history 3a final

induction

• bacon’s method: particular instances → general principles

• easily proven wrong (any contradiction), but only way that interacts w/ the world to find new info

house of salomon

• fictional research institution and utopian brotherhood from bacon’s new atlantis

• collective research society, everyone had their own role

• designed to study/experiment/invent for benefit of humanity

the royal society

• founded 1660

• emphasized baconian experimentalism + empiricism 

  • model for the state to avoid civil wars, opposite of dogmatism, accepted diverse ppl/views

• did NOT like math/rationalism/dogmatism/certainty

the invisible college

• royal society started as unorganized, informal philosophical gathering

• purpose was to study nature but also escape from violence/intolerance to safe haven

  • became a cause to show how ppl w/ different beliefs can work together wo fighting

  • show that seeking common ground + working together benefits everyone

• certain ppl added for social legitimacy + royal support

robert boyle

• prominent member of royal society, explained composition of air w/ air pump + gas laws

• wrote abt mechanical philosophy (god started motion but things move according to their own laws)

• systematic experiments but still avoided certainty (anti-dogmatic RS)

thomas hobbes

• political philosopher/mathematician/rationalist, founded his philosophy on euclidean geometry (no dissent/leviathan state)

• criticized royal society for uncertainty of their results + for allowing dissent (will lead to chaos)

• fellows hate hobbes’s approach as intellectual dead end in science + dangerous approach to state

  • fought w/ leaders of royal society, esp john wallise + robert boyle

• never elected as royal society fellow despite reputation as mathematician/natural philosopher

micrographia

• 1665, written by robert hooke (RS), detailed observations w/ microscope

“letter on light and colors”

• sent by newton to RS in 1672

• theory of light + color (light made of a certain few colors)

  • cannot split colors by running thru prism again– each color is pure

• RS impressed by his experimentation but didn’t like his certainty, wanted to avoid dogmatism even w/  comprehensive evidence

“I think, therefore I am”

• cartesian doubt— reason thru everything to find truth

• cannot doubt one’s existence while thinking/doubting, so one must exist

la geometrie

• descartes’ world is mathematical/geometrical

• book (1637) develops a mathematics to describe such a world

  • every geometric figure in the world can be described thru an algebraic equation

• analytic geometry: defined by relative positions, not axes

isaac beeckman

• introduced descartes to atomism and “physico-mathematical” approach to science

• liked his hypotheses abt particles + mvmts but felt it was too indeterminate (no proof), wanted absolute certainty

discourse on the method

• 1637, detailed descartes’ method of finding truth thru systematic doubt

  • divide into as many parts as possible, simple → complex, only accept what there is evidence for

clear and distinct ideas (descartes)

• foundation of all certain knowledge 

• clear: any idea that is immediately present and fully manifest to a focused mind

• distinct: completely separated from all other ideas without any ambiguity

  • any idea both clear + distinct is definitely true (guaranteed by god)

extension (descartes)

• the fundamental property of physical matter to occupy, or exist in, physical space

• matter = extension in space

  • no other qualities (color, heat, etc)

• res extensa: extended substance (physical body/world), takes up space but cannot think

• res cogitans: thinking substance (mind/soul), thinks but takes up no physical space

vortices (descartes)

• bc all space is matter, motion cannot leave behind empty space

  • space vacated by matter is simultaneously filled w/ matter

• consequently natural motion in the world is a vortex

  • planets carried around in vortex around the sun, all other stars also centers of similar vortices

Uraniborg and Stjerneborg

• revolutionary, custom-built astronomical observatories built by tycho brahe (1570s) on his gifted island; above + below ground

• predated telescopes, so contained giant, complicated instruments

• collected measurements w/ large team of assistants

nova of 1572

• according to aristotelianism, novas were considered atmospheric phenomena

• tycho measures “new star’s” parallax + finds none against background stars

  • therefore must be further than moon, in the heavens— heavens do change after all

comet of 1577

• also seen as atmospheric phenomena in aristotelianism

• tycho finds 0 parallax against background stars again— comets move thru heavens, past moon

  • shatters crystalline spheres idea of heavens, planets float in empty space

• discoveries grant him reputation + island gift from king of denmark

parallax

• apparent shift in an object’s position when viewed from two different lines of sight (depth perception)

• moon has parallax bc relatively close to earth, anything beyond that (heavens) has none

  • ex supernovas, comets, planets, etc

mysterium cosmographicum

• kepler, 1597— believed he’d discovered the most fundamental geometric framework that god used to create the world

• five platonic solids– 3d symmetrical objects w/ identical symmetrical sides

  • place one inside the other, draw circles around each–  planetary orbits fit in the circles

• cute model but ultimately wrong, eventually discovered that orbits were ellipses, not circles

astronomia nova

• kepler, 1609; included mars’ orbit + his first two laws of planetary motion

• first law: shape of orbit of all planets is an ellipse, w/ sun as one of its foci

  • goes against established tradition of perfectly circular orbits, but fits w/ kepler’s belief that god created world according to geometrical pattern

• second law: areas swept by a planet in a given time are always the same regardless of its speed

• 3rd law published 1619: harmonicus mundi (musical harmonies of the heavens)

  • third law: ratio between the square of the period of a planet and its average distance cubed is constant bw all planets

Kepler’s areas law

• an imaginary line connecting a planet to the Sun sweeps out equal areas in equal intervals of time

  • sun’s power greater the closer the planets are, planets move faster the closer they are to the sun

orbit of mars (kepler)

• took him 8 yrs to calculate bc was still trying to adhere to circular standard but actually ellipse

• based on tycho’s v accurate data + followed his strict margin of error

law of falling bodies (galileo)

• in vacuum, all objects dropped form same height will fall at same constant acceleration, regardless of mass/shape/weight

  • gravity causes falling at constantly increasing speed, not steady speed based on weight (aristotle)

doctrine of the two books (Galileo)

• galileo’s argument that religion + science were compatible

• god’s word contained in both Book of Nature + Book of Scripture— cannot contradict each other

  • if appear to conflict, precedence given to nature bc she doesn’t lie

  • bible simplifies things for human understanding + not meant to convey scientific info

cardinal bellarmine

• 1542-1621

• 1615 letter says that motion of earth contradicts bible

  • copernicanism acceptable as hypothesis, not truth

• willing to concede that interpretation of scripture might change, but only catholic church has authority to decide that (counter-reformational principle)

• 1616: sent galileo formal summons to deliver warning abt heliocentric model

sidereus nuncius

• galileo, 1610

• announced his telescopic discoveries

  • moon’s surface

medicean stars

• four largest and brightest moons of Jupiter (io, europa, ganymede, callisto)

• discovered by galileo in 1610, named in honor of his patron, cosimo II de medici, grand duke of tuscany

mountains of the moon (galileo)

• published sketches in sidereus

• disproved aristotelian notion that heavenly bodies were perfectly smooth + fundamentally un-earth-like

  • if moon has geography like earth, earth is more likely to be another planet moving thru space

“[The Universe] is written in the language of mathematics”

• 1623 treatise Il Saggiatore 

• book of nature cannot be understood unless one first learns its language: triangles, circles, and geometry

  • reliably describe, model, predict the behavior of the cosmos w/ math

the council of trent

• 1545-1563, council held by catholic church in response to protestant reformation

• counter-reformation: church reemphasizes its role as conduit of divine grace + source of religious authority

• insists its teachings are superior + true, desseminate thru jesuits

salviati

• galileo’s mouthpiece in dialogue on the two chief world systems, 1632

• conversation on ptolemaic + copernican system bw three friends

  • salviati, simplicio (ptolemaic/aristotelian system, simpleton), sagredo (wise arbitrator)

• book is clear advocacy of copernicanism– salviati (+ sometimes sagredo) scores all convincing points

urban VIII

• galileo dedicated assayer (book on atomism), 1623 to pope urban viii

  • believed w/ friendly pope could go back to copernicanism

• initially galileo’s patron, permitted him to write abt heliocentrism as mathematical hypothesis

  • turned against him after galileo seemingly mocked him in his dialogue (simplicio)

“annus mirabilis” (newton)

• 1665-6 (plague year), newton achieved most of his most important discoveries

  • method of fluxions + fluents (calculus), composition of light, centripetal force formula (mv2/r), inverse square law

inverse square law

• gravitational force between any two objects is directly proportional to the product of their masses + inversely proportional to the square of the distance between them

principia mathematica

• 1687, very impressive + comprehensive scientific work

• covers wide range of phenomena (trajectory of projectiles, motions of comets, etc)

  • all derived from a small number of assumptions precisely + mathematically

  • done mostly thru experiments + mathematics

“de Motu”

• sent halley de motu corporum in gyrum, 1684

• shows that inverse square law of attraction results in ellipse (elliptical orbits also prove the law)

• path would be some conic section (parabola, hyperbola), becomes ellipse below a certain speed

  • then derives kepler’s three laws from the inverse square law

newton’s second law of motion

• acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass

  • explains how much force is required to change the speed or direction of an object— F = Ma

absolute space

• an infinite, immovable, and unchanging void that exists independently of any physical objects

  • served as stationary reference frame for the universe

• prior to matter + independent of it, pervaded by force of gravity

universal gravitation

• every body in the universe attracts every other body in direct proportion to their mass + inverse proportion to the square of their distance

  • key assumption in principia, explains terrestrial gravity + planetary motion