SCIENTIFIC REVOLUTION COURSE NOTES

These notes originated in a course I taught at the American Museum of Natural History’s Hayden Planetarium from 2002 through 2005. My web page there has long since disappeared into the ether(net), so I’m replicating my course outline here as a sort of misguided public service.

Description
Sir Isaac Newton once wrote, “If I have seen further, it is by standing upon the shoulders of giants.” Scientists throughout history have extended the knowledge of their predecessors by tiny increments or by leaps and bounds. From the ancient Greeks to Einstein’s peers, we will trace the paths of paradigm shifts that led to the fundamental ideas of physics. Join us as we climb up on the shoulders of revolutionaries!

This isn’t quite the final version of the web page, but it adds a significant bit to what had been here earlier. First off, take a look at a short bibliography, which will receive more attention as soon as the rest of this page is done. Also, I wanted to direct your attention to a couple science timelines that I like: a fairly exhaustive one as well as a more terse, but easy-to-read synopsis that focuses more on physics and astronomy.

I. What is a “scientific revolution”?

1. In an important sense, there has been only one scientific revolution, the Scientific Revolution:
   • Took place from the 15th to the 18th Centuries, roughly
   • Initial articulation of the scientific method
2. However, the ideas we consider “revolutionary“ occur much more frequently
3. Thomas Kuhn’s The Structure of Scientific Revolutions (1962)
   • Introduces the idea of a “paradigm shift”
   • “To be accepted as a paradigm, a theory must seem better than its competitors, but it need not, and in fact never does, explain all the facts with which it can be confronted”
   • Typically science proceeds incrementally, refining an existing paradigm, but occasionally, anomalies cause a reconsideration or a restructuring of the dominant paradigm
4. Also, revolutions have social as well as scientific dimensions:
   • Paul Johnson quote
   • C.S. Lewis quote
5. This course will tackle the idea of revolutions from a social and scientific perspective. Along the way...
   • Question received knowledge about the functioning of science and the role of certain key characters
   • Reveal flaws in our inherited mythology about science
   • Quote about falling weights sounds like Galileo, but it’s not

II. Observation and Theory in the Ancient World

1. What do we see in the sky?
   • Sun, stars, and everything else rise and set once every 24 hours, so-called “diurnal motion”
   • Moon goes through phases — from new to first quarter to full to third quarter to new — once every month
   • Different stars appear in the sky at different times of year, linked to different seasons
   • Planets wander through the sky, mostly along simple paths, but sometimes changing directions and executing loops
   • Eclipses sometimes blot out the sun and the moon, in a pattern that proves challenging to predict
   • Some events defy prediction — comets, for example
2. Sumerians (3000 B.C.) and Babylonians (1700 B.C. and on)
   • Cuneiform tablets used for detailed record-keeping — in business, accounting, and astronomy
   • Develop number system based on sixty, from which we get our degrees, minutes, and seconds
   • From time of Hammurabi onward, celestial and planetary records fairly complete
   • And accurate — the length of the year known to within four minutes
   • Eventually, they develop predictive capabilities, similar to the manner in which we calculate tide tables, even today
3. Greek philosophers emphasize theoretical speculations over observations
   • Plato quote about observing the sky
4. Thales (624 - 547 B.C.) predicts a solar eclipse
5. Pythagoras (569 - 475 B.C.) and his followers introduce a bit of mathematical mysticism into the works
   • “Music of the Spheres” becomes an influential concept in later thought, influencing everybody from Greek philosophers to Kepler
   • related to concepts of ratios and rationalism
   • recall the Pythagorean ideas about pitch and ratios — e.g., halve the length of a string, and its pitch will go up one octave
   • and in case you don’t believe me, there really is a short film Donald in Mathmagic Land
   • Surmises that the phases of the moon are caused by reflecting the Sun’s light
   • Postulates idea of circular motion — centered on the “central fire,” which is not the Sun
6. Anaxagoras (499 - 427 B.C.) postulates that lunar eclipses are caused by Earth casting a shadow on the Moon
7. Plato (427 BC - 347 B.C.) calls for mathematical exploration of the heavens
   • All celestial bodies are spheres
   • Sublunary versus superlunary; perfection versus imperfection
8. Plato’s student Eudoxus (408 - 355 B.C.) refines the mathematics
   • Develops a system of nested spheres to account for motion of the Sun and planets
   • Discovers 18-year cycle of eclipses — the so-called Saros cycle
9. Aristotle (384 - 322 B.C.) develops unified set of laws that describe the behavior of the Universe
   • Sublunary world made up of four elements — earth, water, air, and fire
   • Superlunary regions made of a fifth element — the quintessence or aether
   • All elements have their natural place in the universe
     • Natural motion of the sublunary elements is toward the center of the universe
     • Natural motion of the superlunary element, aether, is circular motion around the center
   • Earth lies at the center of the Universe
   • Earth’s sphericity is already well-established, but Aristotle articulates reasoning:
     • Only at the surface of a sphere do all falling objects seek the center by falling straight down (not because of gravity, of course, but because of the natural inclination of objects to seek their absolute place in the Universe)
     • Perspective on constellations changes as one travels north or south
     • During lunar eclipses, Earth’s shadow appears curved
   • Planets revolve around the center of the Universe — from the Moon, closest to the Earth, to Saturn, farthest away
   • Outermost sphere of fixed stars represents the boundary of the Universe
10. Eratosthenes (276 - 194 B.C.) calculates the size of the Earth
    • Observing the sun at noon in Alexandria and Syene, he notes that while the sun appears directly overhead in Syrene, 800 kilometers south of Alexandria, it casts a shadow in Alexandria
11. Aristarchus (310 - 230 B.C.) proposes a Sun-centered system
    • Rejected for many reasons:
      • If Earth spins once every 24 hours, why doesn’t everything fly off?
      • If Earth revolves around the Sun, then the stars must be very far away for us not to observe parallax
      • Aristotle’s system very well grounded, so to speak
12. Hipparchus (190 - 120 B.C.)
• cataloged 850 stars, which also originated the system of magnitudes used by astronomers today
• discovered precession of the equinoxes, using observatons from Aristyllus and Timocharis, c. Third Century B.C.
• measured distance to the Moon
• proposed circular planetary orbits
• suggested that the change in brightness of planets implies that their distance varies
13. From the Third Century B.C. to the Fourth Century A.D., Alexandria remains the center for science research
    • Eratosthenes, Aristarchus, and Hipparchus all worked there
    • but the chain of teachers and pupils becomes broken after Hipparchus
    • researchers working in isolation produce little results
    • founding of Constantinople in Fourth Century A.D. shifted intellectual environment further away from Alexandria
14. Claudius Ptolemy (A.D. 85 - 185) systematizes mathematical astronomy
    • produced a work on astronomy known by its Arabic title, the Almagest, although its actual title is Mathematical Syntaxis
    • also composed a lengthier work on astrology, the Tetrabiblos

III. From Ptolemy to Copernicus

1. What about the Romans?
   • the Romans valued Greek learning but placed a greater emphasis on grammar, rhetoric, and logic (which together came to be known as the “trivium”) over arithmetic, geometry, astronomy, and musical theory (known as the “quadrivium”)
   • most literate Romans also read Greek, which eliminated the need for translating the works
   • reduced interest in astronomical topics, as well as the lack of translations of Greek works, left a paucity of material for Medieval scholars to study
2. Islam, on the other hand, inherited regions conquered by Alexander, thus an area already Hellenized in population and culture
   • the literature existed, as well as means to translate it
   • eventually these translations would re-enter Europe, most often through Spain and Sicily
   • note, however, that most translations were also commented upon
   • Hunain ibn Ishaq translated many works in the 9th Century
     • “For the first six books [of a work] only a single manuscript, and besides a very faulty one, was at my disposal at the time. I was therefore unable to produce these books in the manner required. Later I came across another manuscript and collated the text with it and corrected it as much as possible. It would be better if I could collate a third manuscript with it if only I were fortunate enough to find one.”
   • Ibn Yunus (A.D. 950 - 1009) compiles extensive tables of astronomical observations and formulae
3. So what about Medieval Europe?
   • the works of Hipparchus, Ptolemy, and others were unavailable
   • a short list of what survived:
     • Plato’s Timaeus
     • Pliny’s Natural History
     • The Marriage of Philology and Mercury
     • Commentaries of St. Ambrose and St. Augustine
   • Medieval instrumentation showed some improvements, however:
     • obviously, they had no telescopes to work with, but...
     • around the 10th Century, the armillary sphere, Jacob’s staff, and astrolabe all made an appearance
   • Nicole d’ Oresme (A.D. 1323 - 1382) questioned many of Aristotle’s ideas: he redefined the concepts of “time” and “position,” proposed idea of air resistance, and also proposed the idea of a rotating Earth, then rejected it
   • Nicholas of Cusa (A.D. 1401 - 1464) showed a great interest in the idea of infinity and limits (and limits on knowledge)
     • God’s abilities are infinite; therefore, humans can never attain a true knowledge of God, and any idea of God must be incomplete
     • a few of Cusa’s other ideas:
       • the Earth goes around the Sun
       • stars are other suns
       • space is infinite
     • while it’s tempting to see these ideas as prescient, Cusa also submitted them for consideration without any evidence to support them
     • engaged in speculation, but
     • Cusa also wrote about—and recognized the need for—calendar reform
       • the Julian calendar “slips” relative to the seasons—one day for every 129.3 years
       • so who cares?
       • well, it’s terribly important for the calculation of Easter, which is related to both the spring equinox and the lunar calendar
       • if your year is off relative to the spring equinox, so is Easter
       • thus, the Church cares about the calendar, and eventually, the Church revises it (but not until the late 16th Century)
   • Johannes Regiomontanus (A.D. 1436 - 1476) attempts to restore astronomy to its classical footing
     • contributes to major advances in trigonometry
     • has access to original Greek versions of Ptolemy’s Almagest
     • establishes observatory at Nuremburg, where he observes Halley’s comet in 1472 as well as several eclipses of the moon
     • publishes ephemerides—basically a big, boring book of tables that lists the locations of celestial bodies for a series of dates (very necessary for the practical use of the models of Ptolemy and later Copernicus and Kepler)
     • he is also asked to help reform the calendar but dies before he can join in the task
   • Important Aside: The Printing Press
     • when Regiomontanus publishes his ephemerides, he utilizes an innovation in Western technology—the printing press!
     • it’s almost impossible to know the exact effect that printing had on the process of doing science in the 15th and 16th Centuries, but it would seem to have given scientists more time to focus on problems in their fields: relieved of tedious tasks such as copying tables, they would presumably have more time to think about more interesting matters
     • printing certainly broadens the contact between individual researchers
     • also, printing is a corrective process: a handwritten copy introduces errors to a text, but printed volumes correct problems from previous editions
   • Nicolas Copernicus (A.D. 1473 - 1543) publishes De revolutionibus orbium coelestium (On the revolutions of the heavenly spheres) in 1543, basically posthumously
     • a little of his background:
       • he studied law at Krakow—but also mathematics, astronomy and Greek!
       • visited Italy and loved it, stayed there to study medicine as long as he could, but his hometown paid for his education and wanted him back
       • so he spent most of his days as the Canon at Frauenburg, on the outskirts of Roman Europe, in northeastern Poland
       • probably began De revolutionibus in 1514, but he really only got to work on it with the help of his student Rheticus in the 1530s
     • but anyway,...
     • famously postulates that planets revolve around the Sun, not Earth
     • meets Ptolemy on his own turf by presenting mathematical, rather than purely philosophical, arguments
     • but De revolutionibus maintains many Ptolemaic qualities
       • still uses spheres—in fact, Copernicus expressly states that his motivation is to preserve uniform circular motion
       • the epicycles and deferents are still there, too
       • plus, Copernicus’s predictions are no more accurate than Ptolemy’s; however, they provide an alternative set of predictions
     • the effect of printing on Copernicus is hard to gauge, but we know the following:
       • Copernicus purchased copies of various books as a student: Euclid, Alfonsine Tables, and Regiomontanus’s tables
       • when he was a student, he would have had access to one copy of Ptolemy’s Almagest, but when he died, he had three copies!

IV. From Copernicus to Newton

1. Tycho Brahe (A.D. 1546 - 1601) provides accurate and extensive observations for future astronomers
   • Invents instruments to improve accuracy of observations
   • Observes planets throughout their paths and not just at "interesting" points
   • Observations of the nova of 1572 showed no parallax, indicating that it lay farther away than the Moon
   • Likewise, with the Great Comet of 1577, Brahe’s observations show it to be beyond the moon and orbiting the Sun
   • Develops Tychonic model of the universe
     • The Moon and Sun revolve around Earth, but all the other planets revolve around the Sun
     • Functionally equivalent to the Copernican model
2. Johannes Kepler (A.D. 1571 - 1630) extends Copernican ideas
• Makes Copernicus self-consistent:
• works with Brahe’s data on Mars
• publishes extremely accurate Rudolphine Tables, in 1628, based on Brahe’s data and his computational techniques
3. Galileo Galilei
   • makes significant observations with his telescope, published in Siderius Nuncius (The Starry Messenger) in 1610:
     • topography of the Moon
     • phases of Venus
     • moons of Jupiter
     • density of stars
     • point-like nature of stars
   • provides empirical basis for systemized study of kinematics

V. From Newton to Maxwell

1. Isaac Newton gathers numerous threads into a coherent picture
2. What’s So Funny about Phlogiston?
   Phlogiston Theory was popular in the 17th and 18th Century as a way to describe why things burned
   • present in all flammable materials
   • possesses no color, odor, taste, or weight
   • “phlogisticated” substances contain phlogiston
   • on being burned, a substance is “dephlogisticated”
   • ash of burned material is the true material
   But this hints at a fundamental question: What are the inherent properties of matter?
3. Who Discovered Oxygen?
   Candidate Number One: Joseph Priestley
   • proponent of Phlogiston Theory
   • inventor of Priestley’s Tub
   • the basic idea behind his experiments:
     • to isolate a gas emitted when a substance is burned or heated or combined with another substance
     • many experimenters use similar methods around this time
   Candidate Number Two: François Lavoisier
   • proposes Conservation of Matter
   • dismantles phlogiston theory
   • beheaded in 1794 for misuse of funds during the Revolution
   In 1775, Priestley isolates “dephlogisticated” air
   Also in 1775, Lavoisier isolates “air itself entire”
   But from 1777 onward, he sees oxygen as atomic “principle of acidity” which formed a gas when united with “caloric” heat
   Thomas Kuhn points out that “the principle of acidity was not banished from chemistry until after 1810, and the caloric lingered until the 1860s. Oxygen had become a standard chemical substance before either of those dates.”
4. Conservation of Matter
   “Nothing is created, either in the operations of art or in those of nature, and it may be considered as a general principle that in every operation there exists an equal quantity of matter before and after the operation; that the quality and quantity of the constituents is the same, and that what happens is only changes, modifications. It is on this principle that is founded all the art of performing chemical experiments; in all such must be assumed a true equality or equation between constituents of the substances examined, and those resulting from their analysis.” — Antoine Laurent Lavoisier (1785)
5. Electricity and Magnetism
   • the phenomena had been known since ancient times
     • Greeks knew about static electricity and magnets
     • lodestones (magnetite) used for amusement and for ceremonial purposes as well as for navigation
   • In 1600, William Gilbert publishes De Magnete
     • proposes that Earth is magnetic
     • influences Kepler’s thinking
     • sets stage for action at a distance
   • Charles Augustin de Coulomb
     • studies static charges, in part using "Coulomb’s Balance"
     • derives an electrical force similar to Newton’s gravitational force: proportional to charge and decreasing with square of distance
   • In 1780, Luigi Galvani begins experiments with frogs’ legs and electricity
     • static charges cause legs to contract
     • connecting leg between brass hook and iron railing causes similar result
     • postulates “animal electricity” or the “spark of life”
     • Alessandro Volta creates a battery:
       • two different metals layered with a liquid or paste between the two (can also use a frog’s leg)
       • Volta’s battery consists of metal plates, separated by paper soaked in a salt solution, then connected in series, which is fundamentally the same design as modern batteries
       • the battery makes makes steady electrical currents (not just static charges à la Coulomb) available for study
     • Benjamin Franklin proposes fluid theory of electricity
       • may be "positive" or "negative"
       • electrical fluid repels itself and is drawn toward "common matter"
       • lightning rods draw "electric fire" from thunderclouds
       • "And from electric fire thus obtained, spirits may be kindled, and all other electric experiments be performed, which are usually done by the help of a rubbed glass globe or tube, and thereby the sameness of the electric matter with that of lightning be demonstrated." (1752)
     • In 1820, Hans Christian Oersted uses a battery and compass to show that electrical current produces magnetic field
       • electricity and magnetism linked for the first time!
     • André-Marie Ampère made precise measurements of magnetic force created by electrical current
     • Michael Faraday, the premier experimentalist of his time
       • shows that electrical current can be created from changing magnetic force, which is the basis for dynamo and electrical power generators
       • also develops concepts of “fields,” eschewing mathematical “laws,” Faraday creates pictures of his experiments and proposes lines of force that depend on strength and shape of magnet or electrical current
       • the Long Shadow of Isaac Newton
         • the idea of forces and action at a distance
         • the concept of Absolute Space
     • Joseph-Louis Lagrange develops mathematical tools independent of Newton’s
       • allows for generalized coordinates —
       • permits broad mathematical statements to be applied to a variety of particular problems
     • William Rowan Hamilton extends many of Lagrange’s concepts, mostly into optics
       • supplies mathematical basis for much of Einstein’s work, as well as for quantum mechanics
     • James Clerk Maxwell combines various observations into mathematical expression
       • the famed “Maxwell’s equations”
       • Faraday’s Reaction to Maxwell
         “When a mathematician engaged in investigating physical actions and results has arrived at his conclusions may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as I to express them so? Ñ translating them out of their hieroglyphics, that we also might work upon them by experiment.” — Michael Faraday (c. 1864)
     • Hermann von Helmholtz
       • in 1871, initiates systematic tests of existing theories of electricity and magnetism at the University of Berlin in which Maxwell’s equations come out as the clear leader
       • in 1887, opens the Physikalische-Technische-Reichstalt
6. All (Max)well and Good: Light as an Electro-magnetic Phenomenon
   • Maxwell’s equations describe electro-magnetic phenomena with unprecedented accuracy, but they also predict something new:
   • fundamentally, Maxwell’s equations are wave equations:
     • they assume the existence of an “aether” in which waves can propagate
     • electric field and magnetic field exchange energy to produce a self-perpetuating wave
     • equations predict that this wave will propagate at speed of light — what a coincidence!
   • In 1894, Heinrich Hertz conducts experiments the confirm that light is an electro-magnetic phenomenon
     • ...but introduce other problems
   • Guglielmo Marconi produces first radio in 1895
     • i.e., uses electricity to produce radio (light) waves
     • just one year after Hertz showed it could be done
7. Setting the Stage for You-Know-Who
   • This is pretty much where Albert steps in...
   • Michelson-Morley Interferometer
     • from 1878 onward, Albert Abraham Michelson invests much of his time in accurately measuring the speed off light
     • Edward Williams Morley, an American chemist and physicist, specialized in accurate quantitative measurements
     • in 1907, Michelson becomes the first American to receive the Nobel Prize for Physics
   • Ernst Mach
     • tremendous influence on Einstein
     • "No one is competent to predicate things about absolute space and absolute motion; they are pure things of thought, pure mental constructs that cannot be produced in experience."
   • Hendrik Antoon Lorentz describes relative reference frames mathematically
8. Paradigms and Paradigm Shifts
   “In learning a paradigm, the scientist acquires theory, method, and standards together, usually in an inextricable mixture. Therefore, when paradigms change, there are usually significant shifts in the criteria determining the legitimacy both of problems and of proposed solutions.”
   — Thomas Kuhn, The Structure of Scientific Revolutions (1962)
   • Kuhn’s idea of “normal science”
     • science normally operates under a single paradigm
     • when a paradigm begins to fail, solutions initially sought from within
     • as a situation becomes critical, paradigm’s rules become increasingly relaxed, to allow for more creativity
   • Scientists reject a paradigm only when another is available to take its place; otherwise, science could not operate as science
   • A sample paradigm shift can be noted after William Herschel discovered Uranus in 1781
     • the first planet not known by the ancients
     • Herschel initially proposed that it was a comet
     • another researcher, Lexell, suggests that the orbit might be planetary
     • between 1690 and 1781, at least seventeen astronomers had observed Uranus, but no one had reported the observations as a planet
     • then, in the first fifty years of the Nineteenth Century, 20 asteroids (minor planets) were discovered

VI. From Maxwell to Einstein

1. Einstein on “Empty Space”
   “I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept ’empty space’ loses its meaning.”
   — Albert Einstein, “Note to the Fifteenth Edition” of Relativity: The Special and General Theory (1952)
2. Evidence for General Relativity
   • Perihelion of Mercury advances two degrees per century (initially noted by Leverrier in 1859)
   • Light deflection by gravity: predicted by General Theory, then observed by Eddington et al. during solar eclipse of 19 May 1919, when star positions appeared to shift near the Sun’s gravitational influence
   • Gravitational Redshift, in which spectral lines appear shifted toward longer wavelengths: predicted by General Theory, then observed by Adams in 1924
3. Ideas of Space
   • Aristotle considered space to be finite and Earth-centered
     • no such thing as “empty space” — i.e., “nature abhors a vacuum"
   • Newton considered space to be infinite and unbounded
     • absolute space (i.e., absolute frame of reference) required in order to provide meaning for “acceleration,” among other terms
   • Einstein would say that space can be finite or infinite, but it’s probably finite
     • “The concept of the material object was gradually replaced as the fundamental concept of physics by that of the field.”
     • “There is no space without a field.”