Scientific Revolution

Physics and Math in Sixteenth and Seventeenth Centuries in Europe

What were the achievements?

• Discovery of heliocentric view of the heavens• Universal gravitation• Advances in the understanding of:– Light– vacuum– Gases– Body– Microscopic Life

Influences on Revolution

• Effects of Reformation, primarily doubt in divine inspiration (so many people disagreed, that not everyone could be right or divinely inspired)

• Capitalism and emphasis on materialism, money, and interest

• Improved tools and increased levels of precision

Influences Continued

• Discovery of the New World– Geography– Botany– Humanity

On the Importance of the New World

“ ‘It is a striking fact,’ wrote the Parisian lawyer Etienne Pasquier, in the early 1560s, ‘that our classical authors had no knowledge of all this America, which we call New Lands.’ ‘This America’ was not only outside the range of Europe’s experience but was beyond expectation. Africa and Asia, though distant and unfamiliar for most people, had always been known about” (Watson 442).

Role of Math in Scientific Revolution: Why Europe?

• Europe jumped ahead of other civilizations in mathematics

• Arab scholars had no incentive to play with interpretations of data, because a change in understanding could be a threat to religion

• Toby Huff argues that Arab astronomers had all the observations needed, but did not make the connection to the heliocentric model of universe

Math and Science continued

• Chinese and Arabs never developed the = sign• Chinese never believed that empirical

investigation (making investigation based on what senses could perceive) would explain the world around us

• Scholarship in the Muslim world and China was tied to a central authority

• Independence of science from the state allowed Western scientists to be organized in their own way, and skeptical

Why Astronomy?

• In the sixteenth century, scholars believed that “The whole fate of life and everything else was tied up with the movement of the heavens: the heavens ruled the earth. Therefore, whoever understood how the heavens worked, would understand everything on earth.” (Watson 476)

• In other words, the heavens would reveal the mind of God.

Copernicus

• Highly educated in many subjects• Intensely curious• Poor at making accurate observations• He was clever and creative at conceiving of ideas, though.

He realized that the complexity of Ptolemy’s explanation of the universe did not match what else was observed in the natural world.

Copernicus’s Contribution

• 1. There is no center of all circles for heavenly bodies

• 2. The earth is not the center of the universe• 3. The sun is the center of the universe• 4. By mathematical equations, the distance

from the earth to the sun is much less than the relative distance of the height of the firmament, or the distance of more outlying stars and galaxies

Reaction to Copernicus’s Ideas• He sent his book to the

Pope in 1530, who circulated it among his scholar-friends (Landry website on Copernicus)

• Pope recommended that it be printed

• It was not until 1615 that someone objected that Copernicus’s ideas created problems for Christian theology

Tycho Brahe• Danish scientist who came from a

wealthy family• Danish government gave him an

island where he could set up a laboratory, complete with observatory

• Brahe’s contribution was voluminous records of accurate astronomical observations

• In 1599 Brahe left Denmark to work as chief mathematician for the Holy Roman Emperor in Prague Brahe’s lab on the island of

Hveen

Johann Kepler

• Kepler had been an assistant to Brahe• He began with Brahe’s observations, and eventually

abandoned the idea of trying to explain one system for all the planets

• He focused on Mars, and discovered its elliptical orbit; this discovery was applied to other planets, and matched with observations

Implications of Elliptical Theory

• Elliptical orbits led to the study of gravity and dynamics (physics)

• This theory completed refuted Aristotle’s theory of the planets based on hollow concentric crystal balls

Kepler’s Further Discoveries

• Calculated orbits, speeds, and distances of other planets relative to the sun

• Found that the period of rotation and distance from the sun was in the ratio of the square to the cube

• Found a new harmony and pattern in the universe

Galileo

• Professor of mathematics and military engineering, which gave him access to a secret weapon captured from the Dutch—the telescope (used to spy on enemy armies)

• Galileo pointed it at the sky and discovered many more stars than the 2,000 visible to the naked eye

• Galileo saw moons around Jupiter, which were so far away from the Earth that he believed they could work as a measure of absolute time

• This new measurement would allow navigators a new way to find longitude at sea

Galileo and Military Inquiry

• Galileo’s study of the trajectory of cannon balls caused him to study moving objects

• Study of pendulum and swing led to Galileo’s square root law

Galileo’s Writing

• His dialogue written to explain the Ptolemaic and Copernican views of the universe were perceived to mock the Pope—Galileo was jailed by the Inquisition

• In jail he wrote The Two New Sciences, which showed that the path of a projectile is a parabola. Parabola is related to cone and ellipse, which tied together mathematical explanation of observations of ballistics and astronomy.

Isaac Newton

• Spent much time alone as a child in the countryside• Forced to return from Cambridge to his home in

Lincolnshire because of the plague of 1665• In solitude at his country home he made many of his

foundational discoveries

Newton’s Contemporaries: A Brain Trust

• He was familiar with the work of Galileo• Other scholars of his time include: • Gottfried Leibniz (1646-1716)• Nicholas Mercator (1620-1687)• Rene Descartes (1596-1650)• Pierre de Fermat (1601-1665)• Blaise Pascal (1623-1662)• In this time span, the following advances were made in

Math: symbolic expression, the use of letters, mathematical series, new ideas in geometry, logarithms, and calculus

Newton and Calculus• “The calculus is essentially an algebraic method for

understanding (i.e., calculating and measuring) the variation in properties (such as velocities) which may be altered in infinitesimal differences, that is, in properties that are continuous. In our study at home we may have 200 books or 2,000, or 2,001, but we don’t have 200 ¾ books, or 2001 ½. However, when traveling on a train its speed can vary continuously, infinitesimally, from 10 to 186 mph. The calculus concerns infinitesimal differences and is important because it helps explain the way so much of our universe varies” (Watson 481).

• For a time, Newton’s ideas were so advanced that he was the only person who could “differentiate” or calculate the area under a curve.

Gravitation

• Newton’s study of Galileo’s work on pendulums led him to the idea of centrifugal force.

• Centrifugal force led to the idea of the idea that gravity holds the planets in place.

Newton on Optics• Newton believed his more important work related to the study of light• He studied light by examining what happened to it as it passed through

prisms, manipulating it further with mirrors and lenses• Prior to Newton, people believed that light came from human eye to the

object observed• Newton realized that light was more like a projectile, bounced off of the

viewed object

Meet Someone New. . .

• 1671 French astronomer Jean Picard (no relation to Star Trek!) went to the Danish island of Hveen where Tycho Brahe had his laboratory. The lab was in ruins, but he met a young man there who was self-taught about astronomy, Olaus Römer.

• Picard took Römer back to France with him, where Picard taught him more formal processes for studying astronomy.

Römer continued• Römer began examining the observations of

Galileo about Jupiter’s moons, and he discovered that their speed was not constant, as Galileo had recorded. The speed of the moons was relative to Jupiter’s distance from Earth.

• Römer concluded that light has a speed, which idea was accepted by people who had had experience with the speed of sound on battlefields, where they could see a cannonball before they could hear the report from the cannon.

A Genius Generation

• Isaac Newton said, in comparing himself to Descartes,

• “If I have seen farther than Descartes, it is because I have stood on the shoulders of giants.” (Watson 484)

Newton Descartes

Bibliography

• Landry, Peter. “Nicolas Copernicus.” Blupete: Biographies, The Scientists. Feb. 2004. 27 Nov. 2007. <http://www.blupete.com/Literature/Biographies/Science/Copernicus.htm>

• Watson, Peter. “Ideas: A History of Thought and Invention, From Fire to Freud.” New York: Harper Perennial, 2005.