Manganese: atomic number: 25; weight: 54.938044; Transition metal; discovery: 1770-1774.

Torbern Bergman investigated pyrolusite, a mineral containing manganese dioxide, distinguishing it from known elements including lime and magnesia alba, but was unable to isolate the element. His friend Carl Wilhelm Scheele used pyrolusite, as an oxydizing agent to produce chlorine and knew it contained a new element, giving it the namemaganese,but was also unable to isolate it. Johan Gottlieb Gahn, Bergman’s former assistant, was able to isolate the element from the mineral by reducing the dioxide with carbon to obtain this hard brittle silvery metal.

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“Symptoms include apathy, bradykinesia, gait disorder with postural instability, and spastic-hypokinetic dysarthria.”

See also in *The book of science:*

Readings in wikipedia:

]]>In 1768, Johann Heinrich Lambert and Ferdinand von Lindemann proved that it is impossible to ”square the circle.”

The history of π (the ratio of the circumference to the diameter of a circle) is old. The Egyptians knew of it; the Babylonians knew of it; the Greek mathematician Archimedes used a polygon of ninety-six sides to calculate it; the Chinese mathematician Liu Hui knew of it and used polygons of one hundred ninety-two sides and three thousand seventy-two sides, calculating their areas rather than perimeters. Over the centuries, new methods for calculating π have resulted in increasing accuracy— but all decimal representations are approximations of a number that is never ending and never repeating.

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To “square the circle” is to find the length of the
sides of a square with the same area as a circle of a given
radius. The area of a circle of radius *r* is
π*r*^{2}, so success depends on the nature of π. The proofs of Lambert
and Lindemann mean that we know that it is impossible for anyone
to construct on a flat surface a square with the same area as a
given circle using a compass and ruler.

The expression “squaring the circle” means trying to do the impossible.

Archimedes used the “method of exhaustion” to approximate the value of π. The work of both Archimedes and Liu Hui prefigured calculus; Archimedes wrote of infinitesimals and Liu Hui described the use of the limit.

See also in *The book of science:*

- 260 BCE—
*Mechanical advantage*—Archimedes - 628—
*Zero*—Brahmagupta - 1202—
*Number system*—Leonardo Pisano Bigollo (Fibonacci) - 1656—
*Infinite and infinitesimal*—John Wallis - 1683—
*Euler’s number*—Jacob Bernoulli, Leonhard Euler - 1829—
*Non-Euclidean geometry*—Nicolai Lobachevsky, János Bolyai, Bernhard Riemann - 1931—
*Incompleteness theorems*—Kurt Gödel

Readings in wikipedia:

- “Pi”
- “Squaring the circle”
- “Irrational number”
- “Transcendental number”
- “Archimedes”
- “Method of exhaustion” used by Archimedes
- “Liu Hui”
- “Liu Hui’s π algorithm”
- “Calculus”
- “Limit (mathematics)”
- “Johann Heinrich Lambert”
- “Ferdinand von Lindemann”

In 1765, James Watt improved the steam engine, making it more efficient and more useful.

James Watt didn’t invent the steam engine; he improved the Newcomen engine. Newcomen didn’t invent it either; Newcomen combined a vacuum, created by cooling steam, from Thomas Savery, with a piston from Denis Papin. The Newcomen engine rocked a beam up and down, suitable for operating a pump.

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Atmospheric pressure was discovered in 1643 by Evangelista
Torricelli, who invented the mercury barometer. Blaise Pascal was
able to prove that the gap at the end of the barameter was a
vacuum. Newcomen’s engine was called an *atmospheric
engine* because it relied on atmospheric pressure against a vacuum
created by cooling steam in a chamber. The Newcomen engine was not
driven by steam pressure.

See also in *The book of science:*

- 70—
*Windmill*—Hero of Alexandria (Heron) - 1643—
*Atmospheric pressure*—Evangelista Torricelli, Blaise Pascal - 1678-1876—
*Internal combustion engine*—Jean de Hautefeuille, Christiaan Huygens, Denis Papin, François Isaac de Rivaz, Nicéphore Niépce, Claude Niépce, Samuel Brown, William Barnett, Eugenio Barsanti, Felice Matteucci, Étienne Lenoir, Alphonse Beau de Rochas, Nikolaus Otto, Eugen Langen - 1761—
*Latent heat*—Joseph Black - 1805—
*Oruktor Amphibolos*—Oliver Evans - 1816—
*Stirling engine*—Robert Stirling - 1847—
*Laws of thermodynamics*—Benjamin Thompson, Nicolas Léonard Sadi Carnot, James Prescott Joule, Rudolf Clausius - 1871—
*Wind tunnel*—Francis Herbert Wenham - 1885—
*Automobile*—Karl Benz - 1893—
*Diesel engine*—Rudolf Diesel - 1903—
*Airplane*—Wilbur Wright, Orville Wright - 1913—
*Tesla turbine*—Nikola Tesla

Readings in wikipedia:

]]>In 1765, Lazzaro Spallanzani disproved the theory of spontaneous generation. He pasteurized and sealed his samples to prove that microbes cannot grow without the introduction of air that carries microbial endospores.

Maggots grow in cow pies. Tapeworms grow in intestines. Without knowing that flies and worms lay eggs and that stepping barefoot into feces or eating undercooked food can pick them up, people believed that very small creatures were generated spontaneously from decaying plant and animal matter. People like John Needham asserted that a vital principle inhered in such substances that spontaneously generated living things. Lazzaro Spallanzani tried to prove this, sterilizing his samples in sealed flasks, and failed. Realizing that heating and sealing his samples killed anything alive that was already in them and protected them from contamination, Spallanzani demonstrated the principle of pasteurization and scooped Louis Pasteur by ninety-five years.

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Worms have been found in rocks at the bottom of a diamond mine; bacteria has been found deep in volcanic rock.

The theory of spontaneous generation originated with Aristotle, who wrote that the “vital heat” contained in air and water was responsible. Needham exposed his broths to air as they cooled after boiling (insufficiently to kill microbial endospores in the broths), not imagining that air could contain microbes and microbial endospores responsible for what he thought were generated spontaneously.

Apes and chimpanzees have been found to “self-medicate” by eating particular astringent leaves and inner barks to cure themselves of malaria and worms.

See also in *The book of science:*

- 1628—
*Circulation of the blood*—William Harvey - 1668—
*Parasites*—Francesco Redi - 1669—
*Epigenesis*—Jan Swammerdam - 1673—
*Microorganisms*—Robert Hooke, Antonie van Leeuwenhock - 1796—
*Vaccination*—Edward Jenner - 1828—
*Synthesis of urea*—Friedrich Wöhler - 1854—
*Cholera and the pump*—John Snow - 1858—
*Communities of cells*—Rudolf Virchow (cell theory) - 1878—
*Germ theory*—Louis Pasteur - 1953—
*Abiogenesis*—Stanley Miller, Harold Urey

Readings in wikipedia:

]]>In 1763, Thomas Bayes introduced the need to use the base rate in determining a probability.

Intuition disregards the base rate; Bayes taught us to regard it. If you think about whether a mammogram detects breast cancer, you must consider the base rate— the prevalence of breast cancer. If a mammogram shows you have breast cancer and the diagnosis is accurate only 80 percent of the time but only one person in a hundred gets breast cancer, then your chance of having it is only about 7.8 percent.

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It goes by the name of “logic,” but what we mean is trying to overcome our instinctual thought-processes to adhere more closely to reality.

See also in *The book of science:*

Readings in wikipedia:

]]>In 1761, Joseph Black discovered latent heat, recognizing that melting ice didn’t raise the temperature of its water.

Joseph Black measured the temperature and realized after he heated ice to melt it that its water was no warmer. The heat had gone into the ice but only changed its state.

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Latent heat is contrasted with sensible heat, which isn’t hidden, but can be felt.

See also in *The book of science:*

- 1765—
*Steam engine*—James Watt - 1823—
*Liquefaction of gases*—Michael Faraday - 1847—
*Laws of thermodynamics*—Benjamin Thompson, Nicolas Léonard Sadi Carnot, James Prescott Joule, Rudolf Clausius - 1873—
*Gibbs free energy*—Josiah Willard Gibbs - 1876—
*Chemical potential*—Josiah Willard Gibbs - 1963—
*Mpemba effect*—Erasto Batholomeo Mpemba, Denis G. Osborne

Readings in wikipedia:

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