   Second Barbary War                                     Barbary States
1819         Acquisition of Florida
1835  1836   Texas revolution                                       Mexico
1845         Texas annexed
1846         Oregon Territory Acquisition
1846  1848   Mexican-American War                                   Mexico
1848         Acquisition from Mexico
1853         Gadsden Purchase
1861  1865   American Civil War
1865  1891   Indian Wars                                            Indian Tribes
1867         Alaska Purchase
1898         Spanish American War                                   Spain
1898         Hawaii Annexation
1899  1902   Philippine-American War                                PHilippine Republic
1917  1918   World War 1                   UK, France               Germany
1841  1945   World War 2                   UK, France, Russia       Germany, Japan, Italy
1950  1953   Korean War                    South Korea              North Korea
1964  1975   Vietnam War                   South Vietnam            North Vietnam
1998  1999   Intervention in Yugoslavia
2001         Intervention in Afghanistan
2003         Intervention in Iraq
2011         Intervention in Libya
2014         Intervention in Syria

~808       Qing Xuzi publishes a formula resembling gunpower, consisting of
           6 parts sulfur, 6 parts saltpeter, and 1 part birthwort herb (for carbon).
~850       Incendiary property of gunpower discovered
1132       "Fire lances" used in the siege of De'an, China
1241       Mongols use firearms at the Battle of Mohi, Hungary
1338       Battle of Arnemuiden.  First naval battle involving cannons.
           The English had 3.
1346       Cannons used in the Siege of Calais and the Battle of Crecy
1540       Biringuccio publishes "De la pirotechnia", giving recipes for gunpowder
1610       First flintlock rifle
1774       Lavoisier appointed to develop the French gunpowder program.  By 1788
           French gunpowder was the best in the world.
1884       Vieille invents smokeless gunpowder, which was 3 times more powerful
           than black powder and less of a nuisance on the battlefield.

History of music

Music eras
 500 - 1400  Medieval
1400 - 1600  Renaissance
1600 - 1760  Baroque         Monteverdi, Vivaldi, Bach, Handel
1720 - 1770  Galant          Gluck
1730 - 1820  Classical       Mozart
1780 - 1910  Romantic        Beethoven, Brahms, Wagner
1890 -  Now  Modern          Prokofiev, Shostakovich

1567 1643  Monteverdi
1637 1707  Buxtehude
1653 1706  Pachelbel
1659 1695  Purcell
1663 1713  Corelli
1671 1751  Albinoni
1678 1741  Vivaldi
1681 1767  Telemann
1685 1750  Bach
1685 1759  Handel
1732 1809  Haydn
1756 1791  Mozart
1770 1827  Beethoven
1782 1840  Paganini
1797 1828  Schubert
1803 1869  Berlioz
1809 1847  Mendelssohn
1810 1849  Chopin
1810 1856  Schumann
1813 1883  Wagner
1813 1901  Verdi
1833 1897  Brahms
1835 1921  Saint-Saens
1838 1920  Bruch
1840 1893  Tchaikovsky
1841 1904  Dvorak
1858 1924  Puccini
1860 1911  Mahler
1862 1918  Debussy
1864 1949  Strauss
1865 1957  Sibelius
1891 1953  Prokofiev
1906 1975  Shostakovich
1873 1943  Rachmaninov
1882 1971  Stravinsky
1910 1981  Barber

Monteverdi   L'Orfeo                    1607    First opera
Purcell      Dido and Aeneas            1683
Handel       Agrippina                  1710
Handel       Giulio Cesare              1724
Handel       Theodora                   1750
Gluck        Orfeo ed Euridice          1762
Gluck        Iphigenie en Tauride       1779
Mozart       The Marriage of Figaro     1786
Mozart       Don Giovanni               1787
Mozart       The Magic Flute            1791
Beethoven    Fidelio                    1805
Rossini      The Barber of Seville      1616
Rossini      Othello                    1816
Rossini      The Thieving Magpie        1817
Rossini      William Tell               1829
Wagner       The Flying Dutchman        1843
Wagner       Tannhauser                 1845
Wagner       Lohengrin                  1850
Verdi        Rigoletto                  1851
Verdi        The Troubadour             1853
Verdi        La Traviata                1853
Offenbach    Orpheus in the Underworld  1858
Berlioz      Les Troyens                1858
Wagner       Tristan and Isolde         1865
Verdi        Don Carlos                 1867
Wagner       Das Rheingold              1869  Ring cycle 1
Wagner       Die Walkure                1870  Ring cycle 2
Verdi        Aida                       1871
Strauss II   Die Fledermaus             1874
Bizet        Carmen                     1875
Wagner       Siegfried                  1876  Ring cycle 3
Wagner       Gotterdammerung            1876  Ring cycle 4
Saint-Saens  Samson and Delilah         1877
Tchaikovsky  Eugene Onegin              1879
Offenbach    The Tales of Hoffman       1881
Wagner       Parsifal                   1882
Delibes      Lakme                      1883
Verdi        Otello                     1887
Humperdinck  Hansel and Gretal          1893
Puccini      La Boheme                  1896
Puccini      Tosca                      1900
Debussy      Pelleas et Melisande       1902
Puccini      Madama Butterfly           1904
Strauss      Salome                     1905
Strauss      Elektra                    1909
Prokofiev    The Love for Three Oranges 1921
Puccini      Turandot                   1926
Britten      Peter Grimes               1945
Bernstein    Candide                    1956

History of musical instruments

Stone carving from Ancient Ur
Lyra from ~ 1000 CE
First electric guitar

Replica of an early piano
Side view of a modern piano

Broadwood piano hammer design
Erard piano hammer design
Modern piano hammer design

Baroque violin bow
Modern violin bow

-2500  An ensemble of lyres was played in the ancient city of Ur, including
       lyres, harps, flutes, and reed instruments.
 1000  Bowed instruments first developed, such as the Lyre
 1200  The guitar comes into use in Europe
 1555  Amati develops the four-string violin
 1700  Cristofori develops the first piano, an instrument where the string is
       struck by a hammer.  Early pianos had 5 octaves
 1785  Tourte develops the modern bow
 1810  Broadwood develops a 6-octave piano
 1820  Broadwood develops a 7-octave piano
 1821  Erard develops the double-escapement mechanism for the piano, a
       device that permitted repeating a note even if the key had not yet risen
       to its maximum vertical position. This facilitated rapid playing
       of repeated notes.
 1835  Tuba invented
 1847  Boehm advances the design of the flute, including a switch from wood to metal
 1931  Beauchamp builds the first electric guitar

Baroque flute
Meyer flute from somewhere between 1850 and 1890
Modern flute

Floth oboe from 1805
Sydney Town Hall Grand Organ
Electric sitar

Clarinet from 1760
Boehm clarinet
Modern clarinet

Baroque guitar
Baroque violin

A harpshichord string is plucked and a piano string is hammered. A harpsichord can't vary its volume.

The strings in a piano exert a force of 20 tons.

The Sydney Town Hall Grand Organ has pipes that are 64 feet long, which corresponds to a frequency of 8.5 Hertz.

Hermann von Helmholtz

Invented the opthalmascope, an instrument for examining the inside of the eye.

Developed theories of eye focus, depth perception, color vision, and motion perception.

Invented the "Helmholtz resonator" for measuring the frequency spectrum of sound.

Discovered the shape of the oscillation of a violin string.

Demonstrated that different combinations of resonators could mimic vowel sounds.

Measured the speed of neurons.

Developed the principle of conservation of energy and demonstrated that it applies to mechanics, heat, light, electricity and magnetism.

Demonstrated that muscle metabolism conserves energy.

Invented the field of psychology with his student Wilhelm Wundt.

In 1863, Helmholtz published "On the Sensations of Tone", which became the standard reference for the next century.

Students: Max Planck, Heinrich Kayser, Eugen Goldstein, Wilhelm Wien, Arthur Konig, Henry Augustus Rowland, Albert A. Michelson, Wilhelm Wundt, Fernando Sanford and Michael I. Pupin.


Pythagoreans celebrate sunrise, painting by Fyodor Bronnikov (1827-1902)
Pythagoreans on a 3rd century coin

Andrea Amati

Amati (1505-1577) lived in Cremona, Italy, and developed the first violins, violas, and cellos.

This violin, now at the Metropolitan Museum of Art, may have been part of a set made for the marriage of Philip II of Spain to Elisabeth of Valois in 1559, which would make it one of the earliest known violins in existence.

Einstein's comments on composers

1) Bach, Mozart, and some old Italian and English composers are my favorites in music. Beethoven considerably less -- but certainly Schubert.

(2) It is impossible for me to say whether Bach or Mozart means more to me. In music I do not look for logic. I am quite intuitive on the whole and know no theories. I never like a work if I cannot intuitively grasp its inner unity (architecture).

(3) I always feel that Handel is good -- even perfect -- but that he has a certain shallowness. Beethoven is for me too dramatic and too personal.

(4) Schubert is one of my favorites because of his superlative ability to express emotion and his enormous powers of melodic invention. But in his larger works I am disturbed by a certain lack of architectonics.

(5) Schumann is attractive to me in his smaller works because of their originality and richness of feeling, but his lack of formal greatness prevents my full enjoyment. In Mendelssohn I perceive considerable talent but an indefinable lack of depth that often leads to banality.

(6) I find a few lieder and chamber works by Brahms truly signficant, also in their structure. But most of his works have for me no inner persuasiveness. I do not understand why it was necessary to write them.

(7) I admire Wagner's inventiveness, but I see his lack of architectural structure as decadence. Moreover, to me his musical personality is indescribably offensive so that for the most part I can listen to him only with disgust.

(8) I feel that [Richard] Strauss is gifted, but without inner truth and concerned only with outside effects. I cannot say that I care nothing for modern music in general. I feel that Debussy is delicately colorful but shows a poverty of structure. I cannot work up great enthusiasm for something of that sort.

  -5       Birth of Christ
  28       Jesus begins teaching
  33       The Crucifiction
  47       The Church of the East is created by Saint Thomas
  64       Great Fire of Rome. Nero blames and persecutes the Christians.
 100       End of the Apostolic age when John the Apostle dies (the last Apostle)
 313       Edict of Milan. Western Roman Emperor Constantine I and Lucinius
           (controlled the Balkans) declare tolerance for Christianity
 325       First Council of Nicaea convened to unify Christianity
 330       Constantine I moves the capital of the Roman Empire from Rome to
           Byzantium, naming it New Rome
 363       Death of Julian, last non-Christian Roman emperor
 367       Athanasius, Bishop of Alexandria, gives the earliest preserved list of
           the books that would become the New Testament canon.
 380       Emperor Theodosius I declares that Nicene Christianity to be the
           state religion of the Roman Empire. Edict of Thessalonica
 381       Nicene Creed established
 393       The Synod of Hippo approves the New Testament canon
 431       Council of Ephesus. Affirmation of the Nicene Creed and rejection of
           Nestorianism, resulting in a schism between the churches of Constantiople
           and Persia.
 451       Council of Chalcedon, affirming the Council of Ephesus. Declares Jesus
           as both human and divine in one
 455       Sack of Rome by the Vandals
 476       Fall of the Western Roman Empire. Emperor Augustus Deposed
 491       Armenian Orthodox split from the East (Greek) and West (Latin) churches.
 525       Christian Calendar created by Dionysius Exiguus
 538       Western Europe becomes completely Catholic when the Byzantine general
           Belisarius defeats the last Arian kingdom.
 550       Crucifix introduced
 664       Celtic Christianity of the British Isles unites with Roman Catholicism
           at the Synod of Whitby
 698       Fall of Carthage
 718 1492  Reconquista. Iberian Peninsula retaken by Roman Catholic Visigoth monarchs
 732       Battle of Tours. Frankish and Burgundian forces under Charles Martel the
           Hammer defeat the Umayyad army, leading to the expulsion of the Arabs from
 793       Beginning of Viking raids on Christendom
 800       King Charalemagne of the Franks is crowned first Holy Roman Emperor
           of the West by Pope Leo III
 966       Duke Mieszko I of Poland baptized. Poland becomes a Christian country
1000       Saint Stephen crowned king of Hungary and Hungary becomes a Christian country
1030       Battle of Stiklestad, victory of Christianity over Norwegian paganism
1054       East-West Schism between Eastern (Orthodox) and Western (Roman Catholic)
1095       Crusades initiated by Pope Urban II at the Council of Clermont
1113       Knights Hospitaller formalized by Pope Paschal II
1118       Knights Templar founded to defend the Holy Land
1191       Knights Teutonic founded
1274       Thomas Acquinas writes the Summa Theologiae, which later becomes official
           Catholic doctrine
1291       Crusades end
1305 1378  Avignon Papacy. Popes reside in Avignon, France
1312       Catholic Countil of Vienne disbands the Knights Templar
1321       Dante Alighieri completes the Divine Comedy
1378 1418  Western Schism. Separate Popes in Rome & Avignon. Reunified at
           Council of Constance in 1418
1453       Fall of Constantinople. Constantinople, the capital of the Byzantine Empire,
           is captured by the Ottoman Empire. End of the Byzantine Empire.
1455       First Gutenberg Bible printed
1478       Spanish Inquisition established by Pope Sixtus IV
1492       Americas discovered
1517       German Protestant Reformaton begun by Martin Luther when he publishes the
           95 Theses
1521       Luther excommunicated by the Pope
1521       Magellan claims The Philippines for Spain and the conversion to Catholocism
1534       English Reformation. Church of England established by King Henry VIII
1534       Jesuit Order founded, sending missionaries to the Americas, India, and China
1537       Christian III of Denmark decrees Lutheranism as the state religion of
           Norway and Denmark
1588       Spanish Armada defeated in its effort to reconquer England for Catholicism
1611       King James Bible
1688       Glorious Revolution in England as William of Orange becomes king
1689       English Bill of Rights establishes religious liberty
1870       Papal States cease to exist when an Italian army conquers Rome


Time zones


Monarchies and republics



Gross Domestic Product


Speed limit



220 BCE

210 CE











Spanish colonies



British Empire, 1921

British colonies


Japanese Empire, 1942


American Empire


Radio and television
1920  Commercial radio broadcasts begin
1934  Commercial television appears
1941  RCA begins broadcasting 525-line television.  Television becomes widespread
1954  First color television broadcast
1965  Half of broadcasts are in color
1972  All broadcasts are in color
2008  Digital television era begins.  All television is digital by 2010

World War 2

1943 July 1
1943 December 1
1944 May 1

1944 November 1
1945 March 1
1945 August 1

1943 July 1
1943 November 1
1944 July 1

1944 September 1
1944 December 15
1945 May 1


History of logic
1585  Stevin introduces decimal numbers.  (For example, writing 1/8 as 0.125)
1637  Cartesian geometry published by Fermat and Descartes
1684  Leibniz publishes The Calculus
1761  Lambert proves that Pi is irrational
1821  Cauchy publishes the "epsilon-delta" definition of a limit,
      which brought rigor to The Calculus.
1830  Galois publishes "Galois Theory", which explains why
      a general polynomial equation of order n can be solved in terms of radicals
      only if n <= 4.
1844  Louisville proves the existence of transcendental numbers
1851  Louisville constructs the first transcendental number
1854  Riemann publishes the Riemann Integral, the first rigorous definition
      of an integral.
1859  Riemann Hypothesis published
1860  Grassmann studies the question of the axiomatization of arithmetic.
1870  Heine defines "uniform continuity"
1872  Heine proves that a continuous function on an open interval need not be
      uniformly continuous.
1872  Weierstrass publishes the "Weierstrass function", the first example of
      a function that is continuous everywhere but differentiable nowhere.
1873  Hermite proves that "e" is transcendental
1874  Cantor proves that the algebraic numbers are countable and that
      the real numbers are uncountable, using the "diagonal slash" argument.
1874  Cantor publishes the first attempt at a rigorous set theory.
1878  Cantor proves that the transcendental numbers and the real numbers have
      the same cardinality, thus estabilishing the ubiquity of transcendental numbers
1878  Cantor publishes the "Continuum Hypothesis":
      "There is no set whose cardinality is strictly between that of the integers
      and the real numbers."
      In 1900, Hilbert included the question of the Continuum Hypothesis in his
      list of 23 unsolved problems.
1882  Lindemann proves that Pi is transcendental.  A corollary is the imposibility
      of squaring a circle with a compass and straightedge.
1883  Cantor publishes the Cantor Set, a rich source of counterexamples
1887  Poincare discovers the phenomenon of "Chaos" while studying celestial mechanics.
      There exist orbits that are neither unbounded nor limiting to a stable state.
1889  Peano publishes a set of axioms for arithmetic which are now the standard.
1898  Hadamard defines a dynamical system where all orbits exponential diverge from
      each other with a positive Lyapunov exponent.
1900  Hilbert publishes a list of 23 unsolved problems. They include:
      The Continuum Hypothesis           (proved independent of ZFC by Godel)
      Prove that the axioms of arithmetic are consistent.  (proved impossible by Godel)
      The Riemann Hypothesis     (still unresolved)
      What is the densest sphere packing?  (resolved in 1998)
1901  Russell publishes "Russell's Paradox", which shows that Cantor's set theory
      leads to a contradiction.  This was resolved in 1922 by the Zermelo-Fraenkel
      axioms of set theory.
1902  Lebesgue publishes the Lebesque Integral, a generalization of the
      Riemann Integral.
      "Lebesgue Measure" is the standard way of assigning a measure to subsets of
      n-dimensional Euclidean space.  For n = 1, 2, or 3, it coincides with the
      standard measure of length, area, or volume.
      The Lebesgue measure of the set of rational numbers in the interval [0,1]
      is 0, and the real numbers on this interval have measure 1.
      The Cantor set is an example of an uncountable set that has Lebesgue measure zero.
1904  Poincare Conjecture published
1904  Zermelo defines the Axiom of Choice.
      Previously, mathematicians had been using this axiom implicitly without realizing
      Kronecker's opposition to Cantor's theories became the inspiration for
      the mathematical outlook of "Constructivism", which asserts that it is
      necessary to construct a mathematical object to prove that it exists (proving
      its nonexistence does not imply its existence).
      Constructivism is at odds with the Axiom of Choice and the Law of the Excluded
1922  Zermelo-Fraenkel axioms of set theory developed (ZF).  This resolved
      Russell's Paradox.
1924  Banach-Tarsky paradox published, exhibiting a spooky consequence of the
      Axiom of Choice.
1931  Godel proves the Incompleteness Theorems.
      For any set of axioms that are nontrivial and consistent,
      there will exist statements about the natural numbers that are true but
      cannot be proven within the system.
      Also, the system cannot prove its own consistency.
      Cantor's "diagonal slash" argument was an inspiration for these theorems.
1935  Bourbaki textbooks published, with the aim of reformulating mathematics on
      an extremely abstract and formal but self-contained basis.  With the goal
      of grounding all of mathematics on set theory, the authors strove for rigour
      and generality.
1940  Godel proves that the Axiom of Choice and the Continuum Hypothesis cannot be
      disproved with the Zermelo-Fraenkel axioms (ZF).
      He also established that the Continuum Hypothesis cannot be disproved
      even if the Axiom of Choice is added to the Zermelo-Fraenkel axioms (ZFC).
1961  Lorenz finds that computer simulations of weather have extreme sensitivity to
      initial conditions.
1963  Cohen proves that the Axiom of Choice and the Continuum Hypothesis cannot be
      proved with the Zermelo-Fraenkel axioms, establishing that they are
      independent of ZF.
1967  Mandelbrot publishes examples of fractals from nature
1967  Bishop publishes "Foundations of Constructive Analysis", where he proved
      most of the important theorems in real analysis by constructive methods.
1982  Mandelbrot publishes "The Fractal Geometry of Nature"
1983  Langlands Program published
1994  Wiles proves Fermat's Last Theorem
2000  Millenium Prize problems published.  They include:
      The Riemann Hypothesis
      P versus NP
      The Poincare Conjecture
      Navier–Stokes existence and smoothness
2002  Perelman proves the Poincare Conjecture
2009  Chau proves the Fundamental Lemma for the Langlands Program
2013  Zhang and Maynard publish results that constitute progress toward resolving
      the twin prime conjecture.

Define a function between the positive integers and the rational numbers on the interval [0,1].
f(1)   =    0
f(2)   =    1
f(3)   =   1/2
f(4)   =   1/3
f(5)   =   2/3
f(6)   =   1/4
f(7)   =   3/4
f(8)   =   1/5
f(9)   =   2/5
f(10)  =   3/5
f(11)  =   4/5
f(12)  =   1/6
f(13)  =   5/6
f(14)  =   1/7
f(15)  =   2/7
f(16)  =   3/7
Every rational number corresponds to a unique integer and every integer corresponds to a unique rational number (a "bijection").

If a set can be bijected with the integers we say it is "Countable". The rational numbers are countable.

"Algebraic numbers" are numbers that can be expressed as the root of a non-zero n-degree polynomial with integer coefficients. The rational numbers correspond to roots of polynomials of degree 1. The algebraic numbers are countable.

Rational number          Expressible as A/B, where A and B are integers.
Irrational number        Not a rational number.
Algebraic number         Expressible as the root of a non-zero polynomial
                         with integer coefficients.
Transcendental number    Not an algebraic number.
Suppose we attenpt to count the real numbers on the interval [0,1]. Let X=f(I) be a bijection between the positive integers I and the reals X, where every real number X is represented by some integer I. Let g(X,n) be the nth digit of X to the right of the decimal point. Define a number Z such that g(Z,n) = g(f(n),n). Z is not equal to f(I) for any integer I, and so Z is not present in the counting. Any attempt to count the reals will result in at least one missed number, hence the reals are uncountable. We say that the integers are "countably infinite" and the reals are "uncountably infinite".

This is Cantor's "diagonal slash" argument that he used to establish that the real numbers are more numerous than the integers. Godel's theorems are inspired by the diagonal slash argument.

In terms of subsets,

Integers  <  Rational numbers  <  Algebraic numbers  <  Transcendental numbers
A countable set has Lebesgue measure zero. In terms of Lebesgue measure over the interval [0,1],
0  =  Rational numbers  =  Algebraic numbers  <  Transcendental numbers  =  Real numbers  =  1
Two sets have the same "cardinality" if and only if a bijection exists between them. In terms of cardinality,
Integers  =  Rational numbers  =  Algebraic numbers  <  Transcendental numbers  =  Real numbers
In terms of cardinality, real numbers are infinitely more numerous than algebraic numbers.

The Continuum Hypothesis conjectures that there exists no set whose cardinality is strictly between that of the integers and the real numbers. If such a set S existed, its cardinality would be such that

Integers  <  S  <  Real numbers

Hermann Weyl, 1949: "Mathematics with Brouwer gains its highest intuitive clarity. He succeeds in developing the beginnings of analysis in a natural manner, all the time preserving the contact with intuition much more closely than had been done before. It cannot be denied, however, that in advancing to higher and more general theories the inapplicability of the simple laws of classical logic eventually results in an almost unbearable awkwardness. And the mathematician watches with pain the greater part of his towering edifice which he believed to be built of concrete blocks dissolve into mist before his eyes."

Hermann Weyl, 1939: "In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain."

Poincare: "There is no actual infinite; the Cantorians have forgotten this, and that is why they have fallen into contradiction."

Industrial revolution
-3000  Coal is used to smelt copper in Britain
 1700  5/6 of the world's coal is mined in Britain
 1800  Volta invents the battery
 1830  Faraday develops the generator for converting mechanical to electric energy
 1856  Bessemer process developed to transform pig iron to steel
 1882  First commercial electricity plants, using hydro or coal power
 1884  Sir Parsons develops the steam turbine, which today is used for 80% of electrical power

CaO             Calcium oxide          Lime
Al2O3           Aluminum oxide
SiO2            Silicon dioxide        Rock, quartz
CaCO3           Calcium carbonate      Limestone
CO2             Carbon dioxide
Al2O3⋅SiO2       Aluminum silicate      Volcanic ash, andalusite, kyanite, sillimanite
CaSO4⋅2(H2O)                            Gypsum
Fe2O3           Iron(III) oxide        Rust
Non-hydraulic cement hardens upon contact with CO2 in the air and cannot be set in the presence of water.

Hydraulic cement hardens upon contact with water.

Aluminum silicates are compounds derived from aluminum oxide (Al2O3) and silicon dioxide (SiO2) and can be found in volcanic ash.

The Ancient Romans made hydraulic cement from volcanic ash and lime.

Non-hydraulic cement:

CaCO3          →  CaO + CO2           Heat for 10 hours at above 825 Celcius
CaO + H2O      →  Ca(OH)2             Add water and then let dry
Ca(OH)2 + CO2  →  CaCO3 + H2O          Hardens in the presence of CO2
Hydraulic cement is made from a mixture of
2(CaO)⋅SiO2         Belite
3(CaO)⋅SiO2         Alite
3(CaO)⋅Al2O3        Tricalcium aluminate
4(CaO)⋅Al2O3⋅Fe2O3   Brownmillerite
Portland cement is a hydraulic cement.

History of cement:

Ancient Babylon            Bitumen (asphalt). Viscous petroleum
Ancient Egypt              Sand and burnt gypsum
Ancient Greece and Rome    Hydraulic cement
1780                       James Parker advances the art of hydraulic cement
1840                       Aspdin develops "Portland cement"
Portland cement:
CaO      .63
SiO2     .219
Al2O3    .069
Fe2O3    .03
MgO      .025
SO3      .017
Portland cement is the most widely used modern cement. It is made by heating limestone (calcium carbonate) with other materials (such as clay) to 1450 Celsius. The resulting hard substance is ground into powder and mixed with gypsum and water, after which it hardens.

Concrete is cement mixed with gravel and sand.

Glass composition
                Egypt     Rome   Europe    Modern
                1500 BC   0 AD   1300 AD

Silica    SiO2    65      68       53       73
Soda      NaO2    20      16        3       16
Potash    K2O      2        .5     17         .5
Lime      CaO      4       8       12        5
Magnesia  MgO      4        .5      7        3
Numbers are percentages.
Star Trek

                          Seasons    Captain

2151-2155  Enterprise        4       Archer
2256-      Discovery         1       Lorca
2266-2269  Star Trek         3       Kirk
2364-2370  Next Generation   7       Picard
2369-2375  Deep Space 9      7       Sisqo
2371-2404  Voyager           7       Janeway

-2700      Vulcan is in a violent colonial era
-900       Vulcans develop space travel
 400       On Vulcan, Surak introduces logic.  Subsequent wars force
           some Vulcans to flee Vulcan and colonize Romulus, and they become
           the Romulans.
 930       Kahless introduces the concept of honor to a warlike Klingon society
1900       Vulcan civilization stabilizes and interstellar exploration begins
1947       Vulcans develop warp drive
1947       Klingons develop warp drive, possibly from reverse-engineering
1957       Earth launches its first spacecraft, Sputnik. Vulcan begins monitoring
           the Earth
2047       Vulcans warp drives reach a speed of Warp 2
2049-2053  Earth WW III
2050       War begins between Vulcan and Andoria
2063       On Earth, Zefrim Cochrane invents the Warp drive,
           prompting the Vulcans to make official contact with Earth
2151       Klingons encounter Earthlings
2151-2152  Enterprise Season 1    (Captain Archer)
2152       Skirmish between a Federation and Romulan warship
2154-2155  Enterprise Season 4
2156-2160  Earth-Romulan War
2060       Battle of Cheron.  The Federation, Klingons, Andorians, and Tellarites
           defeat the Romulans.  Neutral zone established along the Romulan border.
           Romulans go into isolation.
2161       Founding of the United Federation of Planets, including Earth, Vulcan,
           and Andoria. Enterprise season finale
2256       Discovery Season 1
2258       Star Trek 11.  Timeline forks here to the alternate timeline of Star trek 12.
2266-2267  Star Trek Season 1     (Captain Kirk)
2266       Romulans end their isolation and attacks the Federation
2268-2269  Star Trek Season 3
2271       Klingons defeat the Romulans at the battle of Klach D'Kel Brakt
2285       Wrath of Khan
2285       Klingons acquire cloaking technology from the Romulans
2311       Romulan empire goes into isolation
2344       The Federation and the Klingon Empire negotiate a peace treaty
2347       Federaton-Cardassian war begins
2353       The Borg become aware of the existence of humanity
2353       The Federation and the Klingon Empire form an alliance
2354       The U.S.S. Raven is sent to investigate the Borg and disappears
2364       The Next Generation Season 1 (Captain Picard)
2364       Several Federation and Romulan outposts are destroyed by the Borg,
           prompting the Romulan Empire to come out of isolation and negotiate with
           the Federation.
2364       The Federation makes first contact with the Ferengi
2366       The Borg invade the Alpha Quadrant and attack the Federation
2367       Gowron becomes Chancellor of the Klingon Empire
2367       The Federaton and the Cardassian Union sign a peace treaty
2369       Cardassian occupation of Bajor ends
2369       Starfleet takes posession of Deep Space 9
2369       Bajor wormhole discovered.  Starfleet begins exploring the Gamma Quadrant
2369       Deep Space 9 Season 1 (Captain Sisqo)
2370       The Next Generation Season 7
2370       The Federation encounters the Dominion in the Gamma Quadrant, in which
           the U.S.S. Odyssey is destroyed by a Jem'Hedar ship
2371       The Federation and the Romulans begin cooperating in their struggle
           against the Dominion.  The Romulans give the Federation cloaking technology
2371       Voyager Season 1 (Captain Janeway)
2373       The Dominion invades the Alpha Quadrant and attacks the Federation
           the Klingons, and the Cardassians.  The Cardassian homeworld is captured.
2374       The Romulans enter the war against the Dominion
2375       The Federation, Klingons, Romulans, and Cardassians defeat the Dominion
           and eject them from the Alpha Quadrant
2375       Deep Space 9 Season 7
2387       Romulus destroyed by a supernova
2404       Voyager Season 7

Warp factor   Speed in light units

    1              1
    2             10
    3             39
    4            102
    5            214
    6            392
    7            656
    8           1024
    9           1516
   10         Infinite

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