In 1671, Giovanni Cassini measured the parallax of Mars to calculate the distances between the sun and all the planets.

Cassini stayed in Paris, and sent his assistant, Jean Richer, to Cayenne, ten thousand kilometers away, so they could simultaneously measure the distances between Mars and certain distant planets. Based on the parallax, Cassini calculated the distance between Earth and Mars. Given that distance and known ratios between the planets, Cassini calculated the distances of all the planets to the sun.

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poems* . . .

Because planetary orbits are elliptical, the planets’ distances from the sun depends on their places in their orbits. Kepler’s laws of planetary motion describe these elliptical orbits.

Cassini was not the only famous astronomer before the Enlightenment who cast horoscopes for kings or queens.

See also in *The book of science:*

- 240 BCE—
*Geodesy*—Eratosthenes - 1610—
*Observational astronomy*—Galileo Galilei - 1639—
*Transit of Venus*—Jeremiah Horrocks - 1671—
*Surveying the earth*—Jean Picard - 1671—
*Gravimetry*—Jean Richer - 1781—
*Discovery of Uranus*—William Herschel - 1838—
*Distance to a star*—Friedrich Bessel - 1846—
*Discovery of Neptune*—John Couch Adams, Urbain Jean Joseph Le Verrier, Johann Gottfried Galle

Readings in wikipedia:

]]>In 1670, Nehemiah Grew began the study of pollens and spores, which survive from the earliest forms of life in sedimentary rocks.

The study of strewn particles the dust of plants the dust of centuries. Nehemiah Grew discovered that the pollen of a plant, its size and shape, is characteristic of the plant and necessary for its reproduction. Robert Kidston studied fossil spores related them to living species and used them to correlate coal seams.

*More
poems* . . .

Many scientists have contributed to palynology.
The term *palynology* means “the study of dust,”
and was coined in 1944.

See also in *The book of science:*

- 1669—
*Stratigraphy*—Nicolas Steno - 1694—
*Plant sexuality*—Rudolf Jakob Camerarius - 1812—
*Mohs scale*—Friedrich Mohs - 1815—
*Fossil sequences*—William Smith

Readings in wikipedia:

- “Nehemiah Grew”
- “Robert Kidston”
- “Palynology”
- “Dinocyst”
- “Acritarch”
- “Scolecodont”
- “Chitinozoan”
- “Foraminifera”

Phosphorus: atomic number: 15; weight: 30.973761998; Polyatomic nonmetal; discovery: 1669—Hennig Brand.

Could be Hennig Brand thought kidney stones were sympathetic with the philosopher’s stone that he tried to distill gold from urine . . . or could be the golden color of urine deceived him. At any rate, after letting it rot, evaporating it into a paste, heating the paste, discarding the salts (which included most of the phosphorus), mixing and reheating the rest, and cooling the vapors in water, he produced a white waxy material that glowed in the dark, actually ammonium sodium hydrogen phosphate.

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poems* . . .

Lack of phosphorus in the diet can result in hypophosphatemia, with neurological symptoms and so forth, but too much phosphorus isn’t good either. Vertebrates with teeth should appreciate that phosphorus is essential for growing bones and teeth enamel. Maybe that’s why my sweetheart’s teeth are so bright!

See also in *The book of science:*

Readings in wikipedia:

]]>

In 1669, Rasmus Bartholin observed the birefringence of Iceland spar.

Rasmus Bartholin observed, before Thomas Young explained that light was a wave, before Augustin-Jean Fresnel explained how light could be polarized, that light through a piece of Iceland spar suffered a double refraction. Passing through a crystal of calcite the vertical component of the light is deflected at one angle and the horizontal component is deflected at another.

*More
poems* . . .

Light’s lack of a longitudinal vibration (vibration along its direction of travel) is eventually explained by Albert Einstein—the speed of light is constant.

Many frequencies are inherent in normal, incoherent light in the range perceptible to human eyes, and each of those is a blur of ordinary and extraordinary transverse waves. Some people see ghosts, some see auras, some say they have second sight.

See also in *The book of science:*

- 1666—
*Theory of color*—Isaac Newton - 1800—
*Wave nature of light*—Thomas Young - 1819—
*Wave optics*—Augustin-Jean Fresnel, François Arago - 1828—
*Nicol prism*—William Nicol - 1845-1913—
*Magneto-optic and electro-optic effects*—Michael Faraday, John Kerr, Aimé Cotton, Woldemar Voigt, Pieter Zeeman, Henri Mouton, Johannes Stark, Antonino Lo Surdo - 1914—
*Glossmeter*—Leonard R. Ingersoll - 1925—
*Wave-particle duality*—Werner Heisenberg, Louis de Broglie, Erwin Schrödinger

Readings in wikipedia:

]]>In 1669, Jan Swammerdam, dissecting insects under a microscope, showed that animals can dramatically change form through gradual development and differentiation.

Jan Swammerdam studied their lives and found maggot and fly are phases of the same creature. Insects develop gradually from egg, to larva, to winged adult much the same as humans—from egg, to embryo, to infant, to a creature that can dissect an insect under a microscope to find the underdeveloped wings of the adult in the larva.

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poems* . . .

In addition to studying insects, Jan Swammerdam studied muscle contraction and blood cells. As Galileo was the first to use the telescope in astronomy, Swammerdam was the first to use the microscope in dissections.

See also in *The book of science:*

- 1668—
*Parasites*—Francesco Redi - 1673—
*Microorganisms*—Robert Hooke, Antonie van Leeuwenhock - 1765—
*Spontaneous generation*—Lazzaro Spallanzani - 1817—
*Germ layers*—Heinz Christian Pander - 1826—
*Eggs and embryos*—Karl Ernst von Baer

Readings in wikipedia:

]]>In 1669, Nicolas Steno laid out the fundamentals of stratigraphy, how sedimentary rocks are formed, to explain the similarity of shark teeth to fossil glossopetrae.

To explain how a shark’s tooth had the same shape as fossils known as glossopetræ, “tongue-stones,” Niels Stensen, known as Nicolas Steno, took a year to study how fossils could be derived from living things, embedded in stone, and raised up into mountains. Fabio Colonna had established that glossopetræ had organic origins; Steno explained how this happened and extended this by describing how sedimentary rocks formed in layers, were broken, tilted, covered, and uplifted.

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Nicolas Steno’s four principles of stratigraphy in “Principles” are superposition, original horizontality, lateral continuity, and cross-cutting relationships, according to Michael E. Brookfield. Above, those principles are in his own words as translated by John Garrett Winter.

See also in *The book of science:*

- 1565—
*Fossils*—Conrad Gessner - 1670—
*Palynology*—Nehemiah Grew, Robert Kidston - 1785—
*Earth cycles*—James Hutton - 1812—
*Mohs scale*—Friedrich Mohs - 1815—
*Fossil sequences*—William Smith - 1895—
*Speleology*—Édouard-Alfred Martel

Readings in wikipedia:

]]>In 1668, Isaac Barrow, Isaac Newton’s teacher, proved the fundamental theorem of calculus.

Early Greek and Chinese mathematicians used the “method of exhaustion,” determining a value by disproving a series of approximations. This method foreshadowed the concept of a limit. A limit is the value that the result of a function approaches as its input approaches a given value. Determining limits gave European mathematicians the ability to prove the continuity of functions, and to determine their differentials and integrals. James Gregory and Isaac Barrow showed that the derivative and the integral are inverses of each other. The derivative of velocity is acceleration. The integral of acceleration is the velocity.

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poems* . . .

The work of many mathematicians led to the work of James Gregory and Isaac Barrow. A fuller history could name Eudoxus, Liu Hui, Archimedes, Zu Chongzhi, Alhazen, Pierre de Fermat, Bonaventura Cavalieri, Evangelista Torricelli, and John Wallis. Then there were Isaac Newton and Gottfried Wilhelm Leibniz, who invented calculus as a mathematics of motion and change.

See also in *The book of science:*

- 1656—
*Infinite and infinitesimal*—John Wallis - 1671,1684—
*Calculus*—Isaac Newton, Gottfried Wilhelm Leibniz - 1687—
*Principia Mathematica*—Isaac Newton

Readings in wikipedia:

]]>John Wilkins proposed the metric system and the French Revolution established it.

John Wilkins recognized that a standard system of measurement derived from something natural and measurable would reduce the difficulty of conducting trade between countries and proposed a system of tenths for magnitudes, weights, and values based on the length of a pendulum adjusted to swing every second such that subunits—tenths, hundredths, and multiples of ten, one hundred, and so on— and the standard units for volumes, weights, and values would be derived from the standard unit of length. A hundred years went by until the French revolted against abuse of arbitrary units of measurement by the privileged classes, and established, in 1799, metric units for length, area, and volume, to which were later added units for liquid, mass, and electrical amperage, voltage, resistance, power, capacitance, and charge. The French termmetrewas based on the Greekmétron,which meansmeasure.

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Florence Pretz of Kansas City invented the Billiken in 1908 as “the god of things as they ought to be.” Establishing the metric system was a success against things as they ought not be. So many other aspects of our lives are more irrational and heterogeneous.

After the French revolution, the Commission of Weights and Measures included the Marquis de Condorcet, Pierre-Simon Laplace, Adrien-Marie Legendre, Antoine Lavoisier, and Jean-Charles de Borda. The proper name for the modern metric system is the International System of Units, or, in French, le Système International d’Unités, with the abbreviation SI.

The meter preceded both John Wilkins’ work and the French revolution. Marin Mersenne measured the length of the seconds pendulum in 1644; the Royal Society proposed that it should be the standard unit of length in 1660; Tito Livio Burattini proposed that it should be called a meter in 1675.

See also in *The book of science:*

- 240 BCE—
*Geodesy*—Eratosthenes - 1202—
*Number system*—Leonardo Pisano Bigollo (Fibonacci) - 1742—
*Centigrade scale*—Anders Celsius, Jean-Pierre Christin - 1848—
*Kelvin scale*—William Thomson, Lord Kelvin

Readings in wikipedia:

]]>In 1668, Francesco Redi described about 180 parasites and invented the scientific control.

Francesco Redi described about 180 parasites, animals that live in living animals. They don’t appear out of thin air, but lay eggs in the nostrils of deer, or find a freshwater snail from which they emerge as larva and then we eat raw watercress.

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Francesco Redi described the nasal fly of deer and the sheep liver fluke. In his chemotheraputic experiments with parasites and in his experiments refuting spontaneous generation, Redi introduced the use of a scientific control group.

See also in *The book of science:*

- 1669—
*Epigenesis*—Jan Swammerdam - 1765—
*Spontaneous generation*—Lazzaro Spallanzani - 1858—
*Communities of cells*—Rudolf Virchow - 1897—
*Malarial parasite*—Charles Louis Alphonse Laveran, Patrick Manson, Ronald Ross - 1939—
*DDT*—Paul Hermann Müller

Readings in wikipedia:

]]>In 1666, Isaac Newton showed that sunlight is composed of multiple colors that refract through a prism at different angles.

A glass prism splits light into colors, spreading a circular pinhole of sunlight into an array of colors across an oblong shape. Isaac Newton proved that sunlight was spread in an oblong because it consists of different rays that refract through a prism at different angles. This, he realized, limited the perfection of refracting telescopes and microscopes that rely on curved lenses that transmit light, but suggested that relying on curved mirrors, which reflect all rays in sunlight at equal angles, could create a more focused image.

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Newton explained that the differing refractions of colors in sunlight were responsible for the colors of primary and secondary rainbows, thus completing the inquiry begun by Alhazen in 1025.

Isaac Newton’s first reflecting telescope, finished in late 1668, had an object mirror with a diameter of 2 inches, a length of 6 and a quarter inches, and a small diagonal mirror to reflect the image to an eyepiece at the side of the telescope. He observed that it magnified 35 times.

William Herschel and William Parson followed Newton’s design and built reflecting telescopes with speculum mirrors, but with larger and larger diameters to gather more and more light.

See also in *The book of science:*

- 1025—
*Optics*—Alhazen (Abū-‘Alī al-Ḥasan ibn al-Ḥasan ibn al-Ḥaytham) - 1590—
*Microscope and telescope*—Zacharias Janssen, Hans Lippershey, Jacob Metius, Cornelis Drebbel - 1669—
*Birefringence*—Rasmus Bartholin - 1781—
*Discovery of Uranus*—William Herschel - 1800—
*Wave nature of light*—Thomas Young - 1828—
*Nicol prism*—William Nicol - 1845—
*Spiral galaxies*—William Parsons - 1888-1927—
*Cinematography*—Louis Le Prince, Thomas Edison, Auguste and Louis Lumière - 1916—
*Chemical bond*—Gilbert N. Lewis - 1947—
*Holography*—Dennis Gabor - 1956—
*Visual phototransduction*—George Wald

Readings in wikipedia:

]]>In 1665, Robert Hooke discovered the cell, the unit of all life on earth.

Robert Hooke discovered cork cells in 1665 and named them after the small rooms in a monastery. Antonie van Leeuwenhoek described the blood cells of salmon in 1719 and called their nucleilumen.Robert Brown described orchid cells in 1831 and observed an opaque area that he called theareolaornucleus.

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poems* . . .

The microscope was the key invention for discovering and describing cells. The cell is still being discovered. It didn’t stop with discovery of nuclei, or the Golgi apparatus, or the flagella, cilia, or pili, or the ribosomes, mitochondria, centrioles, chloroplasts, peroxisomes, or lysosomes, or the endoplasmic reticula. We are still working out how these things work.

See also in *The book of science:*

- 1673—
*Microorganisms*—Robert Hooke, Antonie van Leeuwenhock - 1839—
*Cell theory*—Matthias Jakob Schleiden, Theodor Schwann, Barthélemy Charles Joseph Dumortier, Hugo von Mohl, Robert Remak, Rudolf Virchow - 1846-1868—
*Protoplasm*—Hugo von Mohl, Jan Evangelista Purkyně, Thomas Henry Huxley - 1858—
*Communities of cells*—Rudolf Virchow - 1878—
*Mitosis*—Walther Flemming, Edouard Van Beneden, Otto Bütschli, Eduard Strasburger - 1889—
*Nervous system*—Camillo Golgi, Santiago Ramón y Cajal

Readings in wikipedia:

]]>In 1662, Pierre de Fermat claimed rays of light from an object travel through multiple paths to the focus point of a lens in the same time.

An old question in optics is why, if light radiates in all directions, why does it seem as though light travels in a single line from an object to the eyes? Alhazen thought it must be that we see only the rays that hit the eyes perpendicularly. Fermat said, simply, a ray of light always takes the fastest available path, not necessarily the shortest path, as a lifeguard who rescues a swimmer at a beach runs along the shore to a closer point before diving into the waves where he moves more slowly. Or if two rays of light diverge from a distant object and a lens focuses them both at the same point, then the outer ray must have a shorter path in the lens so that the two rays arrive at the same time.

*More
poems* . . .

Light has a constant speed, *c,* only in a vacuum.
In other transparent materials, light travels more slowly.
The ratio of the speed of light in a vacuum to the speed of light in a material
is called the refractive index.
For example, in glass light travels about two-thirds of c,
so its refractive index is about 1.5.

See also in *The book of science:*

- 984,1602,1621,1637—
*Snell’s law*—Ibn Sahl, Thomas Harriot, Willebrord Snellius, René Descartes - 1025—
*Optics*—Alhazen (Abū-‘Alī al-Ḥasan ibn al-Ḥasan ibn al-Ḥaytham) - 1676—
*Speed of light*—Ole Rømer - 1678,1816—
*Huygens—Fresnel principle*—Christiaan Huygens

Readings in wikipedia:

]]>In 1662, Robert Boyle described the relation between pressure and volume of an ideal gas.

For a given mass of confined gas, if you keep its temperature the same, its pressure times its volume is constant. So had Richard Towneley and Henry Power asserted, and so, with the help of Robert Hooke, Robert Boyle established by experiment and published in 1662.

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John Dalton proposed his atomic theory in 1808. Robert Brown discovered Brownian motion in 1837. The controversy over the existence of atoms was not settled until 1908 by Ludwig Boltzmann, Albert Einstein, and Jean Baptiste Perrin.

The works of Bernoulli (1738) and Waterston (1843) were ignored until James Clerk Maxwell, James Prescott Joule, Rudolf Clausius, and Ludwig Boltzmann established the kinetic theory of gases by 1871.

See also in *The book of science:*

- 1638—
*Micrometer*—William Gascoigne - 1678—
*Hooke’s law*—Robert Hooke - 1679—
*Pressure cooker, safety valve*—Denis Papin - 1738—
*Bernoulli’s principle*—Daniel Bernoulli - 1808—
*Atomic theory*—John Dalton - 1847—
*Laws of thermodynamics*—Benjamin Thompson, Nicolas Léonard Sadi Carnot, James Prescott Joule, Rudolf Clausius - 1848—
*Kelvin scale*—William Thomson, Lord Kelvin - 1873—
*Changes of state*—Johannes Diederik van der Waals - 1908—
*Brownian motion*—Robert Brown, Ludwig Boltzmann, Albert Einstein, Jean Baptiste Perrin

Readings in wikipedia:

]]>In 1661, John Evelyn wrote about the air pollution in London and recommended mitigations.

London smog was enough of a problem in 1306 for Edward I to ban the burning of coal in the city. John Evelyn in 1661 published a pamphlet to describe the problem and propose solutions.

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poems* . . .

London is not the only city plagued by air pollution. We also have New Delhi, Beiging, and Los Angeles.

For centuries, climate aggregated and aggravated the effects of air pollution. Today, air pollution is creating climate change.

Burning fossil fuels, incinerating waste, leaving waste to decompose, concentrating animals raised for food, overapplying pesticides and fungicides on crops, leaving farms and ranges susceptible to erosion by water and wind, starting wildfires, allowing nuclear tests and failing to prevent nuclear accidents, choosing construction materials and solvents that emit toxins, and overusing cosmetic products all contribute to air pollution.

Noise pollution, light pollution, and unwanted commercial advertizing combine with air pollution to foul the commons.

See also in *The book of science:*

Readings in wikipedia:

]]>In 1661, Robert Boyle published the principles on which chemistry would be distinguished from alchemy.

Boyle claimed that matter consisted of atoms and clusters of atoms in motion, and he distinguished mixtures from compounds. He defined chemistry as the rational and experimental study of the “Principles of Mixt Bodies,” and he observed that matter was not reducible to only a handful of principle elements, as ancient writers had claimed. Boyle was an alchemist but he believed that one should go about it without hocus pocus.

*More
poems* . . .

Robert Boyle was a charter fellow of the Royal Society of London and is regarded as the first modern chemist.

See also in *The book of science:*

- 335 BCE—
*Science*—Aristotle - 1643—
*Atmospheric pressure*—Evangelista Torricelli, Blaise Pascal - 1662—
*Boyle’s law*—Richard Towneley, Henry Power, Robert Boyle - 1678—
*Hooke’s law*—Robert Hooke - 1774—
*Combustion*—Joseph Priestley, Carl Wilhelm Scheele, Antoine Lavoisier - 1784—
*Hydrogen and water*—Henry Cavendish - 1808—
*Atomic theory*—John Dalton - 1916—
*Chemical bond*—Gilbert N. Lewis

Readings in wikipedia:

]]>In 1657, Christiaan Huygens built the first clock regulated by a pendulum, and gave us the math to understand how it works.

For centuries, clocks were regulated by verge escapements with a balance wheel or foliot, a horizontal bar with adjustable weights. A vertical rod with two pallets engage the teeth of a crown wheel to swing the wheel or foliot first in one direction from a pallet hitting a tooth at the top of the crown, then in the other from the second pallet hitting a tooth at the bottom of the crown.

*More
poems* . . .

The area under a cycloid is exactly three times the area of the circle that is used to generate it. Galileo compared these areas by tracing the curves on sheet metal, cutting them out, and weighing them, but his result was about 3.1, so he mistakenly concluded that the ratio was irrational.

Christiaan Huygens’s father, Constantijn Huygens, was a friend of Marin Mersenne, Descartes, and Galileo. So it is interesting to inquire how many of his interests Christiaan picked up from them. Descartes invented analytic geometry; Christiaan taught analytic geometry to Leibniz. Mersenne was interested in music theory and so was Christiaan, who rediscovered 31 equal temperament. Mersenne and Galileo were interested in vibrating strings and in the cycloid, and so was Christiaan. Galileo was interested in the pendulum and using it to regulate a clock and so was Christiaan. Galileo improved the telescope and so did Christiaan. Galileo was the first to observe the rings of Saturn and Christiaan was the first to identify them as rings. Furthermore, as a student, Christiaan corresponded with Fermat, who with Pascal invented probability theory; well, Christiaan wrote the first book on probability theory. But Christiaan Huygens was also important in the development of the internal combustion engine; Denis Papin was his assistant at one time. Papin contributed to early steam engines.

See also in *The book of science:*

- 1637—
*Mersenne’s laws*—Pythagoras, Vincenzo Galilei, Marin Mersenne - 1638—
*Kinematics*—Galileo Galilei - 1656—
*Rings of Saturn*—Christiaan Huygens, James Clerk Maxwell - 1671—
*Gravimetry*—Jean Richer - 1678—
*Hooke’s law*—Robert Hooke - 1814-1815—
*Metronome*—Dietrich Nikolaus Winkel, Johann Maelzel - 1817—
*Kater’s pendulum*—Christiaan Huygens, Gaspard de Prony, Henry Kater - 1851—
*Foucault’s pendulum*—Léon Foucault

Readings in wikipedia:

- “Christiaan Huygens”
- “Pendulum clock”
- “Pendulum”
- “Seconds pendulum”
- “Turret clock”
- “The tautochrone problem”
- “Cycloid”
- “Verge escapement”
- “Galileo’s escapement”
- “Anchor escapement”
- “Grasshopper escapement”
- “Escapement”
- “Gridiron pendulum”
- “Horologium Oscillatorium: sive de motu pendulorum ad horologia aptato demostrationes geometricae” (Latin: The Pendulum Clock: or geometrical demonstrations concerning the motion of pendula as applied to clocks), by Christiaan Huygens

In 1656, John Wallis gave us our symbol for infinity and used 1/infinity for the infinitesimal.

In 1635, Bonaventura Cavalieri introduced infinitesimals, which he called indivisibles, as a means of calculating areas and volumes. John Wallis’s treatise on conic sections clarified Decartes’ work on analytic geometry and introduced the symbol ∞ for infinity and the symbol 1/∞ for the infinitesimal. Wallis’s workArithmetica Infinitorumfinds the area under a curve by integration and established the principle of interpolation to derive the value of π. Thus Wallis, James Gregory, and Isaac Barrow contributed to the development of integral calculus put to use by Isaac Newton and given modern notation by Gottfried Wilhelm Leibniz.

*More
poems* . . .

James Gregory stated and proved the fundamental theorem of calculus for a special class of curves; Isaac Barrow proved the fundamental theorem in general, showing that differentiation and integration are inverses of each other. Isaac Newton was a student of Isaac Barrow.

See also in *The book of science:*

- 628—
*Zero*—Brahmagupta - 1202—
*Number system*—Leonardo Pisano Bigollo (Fibonacci) - 1668,1669—
*Fundamental theorem of calculus*—James Gregory, Isaac Barrow - 1671,1684—
*Calculus*—Isaac Newton, Gottfried Wilhelm Leibniz - 1687—
*Principia Mathematica*—Isaac Newton - 1768—
*Pi*—Johann Heinrich Lambert, Ferdinand von Lindemann

Readings in wikipedia:

]]>In 1656, Christiaan Huygens was the first to observe that Saturn had rings. In 1855, James Clerk Maxwell proved that they were composed of millions of tiny orbiting particles.

Galileo Galilei observed two children of Saturn in 1619. “I have observed the most distant planet to have a triple form.” In 1656, Christiaan Huygens explained that Saturn was surrounded by thin flat disk. “a thin, flat ring, nowhere touching, and inclined to the ecliptic.” Astronomers thought the disk consisted of solid or liquid rings. Giovanni Cassini discovered a gap in 1675. James Clerk Maxwell did the math in 1855 to prove the rings were made of individually orbiting particles that he called “brick-bats.”

*More
poems* . . .

Maxwell has had the final word on the composition of the rings; however, much fine detail has been discovered and many new questions raised from information beamed back to Earth by NASA’s Pioneer, Voyager, and Cassini spacecrafts.

Mimas, Enceladus, Tethys, Dione, Rhea, Titan, and Iapetus are Saturn’s major moons. In addition to these and the particles and aggregates of the rings, there are fifty-five smaller moons and over a hundred and fifty moonlets.

See also in *The book of science:*

- 1610—
*Observational astronomy*—Galileo Galilei - 1654—
*Probability theory*—Blaise Pascal, Pierre de Fermat - 1657—
*Pendulum clock*—Christiaan Huygens - 1678—
*Hooke’s law*—Robert Hooke - 1705—
*Halley’s comet*—Edmond Halley

Readings in wikipedia:

]]>In 1654, letters between Blaise Pascal and Pierre de Fermat established the basis of probability theory.

Pascal and Fermat corresponded over “the problem of points,” that is, how to fairly divide the stakes of a game if the game were left unfinished. They were the first to realize that fairness depends on the number of possible outcomes left in the game. Fermat drew a tree of all possible outcomes, and counted how many outcomes led to each player winning. Pascal showed how to calculate the number of outcomes and introduced the notion of expected value, the weighted average of all possible outcomes.

*More
poems* . . .

This correspondence between Pascal and Fermat influenced Christiaan Huygens, who published the first book on probability theory three years later. Huygens was the guy who first declared that Saturn has a ring, and who invented the pendulum clock.

Fermat was the first to evaluate the integral of general power functions, which influenced both Newton and Leibnitz in their creation of calculus.

See also in *The book of science:*

- 1656—
*Rings of Saturn*—Christiaan Huygens, James Clerk Maxwell - 1763—
*Bayes’ theorem*—Thomas Bayes - 1889—
*Measuring individuals*—Francis Galton

Readings on wikipedia:

]]>In 1647, Francis Lodwick described a language based on philosophical principles with a phonetic alphabet.

In the seventeenth century several tried to construct a language from first principles. Francis Lodwick designed a phonetic alphabet with his own symbols, showing twenty-nine consonants in a table arranged according to the means of their production, one axis being its place of articulation (labial, dental, palatal, velar, sibilant) and the other by its manner of articulation (voiced, voiceless, aspirated, nasal). Then he added fourteen vowels as diacritics. And in 1647 Lodwick advertised a “Perfect Language” whose phonemes signified their places in a taxonomy of all knowledge, “so that two, not knowing each other’s language, could communicate their minds.”

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poems* . . .

A distinction between a philosophical language and an international auxiliary language can seem artificial, since John Wilkins proposed his “Real Character” to replace Latin as an auxiliary to existing natural languages not only for scholars, but also for diplomats, travelers, and merchants; however, the main difference is that a philosophical language is not derived from existing natural languages, but from philosophical principles.

If you want to understand the value of poetry and the meaning of human life, then think about what these philosophical languages leave out.

See also in *The book of science:*

- 1822—
*Deciphering hieroglyphics*—Jean François Champollion - 1839-1887—
*International auxiliary language*—Joseph Schipfer, Joachim Faiguet de Villeneuve, Jean Pirro, Johann Martin Schleyer, L. L. Zamenhof - 2018—
*Shɑrpεn*—Tom Sharp

Readings in wikipedia:

- “Francis Lodwick”
- “Thomas Urquhart”
- “George Dalgarno”
- “John Wilkins”
- “Gottfried Wilhelm Leibniz”
- “Philosophical language”
- “Pasigraphy”
- “Logopandecteision”
- “An Essay towards a Real Character, and a Philosophical Language”
- “Lingua generalis”
- “Characteristica universalis”
- “Alphabet of human thought”
- “The Analytical Language of John Wilkins” an essay by Jorge Luis Borges
- “Ro (artificial language)”
- “Linguistic relativity” (Sapir–Whorf hypothesis)
- “Loglan”
- “Lojban”
- “Laádan”
- “Ithkuil”
- “Toki Pona”

In 1644, William Playfair invented the first infographics. Florence Nightingale and Charles Joseph Minard extended the science and art.

William Playfair created statistical graphics— the line graph, the bar chart, the pie chart, and the circle graph— to show economic data. * Florence Nightingale used polar area diagrams to persuade Queen Victoria and the parliament that lives could have been saved by improving sanitation in military hospitals. * Charles Joseph Minard visualized Napoleon’s losses during his disasterous Russian campaign in relation to time, distance, temperature, and direction of travel.

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A.K.A. data visualization, descriptive statistics, or statistical graphics, forms include line charts, bar charts, circle graphs, histograms, scatter plots and biplots, box plots, pareto charts, pie charts and doughnut charts, ring or sunburst charts, control charts, run charts, step-and-leaf displays, cartograms, trellis charts (also called small multiples, lattice charts, grid charts, and panel charts), probability plots, spaghetti plots, residual plots, and block plots. Polar area diagrams are also called rose diagrams; almost no one calls them coxcombs any more.

Another noted statistical artist was John Snow, whose map of cholera clusters in London in 1854 helped save lives.

See also in *The book of science:*

Readings in wikipedia:

]]>In 1643, Torricelli invented the mercury barometer; in 1648, Pascal discovered the vacuum of space.

Evangelista Torricelli, a student of Galileo, invented the mercury barometer, but its use created a mystery that scientists before Pascal could not explain. Torricelli showed that if you take a glass tube closed on one end, fill it with mercury, and invert it into a cistern, not all of the mercury leaves the tube, leaving a gap at the closed end. Water barometers had been made before but no one before Torricelli realized that the weight of the atmosphere balanced the weight of the liquid in the tube. The difficulty was that scientists believed that air was weightless and that a vacuum was an impossibility. After all, if nothing was in the gap then what propagated the light? Pascal showed that the gap was a vacuum, that the mechanical weight of the atmosphere decreased as you ascended. If you hike high enough, you would reach the vacuum of space.

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Torricelli was the first scientist to point out that wind is caused by differences of atmospheric pressure.

Pascal’s law applies to liquids and gases. Pressure on a fluid at any point is transmitted undiminished throughout the fluid to all constraining points. Equal areas experience equal pressure, so that the pressure transmitted to an area is proportional to the size of the area.

Otto von Guericke invented the first vacuum pump and conducted his famous Magdeburg hemispheres experiment to demonstrate the force of atmospheric pressure.

See also in *The book of science:*

- 1450,1481—
*Hygrometer*—Nicolaus de Cusa, Leonardo da Vinci - 1661—
*Chymistry*—Robert Boyle - 1661—
*Air pollution*—John Evelyn - 1701—
*Newton scale*—Isaac Newton - 1701—
*Rømer scale*—Ole Christensen Rømer - 1724—
*Fahrenheit scale*—Daniel Gabriel Fahrenheit - 1730—
*Réaumur scale*—René Antoine Ferchault de Réaumur - 1735—
*Trade winds*—George Hadley - 1742—
*Centigrade scale*—Anders Celsius, Jean-Pierre Christin - 1765—
*Steam engine*—James Watt - 1774—
*Combustion*—Joseph Priestley, Carl Wilhelm Scheele, Antoine Lavoisier - 1784—
*Hydrogen and water*—Henry Cavendish - 1848—
*Kelvin scale*—William Thomson, Lord Kelvin - 1863—
*Greenhouse effect*—John Tyndall - 1948—
*Casimir effect*—Hendrik Casimir, Dirk Polder

Readings in wikipedia:

]]>In 1639, Jeremiah Horrocks proposed timing the transit of Venus to triangulate Earth’s distance to the sun.

Jeremiah Horrocks proposed timing the transit of Venus across the face of the sun from different places on Earth to calculate our distance to the sun geometrically. Horrocks measured the transit of Venus in 1639 and roughly estimated the distance to the sun, coming closer to the actual distance than anyone previously had. The next opportunities for making these measurements were long after Horrocks had died. Scientists coordinated their efforts and organized expeditions across the globe over the next two hundred years.

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In 1769, the young Joseph Banks accompanied Captain James Cook on his voyage to Tahiti to measure the transit of Venus. Measurements in 1761 and 1769 improved Horrock’s number but, because of optical problems, were not definitive.

See also in *The book of science:*

- 240 BCE—
*Geodesy*—Eratosthenes - 1610—
*Observational astronomy*—Galileo Galilei - 1671—
*Planetary distances*—Giovanni Domenico Cassini - 1687—
*Principia Mathematica*—Isaac Newton - 1838—
*Distance to a star*—Friedrich Bessel

Readings in wikipedia:

]]>In 1638, William Gascoigne invented the telescopic sight and the micrometer.

William Gascoigne discovered a spider’s web at the focal point of a telescope he was designing and realized that if he added crosshairs at that point it would be easier to locate the center of the field of view. He thus made the first telescopic sight. Then Gascoigne realized that by placing two parallel hairs and adjusting their separation using a fine screw he could measure the size of the image in his view and therefore calculate the relative size of objects in the sky. He thus made the first micrometer.

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Researchers at the University of Virginia report that the Greenwich prime meridian, once bisecting the Airy Transit Circle at the Royal Observatory in Greenwich, is now 102 meters to the east, the original line having been deflected because the local direction of gravitation affected the determination of the vertical.

See also in *The book of science*:

- 1542—
*Nonius*—Pedro Nunes - 1572—
*Supernova*—Tycho Brahe - 1631—
*Vernier scale*—Pierre Vernier - 1662—
*Boyle’s law*—Richard Towneley, Henry Power, Robert Boyle - 1671—
*Surveying the earth*—Jean Picard - 1673—
*Microorganisms*—Robert Hooke, Antonie van Leeuwenhock - 1739—
*Dividing engine*—Henry Hindley

Readings in wikipedia:

]]>In 1638, Galileo discovered the laws of falling and moving objects.

Laws of motion were established by Aristotle, but Aristotle got them wrong. Disregarding Aristotle, and disregarding air resistance, falling objects all fall with the same rate of increase. And disregarding friction, objects that move horizontally can continue to move without anything pushing them. Galileo formulated the mathematical laws of motion, even though Aristotle said that mathematics could describe only abstract immutable things.

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Galileo did not get everything right. He thought that the tides were not related to the moon, as Johannes Kepler had claimed, and he misinterpreted the rings of Saturn. In his defense, one must realize that his best telescope magnified the size of objects only 30 times.

Because falling objects moved too fast to accurately time, instead of dropping metal balls from the Tower of Pisa, Galileo studied pendulums and bronze balls rolling down inclined grooves. He timed these by collecting water released from a reservoir and carefully weighing it.

Isaac Newton incorporated Galileo’s law of horizontal motion, the principle of inertia, into his first law of motion.

Although Christiaan Huygens is credited with inventing the pendulum clock in the 1650s, Galileo realized that a pendulum would provide a more accurate clock and invented an escapement mechanism for it in 1642.

See also in *The book of science:*

- 335 BCE—
*Science*—Aristotle - 260 BCE—
*Mechanical advantage*—Archimedes - 1609—
*Planetary orbits*—Johannes Kepler - 1657—
*Pendulum clock*—Christiaan Huygens - 1687—
*Principia Mathematica*—Isaac Newton - 1699—
*Tribology*—Leonardo da Vinci, Guillaume Amontons

Readings in wikipedia:

]]>Marin Mersenne explained that pitch is inversely proportional to the square root of the heaviness of the string.

Pythagoras understood the first law of vibrating strings— pitch is inversely proportional to the length of the string. Pythagoras also knew that the series of harmonic overtones were related to the series of whole-number multiples. Moving right along, it turned out that musicians knew how to tune their lutes without Pythagoras. Galileo’s father, Vincenzo, a musician, certainly realized that pitch also depends on how tight and how thick the string is. He was the first to describe a natural phenomenon using a non-linear mathematical equation. Specifically, he added the second law of vibrating strings— pitch is proportional to the square root of the tension. Finally, Marin Mersenne added the third law— pitch is inversely proportional to the square root of the heaviness of the string.

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Marin Mersenne published *L’Harmonie Universelle* in 1637.
The work of Pythagoras and Vincenzo Galilei, of course, was earlier.
Pythagoras died around 495 BCE, and Galilei died in 1591.
Some sources say that Galileo Galilei,
independently of Mersenne and about the same time,
discovered all three laws of vibrating strings.

By “a non-linear mathematical equation” we mean that the equation relates two things that are not merely directly or inversely proportional to each other, but that depend on the square or square root, cube or cube root.

See also in *The book of science*:

- 495 BCE—
*Proof of the Pythagorean theorem*—Pythagoras - 1657—
*Pendulum clock*—Christiaan Huygens - 1678—
*Hooke’s law*—Robert Hooke - 1831—
*Faraday wave*—Michael Faraday

Readings in wikipedia:

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