Change, Growth, Decay and Transformation

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Change, Growth, Decay and Transformation.  I learned this from Walter White.

adr

Fermenting beer and wine was done very early in our history.

ala

In fact, there is a whole school of historians who think that the beginnings of agriculture lay more in the need to drink beer than in the need to eat food.

ale

Fermenting is a chemical art as are getting metals from ores, making pottery and glazes, rendering fat into soap, glassmaking, and putting tin and copper together to make bronze.

and

Alchemists who recorded changes and experiments with these processes were the pioneers and precursors of chemistry as we know it today.

Alexa

It wasn’t until the seventeenth, maybe even eighteenth century that a clear difference was established between alchemy and chemistry

andy

The first metals used by humans were those which could be found on the ground in their natural state, such as gold, silver, copper, tin and the iron that came from the sky in the form of meteorites.

ama

People have found natural gold in Spanish caves dating from the Paleolithic (40,000 BCE).

ant

Egyptians made weapons from meteoric iron and they called them “Daggers from Heaven.”

ange

Chemistry is change and nothing effects change more dramatically than fire.

bar

To see water boil, or wood transformed into black charcoal, to see sand turn to glass or metals melt… these must have seemed like magical processes at first and indeed they still seem magical.

ann

Tin, copper and lead can be taken out of rock merely by heating the rock and this began to be done around 5,000, 6,000 BCE in Serbia (Majdanpek, Yarmovac, Plocnik).

ben

At the Belovode site in Serbia, people seem to have done the first smelting of, for example, a copper axe head (5,500 BCE) from the Vinča culture.

bia

Archaeologists have found early metals from the third millennium BCE in Portugal, Spain and England (Stonehenge).

bil

The making of perfume from plants, colors from plants and rocks, these are chemical operations.

bri

Arsenic is brown, copper can be an intense, beautiful blue or an equally attractive green.

bla

Tin can be silvery gray and iron is red brown as we see so often in the earth around us.

brit

People began to adorn themselves with these colors very early on.

 bob a

When it was discovered that copper and tin could be put together into a new better metal, a lot of things changed and this major change was called the Bronze Age (3,500 BCE).

cam

Arsenic was an impurity that occurred in the smelting of bronze.

bob m

Iron was much more difficult to take out of its native ore than were gold, copper and tin.

car

There are substantive claims made for early, very early African iron making, but the traditional account is that Hittites began to work iron in 1,200 BCE and so began the Iron Age.

bob s

The Philistines who lived along the eastern Mediterranean coast and who gave their name to Palestine became a successful people because they learned to extract and work iron.

che

Iron Age metalworking (ferrous metallurgy) began to be done almost worldwide in such places as the Middle East, Near East, Far East, Iran, Egypt, Nubia (Sudan), Anatolia (Turkey), Carthage, Greece, Italy, United Kingdom, China, Japan.

bren

As I have mentioned before, the Chinese invented the blast furnace, cast iron, water powered trip hammers and double acting piston bellows.

chi

How do these metals exist in different forms and how do they change into other forms was a question that thoughtful people asked very early. These questions are the foundations of alchemy and chemistry.

bud

What were the simplest, most fundamental elements?

deb

Air, water, earth and fire seemed to be very basic, and then gold, silver, copper, tin.

budd

There were even early philosphers who posited an atomic basis for everything.

dia

How did they do this?

bul

Did they intuit the presence of atoms?

elaine

Democritus and Leucippus in Greece and Kanada in India (in the Vaisheshika sutras) created a theory of atomism that wasn’t heard of again until John Dalton began postulating a similar idea in the eighteenth century of our time.

byran

Where were the proofs for such an idea as atomism?

ele

The Greeks in their philosophy and Kanada in his sutras talked about atoms, but there was no real clear evidence of atoms until the twentieth century.

cha

This didn’t stop Epicurus in 300 BCE from claiming that there was a universe of tiny, indivisible parts (atoms = a tomos = un cut able).

eli

Where was the empirical evidence for this?

chan

Aristotle, just to name one thinker, denied the existence of atoms completely, and Hippocrates thought and said that the human body was composed of four humors, an idea that lasted well into modern times, almost to the Age of Enlightenment.

elia

The four humors were blood, fire, earth and phlegm, and these created the termperaments.

chr

Blood made for a sanguine temperament or mood.

eliz

Fire was choleric.

cla

Water was phlegmatic and earth was melancholic.

eliza

It was quite an elaborate system and it held sway up into the eighteenth century of our time.

Engrid

We still use these terms, of course, but don’t believe in them literally.

ellen

Sentences such as, She had a sanguine disposition.

dal

He had a choleric nature.

else

So and so was so phlegmatic and in a melancholy mood that day.

dale

Epicurus, on the other hand, not only said that we live in a world of atoms, but that it is incumbent upon us to lead balanced, harmonious lives.

emi

How he went from one of these ideas to the other is very Greek, but it is not at all “epicurean” as we use the word today.

dan

Quite the contrary, in fact.

emm

Lucretius sought to explain the thinking of Epicurus to a Roman audience and so he wrote De Rerum Natura (On the Nature of Things) in 50 BCE, where he explains the idea of atomism, what the mind and soul are, sensations, thought, the development of the physical world and many heavenly phenomena.

dann

The self confidence of these early thinkers is staggering.

erika

They were erecting whole worlds out of thin air.

dav

They would never see an atom.

ess

No one would for a long time, and yet they stated unequivocally that atoms were there and were the basis for everything.

davi

Pliny the Elder took a more practical, concrete approach to all of this and described with accuracy many minerals and properties of earth.

fab

 A Persian who wrote in Arabic, Jabir ibn Hayyan studied Aristotle’s idea of air, earth, fire and water in addition to two philosophical elements: sulphur (combustability) and mercury (the metallic properties) and thus developed the elemental system used in medieval alchemy.

don

The three metallic principles: sulphur to flammability or combustion, mercury to volatility and stability, and salt to solidity became the tria prima of the Swiss alchemist Paracelsus who reasoned that Aristotle’s four element theory appeared in bodies as three principles.

fel

Paracelsus saw these principles as fundamental and justified them by recourse to the description of how wood burns in fire.

doug

Mercury was the cohesive principle, so that when it left in smoke the wood fell apart.

fran

Smoke described the volatility (the mercurial principle), the heat-giving flames described flammability (sulphur), and the remnant ash described solidity (salt).

sfg

Alchemy is defined by the Hermetic quest for the philosopher’s stone, the study of which is steeped in symbolic mysticism, and which differs greatly from modern science.

gab

Alchemists wanted to make transformations on an esoteric (spiritual) and/or exoteric (practical) level.

ell

It was the exoteric aspects of alchemy that contributed heavily to the evolution of chemistry in Greco-Roman (Hellenistic) Egypt, in the Islamic golden age, and then in Europe.

geo

Alchemy and chemistry share an interest in the composition and properties of matter, and prior to the eighteenth century were not separated into distinct disciplines.

eri

The term chymistry has been used to describe the blend of alchemy and chemistry that existed before this time.

eric

The earliest Western alchemists, who lived in the first centuries of the common era, invented chemical apparatus.

gin

The bain-marie, or water bath is named for Mary the Jewess, whose work gives the first descriptions of the tribikos and kerotakis, types of stills.

haz

Cleopatra the alchemist described furnaces and has been credited with the invention of the alembic, although there are several claimants for this title.

gina

Jabir ibn Hayyan set the foundations for the experiments and their methodology which influenced alchemists in the Islamic, and, thus, later the European world in the twelfth century.

irw

In the Renaissance, exoteric alchemy remained popular in the form of Paracelsian iatrochemistry (iatros = doctor, physician) while spiritual alchemy flourished in its Platonic, Hermetic, and Gnostic roots.

gret

The quest for the philosopher’s stone, a legendary substance, allegedly capable of turning inexpensive metals into gold, was not outmoded by scientific advances, but was still the domain of respected scientists and doctors until the early eighteenth century.

jac

Jan Baptist van Helmont, Robert Boyle and Isaac Newton were all alchemists as well as chemists.

hea

They still were searching for a formula that would transform base metals into gold, although Newton warned one colleague about advertising that fact.

jack

The thing about alchemy was that there was no orderly, logical system for naming new compounds and the alchemical language was codified, secretive, esoteric and vague.

heat

Different terms meant different things to different people.

james

Science demands openness and complete honesty.

hilda

There is no place in it for concealment and protection of sources.

jer

From The Fontana History of Chemistry (Brock, 1992):

hop

The language of alchemy soon developed an arcane and secretive technical vocabulary designed to conceal information from the uninitiated. To a large degree, this language is incomprehensible to us today, though it is apparent that readers of Geoffrey Chaucer’s Canon’s Yeoman’s Tale or audiences for Ben Jonson’s The Alchemist understood the alchemical language in these narratives well enough to laugh at it.

jeremiah

Chaucer’s tale exposed the more unethical, hypocritical, thieving side of alchemy, especially the manufacture of counterfeit gold from cheap substances.

jacq

Dante Alighieri banished all alchemists to the Inferno.

jim w

In 1317, the Avignon Pope John XXII ordered all alchemists to leave France because they were counterfeiting money.

jacqu

A law was passed in England in 1403 which made the “multiplication of metals” punishable by death.

joel

Yet royalty and privileged classes still sought to discover the philosopher’s stone and the elixir of life for themselves.

jan

Illusions do not die easily.

joh

Potent is the lure of free money, as we still see today.

jaq

The goal of legitimate scientific inquiry was to make experiments reproducible, but one of the major aims of alchemists was to hide their methods, so there was a basic conflict here

john p

There was a need for an honest scientific method where experiments could be repeated by others  results reported in a clear language that laid out both what was known and unknown.

jen

In the Islamic World, Muslims and Arabic speaking Persians were translating the works of the ancient Greeks and Egypticans they were experimenting with scientific ideas.

john s

An early scientific method for chemistry began to emerge with the work of the 9th century chemist Jabir ibn Hayyan (known as “Geber” in Europe), who is considered as “the father of chemistry,” just as Antoine Lavolisier was centuries later.

jenn

Jabir ibn Hayyan introduced a systematic and experimental approach to scientific research based in the laboratory, in contrast to the ancient Greek and Egyptian alchemists who took a more “magical” approach to their discoveries and findings.

johnny s

Hayyan invented and named the alembic (al-anbiq), chemically analyzed many chemical substances, composed lapidaries, distinguished between alkalis and acids, and manufactured hundreds of drugs.

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Jabir ibn Hayyan proceeded systematically, refining the theory of five classical elements into the theory of seven alchemical elements and  identifying mercury and sulfur as chemical elements.

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Many chemists in the Persian Arabic world detected early the speciousness of alchemy, particularly the “transmutation of metals” aspect.

jenny h

Such heroes of chemistry as Abu al-Rayhan al-Buruni, Avicenna (to use his European name), Al-kindi and al-Tusi who wrote about the conservation of mass, noting that a body of matter can, yes, change, but not disappear.

jos

Or appear for that matter, appear out of nowhere.

jill

Rhazes (بوبکر محمد زکریای رازی  Abū Bakr Muḥammad-e Zakariyā-ye Rāzī) shined the bright light of reason on the Aristotle Hippocrates theory of the four humors and said, in effect, “Oh, come on, you can’t be serious.”

jud

Rhazes went on to design and describe many chemical instruments which are still in use today, the crucible or retort, the alembic and different kinds of chemical stoves.

jilli

Paracelsus (1493–1541), a Swiss alchemist, also rejected the four humors theory and formed a hybrid of alchemy and science (iatrochemistry), where chemicals, whether made in the laboratory or found in plants, were used for healing.

kei

Iatrós ( ἰατρός  ”healer”) is Greek for doctor. It is present in such words as pediatrics, psychiatrist, podiatrist.

joy

Paracelsus was not perfect in making his experiments truly scientific.

kenny

For example, as an extension of his theory that new compounds could be made by combining mercury with sulfur, he once made what he thought was “oil of sulfur”.

jul

This was actually dimethyl ether which contained neither mercury nor sulfur.

kor

Georg Agricola (1494–1555), who published his great work De Re Metallica in 1556, wanted to improve the refining of ores and their extraction to smelt metals

juli

Agricola’s work describes the highly developed and complex processes of mining metal ores, metal extraction and metallurgy of the time.

Big Brother And The Holding Company

Agricola created a practical base upon which others could build by removing the alchemical mysticism from the proceedings.

kaa

De Re Metallica describes the many kinds of furnace used to smelt ore, and the book stimulated interest in minerals and their composition.

kurt

Agricola makes numerous references to the earlier author, Pliny the Elder.

kar

In 1605, Sir Francis Bacon published The Proficience and Advancement of Learning, which is the first clear description of the scientific method.

mar

In 1605, Michal Sedziwój  published the alchemical treatise A New Light of Alchemy which proposed the existence of oxygen.

kare

And in 1615 Jean Beguin published the Tyrocinium Chymicum, an early chemistry textbook,containing the first-ever chemical equation.

marco

René Descartes published Discours de la Méthode (1637), which also outlines the scientific method.

kari

The Dutch chemist Jan Baptist van Helmont’s Ortus medicinae is cited by some as a major transitional work between alchemy and chemistry, and it had an important influence on Robert Boyle.

mark

There are numerous experiments in the book which established an early version of the law of conservation of mass.

karm

Jan Baptist van Helmont, during the time just after Paracelsus and iatrochemistry, suggested that there are insubstantial substances other than air and coined a name for them, “gas” from the Greek word chaos, so think about that the next time you’re running on empty.

marten

Van Helmont conducted several experiments involving gases.

kate l

He is also remembered today largely for his ideas on spontaneous generation and his 5-year tree experiment, as well as being considered the founder of pneumatic chemistry.

 maury

English chemist Robert Boyle (1627–1691) refined the modern scientific method for alchemy and separated chemistry further from alchemy.

kate r

Boyle is regarded today as the first modern chemist, and one of the founders of modern chemistry, a pioneer of the experimental scientific method.

michael santo

He did not actually discover Boyle’s Law, but he presented and formalized it in 1662.

kate

Boyle’s law describes the inversely proportional relationship between the absolute pressure and volume of a gas, given a constant temperature within a closed system.

michael

Boyle wrote The Sceptical Chymist  in 1661, a cornerstone book in chemistry.

katem

In The Sceptical Chymist Boyle posits that every phenomenon is the result of collisions of particles in motion.

mon

Boyle asks for experimentation and he asserts that experiments show that the classic four humors or elements: earth, fire, air, and water are not enough to explain nature.

katey

Boyle also pleads that chemistry cease to be subservient to medicine or to alchemy.

myles

He is really pushing for a rigorous approach to scientific experimentation and he believed that all theories must be proved experimentally before being regarded as true.

kath

The Sceptical Chymist  contains some of the earliest modern ideas of atoms, molecules, and chemical reactions, and marks the beginning of the history of modern chemistry.

nig

Boyle aimed for that classic scientific goal, reproducible results, and he needed purer chemicals for that.

kathy a

He agreed with René Descartes in explaining and quantifying the physical properties and interactions of material substances.

old

Boyle was an atomist, but he preferred the term corpuscle over atoms, so that would make him a corpuscleist, which sounds a bit silly now.

kati

“Atom” merely means uncuttable, and I suppose “corpuscle” would mean a little bodylike thing.

pau

One thing is for sure.

katie c

The atom is very cuttable, so the name atom is not very descriptive now.

pee

The atom has been split so many times now that even its parts have been split many times and there is no end in sight.

kelly s

What is the name of the latest found particle of the atom? Found only within the last year? The Higgs Boson, is that it?

per

There’s a whole universe inside an atom, just as those science fiction writers in the 1950s promised us.

kim

So Boyle thought that the most elemental level of matter was the corpuscle.

pet

He performed numerous investigations with an air pump and noted that the mercury fell as air was pumped out.

lau

He also observed that pumping the air out of a container would extinguish a flame and kill small animals placed inside, and well as causing the level of a barometer to drop.

phi

Boyle was in the vanguard of the chemical revolution with his mechanical corpuscular philosophy.

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He found time to repeat the tree experiment of van Helmont, and was the first to use indicators, those little slips of paper, which changed colors with acidity.

ric

Here is van Helmont’s tree experiment in van Helmont’s own words:

lil

I took an earthen pot and in it placed 200 pounds of earth which had been dried out in

an oven.  This I moistened with rain water, and in it planted a shoot of willow which

weighed five pounds.  When five years had passed the tree which grew from it weighed

169 pounds and about three ounces.  The earthen pot was wetted whenever it was

necessary with rain or distilled water only.  It was very large, and was sunk  in the ground,

and had a tin plated iron lid with many holes punched in it, which covered the edge of

the pot to keep air-borne dust from mixing with the earth.  I did not keep track of the

weight of the leaves which fell in each of the four autumns.  Finally, I dried out the earth

in the pot once more, and found the same 200 pounds, less about 2 ounces.  Thus, 164

pounds of wood, bark, and roots had arisen from water alone.”

rob

So, really? 164 pounds of wood, bark and roots had arisen from 2 ounces of water alone? What is the main igredient, truly the principal ingredient that van Helmont is omitting here? Could it be… solar power?

linda k

Is van Helmont forgetting anything else?

robert y

It’s an interesting experiment, isn’t it?

linda

In 1702, German chemist Georg Stahl coined the name “phlogiston” for the substance believed to be released in the process of burning, and thereby set off a couple of centuries of chemical mischief.

sam

The phlogiston theory postulated a fire-like element called phlogiston, contained within combustible bodies, that is released during combustiuon.

lis

The name comes from the Greek φλογιστόν phlogistón (burning up), from φλόξ phlóx (flame).

sha

The phlogiston theory was first stated in 1667 by Johann Joachim Becher.

lor

The theory attempted to explain burning processes such as combustion and rusting which are now collectively known as oxidation.

shaw

When you buy foods that are rich in anti-oxidants you are trying to keep your insides from rusting and burning, aren’t you?

 lyn

In general, substances that burned in air were said to be rich in phlogiston; the fact that combustion soon ceased in an enclosed space was taken as clear-cut evidence that air had the capacity to absorb only a finite amount of phlogiston. When air had become completely phlogisticated it would no longer serve to support combustion of any material, nor would a metal heated in it yield a calx; nor could phlogisticated air support life, for the role of air in respiration was to remove the phlogiston from the body.

ski

Thus, Becher described phlogiston as a process that was basically the opposite of the role of  oxygen in combustion.

malyn

Daniel Rutherford discovered nitrogen in 1772 and used the phlogiston theory to explain his results.

sku

The residue of air left after burning, in fact a mixture of nitrogen and carbon dioxide, was sometimes referred to as phlogisticated air, having taken up all of the phlogiston.

man

Conversely, when oxygen was first discovered, it was thought to be dephlogisticated air, capable of combining with more phlogiston and thus supporting combustion for longer than ordinary air.

sta

Amazing how an airy nothing of a theory can be so catastrophical to common sense. People believed in this absraction for a long time. They also believed in “ether.” Many serious scientists staked their reputations on the existence of phlogiston and ether.

 mand

Around 1735, Swedish chemist Georg Brandt analyzed a dark blue pigment found in copper ore, and demonstrated that the pigment contained a new element, later named cobalt. 

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In 1751, a Swedish chemist and pupil of Stahl’s named Axel Fredrik Cronstedt identified an impurity in copper ore as a separate metallic element, which he named nickel. 

mari

Cronstedt is one of the founders of modern mineralogy.

stef

Cronstedt also discovered the mineral scheelite in 1751, which he named tungsten, meaning “heavy stone” in Swedish.

maria r

In 1754, Scottish chemist Joseph Black isolated carbon dioxide which he called “fixed air”.

steph

In 1757, Louis Claude Cadet de Gassicourt, while investigating arsenic compounds, created Cadet’s fuming liquid, later discovered to be cacodyl oxide, considered to be the first synthetic organomettalic compound.

maria

In 1758, Joseph Black formulated the concept of latent heat to explain the thermochemistry of phase changes.

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In 1766, English chemist Henry Cavendish isolated hydrogen which he called “inflammable air”.

mbd

Cavendish discovered hydrogen as a colorless, odourless gas that burns and can form an explosive mixture with air, and published a paper on the production of water by burning inflammable air (that is, hydrogen) in dephlogisticated air (now known to be oxygen), the latter a constituent of atmospheric air (according to the phlogiston theory).

ted

In 1773, Swedish chemist Carl Wilhelm Scheele discovered oxygen, which he called “fire air”, but did not immediately publish his findings.

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In 1774, English chemist Joseph Priestly independently isolated oxygen in its gaseous state, calling it “dephlogisticated air”, and published his work before Scheele.

ter

During his lifetime, Priestley’s considerable scientific reputation rested on his invention of soda water, his writings on electricity, and his discovery of several “airs” (gases), the most famous being what Priestley dubbed “dephlogisticated air” (oxygen).

mic

However, Priestley’s determination to defend phlogiston theory and to reject what would become the chemical revoution eventually left him isolated within the scientific community.

terry

In 1781, Carl Wilhelm Scheele discovered that a new acid, tungsten acid could be made from Cronstedt’s scheelite (at the time named tungsten).

mor

Scheele and Torbern Bergman suggested that it might be possible to obtain a new metal by reducing this acid.

till

In 1783, José and Fausto Elhuyar  found an acid made from wolframite that was identical to tungstic acid.

nad

Later that year, in Spain, the brothers succeeded in isolating the metal now known as tungsten by reduction of this acid with charcoal, and they are credited with the discovery of the element.

tim

Oliver Sacks wrote an entire entertaining book Uncle Tungsten (Memories of a Chemical Boyhood) about his family and about this metal.

pat

Antoine-Laurent de Lavoisier is celebrated as the father of modern chemistry.

tom s

Lavoisier demonstrated with careful measurements that transmutation of water to earth was not possible, but that the sediment observed from boiling water came from the container.

paula

Lavoisier burnt phosphorus and sulfur in air, and proved that the products weighed more than the original materials.

tom

Nevertheless, the weight gained was lost from the air.

peg

Thus, in 1789, he established the Law of Conservation of Mass, which is also called “Lavoisier’s Law.”

tommy

The world’s first ice-calorimeter, was used in the winter of 1782-83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat involved in various chemical changes, calculations which were based on Joseph Black’s prior discovery of latent heat.

rac

These experiments mark the foundation of thermochemistry.

vic

Repeating the experiments of Priestley, he demonstrated that air is composed of two parts, one of which combines with metals to form calxes.

roh

In Considérations Générales sur la Nature des Acides (1778), Lavoisier demonstrated that the “air” responsible for combustion was also the source of acidity.

wes

The next year, he named this portion oxygen (Greek for acid-former), and the other azote (Greek for no life).

ron

Lavoisier thus has a claim to the discovery of oxygen along with Preistley and Scheele.

zalan

He also discovered that the “inflammable air” discovered by Cavendish, which he termed hydrogen (Greek for water-former), combined with oxygen to produce a dew, as Priestley had reported, which appeared to be water.

rus

In Reflexions sur le Phlogistique (1783), Lavoisier showed the phlogiston theory of combustion to be inconsistent.

zarles

Mikhail Lomonosov independently established a tradition of chemistry in Russia in the 18th century and he also rejected the phlogiston theory, and anticipated the kinetic theory of gases.

rut

Lomonosov regarded heat as a form of motion, and stated the idea of conservation of matter.

zarlic

Lavoisier worked with Claude Louis Berthollet and others to devise a system of chemical nomenclature which serves as the basis of the modern system of naming chemical compounds.

sal

In his Methods of Chemical Nomenclature (1787), Lavoisier invented the system of naming and classification still largely in use today, including names such as sulfuric acid, sulfates and sulfites.

zarne

In 1785, Berthollet was the first to introduce the use of chlorine gas as a commercial bleach.

san

In the same year he first determined the elemental composition of the gas ammonia.

zarry

Berthollet first produced a modern bleaching liquid in 1789 by passing chlorine gas through a solution of sodium carbonate.

she

The result was a weak solution of sodium hypochlorite.

zaul

Another strong chlorine oxidant and bleach which he investigated and was the first to produce, potassium chlorate(KClO3), is known as Berthollet’s Salt.

shei

Berthollet is also known for his scientific contributions to theory of chemical equilibria via the mechanism of reverse chemical reactions.

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Lavoisier’s Traité Élémentaire de Chimie (Elementary Treatise of Chemistry, 1789) was the first modern chemical textbook, and presented a unified view of new theories of chemistry, contained a clear statement of the Law of Conservation of Mass, and denied the existence of phlogiston.

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In addition, it contained a list of elements, or substances that could not be broken down further, which included oxygen, nitrogen, hydrogen, phosophorus, mercury, zinc and sulfur.

zete

His list, however, also included light and caloric, which he believed to be material substances.

silk

In the work, Lavoisier underscored the observational basis of his chemistry, stating “I have tried…to arrive at the truth by linking up facts; to suppress as much as possible the use of reasoning, which is often an unreliable instrument which deceives us, in order to follow as much as possible the torch of observation and of experiment.”

zicholas

Nevertheless, he believed that the real existence of atoms was philosophically impossible.

sus

Lavoisier demonstrated that organisms disassemble and reconstitute atmospheric air in the same manner as a burning body.

zock

With Pierre-Simon Laplace, Lavoisier used a calorimeter to estimate the heat evolved per unit of carbon dioxide produced.

the

They found the same ratio for a flame and animals, indicating that animals produced energy by a type of combustion.

zoel

Lavoisier believed in the radical theory, believing that radicals, which function as a single group in a chemical reaction, would combine with oxygen in reactions.

zommy

He believed all acids contained oxygen.

tit

Lavoisier also discovered that a diamond is a crystalline form of carbon.

zanesha

Following Lavoisier’s work, chemistry acquired a strict quantitative nature, allowing reliable predictions to be made.

zon

The revolution in chemistry which he brought about was a result of a conscious effort to fit all experiments into the framework of a single theory.

zantea

He established the consistent use of chemical balance, used oxygen to overthrow the phlogiston theory, and developed a new system of chemical nomenclature.

zym

Italian physicist Alessandro Volta constructed a device for accumulating a large charge by a series of inductions and groundings.

zavies

Volta investigated the 1780s discovery “animal electricity” by Luigi Galvani and found that the electric current was generated from the contact of dissimilar metals, and that the frog leg was only acting as a detector.

zelissa

Volta demonstrated in 1794 that when two metals and brine-soaked cloth or cardboard are arranged in a circuit they produce an electric current.

zente

In 1800, Volta stacked several pairs of alternating copper (or silver) and zinc discs (electrodes) separated by cloth or cardboard soaked in vrine (electrolyte) to increase the electrolyte conductivity.

zheri

When the top and bottom contacts were connected by a wire, an electric current flowed through the voltaic pile and the connecting wire.

ziz

Thus, Volta constructed the first electrical battery to produce electricity.

zorg

Volta’s method of stacking round plates of copper and zinc separated by disks of cardboard moistened with salt solution was termed a voltaic pile.

albert ellis

Volta is considered to be the founder of the discipline of electrocheistry.

amy schugar

A Galvanic cell (or voltaic cell) is an electrochemical cell that derives electrical energy from spontaneous redox reaction taking place within the cell.

battery

It generally consists of two different metals connected by a salt bridge, or individual half-cells separated by a porous membrane.

alexander aco kostic

In 1802, French American chemist and industrialist Éleuthère Irénée du Pont, who had learned manufacture of gunpowder and explosives from Antoine Lavoisier, established a gunpowder factory in Delaware known as E.I. du Pont de Nemours and Company.

amy

Wanting to make the best powder possible, du Pont was vigilant about the quality of the materials he used.

andy juke joint

For 32 years, du Pont served as president of E. I. du Pont de Nemours and Company, which eventually grew into one of the largest and most successful companies in America.

angie bowie

Throughout the 19th century, chemistry was divided between those who followed the atomic theory of John Dalton and those who did not, such as Wilhelm Ostwald and Ernst Mach.

bill gavigan

Although such proponents of the atomic theory as Amedeo Avogadro and Ludewig Boltsmann made great advances in explaining the behavior of gases, this dispute was not finally settled until Jean Perrin’s experimental investigation of Einstein’s atomic explanation of Brownian motion in the first decade of the 20th century.

anne herrero

Well before the dispute had been settled, many had already applied the concept of atomism to chemistry.

bo healey

A major example was the ion theory of Svante Arrhenius which anticipated ideas about atomic substructure that did not fully develop until the 20th century.

annie minogue

Michael Faraday was another early worker, whose major contribution to chemistry was electrochemistry, in which (among other things) a certain quantity of electricity during electrolysis or electrodeposition of metals was shown to be associated with certain quantities of chemical elements, and fixed quantities of the elements therefore with each other, in specific ratios.

bodhi setchko

These findings, like those of Dalton’s combining ratios, were early clues to the atomic nature of matter.

betsy

In 1803, English meteorologist and chemistJohn Dalton had proposed Dalton’s law, which describes relationship between the components in a mixture of gases and the relative pressure each contributes to that of the overall mixture.

brad jenkins

This concept, which John Dalton formulated in 1802, is also known as Dalton’s law of partial pressures.

christy jones segale

Dalton also proposed an atomic theory in 1803 which stated that all matter was composed of small indivisible particles termed atoms.

charles schapers

Atoms of a given element possess unique characteristics and weight, and three types of atoms exist: simple (elements), compound (simple molecules), and complex (complex molecules).

daphne graham

In 1808, Dalton first published New System of Chemical Philosophy (1808-1827), in which he outlined the first modern scientific description of the atomic theory.

darrell soltesz

This work identified chemical elements as a specific type of atom, therefore rejecting Newton’s theory of chemical affinities.

dava sheridan

Instead, Dalton inferred proportions of elements in compounds by taking ratios of the weights of reactants, setting the atomic weight of hydrogen to be identically one.

dave archer

Following Jeremias Benjamin Richer (who was known for introducing the term stoichiometry), John Dalton proposed that chemical elements combine in integral ratios.

eileen healey humphreys

This is known as the law of multiple proportions or Dalton’s law, and Dalton included a clear description of the law in his New System of Chemical Philosophy.

david hicks

The law of multiple proportions is one of the basic laws of stoichiometry used to establish the atomic theory.

erika andrew-luzaich

Despite the consideration of atoms as physically real entities and introduction of a system of chemical symbols, New System of Chemical Philosophy devoted almost as much space to the caloric theory as to atomism.

david pangburn

French chemist Joseph Proust proposed the law of definite proportions, which states that elements always combine in small, whole number ratios to form compounds, based on several experiments conducted between 1797 and 1804.

franca bo

Along with the law of multiple proportions, the law of definite proportions forms the basis of stoichiometry.

david roberts

The law of definite proportions and constant composition do not prove that atoms exist, but they are difficult to explain without assuming that chemical compounds are formed when atoms combine in constant proportions.

gayle gannes rosenthal

A Swedish chemist and disciple of Dalton, Jöns Jacob Berzelius embarked on a systematic program to try to make accurate and precise quantitative measurements and insure the purity of chemicals.

ebb eskew

Along with Lavoisier, Boyle, and Dalton, Berzelius is known as one of the fathers of modern chemistry.

gina jacupke

In 1828 he compiled a table of relative atomic weights, where oxygen was assigned the number 100, and which included all of the elements known at the time.

gerry ottesen

This work provided evidence in favor of Dalton’s atomic theory: that inorganic chemical compounds are composed of atoms combined in whole number amounts.

gretchen andrew

He determined the exact elementary constituents of large numbers of compounds.

james patrick penrod

The results strongly confirmed Proust’s Law of Definite Proportions.

jackie eco

In his weights, he used oxygen as a standard, setting its weight equal to exactly 100. He also measured the weights of 43 elements. In discovering that atomic weights are not integer multiples of the weight of hydrogen, Berzelius also disproved Prout’s hypothesis that elements are built up from atoms of hydrogen.

john murray

Motivated by his extensive atomic weight determinations and a desire to aid his experiments, Berzelius introduced the classical system of chemical symbols and notation with his 1808 publishing of Lärbok i Kemien, in which elements are abbreviated by one or two letters to make a distinct abbreviation from their Latin name.

jacque lynn schultz

This system of chemical notation—in which the elements were given simple written labels, such as O for oxygen, or Fe for iron, with proportions noted by numbers—is the same basic system used today. The only difference is that instead of the subscript number used today (e.g., H2O), Berzelius used a superscript (H2O).

john subee

Berzelius is credited with identifying the chemical elements silicon, selenium, thorium and cerium. Students working in Berzelius’s laboratory also discovered lithium and vanadium.

jena rockwood

Berzelius developed the radical theory of chemical combination, which holds that reactions occur as stable groups of atoms called radicals are exchanged between molecules.

keith graves

He believed that salts are compounds of an acid and bases, and discovered that the anions in acids would be attracted to a positive electrode (the anode), whereas the cations in a base would be attracted to a negative electrode (the cathode).

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Berzelius did not believe in the Vitalism Theory, but instead in a regulative force which produced organization of tissues in an organism.

jenda derringer

Berzelius is also credited with originating the chemical terms catalysis, polymer, isomer and allotrope, although his original definitions differ dramatically from modern usage. For example, he coined the term “polymer” in 1833 to describe organic compounds which shared identical empirical formulas but which differed in overall molecular weight, the larger of the compounds being described as “polymers” of the smallest. By this long superseded, pre-structural definition, glucose (C6H12O6) was viewed as a polymer of formaldehyde (CH2O).

English chemist Humphry Davy was a pioneer in the field of electrolysis, using Alessandro Volta’s voltaic pile to split up common compounds and thus isolate a series of new elements. He went on to electrolyse molten salts and discovered several new metals, especially sodium and potassium, highly reactive elements known as the alkali metals.

jennifer espinoza

You may remember a clerihew that I quoted about this man:  Sir Humphry Davy abominated gravy, and deserved the odium of having discovered sodium.

kevin thellen

Potassium, the first metal that was isolated by electrolysis, was discovered in 1807 by Davy, who derived it from caustic potash (KOH).

jessica holmes

Before the 19th century, no distinction was made between potassium and sodium. Sodium was first isolated by Davy in the same year by passing an electric current through molten sodium hydroxide(NaOH).

larry hankin

When Davy heard that Berzelius and Pontin prepared calcium amalgam by electrolyzing lime in mercury, he tried it himself. Davy was successful, and discovered calcium in 1808 by electrolyzing a mixture of lime and mercuric oxide. He worked with electrolysis throughout his life and, in 1808, he isolated magnesium, strontium and barium.

jodi hodgson long

Davy also experimented with gases by inhaling them. This experimental procedure nearly proved fatal on several occasions, but led to the discovery of the unusual effects of nitrous oxide which came to be known as laughing gas. He understood that nitrous oxide had anesthetic properties but didn’t emphasize this fact, and so it was a long time before this compound was used in surgical operations. It is saddening to think of all the needless suffering that happened in the interval between Davy’s discovery of nitrous oxide and its implementation in the medical field.

matty groves

Chlorine was discovered in 1774 by Swedish chemist Carl Wilhelm Scheele, who called it “dephlogisticated marine acid” and mistakenly thought it contained oxygen. Scheele observed several properties of chlorine gas, such as its bleaching effect on litmus, its deadly effect on insects, its yellow-green colour, and the similarity of its smell to that of aqua regia.

julie stein

Scheele was unable to publish his findings at the time, and in 1810, chlorine was given its current name by Humphry Davy (derived from the Greek word for green), who insisted that chlorine was in fact an element.

michael LeValley

Davy also showed that oxygen could not be obtained from the substance known as oxymuriatic acid (HCl solution). This discovery overturned Lavoisier’s definition of acids as compounds of oxygen.

kat

French chemist Joseph Louis Gay-Lussac shared the interest of Lavoisier and others in the quantitative study of the properties of gases.

paul grushkin

From his first major program of research in 1801–1802, he concluded that equal volumes of all gases expand equally with the same increase in temperature: this conclusion is usually called Charles law (Gay-Lussac gave credit to Jacques Charles, who had arrived at nearly the same conclusion in the 1780s but had not published it).

katharine boyd galine MoDemoiselle

Charles law was independently discovered by John Dalton in 1801, although Dalton’s description was less thorough than Gay-Lussac’s.

paul sacca

In 1804 Gay-Lussac made several daring ascents of over 7,000 meters above sea level in hydrogen-filled balloons—a feat not equaled for another 50 years—that allowed him to investigate other aspects of gases. Not only did he gather magnetic measurements at various altitudes, but he also took pressure, temperature, and humidity measurements and samples of air, which he later analyzed chemically.

katie cole

In 1808 Gay-Lussac announced what was probably his single greatest achievement: from his own and others’ experiments he deduced that gases at constant temperature and pressure combine in simple numerical proportions by volume, and the resulting product or products—if gases—also bear a simple proportion by volume to the volumes of the reactants. In other words, gases under equal conditions of temperature and pressure react with one another in volume ratios of small whole numbers. This conclusion subsequently became known as Gay-Lussac’s law or the Law of Combining Volumes.

richard flynn

With his fellow professor at the École Polytechnique, Louis Jacques Thénard, Gay-Lussac also participated in early electrochemical research, investigating the elements discovered by its means. Among other achievements, they decomposed boric acid by using fused potassium, thus discovering the element boron.

kristen capolino

The two also took part in contemporary debates that modified Lavoisier’s definition of acids and furthered his program of analyzing organic compounds for their oxygen and hydrogen content.

richard mott

The element iodine was discovered by French chemist Bernard Courtois in 1811. Courtois gave samples to his friends,Charles Bernard Desormes (1777-1862) and Nicolas Clément (1779–1841), to continue research. He also gave some of the substance to Gay-Lussac and to physicist André-Marie Ampère.

leslie jacobson

On December 6, 1813, Gay-Lussac announced that the new substance was either an element or a compound of oxygen. It was Gay-Lussac who suggested the name “iode”, from the Greek word ιώδες (iodes) for violet (because of the color of iodine vapor).

robbie

Ampère had given some of his sample to Humphry Davy. Davy did some experiments on the substance and noted its similarity to chlorine. Davy sent a letter dated December 10 to the Royal Society of London stating that he had identified a new element. Arguments erupted between Davy and Gay-Lussac over who identified iodine first, but both scientists acknowledged Courtois as the first to isolate the element.

luanne king

In 1815, Humphry Davy invented the Davy lamp, which allowed coal miners to work safely in the presence of flammable gases. There had been many mining explosions caused by firedamp or methane, often ignited by open flames of the lamps then used by miners. Davy thought of using an iron gauze to enclose a lamp’s flame, and so prevent the methane burning inside the lamp from passing out to the general atmosphere.

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Although the idea of the safety lamp had already been demonstrated by William Reid Clanny and by the then unknown (but later very famous) engineer George Stephenson, Davy’s use of wire gauze to prevent the spread of flame was used by many other inventors in their later designs.

meliha nametak-long

There was some discussion as to whether Davy would have discovered the principles behind his lamp without the help of the work of Smithson Tennant, but it was generally agreed that the work of both men had been independent. Davy refused to patent the lamp, and its invention led to his being awarded the Rumford medal in 1816.

stephen long

After Dalton published his atomic theory in 1808, certain of his central ideas were soon adopted by most chemists. However, uncertainty persisted for half a century about how atomic theory was to be configured and applied to concrete situations. Chemists in different countries developed several different incompatible atomistic systems.

minna elena

A paper that suggested a way out of this difficult situation was published as early as 1811 by the Italian physicist Amedeo Avogadro  (1776-1856), who hypothesized that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, from which it followed that relative molecular weights of any two gases are the same as the ratio of the densities of the two gases under the same conditions of temperature and pressure.

steve schuh

Avogadro also reasoned that simple gases were not formed of solitary atoms but were instead compound molecules of two or more atoms. Thus Avogadro was able to overcome the difficulty that Dalton and others had encountered when Gay-Lussac reported that above 100 °C the volume of water vapor was twice the volume of the oxygen used to form it. According to Avogadro, the molecule of oxygen had split into two atoms in the course of forming water vapor.

monica

Avogadro’s hypothesis was neglected for half a century after it was first published. Many reasons for this neglect have been cited, including some theoretical problems, such as Jöns Jacob Berzelius’s “dualism,” which asserted that compounds are held together by the attraction of positive and negative electrical charges, making it inconceivable that a molecule composed of two electrically similar atoms—as in oxygen—could exist.

steven bolstad

An additional barrier to acceptance of Avogadro’s hypothesis was the fact that many chemists were reluctant to adopt physical methods (such as vapour-density determinations) to solve their problems. By mid-century, however, some leading figures had begun to view the chaotic multiplicity of competing systems of atomic weights and molecular formulas as intolerable. Moreover, purely chemical evidence began to mount that suggested Avogadro’s approach might be right after all.

nicole sutton

During the 1850s, younger chemists, such as Alexander Williamson in England, Charles Gerhardt and Charles-Adolphe Wurtz in France, and August Kekulé in Germany, began to advocate reforming theoretical chemistry to make it consistent with Avogadrian theory.

stu robins septoff

In 1825, Friedrich Wöhler and Justus von Liebig performed the first confirmed discovery and explanation of isomers earlier named by Berzelius.

robin drysdale

Working with cyanic acid and fulminic acid, they correctly deduced that isomerism was caused by differing arrangements of atoms within a molecular structure.

terry nails

In 1827, William Prout classified biomolecules into their modern groupings: carbohydrates, proteins and lipids.

rona walstra

After the nature of combustion was settled, another dispute, this one concerning vitalism and the essential distinction between organic and inorganic substances, began. The vitalism question was revolutionized in 1828 when Friedrich Wöhler synthesized urea, thereby establishing that organic compounds could be produced from inorganic starting materials and disproving the theory of vitalism. Never before had an organic compound been synthesized from inorganic material.

thomas israel

This opened a new research field in chemistry, and by the end of the 19th century, scientists were able to synthesize hundreds of organic compounds, the most important among them being mauve, magenta and other synthetic dyes, as well as the widely used drug aspirin. You have probably heard it said of aspirin, that, were it invented today, you would need a prescription for it, since its uses are manifold.

sally

The discovery of the artificial synthesis of urea contributed greatly to the theory of isomerism, as the empirical chemical formulas for urea and ammonium cyanate are identical.

tim gilliland

In 1832, Friedrich Wöhler and Justus von Liebig discovered and explained functional groups and radicals in relation to organic chemistry, as well as first synthesizing benzaldehyde.

shelley champine

Liebig, a German chemist, made major contributions to agricultural and biological chemistry, and worked on the organization of organic chemistry, and he is considered the “father of the fertilizer industry” for his discovery of nitrogen as an essential plant nutrient, and his formulation of the Law of the Minimum which described the effect of individual nutrients on crops.

tim swain

In 1840, Germain Hess proposed Hess’ law, an early statement of the law of conservation of energy, which establishes that energy changes in a chemical process depend only on the states of the starting and product materials and not on the specific pathway taken between the two states.

steph harwood

In 1847, Hermann Kolbe obtained acetic acid from completely inorganic sources, further disproving vitalism.

tomas sclar

In 1848, William Thomson, 1st Baron Kelvin  (commonly known as Lord Kelvin), established the concept of absolute zero, the temperature at which all molecular motion ceases.

teagen leonhart

In 1849, Louis Pasteur discovered that the racemic form of tartaric acid is a mixture of the levorotatory and dextrotatory forms, thus clarifying the nature of optical rotation and advancing the field of stereochemistry.

wayne mesker

In 1852, August Beer proposed Beer’s law, which explains the relationship between the composition of a mixture and the amount of light it will absorb. Based partly on earlier work by Pierre Bouguer and Johann Heinrich Lambert, Beer’s law established the analytical technique known as spectrophotometry.

tina tkalcec

In 1855, Benjaman Silliman, Jr. pioneered methods of petroleum cracking which made the entire modern petrochemical industry possible, so we love him, right?

Zanilo Lopes

Avogadro’s hypothesis was that that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, from which it followed that relative molecular weights of any two gases are the same as the ratio of the densities of the two gases under the same conditions of temperature and pressure.

victoria vanozzi

This hypothesis began to gain broad appeal among chemists only after his compatriot and fellow scientist Stanislao Cannizzarro demonstrated its value in 1858, two years after Avogadro’s death.

Zdoug Bentsen

Cannizzaro’s chemical interests had originally centered on natural products and on reactions of aromatic compounds

Zandy Lynch

In 1853 he discovered that when benzaldehyde is treated with concentrated base, both benzoic acid and benzyl alcohol are produced, a phenomenon known today as the Cannizzaro reaction. In his 1858 pamphlet, Cannizzaro showed that a complete return to the ideas of Avogadro could be used to construct a consistent and robust theoretical structure that fit nearly all of the available empirical evidence. For instance, he pointed to evidence that suggested that not all elementary gases consist of two atoms per molecule—some were monoatomic, but most were diatomic, and a few were even more complex.

Zerry Donald

Another point of contention had been the formulas for compounds of the alkali metals(such as sodium) and the alkaline earth metals (such as calcium), which, in view of their striking chemical analogies, most chemists had wanted to assign to the same formula type.

Zerin Daniels

Cannizzaro argued that placing these metals in different categories had the beneficial result of eliminating certain anomalies when using their physical properties to deduce atomic weights. Unfortunately, Cannizzaro’s pamphlet was published initially only in Italian and had little immediate impact.

Zezio Guaitamacchi

The real breakthrough came with an international chemical congress held in the German town of Karlsruhe in September 1860, at which most of the leading European chemists were present. The Karlsruhe Congress had been arranged by Kékule, Wurtz, and a few others who shared Cannizzaro’s sense of the direction chemistry should go.

Zetz Burkart

Speaking in French (as everyone there did), Cannizzaro made an indelible impression on the assembled body. Moreover, his friend Angelo Pavesi distributed Cannizzaro’s pamphlet to attendees at the end of the meeting; more than one chemist later wrote of the decisive impression the reading of this document provided.

Zikael Kähäri

For instance, Lothar Meyerlater wrote that on reading Cannizzaro’s paper, “The scales seemed to fall from my eyes.” Cannizzaro thus played a crucial role in winning the battle for reform. The system advocated by him, and soon thereafter adopted by most leading chemists, is substantially identical to what is still used today.

Ziane Dupuis

In 1856, Sir William Henry Perkin, age 18, given a challenge by his professor, August Wilhelm von Hofmann, sought to synthesize quinine, the anti-malaria drug from coal tar. In one attempt, Perkin oxidized aniline using potassium dichromate, whose toluidine impurities reacted with the aniline and yielded a black solid—suggesting a “failed” organic synthesis.

Zac Smith

As he was cleaning the flask with alcohol, Perkin noticed purple portions of the solution: a byproduct of the attempt was the first synthetic dye, known as mauveine or Perkin’s mauve. Perkin’s discovery is the foundation of the dye synthesis industry, one of the earliest successful chemical industries.

Zallison McFarland Boring

German chemist August Kekulé von Stradonitz’s most important single contribution was his structural theory of organic composition, outlined in two articles published in 1857 and 1858 and treated in great detail in the pages of his extraordinarily popular Lehrbuch der organischen Chemie (“Textbook of Organic Chemistry”), the first installment of which appeared in 1859 and gradually extended to four volumes.

Zanilo Lopes

Kekulé argued that tetravalent carbon atoms, that is, carbon forming exactly four chemical bonds, could link together to form what he called a “carbon chain” or a “carbon skeleton,” to which other atoms with other valences (such as hydrogen, oxygen, nitrogen, and chlorine) could join. He was convinced that it was possible for the chemist to specify this detailed molecular architecture for at least the simpler organic compounds known in his day.

Zalzara Getz

Kekulé was not the only chemist to make such claims in this era. The Scottish chemist Archibald Scott Couper published a substantially similar theory nearly simultaneously, and the Russian chemist Aleksandr Butlerov  did much to clarify and expand structure theory. However, it was predominantly Kekule’s ideas that prevailed in the chemical community.

Zbarrett Steven

British chemist and physicist William Crookes is noted for his cathode ray studies, fundamental in the development of atomic physics.

Zarianna Dapello Balleto

His researches on electrical discharges through a rarefied gas led him to observe the dark space around the cathode, now called the Crookes dark space. He demonstrated that cathode rays travel in straight lines and produce phosphorescence and heat when they strike certain materials.

Zbenjamin Perkoff

A pioneer of vacuum tubes, Crookes invented the Crookes tube – an early experimental discharge tube, with partial vacuum with which he studied the behavior of cathode rays.

Zbeverly Green

With the introduction of spectrum analysis by Robert Bunsen and Gustav Kirchhoff  (1859-1860), Crookes applied the new technique to the study of selenium compounds. Bunsen and Kirchoff had previously used spectroscopy as a means of chemical analysis to discover caesium and rubidium.

Zbrian Fischer

In 1861, Crookes used this process to discover thallium in some seleniferous deposits. He continued work on that new element, isolated it, studied its properties, and in 1873 determined its atomic weight. During his studies of thallium, Crookes discovered the principle of the Crookes radiometer a device that converts light radiation into rotary motion. The principle of this radiometer has found numerous applications in the development of sensitive measuring instruments.

Zbobbie Fenili

In 1862,Alexander Parkes exhibited Parkesine, one of the earliest synthetic polymers, at the International Exhibition in London. This discovery formed the foundation of the modern plastics industry.

Zchris Smith

In 1864, Cato Maximilian Guldberg and Peter Waage, building on Claude Louis Berthollet’s ideas, proposed the law of mass action.

Zcheyenne Levi

In 1865, Johann Josef Loschmidt determined the exact number of molecules in a mole, later named Avogadro’s number.

Zdavid Aguilar

In 1865, August Kekulé, based partially on the work of Loschmidt and others, established the structure of benzene as a six carbon ring with alternating single and double bonds. Kekulé’s novel proposal for benzene’s cyclic structure was much contested but was never replaced by a superior theory. This theory provided the scientific basis for the dramatic expansion of the German chemical industry in the last third of the 19th century.

Zdaniela Spagnolo

Today, the large majority of known organic compounds are aromatic, and all of them contain at least one hexagonal benzene ring of the sort that Kekulé advocated. Kekulé is also famous for having clarified the nature of aromatic compounds, which are compounds based on the benzene molecule.

Zdavid Bennett Cohen

In 1865, Adolf von Baeyer began work on indigo dye, a milestone in modern industrial organic chemistry which revolutionized the dye industry.

Zjoel Weinberg

Swedish chemist and inventor Alfred Nobel found that when nitroglycerin was incorporated in an absorbent inert substance like kieselguhr (diatomaceous earth) it became safer and more convenient to handle, and this mixture he patented in 1867 as dynamite. Nobel later on combined nitroglycerin with various nitrocellulose compounds, similar to collodion, but settled on a more efficient recipe combining another nitrate explosive, and obtained a transparent, jelly-like substance, which was a more powerful explosive than dynamite.

Zdawn Laurant

Gelignite, or blasting gelatin, as it was named, was patented in 1876; and was followed by a host of similar combinations, modified by the addition of potassium nitrate and various other substances.

Zdre Millz 

An important breakthrough in making sense of the list of known chemical elements (as well as in understanding the internal structure of atoms) was Dmitri Mendeleev’s development of the first modern periodic table, or the periodic classification of the elements.

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Mendeleev, a Russian chemist, felt that there was some type of order to the elements and he spent more than thirteen years of his life collecting data and assembling the concept, initially with the idea of resolving some of the disorder in the field for his students. Mendeleev found that, when all the known chemical elements were arranged in order of increasing atomic weight, the resulting table displayed a recurring pattern, or periodicity, of properties within groups of elements.

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Mendeleev’s law allowed him to build up a systematic periodic table of all the 66 elements then known based on atomic mass, which he published in Principles of Chemistry in 1869. His first Periodic Table was compiled on the basis of arranging the elements in ascending order of atomic weight and grouping them by similarity of properties.

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Mendeleev had such faith in the validity of the periodic law that he proposed changes to the generally accepted values for the atomic weight of a few elements and, in his version of the periodic table of 1871, predicted the locations within the table of unknown elements together with their properties.

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Mendeleev even predicted the likely properties of three yet-to-be-discovered elements, which he called ekaboron (Eb), ekaaluminium (Ea), and ekasilicon (Es), which proved to be good predictors of the properties of scandium, gallium and germanium, respectively, which each fill the spot in the periodic table assigned by Mendeleev.

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At first the periodic system did not raise interest among chemists. However, with the discovery of the predicted elements, notably gallium in 1875, scandium in 1879, and germanium in 1886, it began to win wide acceptance. The subsequent proof of many of his predictions within his lifetime brought fame to Mendeleev as the founder of the periodic law.

Zeck Laura

This organizational system of Mendeleev’s surpassed earlier attempts at classification by Alexandre-Émile Béguyer de Chancourtois, who published the telluric helix, an early, three-dimensional version of the periodic table of the elements in 1862, by John Newlands, who proposed the law of octaves (a precursor to the periodic law) in 1864, and by Lothar Meyer,  who developed an early version of the periodic table with 28 elements organized by valencein 1864.

Zken Lee

Mendeleev’s table did not include any of the noble gases, however, which had not yet been discovered. Gradually the periodic law and table became the framework for a great part of chemical theory. By the time Mendeleyev died in 1907, he enjoyed international recognition and had received distinctions and awards from many countries.

Zerika Alejandra Viana Benitez

In 1873, Jacobus Henricus van’t Hoff and Joseph Achille Le Bel,  working independently, developed a model of chemical bonding that explained the chirality experiments of Pasteur and provided a physical cause for optical activity in chiral compounds.

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Van ‘t Hoff’s publication, called Voorstel tot Uitbreiding der Tegenwoordige in de Scheikunde gebruikte Structuurformules in de Ruimte  (Proposal for the development of 3-dimensional chemical structural formulae) and consisting of twelve pages text and one page diagrams, gave the impetus to the development of stereochemistry.

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The concept of the “asymmetrical carbon atom”, dealt with in this publication, supplied an explanation of the occurrence of numerous isomers, inexplicable by means of the then current structural formulae. At the same time he pointed out the existence of relationship between optical activity and the presence of an asymmetrical carbon atom.

 Zgenevieve Wilkinson

American mathematical physicist J. Willard Gibb’s work on the applications of thermodynamics was instrumental in transforming physical chemistry  into a rigorous deductive science. During the years from 1876 to 1878, Gibbs worked on the principles of thermodynamics, applying them to the complex processes involved in chemical reactions.

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Gibbs discovered the concept of chemical potential, or the “fuel” that makes chemical reactions work. In 1876 he published his most famous contribution, On the Equilibrium of Heterogeneous Substances, a compilation of his work on thermodynamics and physical chemistry which laid out the concept of free energy to explain the physical basis of chemical equilibria.

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In these essays were the beginnings of Gibbs’ theories of phases of matter: he considered each state of matter a phase, and each substance a component. Gibbs took all of the variables involved in a chemical reaction – temperature, pressure, energy, volume, and entropy – and included them in one simple equation known as Gibbs’ phase rule.

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Within this paper was perhaps his most outstanding contribution, the introduction of the concept free energy, now universally called Gibbs’ free energy in his honor. The Gibbs free energy relates the tendency of a physical or chemical system to simultaneously lower its energy and increase its disorder, or entropy, in a spontaneous natural process.

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Gibbs’s approach allows a researcher to calculate the change in free energy in the process, such as in a chemical reaction, and how fast it will happen. Since virtually all chemical processes and many physical ones involve such changes, his work has significantly impacted both the theoretical and experiential aspects of these sciences.

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In 1877, Ludwig Boltzmann established statistical derivations of many important physical and chemical concepts, including entropy, and distributions of molecular velocities in the gas phase. Together with Boltzmann and James Clerk Maxwell, Gibbs created a new branch of theoretical physics called statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of large ensembles of particles.

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Gibbs also worked on the application of Maxwell’s equations to problems in physical optics. Gibbs’s derivation of the phenomenological laws of thermodynamics from the statistical properties of systems with many particles was presented in his highly-influential textbook Elementary Principles in Statistical Mechanics, published in 1902, a year before his death.

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In that work, Gibbs reviewed the relationship between the laws of thermodynamics and statistical theory of molecular motions. The overshooting of the original function by partial sums of Fourier series at points of discontinuity is known as the Gibbs phenomenon.

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German engineer Carl von Linde’s invention of a continuous process of liquefying gases in large quantities formed a basis for the modern technology of refrigerationand provided both impetus and means for conducting scientific research at low temperatures and very high vacuums.

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Von Linde developed a methyl ether refrigerator (1874) and an ammonia refrigerator (1876). Though other refrigeration units had been developed earlier, Linde’s were the first to be designed with the aim of precise calculations of efficiency.

Zhailey Niswanger

In 1895 he set up a large-scale plant for the production of liquid air, and six years later he developed a method for separating pure liquid oxygen from liquid air that resulted in widespread industrial conversion to processes utilizing oxygen (e.g., in steel manufacture).

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In 1883, Svante Arrhenius developed an ion theory to explain conductivity in electrolytes.

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In 1884, Jacobus Henricus van’t Hoff  published Études de Dynamique chimique (Studies in Dynamic Chemisty), a seminal study on chemical kinetics. In this work, van ‘t Hoff entered for the first time the field of physical chemistry. Of great importance was his development of the general thermodynamic relationship between the heat of conversion and the displacement of the equilibrium as a result of temperature variation.

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At constant volume, the equilibrium in a system will tend to shift in such a direction as to oppose the temperature change which is imposed upon the system.

Zhope DeBorse

Thus, lowering the temperature results in heat development while increasing the temperature results in heat absorption. This principle of mobile equilibrium was subsequently (1885) put in a general form by Henry Louis Le Chatelier, who extended the principle to include compensation, by change of volume, for imposed pressure changes.

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The van ‘t Hoff-Le Chatelier principle, or simply Le Chatelier’s principle explains the response of dynamic chemical equilibria to external stresses.

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In 1884,Hermann Emil Fischer proposed the structure of purine, a key structure in many biomolecules, which he later synthesized in 1898. He also began work on the chemistry of glucose and related sugars.

Zkate Richards

In 1885 Eugene Goldstein named the cathode ray, later discovered to be composed of electrons, and the canal ray later discovered to be positive hydrogen ions that had been stripped of their electrons in a cathode ray tube. These would later be named protons.

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The year 1885 also saw the publishing of J. H. van ‘t Hoff’s L’Équilibre chimique dans les Systèmes gazeux ou dissous à I’État dilué (Chemical equilibria in gaseous systems or strongly diluted solutions), which dealt with this theory of dilute solutions. Here he demonstrated that the osmotic pressure in solutions which are sufficiently dilute is proportionate to the concentration and the absolute temperature so that this pressure can be represented by a formula which only deviates from the formula for gas pressure by a coefficient i.

Zkristin Darling

Van’t Hoff also determined the value of i by various methods, for example by means of the vapor pressure and François-Marie Raoult’s results on the lowering of the freezing point. Thus van ‘t Hoff was able to prove that thermodynamic laws are not only valid for gases, but also for dilute solutions.

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His pressure laws, given general validity by the electrolytic dissociation theory of Arrhenius (1884-1887), the first foreigner who came to work with him in Amsterdam (1888), are considered the most comprehensive and important in the realm of natural sciences.

Zleslie Feffer

In 1893, Alfred Werner discovered the octahedral structure of cobalt complexes, thus establishing the field of coordination chemistry.

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The most celebrated discoveries of Scottish chemist William Ramsay were made in inorganic chemistry. Ramsay was intrigued by the British physicist John Strutt, 3rd Baron Rayleigh’s  1892 discovery that the atomic weight of nitrogen found in chemical compounds was lower than that of nitrogen found in the atmosphere. He ascribed this discrepancy to a light gas included in chemical compounds of nitrogen, while Ramsay suspected a hitherto undiscovered heavy gas in atmospheric nitrogen. Using two different methods to remove all known gases from air, Ramsay and Lord Rayleigh were able to announce in 1894 that they had found a monatomic, chemically inert gaseous element that constituted nearly 1 percent of the atmosphere; they named it argon.

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The following year, Ramsay liberated another inert gas from a mineral called cleveite.  This proved to be helium, previously known only in the solar spectrum. In his book The Gases of the Atmosphere (1896), Ramsay showed that the positions of helium and argon in the periodic table of elements indicated that at least three more noble gases might exist. In 1898 Ramsay and the British chemist Morris W. Travers isolated these elements, called neon, krypton and xenon, from air brought to a liquid state at low temperature and high pressure.

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Sir William Ramsay worked with Frederick Soddy to demonstrate, in 1903, that alpha particles (helium nuclei) were continually produced during the radioactive decay of a sample of radium. Ramsay was awarded the 1904 Nobel Prize for Chemistry in recognition of “services in the discovery of the inert gaseous elements in air, and his determination of their place in the periodic system.”

Zonica Brewer

In 1897, J.J. Thomson discovered the electron using the cathode ray tube.

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In 1898, Wilhelm Wien demonstrated that canal rays (streams of positive ions) can be deflected by magnetic fields, and that the amount of deflection is proportional to the mass-to-charge ratio. This discovery would lead to the analytical technique known as mass spectrometry.

Marie Sklodowska-Curie was a Polish-born French physicist and chemist who is famous for her pioneering research on radioactivity.

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She and her husband Pierre are considered to have laid the cornerstone of the nuclear age with their research.

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Marie was fascinated with the work of Henri Becquerel, a French physicist who discovered in 1896 that uranium casts off rays similar to the X-rays discovered by Wilhelm Röntgen.

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Marie Curie began studying uranium in late 1897 and theorized, according to a 1904 article she wrote for Century magazine, “that the emission of rays by the compounds of uranium is a property of the metal itself—that it is an atomic property of the element uranium independent of its chemical or physical state.”

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Curie took Becquerel’s work a few steps further, conducting her own experiments on uranium rays. She discovered that the rays remained constant, no matter the condition or form of the uranium. The rays, she theorized, came from the element’s atomic structure. This revolutionary idea created the field of atomic physics and the Curies coined the word radioactivity to describe the phenomena.

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Pierre and Marie further explored radioactivity by working to separate the substances in uranium ores and then using the electrometer to make radiation measurements to ‘trace’ the minute amount of unknown radioactive element among the fractions that resulted. Working with the mineral pitchblende, the pair discovered a new radioactive element in 1898. They named the element polonium, after Marie’s native country of Poland.

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On December 21, 1898, the Curies detected the presence of another radioactive material in the pitchblende. They presented this finding to the Académie des Sciences on December 26, proposing that the new element be called radium.

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The Curies then went to work isolating polonium and radium from naturally occurring compounds to prove that they were new elements.

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In 1902, the Curies announced that they had produced a decigram of pure radium, demonstrating its existence as a unique chemical element. While it took three years for them to isolate radium, they were never able to isolate polonium.

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Along with the discovery of two new elements and finding techniques for isolating radioactive isotopes, Marie Curie oversaw the world’s first studies into the treatment of neoplasms using radioactive isotopes.

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Marie Curie was awarded the 1903 Nobel Prize for Physics.

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She was the sole winner of the 1911 Nobel Prize for Chemistry.

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She was the first woman to win a Nobel Prize, and she is the only woman to win the award for work in two different fields.

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While working with Marie to extract pure substances from ores, an undertaking that really required industrial resources but that they achieved in relatively primitive conditions, Pierre himself concentrated on the physical study (including luminous and chemical effects) of the new radiations.

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Through the action of magnetic fields on the rays given out by the radium, Pierre Curie proved the existence of particles electrically positive, negative, and neutral.

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Ernest Rutherford would later call these particles alpha, beta, and gamma rays.

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Pierre Curie then studied these radiations by calorimetry and also observed the physiological effects of radium, thus opening the way to radium therapy.

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Among Pierre Curie’s discoveries were that ferromagnetic substances exhibited a critical temperature transition, above which the substances lost their ferromagnetic behavior – this is known as the “Curie point” He was elected to the Academy of Sciences (1905), having in 1903  jointly with Marie received the Royal Society’s prestigious Davy Medal and jointly with her and Becquerel the Nobel Prize for Physics. He was run over by a carriage in the rue Dauphine in Paris in 1906 and died instantly. His complete works were published in 1908.

New Zealand-born chemist and physicist Ernest Rutherford is considered to be “the father of nuclear physics.” Rutherford is best known for devising the names alpha, beta and gamma to classify various forms of radioactive “rays” which were poorly understood at his time (alpha and beta rays are particle beams, while gamma rays are a form of high-energy electromagnetic radiation).

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Rutherford deflected alpha rays with both electric and magnetic fields in 1903. Working with Frederick Soddy, Rutherford explained that radioactivity is due to the transmutation of elements, now known to involve nuclear reactions.

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He also observed that the intensity of radioactivity of a radioactive element decreases over a unique and regular amount of time until a point of stability, and he named the halving time the “half-life”

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In 1901 and 1902 Rutherford worked with Frederick Soddy to prove that atoms of one radioactive element would spontaneously turn into another, by expelling a piece of the atom at high velocity.

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In 1906 at the University of Manchester, Rutherford oversaw an experiment conducted by his students Hans Geiger (known for the Geiger counter and Ernest Marsden. In the Geiger-Marsden experiment, a beam of alpha particles, generated by the radioactive decay of radon was directed normally onto a sheet of very thin gold foil in an evacuated chamber.

1 Ellen Cavanaugh

The alpha particles should all have passed through the foil and hit the detector screen, or have been deflected by, at most, a few degrees.

Zsteve Wolf

However, the actual results surprised Rutherford. Although many of the alpha particles did pass through as expected, many others were deflected at small angles while others were reflected back to the alpha source. Geiger, Marsden and Rutherford observed that a very small percentage of particles were deflected through angles much larger than 90 degrees. The gold foil experiment showed large deflections for a small fraction of incident particles.

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Rutherford realized that, because some of the alpha particles were deflected or reflected, the atom had a concentrated center of positive charge and of relatively large mass. Rutherford later termed this positive center the “atomic nucleus”.

Ztephen Marchese

The alpha particles had either hit the positive center directly or passed by it close enough to be affected by its positive charge. Since many other particles passed through the gold foil, the positive centre would have to be a relatively small size compared to the rest of the atom – meaning that the atom is mostly open space.

1 Jenay Gordon

From these events and conclusions, Rutherford developed a model of the atom that was similar to the solar system, known as Rutherford model.  Like planets, electrons orbited a central, sun-like nucleus. For his work with radiation and the atomic nucleus, Rutherford received the 1908 Nobel Prize in Chemistry.

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In 1903,Mikhail Tsvet invented chromatography, an important analytic technique.

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In 1904,Hantaro Nagaoka proposed an early nuclear model of the atom, where electrons orbit a dense massive nucleus.

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In 1905, Fritz Haber and Carl Bosch developed the Haber process for making ammonia, a milestone in industrial chemistry with deep consequences for agriculture. The Haber process, or Haber-Bosch process, combined nitrogen and hydrogen to form ammonia in industrial quantities for production of fertilizer and munitions. The food production for half the world’s current population depends on this method for producing fertilizer.

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Haber, along with Max Born proposed the Born-Haber cycle as a method for evaluating the lattice energy of an ionic solid. Haber has also been described as the “father of chemical warfare” for his work developing and deploying chlorine and other poisonous gases during World War I.

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In the early twentieth century (1905), Albert Einstein explained Brownian motion in a way that definitively proved atomic theory.

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Leo Baekeland invnted bakelite one of the first commercially successful plastics.

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In 1909, American physicist Robert Andrews Millikan, who had studied in Europe under Walther Nernst and Max Planck, measured the charge of individual electrons with unprecedented accuracy through the oil drop experiment in which he measured the electric charges on tiny falling water (and later oil) droplets. His study established that any particular droplet’s electrical charge is a multiple of a definite, fundamental value,  the electron’s charge, and thus a confirmation that all electrons have the same charge and mass.

1 Kathleen Ferreira Battaglia

Beginning in 1912, Millikan spent several years investigating and finally proving Albert Einstein’s proposed linear relationship between energy and frequency, and providing the first direct photoelectric support for Planck’s constant. In 1923 Millikan was awarded the Nobel Prize for Physics.

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S.P.L. Sørensen invented the pH concept and developed methods for measuring acidity in 1909.

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In 1911, Antonius Van den Broek proposed the idea that the elements on the periodic table are more properly organized by positive nuclear charge rather than atomic weight.

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The first Solvay Conference (1911) was held in Brussels, bringing together most of the most prominent scientists of the day.

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In 1912,William Henry Bragg and William Lawrence Bragg proposed Bragg’s law and established the field of X-ray crystallography, an important tool for elucidating the crystal structure of substances (1912).

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Also in 1912, Peter Debye  developed the concept of molecular dipolarity to describe asymmetric charge distribution in some molecules.

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In 1913,Niels Bohr, a Danish physicist, introduced the concepts of quantum mechanics to atomic structure by proposing what is now known as the Bohr model of the atom, where electrons exist only in strictly defined circular orbits around the nucleus similar to rungs on a ladder.

1 Kristen Browne

The Bohr Model is a planetary model in which the negatively-charged electrons orbit a small, positively-charged nucleus similar to the planets orbiting the sun (except that the orbits are not planar). The gravitational force of the solar system is mathematically akin to the attractive Coulomb (electrical) force between the positively-charged nucleus and the negatively-charged electrons.

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In the Bohr model, however, electrons orbit the nucleus in orbits that have a set size and energy. The energy levels are said to be quantized, which means that only certain orbits with certain radii are allowed. Orbits in between simply don’t exist.

1 Mariee Mel

The energy of the orbit is related to its size – that is, the lowest energy is found in the smallest orbit.

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Bohr also postulated that electromagnetic radiation is absorbed or emitted when an electron moves from one orbit to another. Because only certain electron orbits are permitted, the emission of light accompanying a jump of an electron from an excited energy state to ground state produces a unique emission spectrum for each element.

1 tanya mendoza

Neils Bohr also worked on the principle of complementarity which states that an electron can be interpreted in two mutually exclusive and valid ways. Electrons can be interpreted as wave or particle models. His hypothesis was that an incoming particle would strike the nucleus and create an excited compound nucleus. This formed the basis of his liquid drop model and later provided a theory base for the explanation of nuclear fission.

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In 1913, Henry Mosely working from Van den Broek’s earlier idea, introduced the concept of atomic number to fix inadequacies in Mendeleev’s periodic table, which had been based on atomic weight.

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The peak of Frederick Soddy’s career in radiochemistry was in 1913 with his formulation of the concept of isotopes, which stated that certain elements exist in two or more forms which have different atomic weights but which are indistinguishable chemically. He is remembered for proving the existence of isotopes of certain radioactive elements, and is also credited, along with others, with the discovery of the element protactinium in 1917.

1 Henry Austin Shikongo

In 1913, J. J. Thomson expanded on the work of Wien by showing that charged subatomic particles can be separated by their mass-to-charge ratio, a technique known as mass spectrometry.

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American physical chemist Gilbert N. Lewis laid the foundation of valence bond theory. He was instrumental in developing a bonding theory based on the number of electrons in the outermost “valence” shell of the atom. In 1902, while Lewis was trying to explain valence to his students, he depicted atoms as constructed of a concentric series of cubes with electrons at each corner. This “cubic atom” explained the eight groups in the periodic table and represented his idea that chemical bonds are formed by electron transference to give each atom a complete set of eight outer electrons (an “octet”).

1 Lester Chambers

Lewis’s theory of chemical bonding continued to evolve and, in 1916, he published his seminal article “The Atom of the Molecule”, which suggested that a chemical bond is a pair of electrons shared by two atoms. Lewis’s model equated the classical chemical bond with the sharing of a pair of electrons between the two bonded atoms. Lewis introduced the “electron dot diagrams” in this paper to symbolize the electronic structures of atoms and molecules. Now known as Lewis structures they are discussed in virtually every introductory chemistry book.

2 Lilian Del Solar Oshiro

Shortly after publication of his 1916 paper, Lewis became involved with military research. He did not return to the subject of chemical bonding until 1923, when he masterfully summarized his model in a short monograph entitled Valence and the Structure of Atoms and Molecules.

1 Mark Cubertson

His renewal of interest in this subject was largely stimulated by the activities of the American chemist and General Electric researcher Irving Langmuir, who between 1919 and 1921 popularized and elaborated Lewis’s model. Langmuir subsequently introduced the term covalent bond.

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In 1921, Otto Stern and Walther Gerlach established the concept of quantum mechanical spin in subatomic particles.

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For cases where no sharing was involved, Lewis in 1923 developed the electron pair theory of acids and base.

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Lewis redefined an acid as any atom or molecule with an incomplete octet that was thus capable of accepting electrons from another atom. Bases were, of course, electron donors. His theory is known as the concept of Lewis acids and bases.

2 Mariana Nadal

In 1923, G. N. Lewis and Merle Randall published Thermodynamics and the Free Energy of Chemical Substances, the first modern treatise on chemical thermodynamics.

Djohn Darby Sam

The 1920s saw a rapid adoption and application of Lewis’s model of the electron-pair bond in the fields of organic and coordination chemistry. In organic chemistry, this was primarily due to the efforts of the British chemists Arthur Lapworth, Robert Robinson, Thomas Lowry and Christopher Ingold.

Gladys Acosta

Lewis’s bonding model was promoted through the efforts of the American chemist Maurice Huggins and the British chemist Nevil Sidgwick. 

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In 1924, French quantum physicist Louis de Broglie published his thesis, in which he introduced a revolutionary theory of electron waves based on wave-particle duality in his thesis. In his time, the wave and particle interpretations of light and matter were seen as being at odds with one another, but de Broglie suggested that these seemingly different characteristics were instead the same behavior observed from different perspectives, that particles can behave like waves, and waves (radiation) can behave like particles.

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De Broglie’s proposal offered an explanation of the restriction motion of electrons within the atom. The first publications of de Broglie’s idea of “matter waves” had drawn little attention from other physicists, but a copy of his doctoral thesis chanced to reach Einstein, whose response was enthusiastic. Einstein stressed the importance of de Broglie’s work both explicitly and by building further on it.

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In 1925, Austrian-born physicist Wolfgang Pauli developed the Pauli exclusion principle, which states that no two electrons around a single nucleus in an atom can occupy the same quantum state simultaneously, as described by four quantum numbers.

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Pauli made major contributions to quantum mechanics and quantum field theory, and he was awarded the 1945 Nobel Prize for Physics for his discovery of the Pauli exclusion principle, as well as for solid-state physics, and he successfully hypothesized the existence of the neutrino.

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In addition to his original work, Wolfgang Pauli wrote masterful syntheses of several areas of physical theory that are considered classics of scientific literature.

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In 1926 at the age of 39, Austrian theoretical physicist Erwin Schrödinger  produced the papers that gave the foundations of quantum wave mechanics. In those papers he described his partial differential equation that is the basic equation of quantum mechanics and bears the same relation to the mechanics of the atom as Newton’s equations of motion bear to planetary astronomy.

Darby Engrid Sam

Schrödinger adopted a proposal made by Louis de Broglie in 1924 that particles of matter have a dual nature and in some situations act like waves, and he (Schrödinger) introduced a theory describing the behavior of such a system by a wave equation that is now known as the Schrödinger equation.

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The solutions to Schrödinger’s equation, unlike the solutions to Newton’s equations, are wave functions that can only be related to the probable occurrence of physical events. The readily visualized sequence of events of the planetary orbits of Newton is, in quantum mechanics, replaced by the more abstract notion of probability. (This aspect of the quantum theory made Schrödinger and several other physicists profoundly unhappy, and he devoted much of his later life to formulating philosophical objections to the generally accepted interpretation of the theory that he had done so much to create.)

Tom Red Dog

German theoretical physicist Werner Heisenberg was one of the key creators of quantum mechanics. In 1925, Heisenberg discovered a way to formulate quantum mechanics in terms of matrices. For that discovery, he was awarded the Nobel Prize for Physics for 1932.

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In 1927 Heisenberg published his uncertainty principle, upon which he built his philosophy and for which he is best known. Heisenberg was able to demonstrate that if you were studying an electron in an atom you could say where it was (the electron’s location) or where it was going (the electron’s velocity), but it was impossible to express both at the same time.

Peter Donna

I think of Heisenberg’s principle this way. The very act of observing a sub atomic particle changes that particle. It is impossible to observe a sub atomic particle as it “really” is, because the observing of it changes it.

daniela montanari

Heisenberg also made important contributions to the theories of the hydrodynamics of turbulenty flows, the atomic nucleus, ferromagnetism, cosmic rays and subatomic particles.

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He was instrumental in planning the first West German nuclear reactor at Karlsruhe, together with a research reactor in München (Munich) in 1957.

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Considerable controversy surrounds Werner Heisenberg’s work on atomic research during World War II.

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Some view the birth of quantum chemistry in the discovery of the Schrödinger equation and its application to the hydrogen atom in 1926. However, the 1927 article of Walter Heitler and Fritz Longon is often recognised as the first milestone in the history of quantum chemistry. This is the first application of quantum mechanics to the diatomic hydrogen molecule, and thus to the phenomenon of the chemical bond.

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Werner von Braun was another figure of controversy for the same reason as was that other Werner… Heisenberg. Both men worked with people such as Edward Teller, Robert A. Millikan, Max Born, J. Robert Oppenheimer, Linus Pauling, Erich Hückel, Douglas Hartree and Vladimir Aleksandrovich Fock.

Paula O'Rourke

Skepticism remained as to the general power of quantum mechanics applied to complex chemical systems.

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Hence the quantum mechanical methods developed in the 1930s and 1940s are often referred to as theoretical molecular or atomic physics to underline the fact that they were more the application of quantum mechanics to chemistry and spectroscopy than answers to chemically relevant questions.

jasmyn dawn

In the 1940s many physicists turned from molecular or atomic physics to nuclear physics (J. Robert Oppenheimer or Edward Teller). 

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Clemens C.J. Roothaan wrote a seminal paper on Roothaan equations in 1951 that was a big step toward the solution of the self-consistent field equations for small molecules like hydrogen or nitrogen. Those computations were performed with the help of tables of integrals which were computed on the most advanced computers of the time.

sunni ellis

By the mid 20th century, in principle, the integration of physics and chemistry was extensive, with chemical properties explained as the result of the electronic structure of the atom. Linus Pauling’s book on The Nature of the Chemical Bond used the principles of quantum mechanics to deduce bond angles in ever-more complicated molecules.

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However, though some principles deduced from quantum mechanics were able to predict qualitatively some chemical features for biologically relevant molecules, they were, till the end of the 20th century, more a collection of rules, observations, and recipes than rigorous ab initio quantitative methods.

This heuristic approach triumphed in 1953 when James Watson and Francis Crick deduced the double helical structure of DNA by constructing models constrained by and informed by the knowledge of the chemistry of the constituent parts and the X-ray diffraction patterns obtained by Rosalind Franklin.

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This discovery lead to an explosion of research into the biochemistry of life.

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Rosalind Franklin was seriously taken advantage of in this research on DNA and her story is a sadly typical one. Added to the misogynistic tone of the proceedings, all too common in that era and that place, was a too familiar note of anti Semitism, common in the “upper” classes of that day.

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Rosalind Franklin’s DNA work achieved the most fame because DNA plays an essential role in cell metabolism and genetics, and the discovery of its structure helped her co-workers understand how genetic information is passed from parents to their offspring.

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These co-workers, Watson and Crick, were more than a little unethical in their treatment of Rosalind Franklin. This is very disappointing in people of science.

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Her data were key to determining the structure for formulating Crick and Watson’s 1953 model of the structure of DNA.

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Also in 1953, the Miller-Urey experiment demonstrated that basic constituents of protein, simple amino acids, could themselves be built up from simpler molecules in a simulation of primordial processes on earth. Though many questions remain about the true nature of the origin of life, this was the first attempt by chemists to study hypothetical processes in the laboratory under controlled conditions.

Tiffney Helgerson

I remember being very excited when I heard of these experiments. I was at UC Berkeley in 1965 and a lot of that work was going on there. It seemed as if these scientists were creating the original earth’s atmosphere in a petri dish.  I took LSD and thought about these experiments. It was all very dramatic and intensely interesting.

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In 1983 Kary Mullis devised a method for the in-vitro amplification of DNA, known as  polymerase chain reaction (PCR), which revolutionized the chemical processes used in the laboratory to manipulate it. PCR could be used to synthesize specific pieces of DNA and made possible the sequencing of the DNA  of organisms, which culminated in the huge human genome project.

jenny hoffman

An important piece in the double helix puzzle was solved by one of Pauling’s students Matthew Meselson and Frank Stahl, and the result of their collaboration (the Meselson-Stahl experiment has been called as “the most beautiful experiment in biology”.

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They used a centrifugation technique that sorted molecules according to differences in weight. Because nitrogen atoms are a component of DNA, they were labelled and therefore tracked in replication in bacteria.

jeannie antonelli

In 1970, John Pople developed the Gaussian program which simplified computational chemistry calculations.

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Yves Chauvin offered an explanation of the reaction mechanism ofolefin metathesis reactions in 1973 and in 1975, Karl Barry Sharpless and his group discovered stereoselective oxidation reactions including the Sharpless epoxidation, Sharpless asymmetric dihydroxylation and the Sharpless oxyamination.

bekka bramlett

In 1985, Harold Kroto, Robert Curl and Richard Smalley discovered fullerenes.

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Fullerenes are a class of large carbon molecules superficially resembling the geodesic dome designed by architect R. Buckminster Fuller.

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Sumio Iijima used electron microscopy in 1991 to discover a type of cylindrical fullerene known as a carbon nanotube though earlier work had been done in the field as early as 1951.

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This material is an important component in the field of nanotechnology.

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In 1994, Robert A. Holton and his group achieved the first total synthesis of Taxol.

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Isolated from the bark of the relatively rare and slow-growing pacific yew tree over twenty years ago, taxol is the most promising new antitumor agent for the treatment of ovarian and breast cancers.

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Taxol has a unique mechanism of action, blocking cell division by binding and stabilizing microtubules, structures which comprise the cytoskeleton and the mitotic spindle.

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A few years ago, Holton’s group developed an efficient semisynthesis of taxol which will provide the commercial supply, and this has made it unnecessary to destroy the environment through the harvest of yew trees.

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The yew tree has long been recognized as a tree of strong medicine. Just today I read an account in Julius Caesar of the yew tree’s powers.

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Catuvoleus, rex dimidiae partis Eburonum qui inierat consilium una cum Ambiorige, jam confectus aetate, quum posset non ferre laborem aut belli aut fugae, detestatus Ambiorigem omnibus precibus qui fuisset auctor ejus consilii, exanimavit se taxo (cujus est magna copia in Gallia que Germania).  Liber VI   De Bello Gallico

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Catuvoleus, king of half of the Eburones, who had entered into counsel with Ambiorix, now worn out with age, since he could not bear the fatigue of either war or flight, cursed Ambiorix with all kinds of imprecations since he had been the author of this plan, and then killed himself by  eating yew leaves (the yew grows in great abundance in Gaul and Germany).  Book VI  The Gallic War

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All species of yew contain highly poisonous (and, paradoxically, highly beneficial) alkaloids known as taxanes, with some variation in the exact formula of the alkaloid between the species. All parts of the tree except the arils contain the alkaloid. The arils are edible and sweet, but the seed is dangerously poisonous. Unlike birds’ stomachs, the human stomach can break down the seed coat and release the taxanes into the body.

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The yew is an amazing tree with a long history.  The man found in the ice in Italy who died five thousand years ago, Ötzi, as he is called, carried a bow made of yew. Yew is also associated with Wales and England because of the longbow, an early weapon of war developed in northern Europe, and as the English longbow which was famously used at the battle of Agincourt.

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Yew is the wood of choice for longbow making; the bows are constructed so that the heartwood of yew is on the inside of the bow while the sapwood is on the outside. This takes advantage of the natural properties of yew wood since the heartwood resists compression while the sapwood resists stretching.

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The word yew is from Proto-Germanic.  Baccata is Latin for bearing red berries. The word yew as it was originally used seems to refer to the color brown.

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The yew (μίλος) was known to Theophrastus who noted its preference for mountain coolness and shade, its evergreen character and its slow growth.

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Most romance languages kept a version of the Latin word taxus (Italian tasso, Corsican tassu, Occitan teis, Catalan teix, Gasconic tech, Spanish tejo, Portuguese teixo, Galician teixo and Romanian tisă) from the same root as toxic.

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In Slavic languages, the same root (presumably borrowed from Romanian) is preserved: Russian tiss (тис), Slovenian tisa, Serbiantisa (тиса). In Albanian it is named tis.

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In 1995,Eric Cornell and Carl Wieman produced the first Bose-Einstein condensate, a substance that displays quantum mechanical properties on the macroscopic scale.

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Before the 20th century, chemistry was defined as the science of the nature of matter and its transformations. It was therefore clearly distinct from physics which was not concerned with such dramatic transformation of matter.

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Moreover, in contrast to physics, chemistry was not using much of mathematics. Some scientists, such as Auguste Comte were particularly reluctant to use mathematics within chemistry.

Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry…. if mathematical analysis should ever hold a prominent place in chemistry — an aberration which is happily almost impossible — it would occasion a rapid and widespread degeneration of that science.

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However, in the second part of the 19th century, the situation changed and August Kekulé wrote in 1867:

I rather expect that we shall someday find a mathematico-mechanical explanation for what we now call atoms which will render an account of their properties.

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After the discovery by Rutherford and Bohr of the atomic structure in 1912, and by Marie and Pierre Curie of radioactivity, scientists had to change their viewpoint on the nature of matter.

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The experience acquired by chemists was no longer pertinent to the study of the whole nature of matter but only to aspects related to the electron cloud surrounding the atomic nuclei and the movement of the latter in the electric field induced by the former.

Victor Fondrk

The range of chemistry was thus restricted to the nature of matter around us in conditions which are not too far (or exceptionally far) from standard conditions for temperature and pressure  and in cases where the exposure to radiation is not too different from the natural microwave, visible or UV radiations on Earth. Chemistry was therefore re-defined as the science of matter that deals with the composition, structure, and properties of substances and with the transformations that they undergo.

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However the meaning of matter used here relates explicitly to substances made of atoms and molecules, disregarding the matter within the atomic nuclei and its nuclear reaction or matter within highly ionized plasmas.

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This does not mean that chemistry is never involved with plasma or nuclear sciences or even bosonic fields nowadays.

elizabeth oglesby

Areas such as Quantum Chemistry and Nuclear Chemistry are currently well developed and formally recognized sub-fields of study under the Chemical sciences (Chemistry).

kevin beadles

What is now formally recognized, however, as subject of study under the Chemistry category as a science is always based on the use of concepts that describe or explain phenomena either from matter or to matter in the atomic or molecular scale.

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This includes the study of the behavior of many molecules as an aggregate or the study of the effects of a single proton on a single atom.

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Physicists and not chemists deal with different (more “exotic”) types of matter (e.g. Bose-Einstein condensate, Higgs Boson, dark matter, naked singularity).

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The field of chemistry is still, on our human scale, very broad and the claim that chemistry is everywhere is, of course, accurate.

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The later part of the nineteenth century saw a huge increase in the exploitation of petroleum extracted from the earth for the production of a host of chemicals, which largely replaced the use of whale oil, coal tar and naval stores.

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Large scale production and refinement of petroleum provided feedstocks for liquid fuels such asgasoline and diesel, solvents, lubricants, asphalt and waxes.

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Refined petroleum is also the fundamental ingredient in many of the common materials of the modern world.

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Materials such as synthetic fibers, plastics, paints, detergents, pharmaceuticals, adhesives and for ammonia as fertilizer.

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Many of these required new catalysts to be used practically and this naturally involved chemistry.

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In the mid-twentieth century, control of the electronic structure of semiconductor materials was made precise by the creation of large ingots of extremely pure single crystals of silicon and geranium.

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Accurate control of their chemical composition by doping with other elements made the production of the solid state transistor in 1951.

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Chemistry also made possible the production of the tiny integrated circuits in the machine that I am using to write this. 

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So, here is a salute to all the women and men who worked through all the ages to further the cause of chemistry.

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See you next week?

Sam arms out

Sam Andrew

_____________________________________

The Sheik of Alterity

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Alterity is a latinate way of saying otherness.

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In the phenomenological tradition alterity is usually understood as the entity in contrast to which an identity is constructed.

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The Sheik of Araby” is a song that was written in 1921 by Harry B. Smith, Francis Wheeler with music by Ted Snyder.  It was composed in response to the popularity of the Rudolph Valentino film The Sheik.

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In 1926, to go with the film The Son of the Sheik, Ted Snyder worked parts of the melody into “That Night in Araby”, a related song with words by Billy Rose.

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“The Sheik of Araby” was a Tin Pan Alley hit, and was also adopted by early jazz bands, especially in New Orleans.

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A verse from The Sheik of Araby also appears in the novel The Great Gatsby (1925) by F. Scott Fitzgerald.

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In 1926, Fleischer Studios released a cartoon with The Sheik of Araby, recorded in Phonofilm, as part of their Song Car-Tunes series.

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The appeal to New Orleans bands may have lain in “Araby” sharing the same pronunciation as Arabi, Louisiana, a town down river from New Orleans’ 9th Ward and a center for gambling just outside city limits until the early 1950s.

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The Sheik of Araby is also in the film Valentino (1977) with words of parody by Ken Russell, performed by Chris Ellis.

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Don Albert’s band recorded the first version of The Sheik of Araby with the chant “Without no pants on” between the lines of lyrics. This was and still is a popular bit of hokum with New Orleans bands, but, because of it, Albert’s record was generally banned from radio airplay.

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A whistling version of The Sheik of Araby was recorded by Guido Gialdini in 1923 on the Vox German  label.

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Fats Waller did a beautiful version of The Sheik of Araby in 1939.

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Another Fats, Domino, weighed in on the tune.

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George Lewis’ sinuous clarinet style was perfect for The Sheik of Araby.

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The Beatles thought they would go audition for Decca Records in 1962 and George sang The Sheik of Araby. Pete Best played the drum part.

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Decca, in a genius move, turned the band down. But they went up anyway.

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The Sheik of Araby was done by the Preservation Hall Jazz Band.

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“I Awake Pure Heart” is what “Django Reinhart” means. He played Sheik of Araby a few times.

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And let’s not forget Nelson Riddle.

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Louis Prima did a typically restrained, quiet version of the song. Louis was probably the model for the singer in Broadway Danny Rose.

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And speaking of roses, Jimmy Rosenberg did The Sheik of Araby.

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Harry Connick waited until 2007 to do the tune.

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Leon Redbone performed The Sheik of Araby on several occasions.

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Tim Armstrong put the song on his Tim Timebomb and Friends CD in June 2013.

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Alterity implies the ability to distinguish between self and not-self, and consequently to assume the existence of an alternative viewpoint.

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When I play the changes to Sheik of Araby, I become very happy, and I think of images like this.

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Psyche! from thee they spring O life of Time and alterity!          H. More    1642

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I can’t get this song out of my head.

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Eddie Condon.

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These guys have probably never played The Sheik of Araby, but they could if they wanted to.

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And I love these Sheik of Araby chord changes that are so 1920s.  I like it when the song goes to D7.  Everything seems to lift at that point.

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Makes me want to get out the old ukulele and strum a few happy chords.

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Alterity is a philosophical term meaning “otherness”, strictly being in the sense of the other of two (Latin alter).

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Johnny Hodges played The Sheik of Araby with Duke Ellington in 1932.

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Nicoletta Guaitamacchi at the Trident/Horizons in Sausalito, California, 7 August 2013.

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There was some kind of fascination in the 1920s with Egyptiana and Arabism, probably because Howard Carter found the grave of King Tut at that time.

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Ezio Guatamacchi.

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Tiburon means “shark” in Spanish.

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Like most Arabs Rudy was a whiz on the oud.

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Sayaka.

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Hey, there’s Charlie Christian playing Sheik of Araby. See? That’s the keynote, Bb.

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This is Lillian, and she probably heard Sheik of Araby a few times.

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One of the best presidents we have ever had, pants or no pants.

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Eddie Cantor had to get in the act. He loved makin’ whoopee.

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This person had one of the best comedic deliveries ever.  And Bob wasn’t bad either.

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The Colts recorded The Sheik of Araby in 1957.

Dem

This could be Minoan Crete and she could be singing The Sheik of Araby.

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All he did was make sure the Saudis flew out of here on 9/12/01, a day that no American was allowed to fly. That’s all he did. So, why would they possibly be honoring Bush?

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The chic of Araby.

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Almost no one plays the intro to this tune, which is nonetheless worthwhile and sports a few half tones. It’s a good intro.

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Marti Gregg Demetrion’s very interesting photograph of the underside of the Tour Eiffel.

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Dan

So, did you see that film about backup singers, Twenty Feet From Stardom? Very interesting and affecting.

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Sheik Yerbouti.

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The song has its comic aspects.

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The Sheik of Araby classical ballet interpretation (with a few slight political overtones).

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I will never forget his interpretation of Petite Fleur. Sidney Bechet played The Sheik of Araby in 1941 in one of the first overdubbing recordings at RCA. He played clarinet, soprano saxophone, tenor sax, piano, bass and drums on the song.

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Jimmy Buffet recorded The Sheik of Araby in 1974 on Pencil Thin Mustache.

Bel

Was she the object of the Sheik of Araby’s wild ride over the midnight sands?

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Could be, could be.

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In December 2009 The Original Rabbit Foot Spasm Band put The Sheik of Araby on their CD Gin & Sympathy.

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The mighty Charles Mingus played the Sheik of Araby.

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Peter Albin and I played The Sheik of Araby not so long ago for a documentary that Jay Blakesberg was doing about Jim Marshall. We thought about Django a lot that day.

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Spike Jones did a version of Sheik of Araby that had everything but the kitchen sink… oh, wait, no, it had that too.

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Lou Monte did it.

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I can hear those primitive rhythms now.

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Jimmy Siegel and his Sheiks of Araby.

Chr

Fox Trot.

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John Miller and the Heartbreakers did a punk version of The Sheik of Araby.

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Hmmm, I was on an album like this once. They did Sheik of Araby.

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The Beatles had to play such long hours in Hamburg that they played everything they knew and a lot of things that they didn’t know.

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I have had this experience and it is quite liberating.

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Jo Ann Castle played for years on The Lawrence Welk Show, and she said her most requested tune was The Sheik of Araby.

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In 1991 Ray Stevens did a song called Sheik of R&B about a sheik who becomes dissillusioned with his material possessions and seeks inner peace by traveling the world in an R&B band.

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Oscar Peterson brought his truly fabulous technique to the recording of The Sheik of Araby.

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I  wrote this out by hand, even then the staff lines. It looks cartoonish, doesn’t it?

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Peggy Pettigrew Stewart’s version of Elise Wainani Piliwale.

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Sam Andrew, the Sheik of Araby.

___________________________________________

Grand Guignol

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Guigner is French for wink, to steal a glance at,

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to covet, to peep.

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A guignol is one who does these things.

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The word also means puppet and more specifically Punch as he is known in English (Policinello, Polichinelle in Italian and French).

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The puppet « Guignol » was created by Laurent Mourguet in 1808 and is now the most recognized well known puppet in France.

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Laurent Mourguet (1769-1844), was a silk worker in Lyon before the Revolution.

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After the war, he decided to change his profession and became a dentist or rather an « arracheur de dents » (« puller of teeth »).

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He set up a stall in the market.

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In order to attract patients to his stall, he created a simple « castelet » (puppet theatre) and performed scenes using his own hand made « glove» puppets.

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Monsieur Mourguet was the first person to pioneer this technique. Up until then, puppets had only been manipulated by strings.

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The first characters to appear were Polichinelle and the Devil. At the beginning of the XIXth century he introduced « Gnafron » followed by «Guignol » in 1808.

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In 1820, Laurent Mourguet created a traveling puppet troop which toured the Rhône, Loire and Isère.

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By 1830, they had perfected their technique and the show became a triumph.

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They eventually settled down in Lyon and opened their own Theatre  « Le Caveau des Célestins ».

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Almost a century later, Le Théâtre du Grand-Guignol (The Theatre of the Big Puppet) was founded in 1894 by Oscar Méténier who planned it as a space for naturalist performance.

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With 293 seats, Le Théâtre du Grand-Guignol was the smallest venue in Paris and was located in Pigalle, 20 bis, rue Chaptal.

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Le Théâtre du Grand-Guignol owed its name to Guignol and to the Lyonnais Laurent Mourguet who had joined political satire with a puppet show.

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From its opening in 1897 until its closing in 1962, Le Théâtre du Grand-Guignol specialized in naturalistic horror shows.

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The phrase grand guignol is often used as a general term for graphic, amoral horror entertainment, a genre popular from Elizabethan and Jacobean theatre (for instance Shakespeare’s Titus Andronicus and Webster’s The White Devil) to today’s splatter and snuff films.

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And then the term has expanded to describe generally any sensational and horrific event.

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The theatre’s peak was between World War I and World War II.

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It was often frequented by royalty and celebrities in evening dress.

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A former chapel, the theatre’s previous life was evident in the boxes – which looked like confessionals – and in the “angels” over the orchestra.

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Although the architecture created frustrating obstacles, this interior design that was initially a problem ultimately became a boon for the marketing of the theatre. The heavy furniture and gothic structures placed here and there on the walls of the building exuded a feeling of eeriness.

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People came to this theatre not for a mere show, but for a whole experience and they weren’t disappointed.

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The audience at Le Théâtre du Grand-Guignol endured the terror of the shows because they wanted to feel strong emotions of real intensity.

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There was definitely a sexual component to the drama.

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Underneath the balcony were boxes (originally built for nuns to watch church services) that were available for theatre-goers to rent during performances for whatever purpose.

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The audience members would carry on to such an extent in these boxes, that the actors would sometimes break character and yell “keep it down in there!”

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On the other hand, there were audience members who could not physically handle the brutality of the actions taking place on stage and would sometimes faint and/or vomit during performances.

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Oscar Méténier was the Grand Guignol’s founder and original director. Under his direction, the theater produced plays about a class of people who were not considered appropriate subjects in other venues: prostitutes, criminals, street urchins, and others at the lower end of the Parisian  social echelon.

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Max Maurey served as director from 1898 to 1914. Maurey shifted the theater’s emphasis to the horror plays it would become famous for and judged the success of a performance by the number of patrons who passed out from shock; the average was two faintings each evening.

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Maurey discovered André de Lorde who would become the most important playwright for the theatre and was the theater’s principal playwright from 1901 to 1926. He wrote at least 100 plays for the Grand Guignol and collaborated with experimental psychologist Alfred Binet to create plays about insanity, one of the theater’s frequently recurring themes.

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Camille Choisy served as director from 1914 to 1930. He contributed his expertise in special effects and scenery to the theater’s distinctive style.

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Paula Maxa was one of the Grand Guignol’s best-known performers. From 1917 to the 1930s, she performed most frequently as a victim and was known as “the most assassinated woman in the world”. During her career at the Grand Guignol, Maxa’s characters were murdered more than 10,000 times in at least 60 different ways and raped at least 3,000 times.

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Jack Jouvin served as director from 1930 to 1937. He shifted the theater’s subject matter, focusing performances not on gory horror but psychological drama. Under his leadership the theater’s popularity waned; and after World War II it was not well-attended.

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Charles Nonon was the theater’s last director.

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At the Grand Guignol, patrons would see five or six plays, all in a style that attempted to be brutally true to the theatre’s naturalistic ideals.

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The plays were in a variety of styles, but the most popular and best known were the horror plays, featuring a distinctly bleak worldview as well as notably gory special effects in their notoriously bloody climaxes.

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These plays often explored the altered states, like insanity, hypnosis, panic, under which uncontrolled horror could happen. Some of the horror came from the nature of the crimes shown, which often had very little reason behind them and in which the evildoers were rarely punished or defeated. To heighten the effect, the horror plays were often alternated with comedies in order to, if you will, cleanse the palate between courses.

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Le Laboratoire des Hallucinations, by André de Lorde: When a doctor finds his wife’s lover in his operating room, he performs a graphic brain surgery rendering the adulterer a hallucinating semi-zombie. Now insane, the lover/patient hammers a chisel into the doctor’s brain.

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Un Crime dans une Maison de Fous, by André de Lorde:  Two jealous hags in an insane asylum use scissors to blind a young, pretty fellow inmate.

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L’Horrible Passion, also by André de Lorde:  A nanny strangles the children in her care.

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Le Baiser dans la nuit by Maurice Level: A young woman visits the man whose face she horribly disfigured with acid, and he obtains his revenge.

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Audiences waned in the years following World War II, and the Grand Guignol closed its doors in 1962, the year that I went to live in Paris. Management attributed the closure in part to the fact that the theater’s faux horrors had been eclipsed by the actual events of the Holocaust two decades earlier.

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“We could never equal Buchenwald,” said its final director, Charles Nonon. “Before the war, everyone felt that what was happening onstage was impossible. Now we know that these things, and worse, are possible in reality.”

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The Grand Guignol building still exists. It is occupied by International Visual Theatre, a company devoted to presenting plays in sign language.

Dame Sybil Thorndike at the BBC

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Grand Guignol flourished briefly in London in the early 1920s under the direction of Jose Levy, where it attracted the talents of Sybil Thorndyke and Noël Coward.

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A series of short English “Grand Guignol” films (using original screenplays, not play adaptations) was made at the same time, directed by Fred Paul.

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The Grand Guignol was revived once again in London in 1945, under the direction of Frederick Witney, where it ran for two seasons at the Granville Theatre. These included premiers of Witney’s own work as well as adaptations of French originals.

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In recent years, English director-writer, Richard Mazda, has re-introduced New York audiences to the Grand Guignol. His acting troupe, The Queens Players, have produced 6 mainstage productions of Grand Guignol plays, and Mazda is writing new plays in the classic Guignol style.

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The sixth production, Theatre of Fear, included De Lorde’s famous adaptation of Poe’s Le Système du Dr Goudron et Pr Plume (The System of Doctor Tarr and Professor Feather) as well as two original plays, Double Crossed and The Good Death with The Tell Tale Heart.

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The 1963 mondo film Ecco includes a scene which may have been filmed at the Grand Guignol theatre during its final years.

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American avant-garde composer John Zorn released an album called Grand Guignol by Naked City in 1992, a reference to “the darker side of our existence which has always been with us and always will be”.

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The Washington, D.C.-based Molotov Theatre Group, established in 2007, is dedicated to preserving and exploring the aesthetic of the Grand Guignol. They have entered two plays into the Capital Fringe Festival in Washington, D.C.  Their 2007 show, For Boston, won “Best Comedy”, and their second show, The Sticking Place, won “Best Overall” in 2008.

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The Swiss theatre company, Compagnie Pied de Biche revisits the Grand Guignol genre in contemporary contexts since 2008.

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The company staged in 2010 a diptych Impact & Dr. Incubis, based on original texts by Nicolas Yazgi and directed by Frédéric Ozier.

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More than literal adaptations, the plays address violence, death, crime and fear in contemporary contexts, while revisiting many tropes of the original Grand Guignol corpus, often with humor.

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La Compagnie Pied de Biche defends the idea that theatre is nowadays the best space for audiences to experience genuine fears. As movies have overdone their explorations of the representation of violence, the intimate space of a theatre where actors hurt themselves and each other, at times with extra help from the theatrical illusion, might become again the most genuine stage of fears.

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The company also staged in 2011–12, Si seulement je pouvais avoir peur (If only I could be afraid) a production directed by Julie Burnier of a text by Nicolas Yazgi inspired by the Brothers Grimm.  The play addresses the themes of death, rejection, fear and violence for youth audiences.

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Set in a burlesque expressionist stage design, ghoulish puppets unveil the fate of a young boy who isn’t able to feel fear, because he hasn’t realized what death is.

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The recently formed London-based Grand Guignol company Theatre of the Damned, brought their first production to the Camden Fringe in 2010 and produced the award nominated Grand Guignol in November of that year.

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On May 2, 2011, they announced their new production “Revenge of the Grand Guignol”, which is to be staged in London from October 25 at the Courtyard Theatre, London, as part of the London Horror Festival.

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Also based in London, Le Nouveau Guignol form the UK’s only permanent reperatory Grand Guignol company.

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Plays within their current repertoire include French Guignol classics such as “The Final Kiss”, “Tics… Or Doing the Deed”, “The Lighthouse Keepers”, “Private Room Number Six” and “The Kiss of Blood”.

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Le Nouveau Guignol also encourages new writing, staging several new plays in the Grand-Guignol style, including “Eating For Two”, “Penalty” and “Ways and Means”.

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The Xoregos Performing Company presents Danse Macabre, a contemporary tribute to Grand Guignol at Theater for the New City in New York City. Danse Macabre is a program of four plays of psychological and physical terror and two humorous works, in keeping with Grand Guignol’s programming history.

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The playwrights are Dave DeChristopher, Jack Feldstein, Dylan Guy, Pamela Scott and Joel Trinidad.

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A dance to the famous orchestral score by Camille Saint-Saëns will be performed by the actors.

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There will be six performances between August 18-30, 2013 in the Dream Up Festival at Theater for the New City, Manhattan.

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The Japanese music group ALI Project created the song “Gesshoku Grand Guignol” as the opening for the Bee-Train anime Avenger, while British rock band Duels also named an instrumental track after the theatre.

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While the original Grand Guignol attempted to present naturalistic horror, the performances would seem melodramatic and heightened to today’s audience. For this reason, the term is often applied to films and plays of a stylised nature with heightened acting, melodrama and theatrical effects such as

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What Ever Happened to Baby Jane?

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Hush, Hush, Sweet Charlotte.

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What Ever Happened To Aunt Alice?

helen

What’s The Matter With Helen?

256015.1010.A

Night Watch

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These films form a sub branch of the genre called Grande Dame Guignol because of its use of aging A-list women actors in sensational horror films. On the male side, Vincent Price was the king of grand guignol américain.

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And now, a gallery of contemporary grand guignol themes:

Aguilar guitar

Les Pantins du Vice        Puppets of vice

alert

Ce qu’on lit sur les routes.

ali

La perception extérieure

alice

Définition de la psychologie

andy w

Nouvelles recherches sur les mouvements graphiques

apodaca

Instruction pour étudier la double conscience chez les hystériques

arc

L’obsession ou les deux forces

stanley_aguilar_guitar_front-1

Le Cerveau d’un Imbécile

ari

Une Leçon à la Salpêtrière

arigato

art carles

L’Horrible expérience

artista

I am an artist. That doesn’t mean that I work for free. I have bills to pay too. Thank you for understanding.

azi

L’homme mystériux

big

blumer

Les Invisibles

book

brun

La Maison de la mort

bruno

Crime dans une maison de fous

buon copmpleanno

L’Homme étrange

cam

Le grand mystère

CANDY

Napoléon III

car

L’homme qui a tué la mort

carherine denise

Gott mit uns   (god with us)

carlyon jocelyn

La Cathédrale Engloutie

carmel

Louange à l’éternité

caroline

Elle

cassandra

La Dernière Torture

catharine

Gardiens de phare

cathy

La Veuve

ch

Après coup

che

Sous la lumière rouge

chiara

Le baiser dans la nuit

chichén itzá

Le Jardin des supplices

chr

Le Baiser du sang

coeur

Le Laboratoire des hallucinations

colleen

Le Système du Dr Goudron et Pr Plume

cor

Un Crime dans une maison de fous

cors

Monsieur, Madame et… les autres

cubano

Une bonne farce

dagna

Dans la nuit

dan rick

Madame Blanchard

dan s

Loreau est acquitté

dana

Rêves d’un soir

daniela

L’Affaire Boreau

daniella

La Lettre

de

La Dormeuse

dawn

Doux espoirs

debbie

Hermence de la vertu

dede

Au téléphone

del

La Jeune

della

Attaque nocturne

delphine

L’Idiot

den

Madame Hercule

dena

La Nuit rouge

deutsch

La Victime, ou l’Affaire de l’impasse des Trois-Poulets

ear

elena

Baratrie

fabi

À qui le tour?

flavia

Terre d’épouvante

floyd

Cordon sanitaire

elise gundersen, are you there?

Un concert chez les fous

emma

L’Innocent

emmy

Sur la dalle

españa

Bagnes d’enfants

estelle

Figure de cire

ethel

Le coeur de Floria

eva

La Petite Roque

evelina

Sous les marroniers

evemarie

L’Amour en cage

Érase una vez...

Ernestine est enragée.

fab

Le Truc d’Adolphe

falcon

La Folie au Théâtre

laurie

La Maffia

florencia

La Visiteuse

fed

Le Château de l’amour lente

FIAT

La Bonne amie

Franca

L’Enfant mort

Frieda

Napoléonette

gable

Forfaiture

gene

L’Homme de la nuit

ggate ww2

Un beau tableau

girls

Mon p’tit Tom

good life

green

Le Cerceuil de chair

group

L’Homme aux chèques

jaq

Le Feu de joie

joder

Mon curé chez les riches

jonathan

Le Cabinet du Docteur Caliguri, ou bien Caligari, comme tu veux

juegos reunidos

L’Étrangleuse

kar

Les Nuits rouges de la Tchéka

kelly

La Chambre ardente

lire

Une nuit d’Edgar Poe

Me flipa!

Mon curé chez les pauvres

methec

Dans les dunes

minnie

Le Roman d’une femme de chambre

more fun

Jack l’éventreur

mutande

Magie noire

music meeting

Pour jouer la comédie de salon

nice

Cauchemars

occupy

Rosette, ou l’Amoureuse conspiration

pam

Les Maîtres de la peur

petrizzo

L’Étrange amant du mal

piano

La Galerie des monstres

rossia

Le Second crime de la dame en noir

sal

Dernière conquète

shane

Contes du Grand-Guignol

simone de beauvoir

La Villa solitaire

sophie

La Courroie

susan beth

À la prochaine…

voce

Goodbye till next week, and thank you for reading.

Sam & Lizzy

Sam Andrew

___________________________________________

Mathaíno perissótera.

Learn More Mathaino Perissotera  20 Nov 2009 drawing

Learn more.

2010 26 sept draw

A lifelong motto.

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Mathaíno = I learn.  μάθημα (máthema) = a learned thing.  Mathemata are “learned things.”  This word is at the root of the word “mathematics.”

Adriana

Mathematics and reckoning (numbers, arithmetic) are not the same.

academic horse drawing 23 April 2005 Augsburg

Troy, for example, the town that lay between two continents, Europe and Asia, right in the strait that leads into the Black Sea, has a mathematical design.

Against The Binding Moon 2005

Many turf mazes in England were named Troy TownTroy-town or variations on that theme  presumably because, in popular legend, the walls of the city of Troy were constructed in such a confusing and complex way that any enemy who entered them would be unable to find his way out.

Alberta Edmonton 24 July 2010

Welsh hilltop turf mazes (none of which now exist) were called Caerdroia, which can be translated as “City of Troy” (or perhaps “castle of turns”).

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The name “Troy” has been associated with labyrinths from ancient times. An Etruscan terracotta wine-jar from Tragliatella, Italy, shows a seven-ring labyrinth marked with the word TRUIA (which may refer to Troy). To its left, two armed soldiers appear to be riding out of the labyrinth on horseback, while on the right two couples are shown copulating. The vase dates from about 630 BCE.

A seven-ring Classical labyrinth. The “Troy” mazes at Dalby and Somerton are based on this ancient design.

Medieval labyrinth

Elise Solstice

Of the eight surviving historic turf mazes in England, three have “Troy” names. “The City of Troy” is a small but well-maintained roadside maze near the small villages of Dalby, Brandsby, and Skewsby, not far from Sheriff Hutton in the Howardian Hills of North Yorkshire.

Embrace

“Troy”, a beautiful maze in a private garden at Troy Farm, Somerton, Oxfordshire, is rather larger, and “Troy Town” maze on St Agnes, the Isles of Scilly, is a small maze of turf and small stones and is reputed to have been laid down in 1729 by the son of a local lighthouse keeper.

eye anatomy Forum

All three follow the classical labyrinth pattern (as found on coins from ancient Knossos) rather than the medieval variation.

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This  Troy design may be the oldest town planning scheme that we know. Even older than Jericho.

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This Troy design is a mathematical scheme.

Faustina drawing

There is a range of views even among mathematicians and philosophers as to the exact scope and definition of mathematics.

2006 aug 10 Ft. Collins CO

Galileo Galilei (1564–1642) said, “The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth.”

2006 aug 19 Webster Mass

Richard Feynman made the same point:  When nature speaks to us, she uses the language of mathematics.

2006 feb 26 Sherman Oaks

Carl Friedrich Gauss (1777–1855) referred to mathematics as “the Queen of the Sciences,””

2006 june 17 cuyahoga falls OH

Albert Einstein (1879–1955) stated that “as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

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The most ancient mathematical texts are Plimpton 322 (Babylonian mathematics c. 1900 BCE), the Rhind mathematical papyrus (Egyptian mathematics c. 2000-1800 BCE) and the Moscow mathematical papyrus (Egyptian mathematics c. 1890 BCE).

2006 sept 10 Umea

All of these texts concern the so-called Pythagorean theorem which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. This theorem existed long before Pythagoras himself did. The Chinese and Egyptians knew it.

rib cage (pen and ink) 2003

The study of mathematics begins in the 6th century BCE with the Pythagoreans who coined the term “mathematics” from the ancient Greek μάθημα (mathema), meaning “subject of instruction.”  Note that μάθημα is from the same root as “mathaino perissotera,” (I Learn More) the title of this writing.

2006 aug 29 Leeds

Greek mathematics refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics.

pink Egyptian

Chinese mathematics made very early contributions, including a place value system.

2006 aug 30 Clitheroe, Lancashire

The Hindu-Arabic numerical system and the rules for the use of its operations, in use throughout the world today, likely evolved over the course of the first millennium CE in India and was transmitted to the west via Islamic mathematics.

Libyan

Islamic mathematics developed and expanded the mathematics known to these civilizations.

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Many Greek and Arabic texts on mathematics were then translated into Latin which led to further development of mathematics in medieval Europe.

2006 july 10 St. Louis

From ancient times through the middle ages spurts of mathematical creativity were often followed by centuries of stagnation.

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In 16th century Renaissance Italy, new mathematical developments, interacting with new scientific discoveries, were made at an accelerating pace that continues to the present day.

2005 nov 18

The origins of mathematical thought lie in the concepts of number, magnitude and form.

Alterego 20 Oct 2010

Modern studies of animal cognition have shown that these concepts are not unique to humans.

2006 july 15 Battle Creek

Such concepts would have been part of everyday life in hunter-gatherer societies.

Baja California

The idea of the “number” concept evolving gradually over time is supported by the existence of languages which preserve the distinction between “one”, “two”, and “many”, but not of numbers larger than two.

2006 aug 28 Earby near Manchester

The oldest known possibly mathematical object is the Lebombo bone discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC.

2008 jan 10

The bone consists of 29 distinct notches cut into a baboon’s fibula.

2006 sept 11 Crawley near Gatwick

Also prehistoric artifacts discovered in Africa and France dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.

2006 nov 30 Kihei, Maui

The Ishangi bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone.

2006 sept 9 Uppsala

It is thought that the Ishango bone shows either the earliest known demonstration of sequences of prime numbers or a six-month lunar calendar.

BBHC, green

Peter Rudman argues in How Mathematics Happened: The First 50,000 Years,  that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10,000 BCE, with prime numbers probably not being understood until about 500 BCE.

2006 sept 8 Stockholm

Rudman also writes that “no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10.”

2006 june 14 aspen Zélé

The Ishango bone, according to scholar Alexander Marshack, may have influenced the later development of mathematics in Egypt since, like some entries on the Ishango bone, Egyptian arithmetic also made use of multiplication by 2; this, however, is disputed.

2006 nov 28 Tucson

Predynastic Egyptians of the 5th millennium BCE pictorially represented geometric designs.

2006 july 3 Las Vegas

Megalithic monuments in England and Scotland, dating from the 3rd millennium BCE, incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in their design.

2006 nov 27 Phoenix

The currently oldest undisputed mathematical usage is in Babylonian and dynastic Egyptian sources.

Antea Arianna

Thus it took human beings at least 45,000 years from the time when they became more or less like us and used language to develop mathematics as such.

2006 feb 24 LA

Babylonian mathematics refers to any mathematics of the people of Mesopotamia (modern Iraq) from the days of the early Sumerians through the Hellenistic period and up to the beginning of the Common Era.

Sophia Ramos

The term Babylonian mathematics is used due to the central role of Babylon as the place of study.

2006 sept 1 Glenfarg, Perthshire

During the Arab era, Mesopotamia, especially Baghdad, again became an important center of study for Islamic mathematics.

Joe Freshwater

It’s difficult to find information about Egyptian mathematics, but our knowledge of Babylonian mathematics is derived from more than 400 clay tablets unearthed since the 1850s.

Reason By The Heart  2005

Written in cuneiform, the tablets were inscribed while the clay was moist, and baked hard in an oven or by the heat of the sun.

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Some of these tablets appear to be graded homework.

arm 2005

The first evidence of written mathematics dates back to the ancient Sumerians, who built the earliest civilization in Mesopotamia.

2008 jan 11

The Sumerians developed a complex system of metrology from 3000 BCE.

2009 nov 17

From around 2500 BCE onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems.

Batesville, AR

The earliest traces of the Babylonian numerals also date back to this period.

Beautiful, Illegible

Most of the recovered clay tablets date from 1800 to 1600 BCE, and cover topics which include fractions, algebra, quadratic and cubic equations, and the calculation of regular reciprocal pairs.

Bielefeld

The tablets also include multiplication tables and methods for solving linear and quadratic equations.

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The Babylonian tablet YBC 7289 gives an approximation of √2 accurate to five decimal places.

blue girl hands

Babylonian mathematics were written using a sexagesimal (base-60) numeral system.

Wom Prop

This is where we get the idea of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 x 6) degrees in a circle, as well as the use of seconds and minutes of arc to denote fractions of a degree.

rib cage parts

Babylonian advances in mathematics were facilitated by the fact that 60 has many divisors.

rib cage recling

Unlike the Egyptians, Greeks, and Romans, the Babylonians had a true place-value system, where digits written in the left column represented larger values, much as in the decimal system.

purple woman

The Babylonians had a place-value system, yes, but no kind of decimal point, and so the place value of a symbol often had to be inferred from the context.

rib cage animal

Seen another way, though, this decimal point drawback is equivalent to the modern-day usage of floating point arithmetic.

rib cage animals

Also, the use of base 60 means that any reciprocal of an integer which is a multiple of divisors of 60 necessarily has a finite expansion to the base 60.

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(In our arithmetic, only reciprocals of multiples of 2 and 5 have finite decimal expansions.)

Sam Andrew drawing A Grief Ago  2005

This means that there is a strong argument that the arithmetic Old Babylonian style is considerably more sophisticated than that of our current usage.

Saint Petersburg, Florida  2005

The interpretation of Plimpton 322 (the Babylonian mathematical text from 1900 BCE) was the source of controversy for many years after its significance in the context of Pythagorean triangles was realized.

Sam Andrew, dessin

Problems involving equal-area subdivision of triangular and trapezoidal fields (with integer length sides) quickly convert into the need to calculate the square root of 2, or to solve the “Pythagorean equation” in integers.

rib cage Bargue

Rather than considering a square as the sum of two squares, you can think of it as a difference of two squares. After division, (c-a)(c+a)= bb becomes the product of two rational numbers giving 1: (c/b-a/b)(c/b+a/b) = 1.

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And then you can solve this by looking at a table of reciprocal pairs.

rocket man 2002

Solutions of the original equation are thus parametrized by the choice of a rational number x, from which Pythagorean-triple right-triangles can easily be constructed by integer-scaling a right-triangle with sides of length 2x, xx-1, xx+1 (but only if you wish to do so).

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All Pythagorean triples arise in this way, and the examples provided in Plimpton 322 involve some quite large numbers, by modern standards, such as (4601, 4800, 6649) in decimal notation.

Sam Athens 5 Nov 2009

Egyptian mathematics refers to mathematics written in the Egyptian language. During the Hellenistic period, Greek replaced Egyptian as the written language of Egyptian scholars. Mathematical study in Egypt later continued under the Arab empire as part of Islamic mathematics when Arabic became the written language of Egyptian scholars.

rib cage pen

The most extensive Egyptian mathematical text is the Rhind papyrus(sometimes also called the Ahmes Papyrus after its author), dated to c. 1650 BCE but likely a copy of an older document from the Middle Kingdom of about 2000-1800 BC.

Sam Andrew, cards study

The Rhind papyrus is an instruction manual for students in arithmetic and geometry.

rib cage skeleton

In addition to giving area formulas and methods for multiplication, division and working with unit fractions, it also contains evidence of other mathematical knowledge, including composite and prime numbers; arithmetic, geometric and harmonic means; and simplistic understandings of both the Sieve of Eratosthenes and perfect number theory (namely, that of the number 6).

Sam Andrew, viols

The Rhind papyrus also shows how to solve first order linear equations as well as arithmetic and geometric series.

rib cage sternum boxes

Another significant Egyptian mathematical text is the Moscow papyrus also from the Middle Kingdom period, dated to c. 1890 BCE.

Sculpture model

The Moscow papyrus consists of what are today called word problems or story problems, which were apparently intended as entertainment.

SD figure (pen)

One problem is considered to be of particular importance because it gives a method for finding the volume of a frustum: “If you are told: A truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top. You are to square this 4, result 16. You are to double 4, result 8. You are to square 2, result 4. You are to add the 16, the 8, and the 4, result 28. You are to take one third of 6, result 2. You are to take 28 twice, result 56. See, it is 56. You will find it right.”

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Finally, the Berlin papyrus (c. 1300 BCE) shows that ancient Egyptians could solve a second-order algebraic equation.

Sam Orpheus 4 Nov 2009 drawing

Greek mathematics refers to mathematics written in the Greek language from the time of Thales of Miletus (~600 BCE) to the closure of the Academy of Athens in 529 CE.

Solange

Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to North Africa, but were united by culture and language.

rib cage structure

Greek mathematics of the period following Alexander the Great is often called Hellenistic mathematics.

Tom's Big Brother

Greek mathematics was much more sophisticated than the mathematics that had been developed by earlier cultures.

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All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb.

Camila Coelho

Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them.

carpals 1

Greek mathematics is thought to have begun with Thales of Miletus (c. 624–c.546 BCE) and Pythagoras of Samos (c. 582–c. 507 BCE).

BBHC France

Although the extent of the influence is disputed, Thales and Pythagoras were probably inspired by Egyptian and Babylonian mathematics.

Blues From The Gods

According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests.

Sam Andrew, Fern Hill 2005

Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore.

Spirals Women

He is also credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales’ Theorem.

Blue Head

Thales, therefore, has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed.

Sophia fuschia

Pythagoras established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was “All is number.”

The Sinner's Dust Tongued Bell 2005

It was the Pythagoreans who coined the term “mathematics”, and with whom the study of mathematics for its own sake begins.

Three Graces

The Pythagoreans are credited with the first proof of the Pythagorean theorem.

three heads pen and ink

The statement of the Pythagorean theorem has a long history and was known to Chinese and Egyptian thinkers.

Tiziana Tancredi

The Pythagoreans are also credited with the proof of the existence of irrational numbers.

Sarasota

Archimedes used the method of exhaustion to approximate the value of pi, and that’s what it would take, exhaustion.

We Trembled Listening  2005

I’ll talk a little about the method of exhaustion below.

We Rock the Summer 16 Nov 2009

Plato (428/427 BC – 348/347 BCE) is important as an inspiration in the history of mathematics and as a guide.

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The Platonic Academy in Athens became the mathematical center of the world in the 4th century BCE, and it was this school that produced leading mathematicians of the day such as Eudoxus of Cnidus.

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Plato discussed the foundations of mathematics, clarified some of the definitions (e.g. that of a line as “breadthless length”) and examined the assumptions everyone had up to that point.

virginia city sam

The analytic method of reasoning is ascribed to Plato, and a formula for obtaining Pythagorean triples bears his name.

Victoria drawing

Eudoxus (408–c.355 BCE) developed the method of exhaustion, a precursor of modern integration, and also a theory of ratios that avoided the problem of incommensurable magnitudes

You Green Person You

The method of exhaustion allowed the calculations of areas and volumes of curvilinear figures.

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The theory of ratios enabled subsequent geometers to make significant advances in geometry.

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Aristotle (384—c.322 BCE) contributed significantly to the development of mathematics by laying the foundations of logic, though he made no specific technical mathematical discoveries.

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In the 3rd century BCE, the premier center of mathematical education and research was the Museum of Alexandria.

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It was in Alexandria that Euclid (c. 300 BCE) taught, and wrote the Elements, widely considered the most successful and influential textbook of all time.

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The Elements introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof.

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Most of the contents of the Elements were already known, but Euclid arranged them into a single, coherent logical framework.

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The Elements was known to all educated people in the West until the middle of the 20th century and its contents are still taught in geometry classes today.

Circle Woman 30 September 2011

I remember this book well.

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In addition to teaching the familiar theorems of Euclidean geometry, the Elements was meant as an introductory textbook to all mathematical subjects of the time, such as number theory, algebra and solid geometry, including proofs that the square root of two is irrational and that there are infinitely many prime numbers.

Couple Seattle

Euclid wrote extensively on other subjects, such as conic sections, optics, spherical geometry, and mechanics, but only half of his writings survive.

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The first woman mathematician recorded by history was Hypatia of Alexandria (350 – 415 CE).

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Hypatia succeeded her father as the librarian at the great library of Alexandria and wrote many works on applied mathematics.

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The “Christian” community in Alexandria punished Hypatia for her intellectual “presumption” by stripping her naked and scraping off her skin with clamshells and roofing tiles.

Dido

Apollonius of Perga made significant advances in the study of conic sections.

Dimitra July 2010 drawing

Archimedes (c.287–212 BCE) of Syracuse, widely considered the greatest mathematician of antiquity, used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.

Foot Cincinnatus

Archimedes also showed one could use the method of exhaustion to calculate the value of π with as much precision as desired, and obtained the most accurate value of π then known, 31071 < π < 31070.

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He also studied the spiral that bears his name, obtained formulas for the volumes of surfaces of revolution (paraboloid, ellipsoid, hyperboloid), and an ingenious system for expressing very large numbers.

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While he is also known for his contributions to physics and several advanced mechanical devices, Archimedes himself placed far greater value on the products of his thought and general mathematical principles.

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He regarded as his greatest achievement his finding of the surface area and volume of a sphere, which he obtained by proving these are 2/3 the surface area and volume a cylinder circumscribing the sphere.

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Apollonius of Perga (c. 262-190 BCE) made significant advances to the study of conic sections, showing that one can obtain all three varieties of conic section by varying the angle of the plane that cuts a double-napped cone.

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Apollonius also coined the terminology in use today for conic sections, namely parabola (“place beside” or “comparison”), ellipse (“deficiency”), and hyperbola (“a throw beyond”).

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His work Conics is one of the best known and preserved mathematical works from antiquity, and in it he derives many theorems concerning conic sections that would prove invaluable to later mathematicians and astronomers studying planetary motion.

Flávia França

While neither Apollonius nor any other Greek mathematicians made the leap to coordinate geometry, Apollonius’ treatment of curves is in some ways similar to the modern treatment, and some of his work seems to anticipate the development of analytical geometry by René Descartes.

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Eratosthenes of Cyrene (c. 276-194 BCE) was the one who devised the Sieve of Eratosthenes for finding prime numbers.

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The 3rd century BCE is regarded as the “Golden Age” of Greek mathematics, with advances in pure mathematics henceforth in relative decline.

eye anatomy

In the centuries that followed, however, significant advances were made in applied mathematics, most notably  in trigonometry to help astronomers.

draped nude 2005

Hipparchus of Nicaea (c. 190-120 BCE) is considered the founder of trigonometry because he compiled the first known trigonometric table.

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He was also the first to use systematically the 360 degree circle.

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Heron of Alexandria (c. 10–70 CE) created Heron’s formula for finding the area of a scalene triangle.

E pluribus unum pen

Heron also was the first to recognize the possibility of negative numbers possessing square roots.

hands copied Durer

Menelaus of Alexandria (c. 100 CE) pioneered spherical trigonometry with his Menelaus’ theorem.

Easy Chair

The most complete and influential trigonometric work of antiquity is the Almagest of Ptolemy (c. 90-168 CE), a landmark astronomical treatise whose trigonometric tables would be used by astronomers for the next thousand years.

Elise (charcoal)

Ptolemy also created Ptolemy’s theorem for deriving trigonometric quantities, and the most accurate value of π (3.1416) outside of China until the medieval period in Europe.

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The period between 250 and 350 CE is sometimes referred to as the “Silver Age” of Greek mathematics which had followed a period of stagnation in Greek mathematics.

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During this Silver Age,  Diophantus made significant advances in algebra, particularly indterminate analysis which is also known as Diophantine analysis.

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The study of Diophantine equations and approximations is a significant area of research to this day.

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Diophantus’ main work was the Arithmetica, a collection of 150 algebraic problems dealing with exact solutions to determinate and indeterminate equations.

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The Arithmetica had a significant influence on later mathematicians, such as Pierre de Fermat, who arrived at his famous Last theorem after trying to generalize a problem he had read in the Arithmetica (that of dividing a square into two squares).

Chester Arnold et alia

Diophantus also made significant advances in notation, the Arithmetica being the first instance of algebraic symbolism and syncopation.

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Meanwhile in China,  mathematics was so different from that of other parts of the world  it is logical to assume an independent development of the science.

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The oldest surviving mathematical text from China is the Chou Pei Suan Ching, variously dated to between 1200 BCE and 100 BCE, though a date of about 300 BCE seems the best guess.

Classical Dance

Of particular note is the use in Chinese mathematics of a decimal positional notation system, the so-called “rod numerals” in which distinct ciphers were used for numbers between 1 and 10, and additional ciphers for powers of ten.

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This system may have evolved from looking at an abacus.

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Thus, the number 123 would be written using the symbol for “1″, followed by the symbol for “100″, then the symbol for “2″ followed by the symbol for “10″, followed by the symbol for “3″.

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This was the most advanced number system in the world at the time, in use for several centuries before the common era in Europe and well before the development of the Indian/Arabic numeral system.

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Rod numerals allowed the representation of numbers as large as desired and allowed calculations to be carried out on the suan pan or Chinese abacus.

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When the suan pan was invented is not certain, but the earliest written mention dates from 190 CE, in Xu Yue’s Supplementary Notes on the Art of Figures.

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The oldest Chinese work on geometry is the philosophical Mohist canon c. 330 BCE, compiled by the followers of Mozi (470–390 BCE).

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The Mo Jing described various aspects of many fields associated with physical science, and provided a small number of geometrical theorems as well.

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In 212 BC, the Emperor Qin Shih Huang (Shi Huang-ti) commanded all books in the Qin Empire other than officially sanctioned ones be burned.

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This book burning decree was flouted in some places, but as a consequence of this disastrous decree little is known about ancient Chinese mathematics before this date.

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After the babarian book burning of 212 BCE, the Han dynasty (202 BCE–220 CE) produced works of mathematics which presumably expanded on works that lost during the holocaust.

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(Notice that the Han period corresponds roughly with the time of the Roman empire in Europe. The Han Chinese are, by far, the largest group in China. They call themselves Han as do other peoples around them. The Japanese word for written characters borrowed from China is kanji which means “Han letter” in Japanese.)

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The most important of Han works that expanded on the earlier burned books is The Nine Chapters on the Mathematical Art, the full title of which appeared by 179 CE, but which had existed before under other titles.

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The Nine Chapters consists of 246 word problems involving agriculture, business, employment of geometry to figure height spans and dimension ratios for Chinese pagoda towers, engineering and surveying.

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Material on right triangles and values of  π is also included.

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The Nine Chapters on the Mathematical Art created mathematical proof for the Pythagorean theorem and a mathematical formula for Gaussian elimination.

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Lin Hui commented on the work in the 3rd century CE, and gave a value of π accurate to 5 decimal places.

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Though more of a matter of computational stamina than theoretical insight, in the 5th century CE Zu Chongzhi computed the value of π to seven decimal places, which remained the most accurate value of π for almost the next 1000 years.

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He also established a method which would later be called Cavalieri’s principle to find the volume of a sphere.

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The high-water mark of Chinese mathematics occurs in the 13th century (Sung period), with the development of Chinese algebra.

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The classic text from the later Sung period is the Precious Mirror of the Four Elements by Chu Shih-chieh (fl. 1280-1303), dealing with the solution of simultaneous higher order algebraic equations similar to Horner’s method.

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The Precious Mirror also contains a diagram of Pascal’s triangle with coefficients of binomial expansions through the eighth power, though both appear in Chinese works as early as 1100.

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The Chinese also made use of the complex combinatorial diagram known as the magic square and magic circles, described in ancient times and perfected by Yang Hui (1238–1298 CE).

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Even after European mathematics began to flourish during the Renaissance, European and Chinese mathematics were separate traditions, with significant Chinese mathematical output in decline from the 13th century onwards.

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Jesuit missionaries such as Matteo Ricci carried mathematical ideas back and forth between the two cultures from the 16th to 18th centuries, though at this point far more mathematical ideas were entering China than leaving.

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On the Indian subcontinent was the Indus Valley civilization that flourished between 2600 and 1900 BCE in the Indus River basin.

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The Indus Valley cities were laid out with geometric regularity, but no known mathematical documents survive from this civilization.

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The oldest existing mathematical records from India are the Sulba Sutras, dated variously between the 8th century BCE and the 2nd century CE, appendices to religious texts which give simple rules for constructing altars of various shapes, such as squares, rectangles, parallelograms, and others.

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This preoccupation with temple functions points to an origin of mathematics in religious ritual, as was perhaps the case in Egypt.

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The Sulba Sutras give methods for constructing a circle with approximately the same area as a given square, which implies several different approximations of the value of  π.

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In addition, the Sutras compute the square root of 2 to several decimal places, list Pythagorean triples, and give a statement of the Pythagorean theorem.

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These were all present in Babylonian science, which would seem to indicate a Mesopotamian influence on Indian mathematics.

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It is not known to what extent the Sulba Sutras influenced later Indian mathematicians.

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As in China, there is a lack of continuity in Indian mathematics.

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Significant advances are separated by long periods of inactivity.

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Panini (c. 5th century BCE) formulated the rules for Sanskrit grammar.

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His notation was similar to the mathematical notation of today, andhe  used metarules, transformations and recursion.

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Pingala (roughly 3rd-1st centuries BCE) in his treatise of prosody uses a device corresponding to a binary numeral system.

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His discussion of the combinatrics of meters corresponds to an elementary version of the binomial theorem.

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Pingala’s work also contains the basic ideas of Fibonacci numbers, which he called mātrāmeru).

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The next significant mathematical documents from India after the Sulba Sutras are the Siddhantas, astronomical treatises from the 4th and 5th centuries CE, the Gupta period, showing strong Hellenistic influence.

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They are significant in that they contain the first instance of trigonometric relations based on the half-chord, as is the case in modern trigonometry, rather than the full chord, as was the case in Ptolemaic trigonometry.

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Through a series of translation errors, the words “sine” and “cosine” derive from the Sanskrit “jiya” and “kojiya”.

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In the 5th century CE, Aryabhata wrote the Aryabhatiya, a slim volume, written in verse, intended to supplement the rules of calculation used in astronomy and mathematical mensuration, though with no feeling for logic or deductive methodology.

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Though about half of the entries are wrong, it is in the Aryabhatiya that the decimal place-value system first appears.

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Several centuries later, the Muslim mathematician Abu Rihan Biruni described the Aryabhatiya as a “mix of common pebbles and costly crystals”.

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In the 7th century, Brahmagupta identified the Brahmagupta theorem, Brahmagupta’s identity, and for the first time, in Brahma sphuta siddhanta he lucidly explained the use of zero as both a placeholder and decimal digit and explained the Hindu Arabic numeral system.

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It was from a translation of this Indian text on mathematics (c. 770) that Islamic mathematicians were introduced to this numeral system, which they adapted as Arabic numerals.

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Islamic scholars carried knowledge of this number system to Europe by the 12th century, and it has now displaced all older number systems throughout the world.

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In the 10th century, Halayudha’s commentary on Pingala’s work contains a study of the Fibonacci sequence and Pascal’s triangle and describes the formation of a matrix.

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In the 12th century, Bhaskara II lived in southern India and wrote extensively on mathematics.

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His work contains mathematical objects equivalent or approximately equivalent to infinitesimals, derivatives, the mean value theorem and the derivative of the sine function.

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To what extent he anticipated the invention of calculus is a controversial subject among historians of mathematics.

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In the 14th century, Madhava of Sangamagrama, the founder of the so-called Kerala School of Mathematics, found the Madhava-Leibniz series, and, using 21 terms, computed the value of π as 3.14159265359.

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Madhava also found the Madhava-Gregory series to determine the arctangent, the Madhava-Newton power series to determine sine and cosine and the Taylor approximation for sine and cosine functions.

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In the 16th century, Jyesthadeva consolidated many of the Kerala School’s developments and theorems in the Yukti-bhāṣā.

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However, the Kerala School did not formulate a systematic theory of differentiation and integration, nor is there any direct evidence of their results being transmitted outside Kerala.

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Progress in mathematics along with other fields of science stagnated in India with the establishment of Muslim rule in India.

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The Islamic empire established across Persia, the Middle East,  Central Asia, North Africa, Iberia and in parts of India in the 8th century made significant contributions towards mathematics.

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Although most Islamic texts on mathematics were written in Arabic, most of them were not written by Arabs, since much like the status of Greek in the Hellenistic world, Arabic was used as the written language of non-Arab scholars throughout the Islamic world at the time.

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Persians contributed to the world of Mathematics alongside Arabs.

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In the 9th century, the Persian mathematician Muhammad ibn Musa al-Khwarismi wrote several important books on the Hindu-Arabic numerals and on methods for solving equations.

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His book On the Calculation with Hindu Numerals, written about 825, along with the work of Al-Kindi, were instrumental in spreading Indian mathematics and Indian numerals to the West.

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The word algorhythm is derived from the Latinization of his name, Algoritmi, and the word algebra from the title of one of his works,Al-Kitab al-mukhtasar fihisab al-gabr wa’l-mugabala (The Compendious Book on Calculation by Completion and Balancing).

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He gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots, and he was the first to teach algebra in an elementary form and for its own sake.

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He also discussed the fundamental method of “reduction” and “balancing”, referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.

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This is the operation which al-Khwārizmī originally described asal-jabr.

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His algebra was also no longer concerned “with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study.”

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He also studied an equation for its own sake and “in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems.”

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Further developments in algebra were made by Al-Karaji in his treatise al-Fakhri, where he extends the methodology to incorporate integer powers and integer roots of unknown quantities.

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Something close to a proof by mathematical induction appears in a book written by Al-Karaji around 1000 AD, who used it to prove the binomial theorem, Pascal’s triangle and the sum of integral cubes.

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The historian of mathematics, F. Woepcke, praised Al-Karaji for being “the first who introduced the theory of algebraic calculus.”

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Also in the 10th century, Abul Wafa translated the works of Diophantus into Arabic.

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Ibn al-Haytham was the first mathematician to derive the formula for the sum of the fourth powers, using a method that is readily generalizable for determining the general formula for the sum of any integral powers.

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He performed an integration in order to find the volume of a paraboloid, and was able to generalize his result for the integrals of polynomials up to the fourth degree.

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So he came quite close to finding a general formula for the integrals of polynomials, but he was not concerned with any polynomials higher than the fourth degree.

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In the late 11th century, Omar Khayyam wrote Discussions of the Difficulties in Euclid, a book about what he perceived as flaws in Euclid’s Elements especially the parallel postulate.

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He was also the first to find the general geometric solution to cubic equations. He was also very influential in calendar reform.

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In the 13th century, Nasir al-Din Tusi  (Nasireddin) made advances in spherical trigonometry.

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He also wrote influential work on Euclid’s parallel postulate.

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In the 15th century, Ghiyath al-Kashi computed the value of π to the 16th decimal place.

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Kashi also had an algorithm for calculating nth roots, which was a special case of the methods given many centuries later by Ruffini and Horner.

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Other achievements of Muslim mathematicians during this period include the addition of the decimal point notation to the Arabic numerals, the discovery of all the modern trigonometric notation besides the sine, al-Kindi’s introduction of cryptanalysis and frequency analysis, the development of analytic geometry by Ibn al-Haytham, the beginning of algebraic geometry by Omar Khayyam and the development of an algebraic notation by al-Qalasadi.

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During the time of the Ottoman empire and the Safavid empire, from the 15th century, the development of Islamic mathematics stagnated. Why? What happened? This could be called the Arabic question, just as the problem of why China stopped her phenomenal growth and highly advanced development around the time our own Renaissance began could be called the China question. Are civilizations/cultures like plants? Do they have their own internal clocks?

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Interest in mathematics in Medieval Europe was driven by concerns quite different from those of modern mathematicians.

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People then believed that mathematics would provide the key to understanding the created order of nature, frequently justified by Plato’s Timaeus and the biblical passage (Book of Wisdom) that God had ordered all things in measure, and number, and weight.

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Boethius provided a place for mathematics in the curriculum in the 6th century when he used the term quadrivium to describe the study of arithmetic, geometry, astronomy, and music.

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De institutione arithmetica was Boethius’ free translation from the Greek of Nicomachus’ Introduction to Arithmetic.

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De institutione musica, also by Boethius, derived from Greek sources, especially from a series of excerpts of Euclid’s Elements.

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These works were theoretical, rather than practical, and were the basis of mathematical study until the recovery of Greek and Arabic mathematical works.

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European began to travel south to Spain and Italy by the twelfth century seeking scientific and philosophical Arab texts, including al-Kharizmi’s Compendius Boon on Calculation by Completeion and Balancing, which was then translated into Latin by Robert of Chester.

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The complete text of Euclid’s Elements was translated in various versions by Adelard of Bath, Herman of Carinthia and Gerard of Cremona.

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The new translations aroused a new interest in mathematics.

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Leonardo Pisano Bigollo (1170-1250), better known as Fibonacci, writing in the Liber Abaci (Book of the Abacus), produced the first significant mathematics in Europe since the time of Eratosthenes, a gap of more than a thousand years.

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Fibonacci’s book introduced Hindu/Arabic numerals (modus Indorum, method of the Indians) to Europe, and discussed many other mathematical problems.

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The 14th century saw the development of new mathematical concepts to investigate a wide range of problems.

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One important contribution was development of mathematics of local motion.

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Thomas Bradwardine proposed that speed (V) increases in arithmetic proportion as the ratio of force (F) to resistance (R) increases in geometric proportion.

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Bradwardine expressed this by a series of specific examples, but although the logarithm had not yet been conceived, we can express his conclusion anachronistically by writing: V = log (F/R).

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Bradwardine’s analysis is an example of transferring a mathematical technique used by al-Kindi and Arnald of Villanova to quantify the nature of compound medicines to a different physical problem.

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William Heytesbury (circa 1313 – 1372/1373), one of the 14th-century Oxford calculators, lacking differential calculus and the concept of limits, proposed to measure instantaneous speed “by the path that would be described by [a body] if… it were moved uniformly at the same degree of speed with which it is moved in that given instant.”

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Heytesbury mathematically determined the distance covered by a body undergoing uniformly accelerated motion (today solved by integration), stating that “a moving body uniformly acquiring or losing that increment [of speed] will traverse in some given time a [distance] completely equal to that which it would traverse if it were moving continuously through the same time with the mean degree [of speed]“.

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Nicole Oresme at the Université de Paris and the Italian Giovanni di Casali independently provided graphical demonstrations of this relationship, asserting that the area under the line depicting the constant acceleration, represented the total distance traveled.

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Later, commenting on Euclid’s Elements, Oresme made a more detailed general analysis in which he demonstrated that a body will acquire in each successive increment of time an increment of any quality that increases as the odd numbers.

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Since Euclid had demonstrated the sum of the odd numbers are the square numbers, the total quality acquired by the body increases as the square of the time.

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During the Renaissance, the development of mathematics and of accounting were intertwined were studied at the same time.

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While there is no direct relationship between algebra and accounting, the teaching of the subjects and the books published often intended for the children of merchants who were sent to reckoning schools in Flanders or Germany or abacus schools (known as abbaco in Italy), where they learned the skills useful for trade and commerce.

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In the abacus schools principles of reckoning were taught in the vernacular languages rather than in Latin.

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There is probably no need for algebra in performing bookkeeping operations, but for complex bartering operations or the calculation of compound interest, a basic knowledge of arithmetic was mandatory and knowledge of algebra was very useful.

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The Summa de Arithmetica, Geometria, Proportioni et Proportionalità of Luca Pacioli was first printed and published in Venicein 1494,

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The Summa included a 27-page treatise on bookkeeping “Particularis de Computis et Scripturis” (Details of Calculation and Recording). and was written primarily for, and sold mainly to, merchants who used the book as a reference text, as a source of pleasure from the mathematical puzzles it contained, and to aid the education of their sons.

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Pacioli introduced symbols for plus and minus for the first time in the Summa, symbols that became standard notation in Italian Renaissance mathematics.

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The Summa Arithmetica was also the first known book printed in Italy to contain algebra.

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It is important to note that Pacioli himself had borrowed much of the work of Piero della Francesca whom he plagiarized.

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Long passages in the book are merely a restating of della Francesca’s work.

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In Italy, during the first half of the 16th century, Scipione del Ferro and Niccolò Fontana Tartaglia discovered solutions for cubic equations. (“Tartaglia” means “the stammerer,” because Fontana was injured in a battle against an invading French army which caused his speech defect.)

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Gerolamo Cardano published the cubic equations in his 1545 book Ars Magna together with a solution for the quartic equations discovered by his student Lodovico Ferraro.

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In 1572 Rafael Bombelli published his L’Algebra in which he showed how to deal with the imaginary quantities that could appear in Cardano’s formula for solving cubic equations.

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De Thiende (‘the art of tenths’), by Simon Stevin, first published in Dutch in 1585, contained the first systematic treatment of decimal notation, which influenced all later work on the real number system.

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Stevin is credited with the invention of the decimal point, although, as we have seen, place value notation had long been practiced by the Chinese, Indians, Arabs and others.

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Trigonometry grew to be a major branch of mathematics because large areas of the world needed to be accurately mapped and there were many more ships at sea now.

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Bartholomaeus Pitiscus invented the word “trigonometry,” publishing his Trigonometria in 1595.

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Regiomontanus’s table of sines and cosines was published in 1533.

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During the Renaissance the desire of artists to represent the natural world realistically, together with the rediscovered philosophy of the Greeks, led artists to study mathematics and mathematicians to study art.

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Artists were also the engineers and architects of that time, and so had need of mathematics in any case.

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The art of painting in perspective, and the developments in geometry that involved, were studied intensely.

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The Seventeenth Century was an age of science in Europe.

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Robert Boyle began his experiments during this period and Galileo Galilei observed the moons of Jupiter in orbit about that planet, using a telescope based on a toy imported from Holland.

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Tycho Brahe had gathered an enormous quantity of mathematical data describing the positions of the planets in the sky.

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Johannes Kepler, Brahe’s assistant, was also, to put it mildly, very interested in planetary motion.

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The invention of logarithms by John Napier and Jost Bürgi made Kepler’s calculations a lot easier.

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Kepler succeeded in formulating mathematical laws of planetary motion.

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The analytic geometry of René Descartes (1596–1650) allowed those orbits to be plotted on a graph, as Cartesian coordinates.

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Simon Stevin, as we have mentioned, created the basis for modern decimal notation capable of describing all numbers, whether rational or irrational.

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Isaac Newton discovered the laws of physics explaining Kepler’s laws and brought together the concepts now known as infinitesimal calculus.

In one of those congruencies that happen now and again in human history, Newton and Leibniz independently invented calculus at about the same time.

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Probably most musicians have had the experience of writing something, putting it aside, and then hearing it later on the radio, the work of someone else.

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No one copied anyone.

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The idea was ready to be born and it was born in two places at once.

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Consider the countercultural movement that happened in San Francisco from 1965 to 1970.

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That movement, that questioning of authority, occurred all over the world at about the same time.

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The Red Guards in China were a part of that phenomenon, even though it would have disgusted them to realize that.

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It was the Chinese youth’s mission to do away with the old and to submit all received ideas to the cold light of reëxamination.

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There were excesses as there often are in such profound and universal movements.

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One has only to contemplate the Reign of Terror in the French Revolution to see that lawlessness can very quickly lead to fascism.

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Gottfried Wilhelm Leibniz, who is arguably the most important mathematician of the 17th century, developed this calculus that he and Newton had invented and also much of the calculus notation still in use today.

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In addition to the application of mathematics to the studies of the heavens, applied mathematics began to expand into new areas, as signaled in  the correspondence of Pierre de Fermat and Blaise Pascal.

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Pascal and Fermat set the groundwork for the investigations of probability theory and the corresponding rules of combinatorics in their discussions over a game of gambling.

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Pascal, with his wager, attempted to use the newly developing probability theory to argue for a life devoted to religion, on the grounds that even if the probability of success was small, the rewards were infinite.

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In some sense, this foreshadowed the development of utility theory in the 18th–19th century.

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Leonhard Euler was probably the most influential mathematician of the 18th century.

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His contributions range from founding the study of graph theory with the Seven Bridges of Königsberg problem to standardizing many modern mathematical terms and notations.

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Euler named the square root of minus 1 with the symbol i, and he popularized the use of the Greek letter \pi to stand for the ratio of a circle’s circumference to its diameter.

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He made numerous contributions to the study of topology, graph theory, calculus, combinatorics, and complex analysis, and a multitude of theorems and notations are named for him.

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Joseph Louis Lagrange, who did pioneering work in number theory, algebra, differential calculus, and the calculus of variations, and Laplace who, in the age of Napoléon did important work on the foundations of celestial mechanics and on statistics, were other important eighteenth century mathemaicians.

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In the 19th century mathematics became increasingly abstract.

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Carl Friedrich Gauss (1777–1855), setting aside his many contributions to pure mathematics, did revolutionary work on functions of complex variables, in geometry and on the convergence of series.

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Gauss gave the first satisfactory proofs of the fundamental theorem of algebra and of the quadratic reciprocity law.

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The twentieth century saw the development of the two forms of non Euclidean geometry.

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The Russian mathematician Nikolai Ivanovich Lobachevsky and his rival, the Hungarian mathematician János Bolyai, independently defined and studied hyperbolic geometry where uniqueness of parallels no longer holds.

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In this geometry the sum of angles in a triangle add up to less than 180°.

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Elliptic geometry was developed later in the 19th century by the German mathematician Bernhard Riemann.

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In elliptic geometry, there is no parallel and the angles in a triangle add up to more than 180°.

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Riemann also developed Riemannian geometry which unifies and vastly generalizes the three types of geometry, and he defined the concept of a manifold, which generalizes the ideas of curves and surfaces.

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Hermann Grassmann in Germany gave a first version of vector spaces, and William Rowan Hamilton  in Ireland developed noncommutative algebra.

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The British mathematician George Boole devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were 0 and 1.

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Boolean algebra is the starting point of mathematical logic and has important applications in computer science.

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Agustin-Louis Cauchy, Bernhard Riemann and Karl Weierstrass reformulated the calculus in a more rigorous fashion.

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Niels Henrik Abel, a Norwegian, and Évariste Galois, from France, proved that there is no general algebraic method for solving polynomial equations of degree greater than four (the Abel-Ruffini theorem).

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Other 19th-century mathematicians utilized this in their proofs that straightedge and compass alone are not sufficient to trisect an arbitrary angle.

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Mathematicians had vainly attempted to solve all of these problems since the time of the ancient Greeks.

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The limitation of three dimensions in geometry, however, was surpassed in the 19th century through considerations of parameter space and hypercomplex numbers.

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The Abel and Galois investigations into the solutions of various polynomial equations laid the groundwork for further developments of group theory and the associated fields of abstract algebra.

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Twentieth century physicists and other scientists have seen group theory as the ideal way to study symmetry.

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In the later 19th century, Georg Cantor established the first foundations of set theory, which enabled the rigorous treatment of the notion of infinity and has become the common language of nearly all mathematics.

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Cantor’s set theory, and the rise of mathematical logic in the hands of Peano, L.E.J. Brouwer, David Hilbert, Bertrand Russell and Alfred North Whitehead  initiated a long running debate on the foundations of mathematics.

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A number of national mathematical societies were founded in the nineteenth century: the London Mathematical Society in 1865; the Société Mathématique de France in 1872; the Circolo Matematico di Palermo in 1884; the Edinburgh Mathematical Society in 1883; and the American Mathematical Society in 1888.

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The first international, special-interest society, the Quaternion Society was formed in 1899, in the context of a vector controversy.

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Quaternions are a non-commutative number system that extends the complex numbers.

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Quaternions and their applications to rotations were first described in print by Olinde Rodrigues in all but name in 1840, but independently discovered by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space.

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Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations.

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The 20th century saw mathematics become a major profession.

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Every year, thousands of new Ph.D.s in mathematics were awarded, and jobs were available in both teaching and industry.

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An effort to catalogue the areas and applications of mathematics was undertaken in Klein’s encyclopedia.

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In a 1900 speech to the International Congress of Mathematicians, David Hilbert set out a list of 23 unsolved problems in mathematics.

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These problems, spanning many areas of mathematics, formed a central focus for much of 20th-century mathematics.

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Today, 10 of the 23 problems have been solved, 7 are partially solved, and 2 are still open. The remaining 4 are too loosely formulated to be stated as solved or not.

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In 1976, Wolfgang Haken and Kenneth Appel used a computer to prove the four color theorem.

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Andrew Wiles, building on the work of others, proved Fermat’s Last Theorem in 1995.

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“Paul Cohen was one of the most brilliant mathematicians of the 20th century,” said Princeton Math Professor Peter Sarnak, who received his doctorate from Stanford in 1980 under Cohen’s direction.

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Paul Cohen and Kurt Gödel proved that the continuum hypothesis is independent of (could neither be proved nor disproved from) the standard axioms of set theory.

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In 1998 Thomas Callister Hales proved the Kepler conjecture.

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Mathematical collaborations of unprecedented size and scope were happening.

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The classification of finite simple groups (also called the “enormous theorem”), whose proof between 1955 and 1983 required 500-odd journal articles by about 100 authors, fills tens of thousands of pages.

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A group of French mathematicians, including Jean Dieudonné and André Weil, publishing under the pseudonym “Nicolas Bourbaki,”   attempted to exposit all of known mathematics as a coherent rigorous whole.

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The resulting several dozen volumes has had a controversial influence on mathematical education.

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Differential geometry came into its own when Einstein used it in general relativity.

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Entire new areas of mathematics such as mathematical logic, topology and John von Neumann’s game theory changed the kinds of questions that could be answered by mathematical methods.

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In 2000, the Clay Mathematics Institute announced the seven Millenium Prize Problems.

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And in 2003 the Poincaré conjecture was solved by Grigori Perelman (who declined to accept an award on this point).

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Most mathematical journals now have online versions as well as print versions, and many online-only journals are launched.

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There is an increasing drive towards open access publishing first popularized by the arXiv.

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Sam Andrew

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The Mismeasure of Almost Everything: an homage to the transience of human knowledge

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36, rue de Vaugirard        Paris

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Metre Standard:  The national Convention, in order to spread the use of the metric system, put sixteen marble metre standards in the most frequented places in Paris.  These metres were installed between February 1796 and December 1797. Here is one of the last two that exist in Paris and it is the only one still in its original place.

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The late eighteenth century was a time of revolution.

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The preceding century was an age of science. The leisure classes had laboratories in their homes and did all manner of experiments and tests. The result was an air of skepticism and inquiry into all things.

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After all of this examination of received notions, the nations of Europe and the Americas were ready for radical changes in their lives. People wanted to put their laws, traditions, religions, customs on a more rational, humane and logical basis.

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On the back of the dollar bill and on the Great Seal of the United States is written Novus ordo seclorum, a line from the fourth Eclogue of Virgil, which means “a new order of the ages,” and so it was. Things were changing in radical ways, particularly in France, Great Britain and America.

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So, in this “new order of the ages,” the first thing to be put on a rational basis was time.  The Revolution was a new beginning in human history. The Gregorian Calendar was concerned chiefly with the holy days of saints long dead, and perhaps even non existent.  I had this holy card when I was a child. It depicts St. Christopher (which, after all, means no more than “Christ bearer”) carrying a  German child across a river, the Rhine? The Danube? Both of these rivers arise near Lake Constance in the Alps and are easily fordable there, even carrying a small, holy looking boy.

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One of our recent Popes declared Saint Christopher to be nonexistent, which was very hard on the dashboard/icon sales people.  Anyway, the point is that the Gregorian calendar was identified with the nobility and the clergy of the Ancien Régime, and it was time to put the calendar on a real and rational basis, because this is a Revolution and we have to redo everything, including a lot of things that were working just fine.

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So, now the savants and philosophes are going to make a calendar that is rational and which will accurately describe what the different parts of the year actually feel like.  The new calendar would have twelve months of thirty days each which would be called

vendémiaire               month of the wine harvest              September/October

brumaire                      month of fog                                        October/November

frimaire                        month of frost                                      November/December

nivôse                           month of snow                                    December/January

pluviôse                        month of rain                                      January/February

ventôse                         month of wind                                     February/March

germinal                      month of germination                       March/April

floréal                           month of flowering                            April/May

prairal                           month of meadows                            May/June

messidor                       month of the harvest                         June/July

thermidor                      month of heat                                     July/August

fructidor                        month of fruits                                    August/September

Each month was divided into three ten-day weeks (décades) with a holiday in the middle of each week called quintidi. There would be a festival (sans-culottide) of five days, six in leap years, to ensure that each year begin anew on the autumnal equinox.

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The Revolutionary calendar was born in October 1793 and began with the year II.

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This calendar was abolished early in the year XIV in time to start 1806 on January I.

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The initial big idea in the French Revolution was that the age of reason had arrived. It was time to look at all the old ideas, the nobility, the church, clergy, the status of women, slavery, the calendar, language, weights, measures, everything, and to make sense of these things, to make them reasonable, simpler, more scientific.

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People took the idea of liberty, equality and fraternity seriously. Marie-Olympe de Gouges wrote: ”Why are Black people enslaved? The color of people’s skin only suggests a slight difference. There is no discord between day and night, the sun and the moon and between the stars and dark sky. All is varied; it is the beauty of nature. Why destroy nature’s work?

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There were those in the Assemblée Nationale who believed in rights for blacks and who worked for the abolition of slavery.

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The savants (scientists) in the eighteenth century were also apalled by the lack of uniformity in the weights and measures of their societies. Everything was local and peculiar because it was under the local aristocrat’s control. Measures differed from nation to nation, yes, but also within nations and sometimes even from town to town there were different ideas about what a pint, an ell, a cubit, an inch, a yard was. This diversity made scientific communication very difficult but it was even more disastrous for commerce.

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The savants noted that in the Ancien Régime there were eight hundred terms for measurement that covered an amazing 250,000 different units of weights and measures.

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Thomas Jefferson urged Americans to adopt the decimal metric system in weights and measures and in money. We adopted the metric system for money (10 dimes = a dollar, and so on), but we kept the medieval inch, foot, yard, mile, bushel, peck, and all the rest. The result has been havoc ever since.

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In 1999 a NASA investigation into the failure of the Mars Climate Orbiter showed that one team used “American” units (e.g., inches, feet and pounds) while the other used metric units for a key spacecraft operation. This information was critical to the maneuvers required to place the spacecraft in the proper Mars orbit. The result was a trajectory error of sixty miles. The savants during the French Revolution had created the metric system to avoid just this kind of scientific miscommunication.

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Here are some French measure names from the Ancien Régime:  arpent (acre), aune (ell), lieue ancienne (this is an old French league defined as 10,000, a myriad, feet and it was the official French league until 1674.), lieue de Paris (defined in 1674 as exactly 2000 toises. After 1737, it was also called the “league of bridges and roads” (des Ponts et des Chaussées), Lieue de postes (This league is 2200 toises. It was created in 1737.), ligne (line), perche d’arpent (a “rod,” roughly seven metres),  pied du roi (foot), point (point), pouce (inch, “thumb”), toise (fathom, used in France, but not in England, as a measure on land as well as at sea, six feet).

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The pas (step) had the same value that it had for Julius Caesar who reckoned miles as mille passus, a thousand steps. “Mile” comes from “mille.”

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Lieue de 25 au degré (linked to the circumference of the Earth, with 25 lieues (leagues) making up one degree of a great circle. It was measured by Picard in 1669 to be 2282 toises).

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Lieue tarifaire. This league is 2400 toises. It was created in 1737.

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The perche du roi was the rod used in Québec and Louisiana.

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The vergée was an area measurement of five perches on each side.  This word “vergée” is not only the origin for “verge,” yard, but also for the origin of, “I am on the verge of loving you insanely.”

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Before the Revolution French units of measurement were based on the Carolingian system, introduced by Charlemagne (800 – 814 CE) which in turn were based on ancient Roman measures.

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Charlemagne brought a consistent system to measures across the entire empire. However, after his death the empire fragmented and many rulers introduced their own variants of the units of measure.

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Some of Charlemagne’s units of measure, such as the pied du roi (the king’s foot) remained virtually unchanged for about a thousand years, while others, such as the aune (the ell, used to measure cloth) and the livre (pound) varied dramatically from locality to locality. By the time of the revolution, the number of units of measure had grown to the extent that it was almost impossible to keep track of them.

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The aune (ell), mainly but not always, a cloth measure, varied often within the same town, and often depended on whether the item measured were wool or silk. Insane, but lucrative for wily merchants.

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Flood levels at the pont Wilson at Tours in both metre and pied royal.

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In England the Magna Carta decreed that “there shall be one unit of measure throughout the realm.”   Charlemagne and successive kings had tried but failed to impose such a unified system of measurement in France.

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Now came the juridical revolution of August 1789, when the French nobility were obliged to renounce all privileges, including the authority over weights and measures. This was the time of la Grande Peur, the great fear, and on the morning of the fifth of August, the Assembly abolished the feudal system eliminating many clerical and noble rights and privileges. The August decrees were finally completed a week later.

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The first stipulation put forth by savants, legislators and pamphleteers was the expectation that the new weights and measures would apply equally  throughout France.

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In March 1790, Charles-Maurice de Talleyrand, perhaps with more than a little help from his friend, Condorcet, put forth the most thoughtful and cogent proposals for the new standards of measurement.

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The legislature should derive its fundamental measure from nature, the common heritage of all humanity, which would transcend  the interests of any single nation. The various units of the new measurement (length, area, capacity, weight, volume) should be derived from one source and have one system. A grave, as the gram was then called, would be one cubic centimeter of rainwater weighed in a vacuum at the melting point of ice. Everything, then, was to depend on the final answer:  how long is the metre on which every other measure was to be based?

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All the savants wanted the new measure to be decimal. Simon Stevin, the Flemish engineer, had “invented” the decimal point in the Renaissance.  (The Chinese, Arabs and Indians might have a lot to say about this.)  John Locke and Sébastien Le Prestre de Vauban argued for the virtues of a decimal system.

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Antoine-Laurent de Lavoisier,  who was soon to lose his head in the outrageous excesses of the Revolution, strongly advocated that decimal measurement be adopted.  At the height of the French Revolution, he was accused by Jean-Paul Marat of selling adulterated tobacco and of other crimes, and was eventually guillotined a year after Marat’s death.

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Sketch by Jacques-Louis David of Marie-Antoinette on her way to the guillotine. Stupid, crazy, ridiculous, out of control years. So, right in the middle of all this reason and logic comes one of the most irrational, illogical episodes.  One is reminded of the Chinese curse:  May you live in interesting times.

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The decimal system is natural, because, of course, we have ten digits on our hands, and ten more on our toes.

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The only other numbering system which could rival decimal for naturalness would be the Celtic (and Mayan) vigesimal counting system based on 20. The French don’t say eighty, although they have a word for eighty from Lain (octante). They say quatre vingts (four twentys) because they still remember their Celtic ancestors who counted in twentys. To say 75 in French, you don’t say “septante-cinq” which would seem to be logical, you say soixante-quinze, which is sixty ( 3 twentys) fifteen, again because of the Celts.

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When Abraham Lincoln said “four score and seven years ago,” which was archaic even when he spoke it, he was speaking vigesimally. Not long ago many of us counted in twenties.

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The Mayans also had the vigesimal system for counting.

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Many other systems were proposed… 12 for divisiblity, 11 because eleven is a prime number and can’t be divided  Every number was considered, but the decimal system seemed the most logical because, well, every morning when you look down at your feet, there are ten toes.

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The last big debate among the savants was the nomenclature of prefixes, what were these new measures to be called? In May 1790, citoyen Auguste-Savinien Leblond proposed the name “mètre,” “a name so expressive that I would almost say it was French.” One reason for the expressiveness might be that “mètre” sounds a lot like “maître” (master, expert, capable, basic).

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The proposal for Greek and Latin prefixes (giga-, mega-, kilo-, hecto-, deca-, milli-, centi-) first appeared in a report by the Commission of Weights and Measures in May 1793.

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Now the thing to do was find out how long the mètre actually was.  What was one ten-millionth of the distance from the North Pole to the equator?

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The savants knew that a measure of length taken from a quarter of a meridian divided by ten million would be close to the length of the aune of Paris, that is, about three feet, comfortably on a human scale and familiar to everyone. Indeed, this is what makes the meter easy for us Americans today. The meter is close to the yard which is close to one half the length of the human body.

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The meter/yard is roughly the distance from your nose to the end of the finger on your outstretched hand.

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It wouldn’t be necessary to measure the entire quarter of a meridian to find the length of a meter, but merely an arc, a part of it.

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1.  The selected arc would have to be as long as at least ten degrees of latitude so that there could be an accurate extrapolation to the whole quarter meridian.

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2.  The selected arc would have to be over the 45th parallel, halfway between the pole and the equator.

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3.  The two end points of the “sample,” the selected arc, would have to be located at sea level, and,

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4.  the meridian sample would have to cross a region already fairly well surveyed so that the measurement could proceed rapidly.

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One meridian arc in the entire world met these requirements, the one that ran from Dunkerque (Dunkirk) to Barcelona through Paris.

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In July of 1792 two astronomers left Paris to find the answer to how long the mètre was. Jean-Baptiste-Joseph Delambre headed north from the capital to Dunkerque.

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The cautious, scrupulous Pierre-François-André Méchain traveled to the south, destination Barcelona. The idea was nothing less than the making of a new measure, the meter, which would be one ten-millionth of the distance from the North Pole to the equator. This meter was to be the “one unit of measure throughout the realm,” as the Magna Carta had put it.  All other measurements would flow from the meter, centimeter, millimeter, kilometer, gram, kilogram, hectare and so on.

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The two men, Delambre and Méchain, wanted to measure that part of the meridian arc which ran from Dunkerque through Paris to Barcelona.

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The unit of measure that they thus obtained would be naural, from the earth itself, and would belong to the whole world, since it came from the world.

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For seven years Delambre and Méchain measured along the meridian, trying to find out exactly what one ten-millionth of the distance from the North Pole to the equator would look like.  In the meantime a “provisional metre” was used so that the metric system could be introduced in France and elsewhere. There was a vague idea that the eventual metre would be something like three feet (three pieds du roi).

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This is geodesy or geodetic surveying, the  theory and practice of determining the position of points on the earth’s surface and the dimensions of areas so large that the curvature of the earth must be taken into account. Geodetic surveying is distinguished from plane surveying, the operations of which are executed without regard to the earth’s curvature.

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In geodetic surveying, two points, called stations, many miles apart are selected, and the latitude and longitude of each is determined by astronomical means. The line between these two points, the base line, is measured with a high degree of accuracy. The position of a third station is determined by the angle it makes with each end of the base line. This process, called triangulation, is continued until the whole area to be surveyed is mapped.

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Where the curvature of the earth is great or where there are hills or high trees between stations, towers are built, or tall structures such as churches are used, so that one station may be seen from another. This geodetic station is on Mallorca.

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Ken Alder, an associate professor of history at Northwestern University, has written a book The Measure of All Things about Delambre and Méchain and their trials and tribulations with measuring one ten-millionth of the distance from the north pole to the equator through Paris, and this “through Paris” is an important qualification because, as it turns out, not all meridians are created equal which is the crux of a very big problem.

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In his research for this excellent book, Dr. Alder discovered, apparently for the first time, an error that Pierre-François-André Méchain made while doing his survey near Barcelona.

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Méchain, despite his cautious, precise and almost overly exact approach to his work, made the error in the early years of the expedition and then covered it up, which was not like him at all. (There were extenuating circumstances. Spain was at war with revolutionary, godless France and Méchain was not allowed to reclimb Mont-Jouy near Barcelona harbor and recheck his work.)

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From the Spanish wikipedia:   En 1787 Méchain colaboró con J.D. Cassini y Legendre en la medida precisa de la longitud entre Paris y Greenwich Estos tres científicos visitaron en numerosas ocasiones a William Herschel en su observatório astrónico, Slough (Inglaterra) en el mismo año. Fue destinado a España, para precisar las medidas de este meridiano. Durante una breve estancia en Barcelona, notó un pequeño desvío de tres segundos en un arco del meridiano de Dunkerque-Barcelona. A su llegada a Castellón, se incorporó a un gabinete local liderado por Fausto Vallés encargado de fijar el meridiano 0 de la tierra, a partir del cual nacería al metro.

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(In 1787 Méchain collaborated with J.D. Cassini and Adrien-Marie Legendre on the precise measurement of the longitude between Paris and Greenwich. These three savants (scientists) visited William Herschel, above, on numerous occasions at his astronomical observatory at Slough (England) in the same year. Méchain was headed for Spain to determine with precision the measurements of this meridian. During a brief stay at Barcelona, he noted a small deviation of three seconds in the arc of the meridian from Dunkerque to Barcelona. Upon his arrival in Castellón, he joined a local cabinet led by Fausto Vallés charged with fixing meridian 0 of the earth, from which was born the meter.)

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When my brother Bill and I lived in Paris (1962-1964), one of the places we lived was on rue Legendre, named for Adrien-Marie Legendre, one of these scientists assigned to find the measurement of the longitude between London and Paris.

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A year or two ago in a sentimental moment, I visited this street and took a photo of the nameplate which reads merely Adrien-Marie Legendre, mathématicien.  This is how rue Legendre looked in great grandmother’s day.

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And how it looks now.  Bill and I lived there somewhere in between these two images. We lived there with some “putains allemandes” (German whores) as our landlady (évidemment une commère) so kindly called them. (They were simply two young women who visited us and we spoke about German etymology and dialects across France and the motherland.) I really loved Kristin, as one of them was called and I am sorry I have lost contact with her.  She was very intelligent and good company.

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We never spoke Kristin’s language or ours. All of our conversation was French. Later I visited Germany, and worked there for a while, and upon my return to Paris spoke to Kristin’s parents in German (“Ich bin in der Nähe von Kassel gewesen.” I was near Kassel.), and she said, “Unglaublich! Er hat vorher kein Wort gesprochen.”  (Unbelievable, he didn’t know a single word before.) It was the first time either of us had heard the other speak our native language.

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Our mutual friend Ulrich Roski, with whom I attended the Sorbonne, and who later became a television and music celebrity in Germany, talked about our relationship in a book he wrote published only in Germany.

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Anyway, when I hear the name Legendre, this is what comes to mind. My brother Bill, Ulrich, Kristin and many other close friends.  For years after I returned to the United States, Ulrich and I wrote to each other in Latin.

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Ulrich was a better scholar than I, by far, and  I wish I would have reconnected with him before he died in 2003.

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Ulrich Roski with his daughter Sandra.

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Pierre-François-André Méchain was of course obsessed with his geodetic surveying error and nearly driven mad by his knowledge that he had betrayed the noble cause of Science by a mistake the thickness of two pieces of paper. He died in an attempt to correct himself.  If only he had known that there was no correction possible.

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So, the meter, which was thought to be from and of the earth, is an error, an error that has been repeated with its every new redefinition,

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including our modern view of the meter in terms of distance traveled by light in a fraction of a second.

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But, so what? For one thing, the error is small, very small. For another, how can you really measure a quarter of a meridian anyway? And then derive one ten-millionth of it?  And then who cares? Isn’t it enough that we have a convenient, user friendly measure that everyone agrees on? Isn’t that the main thing? So what if the meter is the mismeasure of almost everything.

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I suspect that none of these considerations would matter at all to Pierre-François-André Méchain. He was a very emotional man, inclined to self doubt and agonies of indecision, and completely devoted to being precise.

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How small is the error? Today’s satellite surveys show that the length of the meridian from the North Pole to the equator is 10,002,290 meters. This means that the meter calculated by Delambre and Méchain is about 0.2 millimeters short, roughly the thickness of two sheets of paper. These are two drill bits, each 0.2 millimeters thick.

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And who says the satellite surveys are correct, for that matter? These are today’s measurements? What will tomorrow’s say? Precision is a non ending quest. Perfect for people with obsessive compulsive disorders.

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By the way, in writing this I kept spelling Méchain “méchant,” which is French for “malicious, wicked, naughty.”

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Do you suppose that this qualifies as a Freudian slip?

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It’s not as if Méchain were the big, bad wolf

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or anything like that.

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To be a little more, pardon the expression, precise, Pierre-François-André Méchain maybe should have been a little more like a wolf. Instead he was so lamblike, real, exposed, passionate, giving that he could not forgive himself for an error that would not have bothered a man like, just to take one example, Jean-Baptiste-Joseph Delambre, who was much more, to use our idiom, “well adjusted,” and who was conducting his triangulations one after the other in the north, peacefully and productively, nearing his goal and waiting for Méchain to finish his work so that they could take their joint calculations to the Académie.

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It seemed for a while as if Méchain had given up on his southern measurements entirely. He sailed to Livorno, which for some inexplicable reason, is known as “Leghorn” in English, and there in Genova (Genoa) made friends with Giuseppe Slop de Cadenburg, the director of the astronomical observatory in the nearby university town of Pisa, ten miles north in Toscano (Tuscany), who proved a sympathetic listener to Méchain’s tale of woe.

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Perhaps a quote from Méchain will make clear his state of mind:  ”Even I, who can claim some experience and competence in geodesy, who know a bit about what methods to use and when to take precautions, even I work in constant fear:  I mistrust myself. I continually solicit the views and intelligence of my colleagues at the Academy and the Bureau of Longitudes, and nothing pains me more than when they respond that they rely entirely on me, and that no one is better placed than I to judge what must be done, to choose the right methods, and to carry them through. At such times I feel as if they are spitting in my face. Nothing comes easily, nothing is simple, when one seeks precision. All it takes to be convinced of this is to do a little observing of one’s own.”

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On 20 September 1804, Pierre-François-André Méchain died of malaria, probably contracted while he was triangulating in the Albufera marshes near Valencia.

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This man was his own worst enemy, tortured, honest, intellectual, precise to a fault, and that cliché never fit anyone more aptly.

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Not all meridians are equal. The earth, as you may have suspected, is lumpy, not perfectly spherical at all, misshapen, a work in progress. Far from being a perfect sphere, the earth is not even an oblate spheroid. It is a piece of mud and rock, different in all places, an organic being, unfinished, very difficult to measure, and not at all the same in different places.

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The meridian at Rome is not the same length as the meridian that runs through Paris. We know that now. They didn’t know that then and they assumed that all meridians were equal since the earth was a perfect sphere.  They searched for perfect uniformity then, but now we know that perfect uniformity is an expensive illusion, as are so many other illusions.

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Méchain did not know that the earth was not a perfect sphere. Neither did Delambre nor anyone else in the world at that time.

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The very planet we live on is pimply and imperfect. Pierre-François-André Méchain did not know that. He was an atheist, a scientist, but he still had the faith that we live on a perfect planet with a uniformly perfect shape and that faith was his undoing.  He never could understand why his measurements went wrong.  They were wrong because the earth is “wrong.”

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It wasn’t Méchain’s fault that his measurements were off. What was his fault was that he tried to cover up his “error.” He wasn’t honest about his findings.

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Honesty in science is a sine qua non. Sine qua non = ”without which nothing.” Science, knowledge, cannot exist without honesty.

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Méchain came from a humble family, but by dint of hard work and study, patient observation and fastidious calculation he had risen to the utmost pinnacle of astronomy in France. Méchain had discovered  eleven comets mainly through a kind of obsinacy about being accurate.

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Méchain was something of a martyr to the endless and fruitless quest for perfection, not out of a search for personal glory, but for the real aim of devotion to science, to the pure pursuit of knowledge.  He was the real thing, the real scientist. It’s just that he was so emotional and tormented by self doubt that he carried his own self destruction around with him.  It’s not an unfamiliar pattern, is it?

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Méchain’s partner, Jean-Baptiste-Joseph Delambre, noted that Méchain sometimes seemed to be late on his mission, melancholy and a martyr to the endless quest for precision.

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Delambre also said, “From this day forth, my most cherished occupation will be to extract from this archive everything that may contribute to the glory of a colleague with whom I was honorably bound in a long common labor. And if I have not succeeded today in painting a picture of the departed astronomer worthy of his merits and the feelings I have for him, I am at least certain that whatever I publish of his work will do far more for his memory than even the most eloquent oration.”

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Thank you for reading.

Sam Time

See you next week.

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