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History of Science Part I Pythagoras - Newton Early mythology Babylonians, Egyptians and Hebrews (6000 BC) Earth in the center of an oyster, covered by dome Water underneath and overhead, closed in on all sides Moderate dimensions Sun, moon and stars progress across dome Universe guided by deity, explained by myth Chaldean priests (3800 BC) Timetables of the motion of the stars and the planets Stars stationary, planets move across a lane in the sky (zodiac) Computed the length of the year Astronomy and astrology, formed calenders Predicted astronomical events Observation without explanation 1 Chap I Greek Heroic Age 1. Ionian philosophers (6th cent BC) Natural causes: not concerned with deities Thales of Miletos: abstract geometry What is the basic material of the Universe? Water Anaximander: universe infinite in time and space: Raw material a substance without definite properties Mechanical model of the universe: Anaximenes: stars attached to a transparent sphere that turns around the earth 2. Pythagoras of Samos (6th cent BC) Founder of science Mathematization of experience: numbers sacred and eternal Highest form of philosophy All things have form, all form defined by numbers 2 Pitch of a note depends on the length of string that produces it Intervals in the scale produced by simple numeric ratios Reality could be reduced to number series and number ratios 16 is a square number, 12 is oblong, 6 a triangle Relations between number-shapes found Addition of successive odd numbers gives square: e.g. 1+3 =4, 4+5=9, 9+7=16, 16+9 =25 Addition of even numbers gives oblong numbers e.g. 2+4 =6, 6+6=12, 12+8=20 etc Similarily, cubic and pyramid numbers obtained. Theorem: Areas of the two smaller squares of the sides of right-angled triangle will equal the area of the larger square Could all the secrets of the Universe be revealed by numbers? Phythagoran astronomy: earth is a sphere (navigation, eclipses) Around it, sun, moon and planets revolve in concentric circles Each planet hums on a different pitch Intervals between orbits governed by the laws of harmony Inspired Kepler 3 3. Downfall of the Pythagoran Brotherhood Discovery of irrational numbers: the diagonal of a square Breakdown in point-to-point correspondence between arithmetic and geometry Tried to keep secret Dissolution of brotherhood (also due to egalitarian practices, socialist nature) Pythagoras: founder of European culture, source of Platonism 4 4. Legacy of Pythagoras Spherical earth (ships on horizon, lunar eclipses, shape of moon and sun) Earth must attract everything to its center Aristarchus of Samos: (310 BC) "On the sizes and distances of the sun and moon" Calculated relative distance of sun and moon Eratosthenes: Measured circumference of earth from summer solstice Deduced relative size of moon (from lunar eclipse) Deduced distance of moon from earth (from geometry) Sun-earth/moon-earth distance (from half-moon) Deduced sun-earth distance Deduced relative size of sun (from solar eclipse) rS/ dS = rM /dM 5 Philolaus and Aristarchus: Earth sphere has motion: rotates about its own axis Daily revolution of the sky caused by earth's own motion Separated day and night, annual motion of the planets Earth orbits sun First suggestion of heliocentric system Quoted by Archimedes: yet heliocentric system was discarded 1. Objects fell towards earth 2. No wind blowing against us 3. No obvious motion of stars (stars too far away to observe stellar parallax) → Heliocentric model rejected Geocentic model retained Snag: motion of planets 6 Chap II Plato and Aristotle Heroic age followed by decline (Should have been Aristarchus - Copernicus, Archimedes-Galileo) Plato: dismissed the visible world, dismissed natural science Philosophy: shape of the world must be a perfect sphere All motion perfect circles at uniform speed Science dominated by Aristotle (logician) Aristotle: God spins the world from outside it, not from center Earth and moon space subject to change: nowhere else All celestial bodies orbit earth in perfect circles 7 2. Academic dogma Planetary motion must be shown to be result of circular motions Aristotle: used 54 spheres to account for motion of the planets Ptolemy (AD 150) : ultimate earth-centered model Complicated epicycle system for circular motion of celestial objects (Ferris Wheel universe) Enshrined in ‘He Magele Syntaxis’ ( later ‘The Almagest’) Kept alive by Islamic scholars during the middle ages Re-introduced to Europe in 1175 - 1600 New dogma dismissed reality: 3 fundamental conceits 1. dualism of celestial and terrestrial motion 2. immobililty of earth in the center 3. all heavenly motion perfectly circular 8 Chap III Middle Ages Platonism adopted by Christianity (St Augustine etc) Ignored early Greeks, adopted only Plato's philosophy: neoplatonism 11cent AD: same view as 5th cent BC Medieval philosophers: Aristotle's 55 spheres, Ptolemy's 40 epicyles replaced by10 revolving spheres: disregarded stellar observation 1000 AD: Portolano charts for navigation 12-16th century: Aristotlean philosophy adopted Muslims: carried fragments of Euclid , Archimedes and Aristotle to Europe Improved Calendric astronomy and planetary tables Important Indian numerals (including zero) and algebra Christianity and Aristotelianism (Thomas Aquinas) Roger Bacon and Albert the Great: study of nature Revival of learning: Universities of Bologna, Paris, Oxford and Cambridge Medieval science divorced mathematics from science Principle: "things only move when they are pushed" handicapped science Aquinas: first proof of God's existence (based on Aristotelian physics) Unmoved mover = God 9 Summary (Chap II-III) By 1500 AD, Europe knew less than Archimedes in 200 BC 1. Splitting of Universe into 2 spheres 2. Geocentric dogma 3.Uniform motion in perfect circles dogma 4.Divorce of mathematics from science 5. Inability to realise tendency of a body in motion to stay in motion These 5 handicaps were to be overcome by Copernicus, Kepler and Galileo 10 Chap IV Renaissance Science Moderns: Roger Bacon, William of Ockham rejected Aristotle William of Occam school: Ockham’s razor philosophy “all other things equal, simpler explanation more likely’’ Nicole d’Oresme: geocentric universe not proven Nicholas of Cusa: earth not hub of universe 1. Canon Nicolas Copernicus (1473-1543) "On the Revolutions of the Heavenly Spheres" Studied at the Universities of Bologna, Padua and Krakow Simple instruments for observing the sky Relied on the observations of the Chaldeans and the Greeks Improved astronomical tables Published Commentariolus (1514) 11 Copernicus - Commentariolus (1514) : 7 axioms 1. Heavenly bodies do not share a common center 2. Earth is not the centre of the universe 3. Centre of the universe is near the sun 4. Earth’s distance to sun negligible compared to distance to stars 5. Daily motion of stars is due to rotation of the earth 6. Earth, planets revolve around sun 7. Observed motion of the planets is due to moving platform (earth) Summ: earth cannot be stationary, Ptotelmy system inconsistent Instead: heliocentric system (influenced by Pythagoras, Aristarchus) Book of the Revolutions of the Heavenly Spheres (1543) Published with aid of Georg von Lauchen (Rheticus) Problems: undermined by preface Ahead of its time (earth just a planet like others) Less accurate predictions of planetary motion Copernican system quite complicated (48 epicycles) Universe de-centralized: no natural center of directions 12 2. Tycho de Brahe (1546-1601) Danish nobleman Lifetime of astronomical observations Observational astronomy to new level (own observatory) Expensive instruments: precise and continuous data Sympathetic to Copernican ideas ‘Mixed’ model of universe (1588): planets orbit sun, sun orbits earth Migrated to Prague (imperial mathematician) Employed Kepler to study Mars: noted interpreter of data Gave data sparingly to Kepler Died from drink (1600) Kepler free to interpret all of Tycho planetary data 13 3. Johannes Kepler (1571-1630) Low born: founder of modern astronomy University of Tubingen Teacher of mathematics and astronomy in Graz, Austria 1. Defended Copernicus while still a young priest Mysterium Cosmographicum (1596): 1st public commitment by professional astronomer to Copernican system 1600: Kepler goes to work with Tycho de Brahe Given Mars project, but limited data Tycho dies after a few months Kepler becomes Imperial Mathematicus (1601-1612) Solved Mars problem in sun-centered model (8 years, not 8 days) Result: "Astronomia Nova " (Kepler, 1609) First accurate sun-centered model of universe 14 Kepler’s planetary laws 1. Planets move in elliptical orbits (not circles) 2. Planets continuously vary their speed (not uniform) 3. Sun is at focus of ellipse (not center of circle) Discovered orbit equation empirically (from data) Natural laws: precise, verifiable statements based on physical data Simple, elegant model Material bodies acted upon by forces Accurate predictions (tides, gravity explained) Ignored by Germans and Italians (incl. Galileo) Accepted by British: (Thomas Harriot, Jeremiah Horrocks, Newton) Kepler’s other work: founded instrumental optics Optics (1604): study of refraction by lenses Light intensity α 1/r2 Principle of sight, spectacles Camera obscura 15 Chap V Galileo and Newton 1. Galileo Galilei (1564-1642) Student: noticed period of pendulum constant (depends only on length, not angle or weight) Invented pendulum timing device Appointed lecturer in mathematics at the University of Pisa (1589) Chair of Mathematics at the University of Padua (1592) Studied mechanics in detail, laid foundations of dynamics Laws of motion of falling bodies Galileo’s Astronomy Improved Dutch model of telescope (mag x 60) Discovered Lunar surface not smooth (contradicts Ptolemy) Discovered moons of Jupiter : (earth not center of all things) Discovered phases of Venus (as predicted by Copernicus) Discovered innumerable stars in Milky Way (unlikely created for man's pleasure) Discovered sunspots: sun subject to decay etc 16 Corresponded with Kepler Private belief in Copernican system Measurements confirmed by Jesuits University Aristotelians opposed Galileo Letter to Grand Duchess Christina Defended Copernican system, suggested scriptures not literal Church Charges brought against Galileo in 1615, dropped Church demanded proof of Copernican system Galileo refused (couldn't prove): ignored Kepler's findings Holy decree (1616): Copernicus's teachings outlawed, Galileo censored 1623: New pope in favour of Galileo 1632: Galileo publishes "Dialogue on the Great World Systems" Propounds Copernican system Pope displeased, felt deceived (many changes over the years) 1633: Church Comission finds Galileo defied decree Interrogated by Inquisition House arrest Dialogue prohibited: smuggled out to Europe 17 After trial Dialogue Concerning Two New Sciences (1636) Magnum Opus - dynamics Postscript: his crusade damaged heliocentric system precipitated the divorce of science from faith 18 Galileo: extra notes Kinematics Careful observation of falling bodies Objects do not fall at rate proportional to their weight s = vt v = gt s = ½ gt2 Inertia principle Body will move forever if not acted upon Projectile motion Resultant of horizontal component (constant) and vertical component (gravity-dependant) 19 Telescopic observation Moons of Jupiter Phases of venus Sunspots Promoted Copernicus Censored Defended Copernican system Dialogue of the Two World Ssytems Tried by the Inquisition (1633) Discourse on Two New Sciences (1637): kinematics No treatment of causes of motion 20 2. Isaac Newton (1642 – 1727) Synthesised all that went before 1. Kepler's laws (planetary motion) 2. Galileo's laws (motion of bodies on earth) Two problems: What were the nature of the forces which drive the planets around? What would a body do if left alone? 1st step “identified Keplerian orbit of moon with Galilean orbit of projectile” Interaction of gravity with centrifugal force: cause of elliptical orbits Law of Gravity (1666) Force of attraction proportional to the masses, inversly proportional to square of separation Dropped for 20 years Developed mechanics and calculus Halley-Hooke-Wren worked on gravity Newton goaded back to problem 21 1686: Newton computes force of earth's attraction for the moon Explained observed motion: repeated for sun Showed orbit produced by inverse-square law was Kepler ellipse Showed Kepler's laws arise as consequence Extended theory to include all motion Newton’s Principia (1687): 4 basic laws for all motion Law of inertia Law of acceleration Law of action and reaction Law of gravity Note: synthesis of celestial and terrestrial dynamics 22 Newton: extra notes Mathematics at Cambridge (TC) 1661 Studies interrupted by plague Invented calculus Elected fellow Reflecting telescope Light made up of components (1666) Lucasian professor of mathematics (1668) Halley : FG α 1/r2 Newton (1684): theoretical basis for Kepler’s laws 1687: Principia published Law 1 Every body continues in its state of rest, or uniform motion in a straight line, unless compelleed to change by forces acting on it Law 2: The change in motion is proportional to the force impressed, and in the direction of the force Law 3: To every action there is always an equal and opposite reaction: the mutual actions of two bodies upon each other are akways equal, and directed to contrary parts 23 First 3 Laws put the planets in elliptical orbits controlled by inverse square law forces: centripetal forces Law 4: Moon held in its orbit by force of gravity (like apple) Compares gravitational pull needed to keep moon in orbit with pendulum data Law 5: Extends to other planets Laws 6 and 7: Universal Law of Gravitation FG = Gm1m2/r2 Optics (1704) Experimental foundations of optics Relection, refraction Diffraction Interference (Newton’s rings) Light rays trajectories of small particles Optical forces different in different media Optical and grav phenomena transported by the ether Suggests Atomism By 1830, wave theory of Young supreme 24 Postscript 3. Albert Einstein (1867-1955) Special Relativity (1905): Breakdown of Newtonian mechanics for bodies at high velocity All motion is relative Speed of light = fundamental const, limit Distance, time and mass depend on velocity Space+time = spacetime General relativity (1915): Breakdown of Newtonian mechanics for bodies in high gravitational fields Gravity = distortion of space-time Mass distorts spacetime, causes other mass to move along curve 25 4. Schrodinger, Heisenberg and Dirac Quantum Theory (1925-) Breakdown of Newtonian mechanics at the atomic scale Wave-particle duality of radiation (Planck, Einstein, Bohr) Wave-particle duality of matter (de Broglie) Schrodinger: wave equation, wave mechanics Born: probability amplitude Heisenberg: matrix mechanics, uncertainty principle Dirac: quantum field theory (relativistic) New ideas: Indeterminancy Probability Entanglement 26