# 2: Calculus in the 17th and 18th Centuries

• 2.1: Newton and Leibniz Get Started
The rules for calculus were ﬁrst laid out in Gottfried Wilhelm Leibniz’s 1684 paper Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales, quantitates moratur, et singulare pro illi calculi genus (A New Method for Maxima and Minima as Well as Tangents, Which is Impeded Neither by Fractional Nor by Irrational Quantities, and a Remarkable Type of Calculus for This).
• 2.2: Power Series as Infinite Polynomials
Applied to polynomials, the rules of diﬀerential and integral calculus are straightforward. Indeed, diﬀerentiating and integrating polynomials represent some of the easiest tasks in a calculus course. Unfortunately, not all functions can be expressed as a polynomial. A standard technique is to write such functions as an “inﬁnite polynomial,” what we typically refer to as a power series. Such “inﬁnite polynomials” are much more subtle object than mere polynomials, which by deﬁnition are ﬁnite.
• 2.E: Calculus in the 17th and 18th Centuries (Exercises)

Thumbnail: Engraving of Gottfried Wilhelm Leibniz. (Public Domain; Pierre Savart)

## Constructed language

A constructed language (sometimes called a conlang) [2] is a language whose phonology, grammar, and vocabulary, instead of having developed naturally, are consciously devised or invented as a work of fiction. Constructed languages may also be referred to as artificial languages, planned languages or invented languages [3] and in some cases, fictional languages. Planned languages are languages that have been purposefully designed. They are the result of deliberate controlling intervention, thus of a form of language planning. [4]

There are many possible reasons to create a constructed language, such as to ease human communication (see international auxiliary language and code) to give fiction or an associated constructed setting an added layer of realism for experimentation in the fields of linguistics, cognitive science, and machine learning for artistic creation and for language games. Some people make constructed languages simply because they like doing it.

The expression planned language is sometimes used to indicate international auxiliary languages and other languages designed for actual use in human communication. Some prefer it to the adjective artificial, as this term may be perceived as pejorative. Outside Esperanto culture, the term language planning means the prescriptions given to a natural language to standardize it in this regard, even a "natural language" may be artificial in some respects, meaning some of its words have been crafted by conscious decision. Prescriptive grammars, which date to ancient times for classical languages such as Latin and Sanskrit, are rule-based codifications of natural languages, such codifications being a middle ground between naïve natural selection and development of language and its explicit construction. The term glossopoeia is also used to mean language construction, particularly construction of artistic languages. [5]

Conlang speakers are rare. For example, the Hungarian census of 2011 found 8,397 speakers of Esperanto, [6] and the census of 2001 found 10 of Romanid, two each of Interlingua and Ido and one each of Idiom Neutral and Mundolinco. [7] The Russian census of 2010 found that there were in Russia about 992 speakers of Esperanto (on place 120), nine of Ido and one of Edo. [8]

## 2: Calculus in the 17th and 18th Centuries

At first glance, there may not seem to be much of a connection between the "Scientific Revolution" that took place in Western Europe starting in the 17th century CE, and the political revolutions that took place in Western Europe and its colonies beginning in the late 18th century. What could the development of calculus and the discovery of laws of physics (such as gravitation) possibly have to do with the overthrow of monarchical and colonial governments and the establishment of new democracies?

In fact, they have a lot to do with one another. In order to understand the connection, and also to understand both the scientific and the political developments better, we must look to the philosophical ideas they share.

There are 2 ideas that are fundamental to both the "Scientific Revolution" and the political revolutions. These 2 ideas appear in one form or another in the basic documents of both. They are:

the idea that the universe and everything in it work according to "laws of nature." These laws are established by the Divine Being (generally the God of Judaism, Christianity, and Islam). (1) Thus the universe is ultimately run by a divine being, but this divine being does not do things at random or capriciously rather, the divine being makes things work in an orderly and regular fashion. This idea is accompanied by

Now, the idea that we can learn true things about the universe by means of observation and reasoning has important implications for politics, thought, and life in general. First, everyone is capable of observing things, and everyone is capable of reasoning. If we were not able to observe and reason, we could not be expected to make choices, obey laws and religious rules and moral standards, etc. Of course, some people lack the ability to observe certain things (blind people cannot observe colors, for example), but everyone can observe something.

If we all have the ability to observe and reason, then in principle we all have the ability to learn true things about the universe, according to the writers of the Scientific Revolution and the European "Enlightenment." In other words, if we want to learn about how the universe works - from how volcanoes form to how diseases occur to how stars develop to what kinds of laws are fair to humans - we can do it by training our powers of observation and reasoning. We can train our powers of observation and reasoning by learning mathematics (arithmetic, algebra, geometry) and logic, by carefully recording and checking our observations, and by doing experiments. All humans are capable of doing these things. And, if we write down our findings and show our reasoning carefully, others can check our results.

Galileo (1564-1642 Italian) is an example of a writer who put forth these ideas.

In his book The Assayer, written in 1623, Galileo said, "Philosophy is written in this grand book of the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and to read the alphabet in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures, without which it is humanly impossible to understand a single word of it without these, one wanders in a dark labyrinth."

(By 'philosophy' Galileo means both what we would call philosophy and also natural sciences, which were in his time studied as part of philosophy. For more on the great astronomer, physicist, and mathematician Galileo, see the excellent web site of Prof. Fowler at the University of Virginia.)

What Galileo is saying is that the workings of the universe are understandable, and that we need mathematics in order to understand them. This may seem to many people today to be a very obvious point: of course we need to learn mathematics in order to understand things so many fields rely on measurements, statistics, "facts and figures." But it was not so obvious in Galileo's time, and he was tried and imprisoned for his theories that were based on this idea.

Why would anyone want to punish Galileo for this?

Galileo was punished by certain important members of the Catholic Church. Remember that in Europe in Galileo's time, there was no separation of church and state the religious authorities ran the universities and could censor publications, and worked hand-in-hand with the governments of the various countries. Galileo lived in Italy, which was Catholic, and got into trouble with some people close to the Pope.

The basic problem that these religious authorities found was that some of Galileo's scientific discoveries appeared to contradict the official Catholic interpretation of Christian scripture, or to contradict the official Catholic interpretation of Aristotle. (Why the Catholic Church accepted the works of Aristotle is a long story here I will say only that the 17th-century Church interpretation of Aristotle's scientific work is not necessarily what Aristotle intended.) For example, Galileo discovered more stars in the sky than are mentioned in the Bible or Aristotle, because he had a telescope and Aristotle and the ancient Hebrews did not. Galileo discovered that a heavier object falls no faster than a lighter one (the Church interpreted Aristotle as saying that heavy objects fall faster than light ones a close examination of Aristotle's texts suggests that this is a misunderstanding or a mistranslation of Aristotle's words). Therefore the Church authorities claimed that Galileo had contradicted sacred truths. They believed that if human observation and reasoning seemed to say something different from holy scripture (or from their interpretation of holy scripture), then the human observation and reasoning must be wrong. (2)

Galileo pointed out that he was not denying God's perfection or role as a creator that the Bible did not specify exactly how many stars there were that some statements in the Bible are not understood literally (for example, even the Church agreed that the sun does not literally "rise").

But Galileo was unable to convince the Church authorities of this, even though Aristotle himself would have agreed with Galileo about the need for independent investigation, reasoning, and proof. What was really at stake here was what counts as knowledge, and why who can get new knowledge, and how. The Church held that knowledge was revealed in Scripture that a person with a religious calling and lots of training in accepted interpretations could learn. Other people should be content to hear these trained religious people explain things. The Church was more interested in the ultimate nature of things (as revealed by God) and in how to achieve salvation than in the everyday workings of things, so a lot of areas were just not covered by Church teachings. Galileo and the Scientific Revolution argued that perhaps religious revelation was needed in order to learn the ultimate meaning of things and the way to salvation, but that observation and reasoning would tell us about how things work on an everyday basis and that any human could learn these things if he or she worked hard enough.

This sets the stage for Rene Descartes (1596-1650 French).

Descartes set himself a dual task: (1) Show that Galileo was right about how to seek knowledge and (2) Avoid getting imprisoned or executed for this.

This meant that Descartes had to show (1') that true things can be discovered by means of observation and reasoning and (2') that this independent inquiry does not violate any religious or moral rules.

Descartes was uniquely equipped for this project in that he was a mathematical genius (he invented analytic geometry, or what became analytic geometry the Cartesian coordinate system is named after him), a scientist (he did work in optics and physics), and a philosopher. He was educated in Catholic schools and knew their teachings well.

Descartes argued that the very essence of being human was the ability to think or reason (see for example Discourse Part Four Meditation Two). The Catholic Church could not deny that this ability had been given to us by God, since only by means of this ability can we have an idea of God, understand scripture, worship, etc. Descartes continued by saying that "we should never allow ourselves to be persuaded except by the evidence of our reason" (3) (22). The senses and imagination, Descartes felt, could be important sources of raw information, but they might give us erroneous information, so we must be careful always to examine our sensory impressions and ideas by using reason. Some of our ideas may turn out not to be true, Descartes says, but "all our ideas or notions ought to have some foundation of truth, for it would not be possible that God, who is all-perfect and all-truthful, would have put them in us without that." (4) Note that Descartes does not claim that all of our ideas are true, but rather that even the false ones have some basis in truth. Our false ideas come from our reactions to real things or to our impressions of real things, and our reactions and impressions may be confused, or we may have insufficient information to make a true judgment, etc. Through reason, he says, we can find out the truth.

How are we to find out the truth? Descartes provides a method of reasoning that is very much like today's mathematical and scientific methods (see Discourse Part Two).

What truths will we find out? Descartes says in Part Five of the Discourse that he has "showed what the laws of nature were": There are, he says, "certain laws that God has so established in nature and of which he has impressed in our souls such notions, that, after having reflected sufficiently on these matters, we cannot deny that they are strictly adhered to in everything that exists or occurs in the world." 5 God has made the universe work according to laws, Descartes holds and God has given us impressions of these laws. By reflection and reasoning, we can gain clear knowledge of these laws. The laws Descartes is talking about are such things as the laws of physics, the principles of respiration and circulation, and so on.

Descartes was very careful in his publishing, and got into only minimal trouble with religious authorities. Times were beginning to change politically. But Descartes had to stay out of certain countries for his own safety. He found safe havens in places with more tolerant regimes, and even served as a sort of professor to the Queen of Sweden, who was a very able philosopher and scientist in her own right. Descartes also sent his work informally to philosophers and scientists who he thought would be sympathetic to his projects, and this got the word out. In addition, he did something new and clever: he put his work out in French as well as in Latin. Latin was the language of the Catholic Church and the universities, so it was important for Descartes to use it. But many people in Europe knew only minimal Latin, and some of these people were able to be very helpful. The people who knew Latin well were Catholic (and some Protestant) clergy, and those who could study at universities. But most of the people at universities were nobility, and all were men. There was a growing number of noblewomen, and members of the merchant and artisan classes of both sexes, who had the resources and the interest to study philosophy and science. They had not had much of a chance so far. French was a language that many people knew it was used often outside of France. So these people read Descartes with great interest, and provided him with scholarly discussion as well as in some cases political and financial support.

But what does that have to do with political revolutions?

One immediate connection can be seen in the fact that Descartes was arguing that reasoning was an ability all people have, and that this ability we all have is exactly what we need in order to learn about the world. We don't need a special upbringing or education or religion (Descartes reached out to people of all religions that he knew). And Descartes made sure that every human who could read French would have a chance to try. In this way, he was very egalitarian. This was very much different from the way most institutions worked in his time, where only a small number of people had any political power or religious authority, and others did not have a chance to try for it.

The idea of natural equality and rule by reason was also getting an explicitly political interpretation at this time. Thomas Hobbes (1588-1679 English) wrote in Leviathan (1651), "Nature hath made men so equal, in the faculties of body and mind as that, though there be found one man sometimes manifestly stronger in body or of quicker mind than another, yet when all is reckoned together, the difference between man and man is not so considerable, as that one man can thereupon claim to himself any benefit, to which another may not pretend as well as he. From this equality of ability, ariseth equality of hope in the attaining of our ends" (6) (Chapter XIII). Given scarcity of resources, people tend to fight for survival, power, and protection and the result, according to Hobbes, is that the "state of nature" is a state of war. But we don't have to remain always at war, because nature itself gives us a way out, and that way out is discoverable by reason: "The passions that incline men to peace are fear of death, desire of such things as are necessary to commodious living, and a hope by their industry to attain them. And reason suggesteth convenient articles of peace. These articles are they wich otherwise are called the Laws of Nature. " (also Chapter XIII).

According to Hobbes (Ch. XIV), a law of nature is "a precept or general rule, found out by reason, by which a man is forbidden to do what is destructive of life, or taketh away the means of preserving the same and to omit that by which he thinketh it may be best preserved."

The first two laws of nature, according to Hobbes, are (1) "that every man ought to endeavor peace, as far as he has hope of attaining it and when he cannot obtain it, that he may see and use all the helps and advantages of war" and (2) "that a man be willing, when others are so too, as far forth as for peace and defense of himself he shall think it necessary, to lay down this right to all things and be contented with so much liberty against other men, as he would allow other men against himself" (Ch. XIV). Hobbes explicitly connects the second law with Chritian scripture.

Now, it is true that Christian writers in Europe had been saying for over a millennium that all people were equal in the sight of God. What was so different here?

-- First, some Christian writers had allowed for the "divine right of kings" and secondarily for the special rights of aristocrats: the kings, assisted by the aristocrats, were supposed to be those who ruled the earth according to God's will. Kings and aristocrats had special responsibilities (which some took seriously and some did not), but also special rights and privileges. Hobbes is saying that no one can rightly claim special status by birth one can only be a leader by the agreement of those who are to be led. No one is to violate certain natural rights no king is to take land from a person just because the king wants to, for example. As Hobbes says in Ch. XV, it is a law of nature that everyone must acknowledge the others as one's equals by nature.

-- Second, Hobbes is claiming that the laws of nature are discoverable by reason. You don't need special instruction in interpreting scripture in order to discover these laws and they apply to everyone no matter what their religion. Hobbes thinks his laws are in keeping with Christian religious law, or with its true spirit. But he thinks that this is because Christian teachings follow the laws of nature, not the other way around.

John Locke (1632-1704 English) took these ideas even further.

John Locke was familiar with the work of Descartes and Hobbes, and was himself a source of many ideas of the French Enlightenment, the American Revolution, and the French Revolution. Here are some passages from his Second Treatise of Government (1690), illustrating once again the idea of laws of nature discoverable by reason.

Like Hobbes, Locke begins from a picture of the "state of nature" or "natural state" of humans but Locke's picture of it is less harsh than Hobbes' picture: The state of nature for all men, he says, "is a state of perfect freedom to order their actions and dispose of their possessions as they think fit, within the bounds of the law of nature, without asking leave, or depending on the will of any other man. A state also of equality, wherein all power and jurisdiction is reciprocal, no one having more than another. "(Chapter II). This is not necessarily a state of war, Locke thinks.

According to Locke, "The state of nature has a law of nature to govern it, which obliges everyone and reason, which is that law, teaches all mankind who will but consult it, that, being all equal and independent, no one ought to harm another in his life, health, liberty, or possessions" (Chapter II). Locke is explicit that slavery is against the law of nature and argues that it should therefore be against civil laws too (Chapter IV).

Compare these passages from Locke and Hobbes with some articles of the Declaration of the Rights of Man and Citizen (French Revolution):

Article 1: Men are born and remain free and equal in rights.

Article 2: The purpose of all political association is the preservation of the natural and imprescriptible rights of man. These rights are liberty, property, security, and resistance to oppression.

Article 4: Liberty consists in the ability to do whatever does not harm another.

Article 12: The safeguard of the rights of man and the citizen requires public powers. These powers are therefore instituted for the advantage of all, not for the private benefit of those to whom they are entrusted.

1. Most of the scientists, philosophers, and political activists in Western Europe and its colonies at this time were Christians of some sort (various kinds of Protestants, as well as Catholics). Some were Jewish. (Remember that there were very few Muslims left in Western Europe at this time.) However, the descriptions of the divine being that these scientists, philosophers, and political activists used would fit the beliefs of Judaism, Christianity, AND Islam. That is, the revolutionary writings describe a divine being who is all-powerful, all-knowing, all-good, and the creator of the universe. Most do not say anything that is specific to any one monotheistic religion. An excellent example of this is found in Descartes' Discourse on the Method for Rightly Conducting One's Reason and Seeking Truth in the Sciences, Part Four.

2. It is important to note that some Catholic theologians saw nothing wrong with what Galileo was doing, and even supported it. However, the ones who supported Galileo were not the most powerful politically.

3. All quotations from Descartes are from Discourse on the Method for Rightly Conducting One's Reason and Seeking Truth in the Sciences, translated by Donald Cress. The edition used here is Discourse on Method and Meditations on First Philosophy, fourth edition (Hackett Publishing Co., 1998). The quotation is from Part Four of the Discourse. The page in that edition is 22 if you are using another edition of the same translation your page numbers may be different.

4. Also from Part Four page 22 in the edition noted above.

5. Quotations are from pages 24 and 23, respectively, in the edition noted above.

6. Hobbes generally uses the word 'man' in a way that suggests that he refers to all humans. Great debate ensued as to whether the notion that all "men" were equal should entail that women should have the same political, social, and economic rights as men. Similarly, over the next couple of centuries, debates arose as to whether all peoples of the world should have the same rights.
Quotations from Hobbes come from the version of the text used in this class: http://ebooks.adelaide.edu.au/h/hobbes/thomas/h68l/

7. All quotations from Locke on this page come from the version of the text used in this class: http://ebooks.adelaide.edu.au/l/locke/john/l81s/

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## Contents

(c. 310 – c. 230 BCE) was the first known originator of a heliocentric (solar) system. Such a system was formulated again some 18 centuries later by Nicolaus Copernicus (1473–1543). [7][8]
• 1242 – first description of the function of pulmonary circulation, in Egypt, by Ibn al-Nafis. Later independently rediscovered by the Europeans Michael Servetus (1553) and William Harvey (1616).
: Nicole Oresme (c. 1370) Nicolaus Copernicus (1519) [9]Thomas Gresham (16th century) Henry Dunning Macleod (1857). Ancient references to the same concept include one in Aristophanes' comedy The Frogs (405 BCE), which compares bad politicians to bad coin (bad politicians and bad coin, respectively, drive good politicians and good coin out of circulation). [10]
and Simon Stevin: heavy and light balls fall together (contra Aristotle).
• Galileo Galilei and Simon Stevin: Hydrostatic paradox (Stevin c. 1585, Galileo c. 1610). (1520) and Niccolò Tartaglia (1535) independently developed a method for solving cubic equations. (the "dark-night-sky paradox") was described by Thomas Digges in the 16th century, by Johannes Kepler in the 17th century (1610), by Edmond Halley and by Jean-Philippe de Chéseaux in the 18th century, by Heinrich Wilhelm Matthias Olbers in the 19th century (1823), and definitively by Lord Kelvin in the 20th century (1901) some aspects of Kelvin's argument had been anticipated in the poet and short-story writer Edgar Allan Poe's essay, Eureka: A Prose Poem (1848), which also presaged by three-quarters of a century the Big Bang theory of the universe. [11][12][13] , in varying independent iterations, was proposed by Abraham Ortelius (Ortelius 1596) harv error: no target: CITEREFOrtelius1596 (help) , [14] Theodor Christoph Lilienthal (1756), [15]Alexander von Humboldt (1801 and 1845), [15]Antonio Snider-Pellegrini (Snider-Pellegrini 1858) harv error: no target: CITEREFSnider-Pellegrini1858 (help) , Alfred Russel Wallace, [16]Charles Lyell, [17] Franklin Coxworthy (between 1848 and 1890), [18]Roberto Mantovani (between 1889 and 1909), William Henry Pickering (1907), [19]Frank Bursley Taylor (1908), [20] and Alfred Wegener (1912). [21] In addition, in 1885 Eduard Suess had proposed a supercontinent Gondwana[22] and in 1893 the Tethys Ocean, [23] assuming a land-bridge between the present continents submerged in the form of a geosyncline and in 1895 John Perry had written a paper proposing that the earth's interior was fluid, and disagreeing with Lord Kelvin on the age of the earth. [24]
– Thomas Harriot (England, 1610), Johannes and David Fabricius (Frisia, 1611), Galileo Galilei (Italy, 1612), Christoph Scheiner (Germany, 1612). – John Napier (Scotland, 1614) and Joost Bürgi (Switzerland, 1618). – René Descartes, Pierre de Fermat. solved by both Pierre de Fermat (France, 1654), Blaise Pascal (France, 1654), and Huygens (Holland, 1657). – Gottfried Wilhelm Leibniz and Seki Kōwa. – Isaac Newton, Gottfried Wilhelm Leibniz, Pierre de Fermat and others. [25] (sometimes referred to as the "Boyle-Mariotte law") is one of the gas laws and basis of derivation for the Ideal gas law, which describes the relationship between the product pressure and volume within a closed system as constant when temperature remains at a fixed measure. The law was named for chemist and physicistRobert Boyle who published the original law in 1662. The French physicist Edme Mariotte discovered the same law independently of Boyle in 1676. – Joseph Raphson (1690), Isaac Newton (Newton's work was written in 1671, but not published until 1736). problem solved by Johann Bernoulli, Jakob Bernoulli, Isaac Newton, Gottfried Wilhelm Leibniz, Guillaume de l'Hôpital, and Ehrenfried Walther von Tschirnhaus. The problem was posed in 1696 by Johann Bernoulli, and its solutions were published next year. : Patent granted to Thomas Savery in 1698. The invention has often been credited to Thomas Newcomen (1712). Other early inventors have included Taqī al-Dīn (1551), Jerónimo de Ayanz y Beaumont (1606), Giambattista della Porta, [citation needed] Giovanni Branca (1629), Cosimo de' Medici (1641), [citation needed] Evangelista Torricelli (1643), Otto Von Guericke (1672), Denis Papin (1679), and many others.
– Antonio de Ulloa and Charles Wood (both in the 1740s). – Ewald Georg von Kleist (1745) and Pieter van Musschenbroek (1745–46). [26] – Benjamin Franklin (1749) and Prokop Diviš (1754) (debated: Diviš's apparatus is assumed to have been more effective than Franklin's lightning rods in 1754, but was intended for a different purpose than lightning protection). – discovered by Mikhail Lomonosov, 1756 [27] and independently by Antoine Lavoisier, 1778. [28] – Carl Wilhelm Scheele (Uppsala, 1773), Joseph Priestley (Wiltshire, 1774). The term was coined by Antoine Lavoisier (1777). Michael Sendivogius (Polish: Michał Sędziwój 1566–1636) is claimed as an earlier discoverer of oxygen. [29] theory – John Michell, in a 1783 paper in The Philosophical Transactions of the Royal Society, wrote: "If the semi-diameter of a sphere of the same density as the Sun in the proportion of five hundred to one, and by supposing light to be attracted by the same force in proportion to its [mass] with other bodies, all light emitted from such a body would be made to return towards it, by its own proper gravity." [30] A few years later, a similar idea was suggested independently by Pierre-Simon Laplace. [31] – Thomas Robert Malthus (1798), Hong Liangji (1793). [32]
• A method for measuring the specific heat of a solid – devised independently by Benjamin Thompson, Count Rumford and by Johan Wilcke, who published his discovery first (apparently not later than 1796, when he died).
• In a treatise [33] written in 1805 and published in 1866, Carl Friedrich Gauss describes an efficient algorithm to compute the discrete Fourier transform. James W. Cooley and John W. Tukey reinvented a similar algorithm in 1965. [34] – Geometrical representation of complex numbers was discovered independently by Caspar Wessel (1799), Jean-Robert Argand (1806), John Warren (1828), and Carl Friedrich Gauss (1831). [35] – Friedrich Strohmeyer, K.S.L Hermann (both in 1817). (aka the Principle of Photochemical Activation) – first proposed in 1817 by Theodor Grotthuss, then independently, in 1842, by John William Draper. The law states that only that light which is absorbed by a system can bring about a photochemical change. – Friedrich Wöhler, A.A.B. Bussy (1828). was discovered by Michael Faraday in England in 1831, and independently about the same time by Joseph Henry in the U.S. [36] – Samuel Guthrie in the United States (July 1831), and a few months later Eugène Soubeiran (France) and Justus von Liebig (Germany), all of them using variations of the haloform reaction.
• Non-Euclidean geometry (hyperbolic geometry) – Nikolai Ivanovich Lobachevsky (1830), János Bolyai (1832) preceded by Gauss (unpublished result) c. 1805. , aka Lobachevsky method – an algorithm for finding multiple roots of a polynomial, developed independently by Germinal Pierre Dandelin, Karl Heinrich Gräffe, and Nikolai Ivanovich Lobachevsky. – Charles Wheatstone (England), 1837, Samuel F.B. Morse (United States), 1837. – In the late 19th century, various scientists independently stated that energy and matter are persistent, although this was later to be disregarded under subatomic conditions. Hess's Law (Germain Hess), Julius Robert von Mayer, and James Joule were some of the first.
• 1846: Urbain Le Verrier and John Couch Adams, studying Uranus's orbit, independently proved that another, farther planet must exist. Neptune was found at the predicted moment and position. [37][a] – The process of removing impurities from steel on an industrial level using oxidation, developed in 1851 by American William Kelly and independently developed and patented in 1855 by eponymous Englishman Sir Henry Bessemer.
• The Möbius strip was discovered independently by the German astronomer–mathematician August Ferdinand Möbius and the German mathematician Johann Benedict Listing in 1858. by natural selection – Charles Darwin (discovery about 1840), Alfred Russel Wallace (discovery about 1857–58) – joint publication, 1859.
• 1862: 109P/Swift–Tuttle, the comet generating the Perseid meteor shower, was independently discovered by Lewis Swift on 16 July 1862, and by Horace Parnell Tuttle on 19 July 1862. The comet made a return appearance in 1992, when it was rediscovered by Japanese astronomerTsuruhiko Kiuchi.
• 1868: French astronomer Pierre Janssen and English astronomer Norman Lockyer independently discovered evidence in the solar spectrum for a new element that Lockyer named "helium". [39] (The formal discovery of the element was made in 1895 by two Swedish chemists, Per Teodor Cleve and Nils Abraham Langlet, who found helium emanating from the uraniumorecleveite.)
• 1869: Dmitri Ivanovich Mendeleyev published his periodic table of chemical elements, and the following year (1870) Julius Lothar Meyer published his independently constructed version.
• 1873: Bolesław Prus propounded a "law of combination" describing the making of discoveries and inventions: “Any new discovery or invention is a combination of earlier discoveries and inventions, or rests on them.” [40] In 1978, Christopher Kasparek independently proposed an identical model of discovery and invention which he termed "recombinant conceptualization." [41]
• 1876: Oskar Hertwig and Hermann Fol independently described the entry of sperm into the egg and the subsequent fusion of the egg and sperm nuclei to form a single new nucleus.
• 1876: Elisha Gray and Alexander Graham Bell independently, on the same day, filed patents for invention of the telephone.
• 1877: Charles Cros described the principles of the phonograph that was, independently, constructed the following year (1878) by Thomas Edison.
• British physicist-chemist Joseph Swan independently developed an incandescent light bulb at the same time as American inventor Thomas Edison was independently working on his incandescent light bulb. [42] Swan's first successful electric light bulb and Edison's electric light bulb were both patented in 1879. [43]
• Circa 1880: the integraph was invented independently by the British physicist Sir Charles Vernon Boys and by the Polish mathematician, inventor, and electrical engineer Bruno Abakanowicz. Abakanowicz's design was produced by the Swiss firm Coradi of Zurich.
• 1886: The Hall–Héroult process for inexpensively producing aluminum was independently discovered by the American engineer-inventor Charles Martin Hall and the French scientist Paul Héroult. [44]
• 1895: Adrenaline was discovered by the Polish physiologist Napoleon Cybulski. [45] It was independently discovered in 1900 by the Japanese chemist Jōkichi Takamine and his assistant Keizo Uenaka. [46][47]
• 1896: Two proofs of the prime number theorem (the asymptotic law of the distribution of prime numbers) were obtained independently by Jacques Hadamard and Charles de la Vallée-Poussin and appeared the same year.
• 1896: Discovery of radioactivity independently by Henri Becquerel and Silvanus Thompson. [48]
• 1898: Discovery of thoriumradioactivity by Gerhard Carl Schmidt and Marie Curie. [49]Filip Fyodorovich Fortunatov and Ferdinand de Saussure independently formulated the sound law now known as the Saussure–Fortunatov law. [50][51] was invented independently by the American, Josiah Willard Gibbs (1839–1903), and by the Englishman, Oliver Heaviside (1850–1925).
• 1902: Walter Sutton and Theodor Boveri independently proposed that the hereditary information is carried in the chromosomes.
• 1902: Richard Assmann and Léon Teisserenc de Bort independently discovered the stratosphere. , though only Einstein provided the accepted interpretation – Henri Poincaré, 1900 Olinto De Pretto, 1903 Albert Einstein, 1905 Paul Langevin, 1906. [52] was independently explained by Albert Einstein (in one of his 1905 papers) and by Marian Smoluchowski in 1906. [53]
• The Einstein Relation was revealed independently by William Sutherland in 1905, [54][55] by Albert Einstein in 1905, [56] and by Marian Smoluchowski in 1906. [53]
• 1904: Epinephrine synthesized independently by Friedrich Stolz and by Henry Drysdale Dakin.
• 1905: The chromosomalXY sex-determination system—that males have XY, and females XX, sex chromosomes—was discovered independently by Nettie Stevens, at Bryn Mawr College, and by Edmund Beecher Wilson at Columbia University. [57]
• 1907: Lutetium discovered independently by French scientist Georges Urbain and by Austrian mineralogist Baron Carl Auer von Welsbach.
• 1907: Hilbert space representation theorem, also known as Riesz representation theorem, the mathematical justification of the Bra-ket notation in the theory of quantum mechanics – independently proved by Frigyes Riesz and Maurice René Fréchet.
• The Hardy–Weinberg principle is a principle of population genetics that states that, in the absence of other evolutionary influences, allele and genotype frequencies in a population will remain constant from generation to generation. This law was formulated in 1908 independently by German obstetrician-gynecologist Wilhelm Weinberg and, a little later and a little less rigorously, by British mathematician G.H. Hardy.
• The Stark–Einstein law (aka photochemical equivalence law, or photoequivalence law) – independently formulated between 1908 and 1913 by Johannes Stark and Albert Einstein. It states that every photon that is absorbed will cause a (primary) chemical or physical reaction. [58] in radio work was described by Johannes Zenneck (1908), Leonard Danilewicz (1929), [59]Willem Broertjes (1929), and Hedy Lamarr and George Antheil (1942 US patent).
• By 1913, vitamin A was independently discovered by Elmer McCollum and Marguerite Davis at the University of Wisconsin–Madison, and by Lafayette Mendel and Thomas Burr Osborne at Yale University, who studied the role of fats in the diet. (viruses that infect bacteria) – Frederick Twort (1915), Félix d'Hérelle (1917). – Theo A. van Hengel and R.P.C. Spengler (1915) Edward Hebern (1917) Arthur Scherbius (Enigma machine, 1918) Hugo Koch (1919) Arvid Damm (1919). – Joseph Tykociński-Tykociner (1922), Lee De Forest (1923).
• The Big Bang theory of the universe—that the universe is expanding from a single original point—was developed from the independent derivation of the Friedmann equations from Albert Einstein's equations of general relativity by the Russian, Alexander Friedmann, in 1922, and by the Belgian, Georges Lemaître, in 1927. [60] The Big Bang theory was confirmed in 1929 by the American astronomer Edwin Hubble's analysis of galactic redshifts. [61] But the Big Bang theory had been presaged three-quarters of a century earlier in the American poet and short-story writer Edgar Allan Poe's then much-derided essay, Eureka: A Prose Poem (1848), [11][62][63] is credited with discovering as early as 1923 that cervical cancer cells can be detected microscopically, though his invention of the Pap test went largely ignored by physicians until 1943. Aurel Babeş of Romania independently made similar discoveries in 1927. [64]
• "Primordial soup" theory of the abiogenetic evolution of life from carbon-based molecules – Alexander Oparin (1924), J.B.S. Haldane (1925). was detected in the 1920s by Japanese meteorologistWasaburo Oishi, whose work largely went unnoticed outside Japan because he published his findings in Esperanto. [65][66] Often given some credit for discovery of jet streams is American pilot Wiley Post, who in the year before his 1935 death noticed that at times his ground speed greatly exceeded his air speed. [67] Real understanding of the nature of jet streams is often credited to experience in World War II military flights. [68][69] , an algorithm for finding a minimum spanning tree in a graph, was first published in 1926 by Otakar Borůvka. The algorithm was rediscovered by Choquet in 1938 again by Florek, Łukasiewicz, Perkal, Steinhaus, and Zubrzycki and again by Sollin in 1965.
• 1927: The discovery of phosphocreatine was reported by Grace Palmer Eggleton and Philip Eggleton of the University of Cambridge[70] and separately by Cyrus H. Fiske and Yellapragada Subbarow of Harvard Medical School. [71]
• 1929: Dmitri Skobeltsyn first observed the positron in 1929. [72]Chung-Yao Chao also observed the positron in 1929, though he did not recognize it as such. , an important limitative result in mathematical logic – Kurt Gödel (1930 described in a 1931 private letter, but not published) Alfred Tarski (1933). —published by Subramanyan Chandrasekhar (1931–35) also computed by Lev Landau (1932). [73]
• A theory of protein denaturation is widely attributed to Alfred Mirsky and Linus Pauling, who published their paper in 1936, [74] though it had been independently discovered in 1931 by Hsien Wu, [75] whom some now recognize as the originator of the theory. [76] in silicon carbide, now known as the LED, was discovered independently by Oleg Losev in 1927 and by H.J. Round in 1907, and possibly in 1936 in zinc sulfide by Georges Destriau, who believed it was actually a form of incandescence.
• 1934: Natural deduction, an approach to proof theory in philosophical logic – discovered independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934.
• The Gelfond–Schneider theorem, in mathematics, establishes the transcendence of a large class of numbers. It was originally proved in 1934 by Aleksandr Gelfond, and again independently in 1935 by Theodor Schneider.
• The Penrose triangle, also known as the "tribar", is an impossible object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. The mathematicianRoger Penrose independently devised and popularised it in the 1950s.
• 1936: In computer science, the concept of the "universal computing machine" (now generally called the "Turing Machine") was proposed by Alan Turing, but also independently by Emil Post, [77] both in 1936. Similar approaches, also aiming to cover the concept of universal computing, were introduced by S.C. Kleene, Rózsa Péter, and Alonzo Church that same year. Also in 1936, Konrad Zuse tried to build a binary electrically driven mechanical calculator with limited programability however, Zuse's machine was never fully functional. The later Atanasoff–Berry Computer ("ABC"), designed by John Vincent Atanasoff and Clifford Berry, was the first fully electronicdigitalcomputing device [78] while not programmable, it pioneered important elements of modern computing, including binary arithmetic and electronic switching elements, [79][80] though its special-purpose nature and lack of a changeable, stored program distinguish it from modern computers.
• The atom bomb was independently thought of by Leó Szilárd, [81]Józef Rotblat[82] and others.
• The jet engine, independently invented by Hans von Ohain (1939), Secondo Campini (1940) and Frank Whittle (1941) and used in working aircraft.
• In agriculture, the ability of synthetic auxins2,4-D, 2,4,5-T, and MCPA to act as hormone herbicides was discovered independently by four groups in the United States and Great Britain: William G. Templeman and coworkers (1941) Philip Nutman, Gerard Thornton, and Juda Quastel (1942) Franklin Jones (1942) and Ezra Kraus, John W. Mitchell, and Charles L. Hamner (1943). All four groups were subject to various aspects of wartime secrecy, and the exact order of discovery is a matter of some debate. [83]
• The point-contact transistor was independently invented in 1947 by Americans William Shockley, John Bardeen and Walter Brattain, working at Bell Labs, [84] and in 1948 by German physicists Herbert Mataré and Heinrich Welker, working at the Compagnie des Freins et Signaux, a Westinghouse subsidiary located in Paris. [85] The Americans were jointly awarded the 1956 Nobel Prize in Physics "for their researches on semiconductors and their discovery of the transistor effect." [86]
• 1949: A formal definition of cliques was simultaneously introduced by Luce and Perry (1949) and Festinger (1949). [87][88] was independently developed in the late 1940s and early 1950s by the Purcell group at Harvard University and the Bloch group at Stanford University. Edward Mills Purcell and Felix Bloch shared the 1952 Nobel Prize in Physics for their discoveries. [89] (1950–63): Hilary Koprowski, Jonas Salk, Albert Sabin.
• The integrated circuit was devised independently by Jack Kilby in 1958 [90] and half a year later by Robert Noyce. [91] Kilby won the 2000 Nobel Prize in Physics for his part in the invention of the integrated circuit. [92]
• The QR algorithm for calculating eigenvalues and eigenvectors of matrices was developed independently in the late 1950s by John G. F. Francis and by Vera N. Kublanovskaya. [93] The algorithm is considered one of the most important developments in numerical linear algebra of the 20th century. [94] and renormalization (1930s–40s): Ernst Stueckelberg, Julian Schwinger, Richard Feynman, and Sin-Itiro Tomonaga, for which the latter 3 received the 1965 Nobel Prize in Physics.
• The maser, a precursor to the laser, was described by Russian scientists in 1952, and built independently by scientists at Columbia University in 1953. The laser itself was developed independently by Gordon Gould at Columbia University and by researchers at Bell Labs, and by the Russian scientist Aleksandr Prokhorov. , also known as "Kolmogorov–Chaitin complexity", descriptive complexity, etc., of an object such as a piece of text is a measure of the computational resources needed to specify the object. The concept was independently introduced by Ray Solomonoff, Andrey Kolmogorov and Gregory Chaitin in the 1960s. [95]
• The concept of packet switching, a communications method in which discrete blocks of data (packets) are routed between nodes over data links, was first explored by Paul Baran in the early 1960s, and then independently a few years later by Donald Davies.
• The principles of atomic layer deposition, a thin-film growth method that in the 2000s contributed to the continuation of semiconductor-device scaling in accord with Moore's law, were independently discovered in the early 1960s by the Soviet scientists Valentin Aleskovsky and Stanislav Koltsov and in 1974 by the Finnish inventor Tuomo Suntola. [96][97][98] is a popular model in finance for trading off risk versus return. Three separate authors published it in academic journals and a fourth circulated unpublished papers.
• 1963: In a major advance in the development of plate tectonics theory, the Vine–Matthews–Morley hypothesis was independently proposed by Lawrence Morley, and by Fred Vine and Drummond Matthews, linking seafloor spreading and the symmetric "zebra pattern" of magnetic reversals in the basalt rocks on either side of mid-ocean ridges. [99] as a signature of the Big Bang was confirmed by Arno Penzias and Robert Wilson of Bell Labs. Penzias and Wilson had been testing a very sensitive microwave detector when they noticed that their equipment was picking up a strange noise that was independent of the orientation (direction) of their instrument. At first they thought the noise was generated due to pigeon droppings in the detector, but even after they removed the droppings the noise was still detected. Meanwhile, at nearby Princeton University two physicists, Robert Dicke and Jim Peebles, were working on a suggestion of George Gamow's that the early universe had been hot and dense they believed its hot glow could still be detected but would be so red-shifted that it would manifest as microwaves. When Penzias and Wilson learned about this, they realized that they had already detected the red-shifted microwaves and (to the disappointment of Dicke and Peebles) were awarded the 1978 Nobel Prize in physics. [31] : Between 1963 and 1977, doped and oxidized highly conductive polyacetylene derivatives were independently discovered, "lost", and then rediscovered at least four times. The last rediscovery won the 2000 Nobel prize in Chemistry, for the "discovery and development of conductive polymers". This was without reference to the previous discoveries. Citations in article "Conductive polymers."
• 1964: The relativistic model for the Higgs mechanism was developed by three independent groups: Robert Brout and François Englert Peter Higgs and Gerald Guralnik, Carl Richard Hagen, and Tom Kibble. [100] Slightly later, in 1965, it was also proposed by Soviet undergraduate students Alexander Migdal and Alexander Markovich Polyakov. [101] The existence of the "Higgs boson" was finally confirmed in 2012 Higgs and Englert were awarded a Nobel Prize in 2013.
• The Cocke–Younger–Kasami algorithm was independently discovered three times: by T. Kasami (1965), by Daniel H. Younger (1967), and by John Cocke and Jacob T. Schwartz (1970).
• The Wagner–Fischer algorithm, in computer science, was discovered and published at least six times. [102] : 43
• The affine scaling method for solving linear programming was discovered by Soviet mathematician I.I. Dikin in 1967. It went unnoticed in the West for two decades, until two groups of researchers in the U.S. reinvented it in 1985. was introduced by a Japanese biologist, Motoo Kimura, in 1968, and independently by two American biologists, Jack Lester King and Thomas Hughes Jukes, in 1969.
• 1969: Thyrotropin-releasing hormone (TRH) structure was determined, and the hormone synthesized, independently by Andrew V. Schally and Roger Guillemin, who shared the 1977 Nobel Prize in Medicine. [103]
• 1970: Howard Temin and David Baltimore independently discovered reverse transcriptase enzymes.
• The Knuth–Morris–Prattstring searching algorithm was developed by Donald Knuth and Vaughan Pratt and independently by J. H. Morris.
• The Cook–Levin theorem (also known as "Cook's theorem"), a result in computational complexity theory, was proven independently by Stephen Cook (1971 in the U.S.) and by Leonid Levin (1973 in the USSR). Levin was not aware of Cook's achievement because of communication difficulties between East and West during the Cold War. The other way round, Levin's work was not widely known in the West until around 1978. [104] (compactin ML-236B) was independently discovered by Akira Endo in Japan in a culture of Penicillium citrinium[105] and by a British group in a culture of Penicillium brevicompactum. [106] Both reports were published in 1976.
• The Bohlen–Pierce scale, a harmonic, non-octave musical scale, was independently discovered by Heinz Bohlen (1972), Kees van Prooijen (1978) and John R. Pierce (1984). , an algorithm suitable for signing and encryption in public-key cryptography, was publicly described in 1977 by Ron Rivest, Adi Shamir and Leonard Adleman. An equivalent system had been described in 1973 in an internal document by Clifford Cocks, a British mathematician working for the UK intelligence agency GCHQ, but his work was not revealed until 1997 due to its top-secret classification.
• 1973: Asymptotic freedom, which states that the strong nuclear interaction between quarks decreases with decreasing distance, was discovered in 1973 by David Gross and Frank Wilczek, and by David Politzer, and was published in the same 1973 edition of the journal Physical Review Letters. [107] For their work the three received the Nobel Prize in Physics in 2004.
• 1974: The J/ψ meson was independently discovered by a group at the Stanford Linear Accelerator Center, headed by Burton Richter, and by a group at Brookhaven National Laboratory, headed by Samuel Ting of MIT. Both announced their discoveries on 11 November 1974. For their shared discovery, Richter and Ting shared the 1976 Nobel Prize in Physics.
• 1975: Endorphins were discovered independently in Scotland and the US in 1975.
• 1975: Two English biologists, Robin Holliday and John Pugh, and an American biologist, Arthur Riggs, independently suggested that methylation, a chemical modification of DNA that is heritable and can be induced by environmental influences, including physical and emotional stresses, has an important part in controlling gene expression. This concept has become foundational for the field of epigenetics, with its multifarious implications for physical and mental health and for sociopolitics. [108]
• 1980: The asteroid cause of the Cretaceous-Tertiary extinction that wiped out much life on Earth, including all dinosaurs except for birds, was published in Science[109] by Luis and Walter Alvarezet al. and independently 2 weeks earlier, in Nature, by Dutch geologist Jan Smit and Belgian geologist Jan Hertogen. [110]
• 1983: Two separate research groups led by American Robert Gallo and French investigators Françoise Barré-Sinoussi and Luc Montagnier independently declared that a novel retrovirus may have been infecting AIDS patients, and published their findings in the same issue of the journal Science. [111][112][113] A third contemporaneous group, at the University of California, San Francisco, led by Dr. Jay Levy, in 1983 independently discovered an AIDS virus [114] which was very different from that reported by the Montagnier and Gallo groups and which indicated, for the first time, the heterogeneity of HIV isolates. [115] —the first cryptographic method to rely not on mathematical complexity but on the laws of physics—was first postulated in 1984 by Charles Bennett and Gilles Brassard, working together, and later independently, in 1991, by Artur Ekert. The earlier scheme has proven the more practical. [116]
• 1984: Comet Levy-Rudenko was discovered independently by David H. Levy on 13 November 1984 and the next evening by Michael Rudenko. (It was the first of 23 comets discovered by Levy, who is famous as the 1993 co-discoverer of Comet Shoemaker-Levy 9, the first comet ever observed crashing into a planet, Jupiter.) [117]
• 1985: The use of elliptic curves in cryptography (Elliptic curve cryptography) was suggested independently by Neal Koblitz and Victor S. Miller in 1985.
• 1987: The Immerman–Szelepcsényi theorem, another fundamental result in computational complexity theory, was proven independently by Neil Immerman and Róbert Szelepcsényi in 1987. [118]
• In 1989, Thomas R. Cech (Colorado) and Sidney Altman (Yale) won the Nobel Prize in chemistry for their independent discovery in the 1980s of ribozymes – for the "discovery of catalytic properties of RNA" – using different approaches. Catalytic RNA was an unexpected finding, something they were not looking for, and it required rigorous proof that there was no contaminating protein enzyme.
• In 1993, groups led by Donald S. Bethune at IBM and Sumio Iijima at NEC independently discovered single-wallcarbon nanotubes and methods to produce them using transition-metal catalysts.
• 1998: Saul Perlmutter, Adam G. Riess, and Brian P. Schmidt—working as members of two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team—simultaneously discovered in 1998 the accelerating expansion of the universe through observations of distant supernovae For this, they were jointly awarded the 2006 Shaw Prize in Astronomy and the 2011 Nobel Prize in Physics. [119][120]
• In 2001 four different authors published different implementations of a distributed hash table.
• The Super Kamiokande and SNOLAB collaborations, whose findings were published in 1998 and 2001 respectively, both proved that neutrinos have mass. The 2015 Nobel Prize in Physics was shared by Takaaki Kajita of Japan and Arthur B. McDonald of Canada as a result. [121] of MD Anderson Cancer Center at the University of Texas at Houston discovered a mechanism enabling cancer immunotherapy in 1996. Tasuku Honjo of Kyoto University discovered another such mechanism in 2002. This outcome, which led to them sharing the 2018 Nobel Prize in Physiology or Medicine, has been described as follows: "Each independently discovered that our immune system is restrained from attacking tumors by molecules that function as 'brakes.' Releasing these brakes (or 'brake receptors') allows our body to powerfully combat cancer." [122]
• In 2014, Paul Erdős' conjecture about prime gaps was proved by Kevin Ford, Ben Green, Sergei Konyagin, and Terence Tao, working together, and independently by James Maynard. [123][124]
• 2020: half of the 2020 Nobel Prize in Physics was awarded to Reinhard Genzel and Andrea Ghez, who each have led a group of astronomers focused since the early 1990s on a region at the center of the Milky Way galaxy called Sagittarius A*, finding an extremely heavy, invisible object (black hole) that pulls on a jumble of stars, causing them to rush around at dizzying speeds. Some 4 million solar masses are packed together in a region no larger than our solar system. [125]

"When the time is ripe for certain things, these things appear in different places in the manner of violets coming to light in early spring."

"[Y]ou do not [make a discovery] until a background knowledge is built up to a place where it's almost impossible not to see the new thing, and it often happens that the new step is done contemporaneously in two different places in the world, independently."

"[A] man can no more be completely original [. ] than a tree can grow out of air."

I never had an idea in my life. My so-called inventions already existed in the environment – I took them out. I've created nothing. Nobody does. There's no such thing as an idea being brain-born everything comes from the outside.

## History of Pain: A Brief Overview of the 17th and 18th Centuries

You might be asking yourself, why is the history of pain important to me? How can history help me provide more effective pain treatment for my patients?

Pain can be scary and it triggers superstitious thinking that leads to fear. Fearful pain patients are often their own worst enemies because they feel like they have no control over their bodies, which only adds to their fear. Knowledge is a powerful tool and my initial goal with every pain patient is to share creditable information about pain. I want to temper that fear with knowledge and guide the patient in becoming his or her own best friend and advocate.

A history of pain will help you understand the nature of pain and how providers and researchers arrived at the current range of treatment options. Part 1 of this series will review pain management practices from the 17th and 18th centuries.

### René Descartes and the Dualistic Nature of Pain

We begin our journey of discovery in the 17th century with René Descartes (1596-1650), whose research and influence initiated new thinking about pain that has transcended three centuries. Not only did he impact how we think about pain, but his contributions to science and medicine were so influential that they are still evident in Western medical practice today.

In 1644, Descartes’ Principles of Philosophy was published, in which he discussed pain in phantom limbs. From his observations, he deduced that pain was felt in the brain, not the phantom limb. He introduced his concept of the soul: that the soul of pain was located in the pineal gland. He argued that persistent agitation of the nerves from the phantom limb produced sensations as if the phantom limb was still intact. However, Church thinking at that time considered pain closely linked to original sin, and had a very strong power over scientific thought. 1 Descartes was aware of the Church’s influence and, therefore, placated the Church by introducing the soul into his thinking.

Descartes believed the pain from the phantom limb was real and not imaginary. Pain was a perception of the soul. Further, he felt that pain was somehow limited to touch and that pain was not a specific sensation, but a more general mode of animal spirits. It is generally believed that Descartes incorporated the notion of the soul to avoid trouble with the Church, being well aware of what had happened to Galileo!

The influence of the Church persisted and was evident up to the 19th century. Traditional Catholic religion maintained that pain was rooted in the passion and death of Christ that suffering individuals were closer to Christ and that their anguish could be offered up in penance for earthly sins.

In Descartes’ L’Homme (1644), which was published 14 years after his death, Descartes presented a model of pain in the form of a boy sticking his foot in a fire. This well-known model has had profound influence on subsequent pain research. 2 Descartes believed that as the fire came close to the foot, the painful stimulus resulted in the pulling of a delicate thread that ran up the boy’s leg to the brain by the shortest route.

Descartes expanded William Harvey’s (1628) model of circulation, which embodied the movement of spirits via valves. Harvey’s main contribution to medicine was his study of the heart and the movement of blood around the body. According to his theories, these valves acted as little doors opening to let the spirits through and, thus, prevented reflux. 3

Descartes’ model of the dualistic nature of pain suggests that pain is primarily a sensory phenomenon that is separated from higher order (neocortical) influences. It is the either/or school of thinking: either pain is physical or it is of psychic origin they are mutually exclusive of one another.

### Descartes’ Error

About 20 years ago, I had the opportunity to listen to a lecture in Portland, Oregon, by Antonio Damasio, MD, the M.W. Van Allen Professor of Neurology and Chairman of the Department of Neurology at the University of Iowa, College of Medicine. He had just published Descartes’ Error: Emotion, Reason, and the Human Brain, in which he stated, “The error is the abysmal separation between body and mind. The suffering that comes from physical pain or emotional upheaval might exist separately from the body.” 4 Damasio stated quite emphatically that medical schools in the United States largely ignore human dimensions and instead concentrate on the physiology and pathology of the body proper. Further, Damasio felt that this neglect stems from a Cartesian dualistic view of humanity that has persisted for 3 centuries.

The true value of Descartes’ research and thinking is that he opened the way to subsequent research on the localization of cerebral functions. He tried to dispel the confusion between pain and sadness. He felt that sadness always followed pain because the soul recognized the weakness of the body and its inability to resist the injuries that afflicted it. 1

Descartes’ work marked a major milestone in pain research and application. He created controversy in the world of pain research, which contributed to more debate and, ultimately, progress. His research at that time was revolutionary, especially when you consider the level of technology available. His theories were very different and far-reaching as represented by the example of the boy who stuck his foot in the fire.

Damasio’s critique of Cartesian dualism is relevant today, especially since there are still many pain providers who feel that pain is only a sensory event. Damasio’s observations were very important, especially considering that the British school of research was influenced by Francis Bacon—considered to be the creator of empiricism and the scientific method—to advance science through inductive reasoning, and France was influenced by Descartes’ reductive mechanistic philosophy. These differences carried on throughout the 18th century.

### Progress in the 18th Century: Shifts in Medical Philosophies

The 18th century is often referred to as the Age of Enlightenment. A shift in thinking, associated with the decrease of Church influence, was taking place in the secularization of thought and the separation between science and metaphysics. Additionally, thoughts and sentiments were shifting regarding the perception and definition of pain. 1 In The History of Pain, Roselyne Rey observed that there were three different medical philosophies in the 18th century:

• First, there was the mechanical school of thought—those who wanted to return to the notion that the human body functions as a simple machine—which was popular up until the middle of the 18th century.
• Second, there was the vitalist school of thinking, which was more dominant toward the end of the century. Those thought leaders adopted the concept of sensitivity, which included the simultaneous concepts of physiology and psychology.
• Third, the minority school of thought (animism) felt that nature was more passive. Those believers accepted mechanical explanations and considered the soul to be directly responsible for all organic functions. Further, they believed it made pain an important sign in illness as a result of internal strife. 1

### Albrecht von Haller

The first major contributor to this shift in thinking was Albrecht von Haller (1708-1777). He was interested in the reactions of fibers and how to distinguish between the irritability of muscle fiber (which he called the contractibility) and the excitability of nerve fibers (which he called sensitivity). (In today’s vernacular, this would be considered “hyperesthesia” in extreme forms.) In von Haller’s work, only the nerves are sensitive, while muscle fibers are irritable. Von Haller felt strongly about a strict dichotomy between sensitivity, which was associated with consciousness, and irritability, which was independent of consciousness. Von Haller was the first person to discover that only nerves produce sensation and only those parts of the body connected to the nervous system can undergo a sensation.

As knowledge and research progressed in the 18th century, a major trend started to develop where research focused on more specific aspects of pain. The specific aspects of pain for von Haller were the roles of muscle fibers and nerves. This is still an area of interest in today’s pain research. I would suggest that von Haller’s work was the beginning of what we now consider “myofascial” pain.

### Pierre Jean George Cabanis

Toward the second half of the 18th century, there was a reaction against von Haller’s theory of pain, which was lead by Pierre Jean George Cabanis (1757-1808). Cabanis’ work incorporated a psychophysiological approach to pain, which included the emotional component. For Cabanis, sensitivity could not be defined outside the realm of pleasure and pain, since what affects us can never be indifferent to us. 1 In Cabanis’ view, pain was useful it instilled stability, balance, and equilibrium to the nerves and muscular systems. The idea of the usefulness of pain led to the therapeutic techniques of electrical shock and stimulation.

Cabanis also felt that sensations (pain) could be generated spontaneously in the brain and provoke pains that were real. This notion is where Cabanis introduced the concept of hypochondria and pain: pain is not a pure physiological reaction to a stimulus, but requires the mental activity of the patient. It seems to me that Cabanis was either extending Cartesian dualism—pain separate from the physiological perception (dualism)—or was inferring that pain was somehow a combination of physiology and psychology. According to Rey, 1 the work of Cabanis focused on sensitivity as the cornerstone for life, and pain provided the ideal experience to study the relationship between the physical and mental.

Cabanis’ questions about the psychophysiological conditions necessary for pain to reach consciousness led him to view the perception of pain as being a complex, chronologically staged process. During this process, any given sensation at any given time could be absorbed by another sensation. He proposed a competitive model between external and internal feelings, where the weakest sensations were absorbed by the strongest. 1

Cabanis’ research and ideas were a major step forward in how the pain patient was treated. His work led to new techniques, such as using electrical stimulation for the treatment of pain. He introduced the concepts of psychophysiology and the emotional components of pain. These concepts continued to grow well into the 19th century, even though his thinking contradicted von Haller’s theories.

### Xavier Bichat

The next major contributor to consider is Xavier Bichat (1771-1802). Bichat’s work represented a passage from organic sensitivity to animal sensitivity and the “threshold concept.” His work on the two nervous systems and their relationship to the understanding of pain was an important contribution. He separately studied the sympathetic and parasympathetic systems, which, in the 18th century, was highly significant. He believed the two systems were very distinct, each having two principal centers: one in the brain and the other in the ganglions. Pain coming from the ganglions was very different than pain coming from the spinal nerves. This distinction agreed with the vitalists—those who believed living organisms are fundamentally different from non-living entities because they contain some non-physical element or are governed by different principles—but differed from von Haller’s thinking. This debate between Bichat and von Haller persisted for more than a half century and had major consequences for physiology and the treatment of pain. Bichat’s contribution to pain medicine was his discovery of the importance of the sympathetic nervous system.

Bichat’s work complemented the work of Cabanis, which led to a more global psychophysiological approach to pain treatment. This approach also led to the increasing use of opium as a treatment option, which was not present in the 17th century. 1 The work of Cabanis and Bichat represented the beginning of an important trend in pain treatment: the holistic and multidisciplinary approach.

### Conclusion

This article was a brief overview of the history of pain in the 17th and 18th centuries. Part 2 will cover pain management in the 19th and 20th centuries. In this article, I have imposed arbitrary parameters and left out many contributors who have played an important role in adding to our understanding of the pain experience. I attempted to include the major contributors who appeared to build on one another’s work. The framework for this article came largely from Roselyne Rey’s book titled, The History of Pain

Note: All of the major contributors covered in this article are available online. For those who are interested in more information about the history of pain, I would recommend you visit The John C. Liebeskind History of Pain Collection at the Louise M. Darling Biomedical Library at the University of California, Los Angeles.

## What Were Some Inventions in the 17th Century?

The 17th century, or the time between 1601 and 1700, was revolutionary. This was the time period when science, math, and reason all began to emerge from the shadow of mysticism and superstition. It was during this period that the great thinkers who would inspire the industrial revolution began making themselves known. This was the time of Galileo, Blaise Pascal, and Isaac Newton. These are names that are often mentioned during lectures on math and astronomy, but most people think they were isolated in a period of scientific darkness. This is completely untrue. There were numerous inventions and discoveries made during the 17th century.

What were some of the inventions of the 17th century?

1608 The refracting telescope is invented by Hans Lippershey.

1609 Galileo Galilei was the first person to observe the skies with a telescope.

1620 First submarine invented by Cornelis Drebbel.

1624 The slide rule is invented by William Oughtred.

1626 St. Peter’s Basilica completed.

1629 The steam turbine is invented by Giovanni Branca.

1636 The micrometer is invented by W. Gascoigne.

1642 The adding machine is invented by Blasie Pascal.

1643 The barometer is invented by Evangelista Torricelli.

1650 The air pump is invented by Otto von Guericke.

1656 The pendulum clock is invented by Christian Huygens.

1663 The reflecting telescope is invented by James Gregory.

1668 A reflecting telescope is invented by Isaac Newton.

1670 Champagne is invented by Dom Perignon.

1671 A calculating machine is invented by Gottfried Wilhelm Leibniz.

1674 Bacteria is first seen and described in a microscope by Anton Van Leeuwenhoek.

1675 The pocket watch is invented by Christian Huygens.

1676 The universal joint is created by Robert Hooke.

1679 The pressure cooker is created by Denis Papin.

1684 Newton completes calculations on gravity.

1684 Gottfried Leibniz published his theories and work on calculus.

1693 Isaac Newton published his work on calculus.

1698 The steam pump is invented by Thomas Savery.

Many of the greatest inventions of the 17th century were theoretical in nature. Understanding gravity, creating a form of math to understand physics, and having the ability to study the stars and planets are all advances future scientists and mathematicians would build upon. Without these advances, the industrial revolution would not have been possible. Advances in medicine such as the microscope, identification of bacteria, and the ability to transfuse blood all revolutionized the medical field and made true medicine possible.

While the Industrial Revolution gets much of the credit for altering everyday life, without some of the inventions of the 17th century the famous advances of later centuries in science, math, and medicine would not have been possible.

## Slave Rebellions

Rebellionsਊmong enslaved people did occur—notably ones led by Gabriel Prosser in Richmond in 1800 and by Denmark Vesey in Charleston in 1822𠅋ut few were successful.

The revolt that most terrified enslavers was that led by Nat Turner in Southampton County, Virginia, in August 1831. Turner’s group, which eventually numbered around 75 Black men, murdered some 55 white people in two days before armed resistance from local white people and the arrival of state militia forces overwhelmed them.

Supporters of slavery pointed to Turner’s rebellion as evidence that Black people were inherently inferior barbarians requiring an institution such as slavery to discipline them, and fears of similar insurrections led many southern states to further strengthen their slave codes in order to limit the education, movement and assembly of enslaved people.

## The Early Enlightenment: 1685-1730

The Enlightenment’s important 17th-century precursors included the Englishmen Francis Bacon and Thomas Hobbes, the Frenchman René Descartes and the key natural philosophers of the Scientific Revolution, including Galileo Galilei, Johannes Kepler and Gottfried Wilhelm Leibniz. Its roots are usually traced to 1680s England, where in the span of three years Isaac Newton published his “Principia Mathematica” (1686) and John Locke his 𠇎ssay Concerning Human Understanding” (1689)—two works that provided the scientific, mathematical and philosophical toolkit for the Enlightenment’s major advances.

Did you know? In his essay &aposWhat Is Enlightenment?&apos (1784), the German philosopher Immanuel Kant summed up the era&aposs motto in the following terms: &aposDare to know! Have courage to use your own reason!&apos

Locke argued that human nature was mutable and that knowledge was gained through accumulated experience rather than by accessing some sort of outside truth. Newton’s calculus and optical theories provided the powerful Enlightenment metaphors for precisely measured change and illumination.

There was no single, unified Enlightenment. Instead, it is possible to speak of the French Enlightenment, the Scottish Enlightenment and the English, German, Swiss or American Enlightenment. Individual Enlightenment thinkers often had very different approaches. Locke differed from David Hume, Jean-Jacques Rousseau from Voltaire, Thomas Jefferson from Frederick the Great. Their differences and disagreements, though, emerged out of the common Enlightenment themes of rational questioning and belief in progress through dialogue.

## Binary Number System

During the 1670s, Leibniz worked on the invention of a practical calculating machine, which used the binary system and was capable of multiplying, dividing and even extracting roots, a great improvement on Pascal’s rudimentary adding machine and a true forerunner of the computer.

He is usually credited with the early development of the binary number system (base 2 counting, using only the digits 0 and 1), although he himself was aware of similar ideas dating back to the I Ching of Ancient China. Because of the ability of binary to be represented by the two phases “on” and “off”, it would later become the foundation of virtually all modern computer systems, and Leibniz’s documentation was essential in the development process.

Leibniz is also often considered the most important logician between Aristotle in Ancient Greece and George Boole and Augustus De Morgan in the 19th Century. Even though he actually published nothing on formal logic in his lifetime, he enunciated in his working drafts the principal properties of what we now call conjunction, disjunction, negation, identity, set inclusion and the empty set.

## LIFE IN THE 18th CENTURY

In the late 18th century life the industrial revolution began to transform life in Britain. Until then most people lived in the countryside and made their living from farming. By the mid 19th century most people in Britain lived in towns and made their living from mining or manufacturing industries.

From 1712 a man named Thomas Newcomen (1663-1729) made primitive steam engines for pumping water from mines. In 1769 James Watt (1736-1819) patented a more efficient steam engine. In 1785 his engine was adapted to driving machinery in a cotton factory. The use of steam engines to drive machines slowly transformed industry.

Meanwhile during the 1700s Britain built up a great overseas empire. The North American colonies were lost after the War of Independence 1776-1783. On the other hand, after the Seven Years War 1756-1763, Britain captured Canada and India. Britain also took Dominica, Grenada, St Vincent, and Tobago in the West Indies. In 1707 the Act of Union was passed. Scotland was united with England and Wales. England became part of Great Britain.

Owning land was the main form of wealth in the 18th century. Political power and influence were in the hands of rich landowners. At the top were the nobility. Below them was a class of nearly rich landowners called the gentry. In the early 18th century there was another class of landowners called yeomen between the rich and the poor. However, during the century this class became less and less numerous. But other middle-class people such as merchants and professional men became richer and more numerous, especially in the towns.

Below them were the great mass of the population, craftsmen, and laborers. In the 18th century probably half the population lived at subsistence or bare survival level.

In the early 18th century England suffered from gin drinking. It was cheap and it was sold everywhere as you did not need a license to sell it. Many people ruined their health by drinking gin. Sadly for many poor people drinking gin was their only comfort. The situation improved after 1751 when a tax was imposed on gin.

At the end of the 1700s, a group of Evangelical Christians called the Clapham Sect was formed. They campaigned for an end to slavery and cruel sports. They were later called the Clapham Sect because so many of them lived in Clapham.

Population in 18th Century Britain

At the end of the 17th century, it was estimated the population of England and Wales was about 5 1/2 million. The population of Scotland was about 1 million. The population of London was about 600,000. In the mid 18th century the population of Britain was about 6 1/2 million. In the late 18th century it grew rapidly and by 1801 it was over 9 million. The population of London was almost 1 million.

During the 18th-century towns in Britain grew larger. Nevertheless, most towns still had populations of less than 10,000. However, in the late 18th century new industrial towns in the Midland and the North of England mushroomed. Meanwhile, the population of London grew to nearly 1 million by the end of the century.

Towns in 18th Century England

In the later 18th century bodies of men called Paving or Improvement Commissioners were formed in many towns. They had the power to pave and clean the streets and sometimes to light them with oil lamps. Some also arranged collections of rubbish. Since most of it was organic it could be sold as fertilizer.

Agriculture in 18th Century England

During the 18th century, agriculture was gradually transformed by an agricultural revolution. Until 1701 seed was sown by hand. In that year Jethro Tull invented a seed drill, which sowed seed in straight lines. He also invented a horse-drawn hoe that hoed the land and destroyed weed between rows of crops.

Furthermore, until the 18th century, most livestock was slaughtered at the beginning of winter because farmers could not grow enough food to feed their animals through the winter months.

Until the 18th century most land in England was divided into 3 fields. Each year 2 fields were sown with crops while the third was left fallow (unused). The Dutch began to grow swedes or turnips on land instead of leaving it fallow. (The turnips restored the soil’s fertility). When they were harvested the turnips could be stored to provide food for livestock over the winter. The new methods were popularized in England by a man named Robert ‘Turnip’ Townshend (1674-1741).

Under the 3 field system, which still covered much of England, all the land around a village or small town, was divided into 3 huge fields. Each farmer owned some strips of land in each field. During the 18th century land was enclosed. That means it was divided up so each farmer had all his land in one place instead of scattered across 3 fields. Enclosure allowed farmers to use their land more efficiently. Also in the 18th-century farmers like Robert Bakewell began scientific stock breeding (selective breeding). Farm animals grew much larger and they gave more meat, wool, and milk.

There was little change in food in the 18th century. Despite the improvements in farming food for ordinary people remained plain and monotonous. For them, meat was a luxury. In England, a poor person’s food was mainly bread and potatoes. In the 18th-century drinking tea became common even among ordinary people.

Houses in the 18th Century

In the 18th century, a tiny minority of the population lived in luxury. The rich built great country houses. A famous landscape gardener called Lancelot Brown (1715-1783) created beautiful gardens. (He was known as ‘Capability’ Brown from his habit of looking at land and saying it had ‘great capabilities’). The leading architect of the 18th century was Robert Adam (1728-1792). He created a style called neo-classical and he designed many 18th-century country houses.

In 18th century Britain the wealthy owned comfortable upholstered furniture. They owned beautiful furniture, some of it veneered or inlaid. In the 18th century, much fine furniture was made by Thomas Chippendale (1718-1779), George Hepplewhite (?-1786), and Thomas Sheraton (1751-1806). The famous clockmaker James Cox (1723-1800) made exquisite clocks for the rich.

However the poor had none of these things. Craftsmen and laborers lived in 2 or 3 rooms. The poorest people lived in just one room. Their furniture was very simple and plain.

In the 18th-century men wore knee-length trouser-like garments called breeches and stockings. They also wore waistcoats and frock coats. They wore linen shirts. Both men and women wore wigs and for men three-cornered hats were popular. Men wore buckled shoes.

Women wore stays (a bodice with strips of whalebone) and hooped petticoats under their dresses. Women in the 18th century did not wear knickers. Fashionable women carried folding fans. Fashion was very important for the rich in the 18th century but poor people’s clothes hardly changed at all.

Leisure in the 18th Century

Traditional games remained popular in the 18th century. These included games such as chess, draughts, and backgammon. They also tennis and a rough version of football. It is believed dominoes was invented in China. It reached Europe in the 18th century. Then in 1759, a man named John Jeffries invented an entirely new board game called A Journey Through Europe or The Play of Geography in which players race across a map of Europe.

Horse racing was carried on for centuries before the 18th century but at this time it became a professional sport. The Jockey Club was formed in 1727. The Derby began in 1780.

For the well off card games and gambling were popular. The theatre was also popular. In the early 18th century most towns did not have a purpose-built theater and plays were staged in buildings like inns. However, in the late 18th-century theatres were built in most towns in England. Assembly rooms were also built in most towns. In them, people played cards and attended balls. In London, pleasure gardens were created.

Moreover, a kind of cricket was played long before the 18th century but at that time it took on its modern form. The first cricket club was formed at Hambledon in Hampshire about 1750.

Also in the 18th century rich people visited spas. They believed that bathing in and/or drinking spa water could cure illness. Towns like Buxton, Bath, and Tunbridge prospered. At the end of the 18th century, wealthy people began to spend time at the seaside. (Again they believed that bathing in seawater was good for your health). Seaside resorts like Brighton and Bognor boomed.

Reading was also a popular pastime in the 18th century and the first novels were published at this time. Books were still expensive but in many towns, you could pay to join a circulating library. The first daily newspaper in England was printed in 1702. The Times began in 1785.

Many people enjoyed cruel ‘sports’ like cockfighting and bull baiting. (A bull was chained to a post and dogs were trained to attack it). Rich people liked fox hunting. Public executions were also popular and they drew large crowds. Boxing without gloves was also popular (although some boxers began to wear leather gloves in the 18th century). Puppet shows like Punch and Judy also drew the crowds. Furthermore, in the late 18th century the circus became a popular form of entertainment.

Smoking clay pipes was popular in the 18th century. So was taking snuff. Wealthy young men would go on a ‘grand tour’ of Europe lasting one or two years.

Education in the 18th Century

In the early 18th-century charity schools were founded in many towns in England. They were sometimes called Blue Coat Schools because of the color of the children’s uniforms. Boys from well-off families went to grammar schools. Girls from well-off families also went to school. However, dissenters (Protestants who did not belong to the Church of England) were not allowed to attend most public schools. Instead, they went to their own dissenting academies.

Transport in the 18th Century

Transport was greatly improved during the 18th century. Groups of rich men formed turnpike trusts. Acts of Parliament gave them the right to improve and maintain certain roads. Travelers had to pay tolls to use them. The first turnpikes were created as early as 1663 but they became far more common in the 18th century.

Transporting goods was also made much easier by digging canals. In the early 18th century goods were often transported by packhorse. Moving heavy goods was very expensive. However, in 1759 the Duke of Bridgewater decided to build a canal to bring coal from his estate at Worsley to Manchester. He employed an engineer called James Brindley. When it was completed the Bridgewater canal halved the price of coal in Manchester. Many more canals were dug in the late 18th century and the early 19th century. They played a major role in the industrial revolution by making it cheaper to transport goods.

Travel in the 18th century was made dangerous by highwaymen. The most famous is Dick Turpin (1705-1739). Originally a butcher Turpin does not deserve his romantic reputation. In reality, he was a cruel and brutal man. Like many of his fellow highwaymen, he was hanged. Smuggling was also very common in the 18th century. It could be very profitable as import duties on goods like rum and tobacco were very high.

Medicine in the 18th Century n Knowledge of anatomy greatly improved in the 18th century. The famous 18th-century surgeon John Hunter (1728-1793) is sometimes called the Father of Modern Surgery. He invented new procedures such as tracheotomy. Among other advances, a Scottish surgeon named James Lind discovered that fresh fruit or lemon juice could cure or prevent scurvy. He published his findings in 1753.

A major scourge of the 18th century was smallpox. Even if it did not kill you it could leave you scarred with pox marks. Then, in 1721 Lady Mary Wortley Montagu learned inoculation from the Turks. You cut the patient then introduced matter from a smallpox pustule into the wound. The patient would (hopefully!) develop a mild case of the disease and be immune in the future. Some people realized that milkmaids who caught cowpox were immune to smallpox. A doctor named Jenner introduced vaccination. The patient was cut then matter from a cowpox pustule was introduced. The patient gained immunity to smallpox. (Jenner was not the first to think of this idea but because of his work it became a common practice).

In 1700 many people believed that scrofula (a form of tubercular infection) could be healed by a monarch’s touch. (Scrofula was called the kings evil). Queen Anne (1702-1714) was the last British monarch to touch for scrofula. However, there were still many quacks in the 18th century. Limited medical knowledge meant many people were desperate for a cure. One of the most common treatments, for the wealthy, was bathing in or drinking spa water, which they believed could cure all kinds of illnesses.

Art and Science in the 18th Century

During the 18th century, England produced two great portrait painters, Thomas Gainsborough (1727-1788) and Sir Joshua Reynolds (1723-1792). Meanwhile, the artist William Hogarth (1697-1764) painted scenes showing the harsh side of 18th-century life. The Royal Academy of Arts was founded in 1768. In theatre, the greatest actor of the 18th century was David Garrick (1717-1779).

In science Joseph Priestley (1733-1804) discovered oxygen. Henry Cavendish (1731-1810) discovered hydrogen. He also calculated the mass and density of the earth. William Herschel (1738-1822) discovered Uranus. The Scottish engineer Thomas Telford (1757-1834) built roads, canals, and the Menai suspension bridge.

Technology in the 18th Century

In the late 18th century technology advanced rapidly as Britain industrialized. From 1712 Thomas Newcomen made steam engines to pump water from mines. Then, in 1769, James Watt patented a more efficient steam engine and in the 1780s it was adapted to power machinery. The first industry to become mechanized was the textile industry. In 1771 Richard Arkwright opened a cotton-spinning mill with a machine called a water frame, which was powered by a water mill. Then, in 1779, Samuel Crompton invented a new cotton-spinning machine called a spinning mule. Finally, in 1785 Edmund Cartwright invented a loom that could be powered by a steam engine.

As a result of these new inventions, cotton production boomed. n Iron production also grew rapidly. In 1784 a man named Henry Cort (1740-1800) invented a much better way of making wrought iron. Until then men had to beat red hot iron with hammers to remove impurities. In 1784 Cort invented the puddling process. The iron was melted in an extremely hot furnace and stirred of ‘puddled’ to remove impurities. The result was a vast increase in iron production.

Religion in the 18th Century

The early 18th century was noted for its lack of religious enthusiasm and the churches in England lacked vigor. However, in the mid-18th century, things began to change. In 1739 the great evangelist George Whitefield (1714-1770) began preaching. Also in 1739, John Wesley (1703-1791) began preaching. He eventually created a new religious movement called the Methodists. His brother Charles Wesley (1707-1788) was a famous hymn writer.

John Wesley traveled all over the country, often preaching in open spaces. People jeered at his meetings and threw stones but Wesley persevered. He never intended to form a movement separate from the Church of England. However, the Methodists did eventually break away. After 1760 Methodism spread to Scotland.

In Wales there was a great revival in the years 1738-1742. Howell Harris (1714-1773) was a key figure. Scotland was also swept by a revival in the mid-18th century. William McCulloch and James Robe were the leading figures.