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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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)

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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

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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

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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

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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

Chap V Galileo and Newton

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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

Corresponded with Kepler

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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

After trial

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Dialogue Concerning Two New Sciences (1636)

Magnum Opus - dynamics

Postscript: his crusade damaged heliocentric system

precipitated the divorce of science from faith

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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 motionResultant of horizontal component (constant) and vertical component (gravity-dependant)

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Telescopic observation

Moons of JupiterPhases of venus

Sunspots

Promoted CopernicusCensored

Defended Copernican system Dialogue of the Two World Ssytems

Tried by the Inquisition (1633)

Discourse on Two New Sciences (1637): kinematicsNo treatment of causes of motion

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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

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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

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Newton: extra notes

Mathematics at Cambridge (TC) 1661Studies interrupted by plagueInvented calculusElected fellow

Reflecting telescopeLight made up of components (1666)Lucasian professor of mathematics (1668)

Halley : FG α 1/r2

Newton (1684): theoretical basis for Kepler’s laws1687: 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

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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 opticsRelection, refractionDiffractionInterference (Newton’s rings)

Light rays trajectories of small particlesOptical forces different in different media

Optical and grav phenomena transported by the etherSuggests Atomism

By 1830, wave theory of Young supreme

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Postscript

3. Albert Einstein (1867-1955)

Special Relativity (1905): Breakdown of Newtonian mechanics for bodies at high velocity

All motion is relativeSpeed of light = fundamental const, limitDistance, time and mass depend on velocitySpace+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

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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 mechanicsBorn: probability amplitudeHeisenberg: matrix mechanics, uncertainty principleDirac: quantum field theory (relativistic)

New ideas: IndeterminancyProbabilityEntanglement

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