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  • Lorenzo the Magnificent

    ordered Greek manuscripts, like Plato, to be translated into Latin and Italian


    Plato liked math and believed that math is the idea itself, not the appearance

    Hermes Trimegistus

    Platonist who made up numerology, magic, and astrology (provides money for astronomers)


    eventually every paradigm has questions it is unable to answer; Ptolemaic calendar stops working; usually, the solution is to add more epicycles; Clement V calls a meeting to mathematically adjust the model because they don't believe there are that many epicycles


    cathedral clerk; uncle was a bishop (nepotism); neo platonist - convinced math shows truth; revises ptolemaic model and convinced whole model needs to be fixed because its so confusing

    Copernican Universe

    resurrects Aristarchus' sun centered universe with earth in third position; retrograde motion is a matter of appearance (earth moves twice as fast as mars); earth turns once on axis per day and once around sun per year; Problem : still no quid; he's not denying the need for a quid he is just reversing the order; he's changing the order from quid -> idea to idea -> quid

    Gutenberg Printing Press

    anything anyone says can be put into print; offices for censorship are created

    Holy Office of Inquisition

    Roman; examines IDEAS to see if they are heretical; run by Dominicans

    Sacred Congregation of the Index

    in charge of censorship; rounds up copies of heretical writing and burns then, as well as puts them on the list (=the index) of books that the faithful should not read

    End of Copernicus' Life

    Copernicus doesn't put his ideas into writing until the end of his life; a volume of his book, "De Revolutionibus orbium caelestium" ("concerning the revolutions of heavenly spheres") is placed into his hands on his death bed

    Ossiander Preface

    written by Andreas Ossiander; enough to convince the censors that the book is okay; says sun-centered universe is hypothetical for calculation; it is a hypotheses not asserted to be true; Copernicus does not actually agree;

    Dedication to Pope Paul III

    flattery; justifies his move and takes shots at Aristotelians; Copernican model is same as Ptolemaic model just simpler and more precise; still assumes circular movement (still has problem of things appearing closer and farther away; doesn't care whether planets move on spheres; he just cares where they are

    Introduction and Book

    not many people read it; it is basically a giant math proof for other mathematician astronomers; proves what Ptolemy said but with a different position; goes through proofs that everyone knows (horizon and ship etc.); separates diurnal and annual motion; diurnal belongs to earth alone; annual belongs to planets and us; a.) natural motion of spheres is a circle, b.) earth is a sphere, c.) natural motion of earth is a circle; the universe is huge and earth is so small that it looks like we are in the center

    Inferior Planets

    planets between earth and sun

    Superior Planets

    planets beyond earth


    superior planets; earth, planet and sun are in the same line; 6 hours after sunset, 6 hours before sunrise


    planet and earth are at a right angle from the sun; superior planets


    inferior planets; can't see it because it's below the horizon; once every six months; right angles; similar to quadrature

    F = frequency; T = period;

    frequency = 1/T orbits per year


    orbit per year


    in earth years; earth's period is 1

    Tyco Brahe

    Dane; German Protestant; best naked eye astronomer in Europe; minor nobility; convinces king to build him an observatory in the Baltic; builds a wall to act as a horizon; spent 15 years here completing research

    Brahe's discoveries

    universe DOES change!; stella nova ("new star") : burns day and night, shows no parallax because its very far away; super nova : an exploding star, way far out among the fixed stars; comets : previously people said it was only between the earth and the moon, but he said it was far away then moved closer and showed parallax; no crystaline spheres

    Brahe's Universe

    earth centered; sun orbits the earth and all the planets orbit around the sun; no one believed him


    after Brahe's falling out with the king, Rudolph, the holy roman emperor gives him a job because of a horoscope that came true predicting a successful campaign against the turks

    Johannes Kepler

    hired as Brahe's assistant; Lutheran; poor German; left Lutheran seminary; good at math; copernican; he had the job of computing the orbit of mars with Tyco's data; took way longer than estimated; within hours of Brahe's death, steals his data;

    Kepler's discoveries

    orbits were ellipses; no one believes it

    Kepler's Laws of Planetary Motion

    planetary orbit is an ellipse with the sun at one focus; an imaginary line drawn from the sun to any planet will sweep out equal areas in equal time; (Ta/Tb) squared = (Ra/Rb) cubed (*a = planet 1; b = planet 2; r = radii; T = period*)

    Kepler's books

    includes his laws; thinks he can solve the universe with numbers; first to write science fiction about a trip to the moon


    sun is somehow influencing the planets; calls the sun the "anima matrix" = motor soul; sun exerts force on planets - the closer a planet the more force and vice versa; he is getting closer to the idea of gravity

    Kepler's death

    he is almost completely unknown

    Galileo Galilei

    most famous mathematician astronomer in Europe; musician; studied at university of Padua ( a college of math and medicine ); gets degrees, teaches, and casts horoscopes; not a good teacher because he wants to do research; interested in motion and wants to use the new math to answer questions like "how fast?"; neo platonist

    Galileo's discoveries

    mass has nothing to do with the rate at which things fall; moon is not smooth; light of sun hits top of moon first then spreads to valleys (just like the earth); believes things fall the same way on the moon as they do on the earth; we can see the moon when there is no sun because if you are standing on the moon, the earth reflects the light of the sun; describes the Milky way as "the galaxy" (=big collection of stars; stars are at an immense distance because they still twinkle through the telescope just appear slightly bigger; planets are spherical like earth; 4 moons around Jupiter, they all like on same line sometimes on one side of Jupiter, thus they revolve around it, this is important because it implies that not everything revolves around the earth; Jupiter is seen as the model of the Copernican universe (but its not a quid demonstration)

    inclined plane

    he put ball bearings at the top and watched them roll down; set up bells to measure time (more and more rings as balls went down);

    Galileo's protection

    lived in Padua; Padua belonged to Venice; Venice had no relationship with the papacy


    Galileo finds a Dutch spy glass and makes a better one; shows it to Venetian hierarchy and they buy some; makes himself a really nice one; he has invented the telescope

    Sidericus Nuntius

    starry messenger; 40 page pamphlet; written in Italian; popular; dedicated to prince Lorenzo de Medici because Galileo wants a job

    Kepler and Galileo

    kepler requests a telescope and sends Galileo the book "Astronomica Nova" which says that orbits are elliptical; galileo ignores this;

    Inquisition and Copernicus

    investigates the copernican system; contradicts scripture; by saying the universe is one way and not another is saying God can only make it one way and it limits the power of God; after "The Dialogue" incident Galileo is summoned to Rome and examined without torture; he says he doesn't remember being told not to defend Copernican system; given 2 choices - 1. publicly disavow Copernican system, 2.) go to prison for life; so, he kneels and recants; rest of his life is under house arrest

    "The Dialogue"

    Galileo was told not to defend Copernican system so he gives both a "fair hearing"; involves three characters - 1. salviati, an apologist for the Copernican system; 2. simplicius, an apologist for Ptolemy/Aristotle; 3. Sagredo, a neutral and honest judge; Salviati gets the good arguments and presents the quid - the motion of tides is caused by motion of planet on axis (WRONG); kepler writes him a letter saying this is wrong; approved by censorship and translated into many languages; mainstream and had little math; pope realizes that his opinion comes out of simplicius' mouth; the pope orders cessation of book's publication and fires head of Sacred Congregation of the Index;

    "De Motu"

    galileo writes while under house arrest; on mechanics; smuggled out after death and published in Holland; available everywhere except Italy

    Isaac Newton

    sums up everything that happened in past century; gives his name to new paradigm;used mathematical equations to define the way things happened; invented calculus; did work in 18 months during early 20s; dabbled in alchemy; wrote more on that than physics; didn't believe in divinity of christ and wouldn't swear by 39 articles of faith; Oxford gave him a position anyway


    written by Newton; mathematical principles of natural philosophy; considered by Einstein, to be greatest work of physics ever; science = math; used geometry even though he had calculus; atoms and void; difference between mass and weight; weight is a force and changes with gravity; mass doesn't change

    momentum = P

    P = mass (velocity)


    innate property of matter to resist change in velocity; vis insita; more mass, more inertia


    only on something as long as its in your hand, then it moves by inertia and is pulled back by gravity; he thinks gravity and magnets attracting each other are the same (hes wrong); gravitational pull cannot make circles, it makes an ellipse; he doesn't know what gravity is and neither do we; "I do not show hypotheses"; how can there be force if things are not touching

    Euclidean space

    straight lines

    absolute space

    space with nothing in it; but there is stuff in it so space = distance between two things; one can only see absolute space and time from outside of space (God)

    Newton puts God "out of work"

    the universe runs itself with laws; god sees things at rest and in motion; we only see them relatively (wrong - time and space are not absolute)

    Newton as a deist

    religion of the enlightenment; Newton was partly responsible for this religion which claimed that God is watching space and time and can perform miracles to mess with the laws if he wants

    movement and Newton

    if you are sitting on a ship, you are not moving with relation to the ship, but you are moving with respect to the water

    Newton's laws of motion

    1. something with matter resists change in velocity - inertia!; more mass, more inertia; a property of things, not a force; 2. F = ma (force = mass (acceleration), 3. for every action, there is an equal and opposite reaction;

    Rules of Reasoning and Philosophy

    1. the simplest equation explaining phenomena is the truth 2. same things have same causes (light bulb vs. sun) 3. whatever the laws of science are, they apply across the entire universe (if there are other intelligent beings, they must come up with same equations); 4. scientific method - arrive at truth by induction, for a testable hypothesis, science cannot say anything is absolutely true

    Demonstratio Propter Quid

    modern science still requires it, but approach is different; something is proposed and accepted as true then the search for the quid begins

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