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11Math 1700 – Newton2

The Newtonian SynthesisThe Newtonian Synthesis

The Mathematical Principles of The Mathematical Principles of Natural PhilosophyNatural Philosophy


The Falling AppleThe Falling Apple

According to Newton, it According to Newton, it was while he was in the was while he was in the orchard at orchard at WoolsthorpeWoolsthorpeduring the plague years of during the plague years of 16651665--1666 that he noticed 1666 that he noticed an apple fall and realized an apple fall and realized that whatever made it fall that whatever made it fall also kept the Moon in its also kept the Moon in its orbit around the Earth.orbit around the Earth.

The orchard at Woolsthorpe Manor.


From Falling Apple to From Falling Apple to PrincipiaPrincipia

The falling apple insight started Newton on The falling apple insight started Newton on the path that brought together the insights the path that brought together the insights of Renaissance astronomy and physics of Renaissance astronomy and physics into a comprehensive system.into a comprehensive system.It took another 20 years before he was It took another 20 years before he was ready to put it all together in ready to put it all together in Principia Principia Mathematica Mathematica –– The Mathematical The Mathematical Principles of Natural Philosophy.Principles of Natural Philosophy.

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Concepts considered by NewtonConcepts considered by Newton

Kepler's Laws:Kepler's Laws:1. Elliptical orbits of planets.1. Elliptical orbits of planets.2. Planets sweep out equal areas in equal 2. Planets sweep out equal areas in equal times.times.3. Harmonic law: 3. Harmonic law: DD33//TT22 = K, providing a = K, providing a formula that relates the period of formula that relates the period of revolution of a planet, revolution of a planet, TT, to its distance , to its distance from the Sun, from the Sun, DD..


Concepts considered by Newton, 2Concepts considered by Newton, 2

Galileo's findings:Galileo's findings:1. Times square law for falling bodies.1. Times square law for falling bodies.2. Projectiles in parabolic path.2. Projectiles in parabolic path.3. Galilean relativity.3. Galilean relativity.


Concepts considered by Newton, 3Concepts considered by Newton, 3

Descartes' Principles:Descartes' Principles:1. Motion is natural.1. Motion is natural.2. Inertia: Bodies in motion tend to stay in 2. Inertia: Bodies in motion tend to stay in motion in a straight line motion in a straight line —— unless forced unless forced from it.from it.3. All motion due to impact.3. All motion due to impact.

Forces are occult Forces are occult –– i.e., forbidden in a i.e., forbidden in a mechanical system.mechanical system.

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Aristotle's philosophical approach Aristotle's philosophical approach to physicsto physics

1. Two separate realms: 1. Two separate realms: The heavens and the earth.The heavens and the earth.

2. Heavenly motions:2. Heavenly motions:Eternal, changeless, and always circular.Eternal, changeless, and always circular.

3. Earthly motions:3. Earthly motions:Either natural or forced.Either natural or forced.Natural motion either up (light things) or down (heavy Natural motion either up (light things) or down (heavy things) things) –– bodies seek their natural places.bodies seek their natural places.Forced motions caused by pushes Forced motions caused by pushes –– Cannot occur Cannot occur "naturally.""naturally."


Euclid's Mathematical approach to Euclid's Mathematical approach to certain knowledgecertain knowledge

Axiomatic Structure:Axiomatic Structure:DefinitionsDefinitionsAxioms & PostulatesAxioms & PostulatesRules of reasoningRules of reasoning

Begin from reasonable assumptions and Begin from reasonable assumptions and through logic and other strict rules of through logic and other strict rules of inference, build up a body of knowledgeinference, build up a body of knowledge..


The The LucasianLucasian Professor of Professor of MathematicksMathematicks

Newton returned to Cambridge after the Newton returned to Cambridge after the plague.plague.After a few years his former mathematics After a few years his former mathematics professor, Isaac Barrow, resigned his professor, Isaac Barrow, resigned his position, and recommended that Newton position, and recommended that Newton be his replacement.be his replacement.Newton became the 2Newton became the 2ndnd LucasianLucasianProfessor of Professor of MathematicksMathematicks, a position he , a position he held for 27 years.held for 27 years.

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NewtonNewton’’s sporadic outputs sporadic output

Over the next 15Over the next 15--20 years, Newton 20 years, Newton published a work on the calculus, the published a work on the calculus, the ideas of which he was accused of stealing ideas of which he was accused of stealing from Leibniz, and some of his work on from Leibniz, and some of his work on light, which Robert Hooke claimed he had light, which Robert Hooke claimed he had conceived of first.conceived of first.Newton, disgusted, retreated into his own Newton, disgusted, retreated into his own studies, publishing nothing.studies, publishing nothing.


Edmund HalleyEdmund Halley’’s Visits Visit

One of NewtonOne of Newton’’s few friends was the s few friends was the astronomer, Edmund Halley.astronomer, Edmund Halley.In 1684, Halley and architect Christopher In 1684, Halley and architect Christopher Wren, speculated that the force that held Wren, speculated that the force that held the planets in their orbits must be inversely the planets in their orbits must be inversely related to their distance from the sun.related to their distance from the sun.Halley thought Newton might be able to Halley thought Newton might be able to settle the matter.settle the matter.


HalleyHalley’’s questions question

Instead of asking Newton what kind of Instead of asking Newton what kind of force would hold the planets in their orbits, force would hold the planets in their orbits, Halley asked Newton what curve would be Halley asked Newton what curve would be produced by a force of attraction that produced by a force of attraction that diminished with the square of the distance.diminished with the square of the distance.Newton replied immediately, Newton replied immediately, ““An Ellipse.An Ellipse.””

Halley asked for the proof, but Newton could Halley asked for the proof, but Newton could not find it, and promised to send it to him.not find it, and promised to send it to him.

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NewtonNewton’’s first drafts first draft

Newton sent Halley a nine page proof Newton sent Halley a nine page proof three months later.three months later.Halley urged Newton to publish it, but Halley urged Newton to publish it, but Newton refused, realizing that the Newton refused, realizing that the consequences were far greater than the consequences were far greater than the solution to that problem.solution to that problem.For 18 months, Newton developed the For 18 months, Newton developed the theory farther.theory farther.


The PrincipiaThe Principia

Finally, three years after HalleyFinally, three years after Halley’’s visit, s visit, NewtonNewton’’s results were publisheds results were published——at at HalleyHalley’’s expenses expense——in the single most in the single most important work in the history of science:important work in the history of science:PhilosophiPhilosophiææ NaturalisNaturalis Principia Principia Mathematica, Mathematica, translated as translated as The The Mathematical Principles of Natural Mathematical Principles of Natural Philosophy,Philosophy, published in 1687.published in 1687.


The title tells allThe title tells all……

DescartesDescartes’’ attempt at a new system of attempt at a new system of philosophy was philosophy was The Principles of The Principles of Philosophy.Philosophy.Newton adds two words:Newton adds two words:

Natural Natural –– referring to the physical world only, referring to the physical world only, not to not to res cogitans.res cogitans.Mathematical Mathematical –– perhaps not perhaps not allall of the of the principles of philosophy, just the mathematical principles of philosophy, just the mathematical ones.ones.

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The Axiomatic Structure of The Axiomatic Structure of Newton's Newton's PrincipiaPrincipia

Definitions, axioms, rules of reasoning, Definitions, axioms, rules of reasoning, just like Euclid.just like Euclid.Examples:Examples:

DefinitionDefinition1. The quantity of matter is the measure of the 1. The quantity of matter is the measure of the same, arising from its density and bulk same, arising from its density and bulk conjunctly.conjunctly.

How Newton is going to use the term How Newton is going to use the term ““quantity of quantity of matter.matter.””


Rules of ReasoningRules of Reasoning

1. We are to admit no more causes of 1. We are to admit no more causes of natural things than such as are both true natural things than such as are both true and sufficient to explain their and sufficient to explain their appearances.appearances.

This is the wellThis is the well--known Principle of Parsimony, known Principle of Parsimony, also known as Ockhamalso known as Ockham’’s Razor. In short, it s Razor. In short, it means that the best explanation is the means that the best explanation is the simplest one that does the job.simplest one that does the job.


The AxiomsThe Axioms

1. Every body continues in its state of rest 1. Every body continues in its state of rest of or uniform motion in right line unless it of or uniform motion in right line unless it is compelled to change that state by is compelled to change that state by forces impressed upon it.forces impressed upon it.

This is DescartesThis is Descartes’’ principle of inertia. It principle of inertia. It declares that straightdeclares that straight--line, constant speed, line, constant speed, motion is the natural state. Force is motion is the natural state. Force is necessary to change that motion.necessary to change that motion.Compare this to AristotleCompare this to Aristotle’’s need to explain s need to explain motion.motion.

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The Axioms, 2The Axioms, 2

2. The change in motion is proportional to 2. The change in motion is proportional to the motive force impressed and is made the motive force impressed and is made in the direction of the right line in which in the direction of the right line in which that force is impressed.that force is impressed.

A force causes a change in motion, and does A force causes a change in motion, and does so in the direction in which the force is so in the direction in which the force is applied.applied.


The Axioms, 3The Axioms, 3

3. To every action there is always 3. To every action there is always opposed an equal reaction; or, the mutual opposed an equal reaction; or, the mutual actions of two bodies upon each other are actions of two bodies upon each other are always equal and directed to contrary always equal and directed to contrary parts.parts.

Push against any object; it pushes back at Push against any object; it pushes back at you. This is how any object is held up from you. This is how any object is held up from falling, and how a jet engine works.falling, and how a jet engine works.


Known Empirical Laws DeducedKnown Empirical Laws Deduced

Just as Euclid showed that already known Just as Euclid showed that already known mathematical theorems follow logically mathematical theorems follow logically from his axioms, Newton showed that the from his axioms, Newton showed that the laws of motion discerned from laws of motion discerned from observations by Galileo and Kepler observations by Galileo and Kepler followed from his axiomatic structure.followed from his axiomatic structure.

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GalileoGalileo’’s Lawss Laws

GalileoGalileo’’s laws about physics on Earth:s laws about physics on Earth:The law of free fall.The law of free fall.

Galileo asserts that falling bodies pick up speed at Galileo asserts that falling bodies pick up speed at a uniform rate.a uniform rate.Newton shows that a constant force acting in line Newton shows that a constant force acting in line with inertial motion would produce a constant with inertial motion would produce a constant acceleration. This is implied by his first 2 axioms.acceleration. This is implied by his first 2 axioms.

The parabolic path of a projectile.The parabolic path of a projectile.Likewise, if a body is initially moving Likewise, if a body is initially moving inertiallyinertially (in (in any direction), but a constant force pushes it any direction), but a constant force pushes it downwards, the resulting path will be a parabola.downwards, the resulting path will be a parabola.


KeplerKepler’’s Lawss Laws

NewtonNewton’’s very first proposition is Keplers very first proposition is Kepler’’s s 22ndnd law (planets sweep out equal areas in law (planets sweep out equal areas in equal times).equal times).It follows from NewtonIt follows from Newton’’s first two axioms s first two axioms (inertial motion and change of motion in (inertial motion and change of motion in direction of force) and Eucliddirection of force) and Euclid’’s formula for s formula for the area of a triangle.the area of a triangle.


KeplerKepler’’s 2s 2ndnd Law illustratedLaw illustratedIn the diagram, a planet In the diagram, a planet is moving is moving inertiallyinertially from from point point AA along the line along the line ABAB. . S is the Sun. S is the Sun. Consider Consider the triangle the triangle ABS ABS as as ““swept outswept out”” by the planet.by the planet.When the planet gets to When the planet gets to B, B, Newton supposes a Newton supposes a sudden force is applied to sudden force is applied to the planet in the direction of the sun. the planet in the direction of the sun. This will cause the planetThis will cause the planet’’s inertial motion to shift in the s inertial motion to shift in the direction of point C.direction of point C.

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KeplerKepler’’s 2s 2ndnd Law illustrated, 2Law illustrated, 2Note that if instead of Note that if instead of veering off to C, the veering off to C, the planet continued in a planet continued in a straight line it would straight line it would reach c (follow the reach c (follow the dotted line) in the dotted line) in the same time.same time.Triangles ABS and Triangles ABS and BcSBcS have equal area.have equal area.

Equal base, same Equal base, same height.height.


KeplerKepler’’s 2s 2ndnd Law illustrated, 3Law illustrated, 3Newton showed that Newton showed that triangles BCS and triangles BCS and BcSBcSalso have the same also have the same area. area.

Think of BS as the Think of BS as the common base. C and c common base. C and c are at the same height are at the same height from BS extended.from BS extended.

Therefore ABS and BCS are equal areas.Therefore ABS and BCS are equal areas.Things equal to the same thing are equal to each Things equal to the same thing are equal to each other.other.


KeplerKepler’’s 2s 2ndnd Law illustrated, 4Law illustrated, 4Now, imagine the sudden Now, imagine the sudden force toward the sun force toward the sun happening in more happening in more frequent intervals. frequent intervals.

The smaller triangles would The smaller triangles would also be equal in area. also be equal in area.

In the limiting case, the In the limiting case, the force acts continuously and any section taking force acts continuously and any section taking an equal amount of time carves out an equal an equal amount of time carves out an equal area.area.

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The Same Laws of Motion in the The Same Laws of Motion in the Heavens and on EarthHeavens and on Earth

NewtonNewton’’s analysis s analysis showed that from the showed that from the same assumptions same assumptions about motion, he about motion, he could account for the could account for the parabolic path of a parabolic path of a projectile on Earth projectile on Earth and for a planet (or and for a planet (or the Moon) in orbit.the Moon) in orbit.

Newton’s illustration of the relationship between a projectile and an object in orbit.


A Mechanical systemA Mechanical system

Newton's axiomatic "principles" implied a Newton's axiomatic "principles" implied a mechanistic model of the universe.mechanistic model of the universe.

This was all that made sense to Newton.This was all that made sense to Newton.The Clockwork UniverseThe Clockwork Universe

God makes clock and winds it up.God makes clock and winds it up.


Universal GravitationUniversal Gravitation

A deduced effectA deduced effectThat which makes apples fall and the moon That which makes apples fall and the moon stay in orbit. stay in orbit. And the planets, and projectiles, etc.And the planets, and projectiles, etc.

The gravitational force:The gravitational force:G = g(MG = g(M11MM22/d/d22))

The force varies inversely with square of The force varies inversely with square of distance.distance.

It gets much weaker as the distance between It gets much weaker as the distance between objects is greater, but never disappears entirely.objects is greater, but never disappears entirely.

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Action at a DistanceAction at a Distance

Gravity, and magnetism too, operate over Gravity, and magnetism too, operate over apparently empty space.apparently empty space.

Is this an occult force?Is this an occult force?Newton postulates an "Aether" to transmit Newton postulates an "Aether" to transmit gravity, magnetism, etc.gravity, magnetism, etc.

Makes empty space no longer empty.Makes empty space no longer empty.Note the return to ParmenidesNote the return to Parmenides’’ and Aristotleand Aristotle’’s s denial of the existence of denial of the existence of ““nothing.nothing.””


Hypotheses non Hypotheses non fingofingo

Unlike Aristotle (but like Galileo), Newton Unlike Aristotle (but like Galileo), Newton did not claim to have an explanation for did not claim to have an explanation for everything.everything.

For example, he described how gravity works, For example, he described how gravity works, on the basis of the effects seen. He does not on the basis of the effects seen. He does not say what gravity is.say what gravity is.On this an other mystery subjects, Newton On this an other mystery subjects, Newton said that he said that he ““frames no hypotheses.frames no hypotheses.””


How the Newtonian world How the Newtonian world view transformed our view of view transformed our view of

NatureNatureDifferent ways of doing scientific Different ways of doing scientific

workwork

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The Whig Interpretation of The Whig Interpretation of HistoryHistory

Seeing (British) history as a battle Seeing (British) history as a battle betweenbetween

the progressive, forwardthe progressive, forward--looking Whigslooking Whigsandand

the reactionary, backwardthe reactionary, backward--looking Tories.looking Tories.


Herbert ButterfieldHerbert Butterfield

The Whig Interpretation of The Whig Interpretation of HistoryHistory

London, 1931.London, 1931.

Butterfield showed that the Butterfield showed that the ““whigwhig interpretationinterpretation”” was a was a fundamental problem in fundamental problem in writing political history.writing political history.


The Whig Interpretation of The Whig Interpretation of ScienceScience

The same flaw occurred in writing the The same flaw occurred in writing the history of science.history of science.Even more acute in the history of science Even more acute in the history of science because of the inevitable conclusion that because of the inevitable conclusion that present day science is right and past present day science is right and past science was wrong.science was wrong.

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Hugh KearneyHugh Kearney

Science and ChangeScience and Change, , 15001500--1700.1700.

New York, 1971.New York, 1971.

An attempt to combat An attempt to combat a a whigwhig interpretation interpretation of the scientific of the scientific revolution.revolution.


KearneyKearney’’s Three Traditions in s Three Traditions in ScienceScience

The Organic. The Magical. The Mechanist.The Organic. The Magical. The Mechanist.


The Organic ViewpointThe Organic ViewpointCommon sense.Common sense.Empirical.Empirical.Coherent and logical.Coherent and logical.The goal was to explain The goal was to explain the purpose (why) of the purpose (why) of something in nature.something in nature.Focus on cycles.Focus on cycles.

Life cycles.Life cycles.Generation and corruption.Generation and corruption.

Planetary cycles.Planetary cycles.Ignored accident.Ignored accident.

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The Organic Tradition in The Organic Tradition in AntiquityAntiquity

AristotleAristotleBiological interestsBiological interestsHistory of AnimalsHistory of AnimalsPurpose the ultimate causePurpose the ultimate cause

PtolemyPtolemyCycles of the planets and the heavensCycles of the planets and the heavens

GalenGalenPhysiologyPhysiology


The Organic Tradition in the The Organic Tradition in the Middle AgesMiddle Ages

Dominated the Middle Ages and the early Dominated the Middle Ages and the early Renaissance, especially in Europe.Renaissance, especially in Europe.Scholasticism, 14Scholasticism, 14thth century.century.

William of Ockham, OckhamWilliam of Ockham, Ockham’’s Razor.s Razor.


Padua in the 15Padua in the 15thth and 16and 16thth

centurycentury

Andreas VesaliusAndreas VesaliusDe De FabricaFabrica, 1543, 1543

William HarveyWilliam HarveyDe De MotuMotu CordisCordis, , 16281628

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The Organic Tradition in the The Organic Tradition in the Scientific RevolutionScientific Revolution

Spokesman: Spokesman: Francis BaconFrancis Bacon

Popularized Popularized experiment (i.e. experiment (i.e. observation).observation).Criticized acceptance Criticized acceptance of authority.of authority.Science as induction Science as induction from particulars.from particulars.Ignored mathematics.Ignored mathematics.

Title page of Bacon’s Great Instauration


The Magical ViewpointThe Magical Viewpoint

The search for secrets.The search for secrets.Solving the riddle of nature.Solving the riddle of nature.Hidden structures, forces.Hidden structures, forces.Magical powers.Magical powers.The scientist as wizard, The scientist as wizard, sorcerer, high priest, sorcerer, high priest, soothsayer.soothsayer.


The Magical Tradition in The Magical Tradition in AntiquityAntiquity

PythagorasPythagorasNumber magicNumber magicSecretive cultSecretive cult

PlatoPlatoUpper part of the Upper part of the Divided LineDivided LineMathematics the key Mathematics the key to higher to higher understanding.understanding.

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The Magical Tradition in The Magical Tradition in Antiquity, 2Antiquity, 2

Hermes Hermes TrismegistusTrismegistus

A mythical figure.A mythical figure.Held that the Sun Held that the Sun was God, or a was God, or a symbol of God.symbol of God.Light, the source Light, the source of life.of life.Mathematical Mathematical harmony in the harmony in the cosmos.cosmos.


The Magical Tradition in the The Magical Tradition in the Middle Ages and RenaissanceMiddle Ages and RenaissanceThe Magical Tradition has never The Magical Tradition has never dominated, but has never been totally dominated, but has never been totally ignored.ignored.NeoplatonismNeoplatonism..HermeticismHermeticism..Alchemy.Alchemy.Astrology.Astrology.


The Magical Tradition viewed as The Magical Tradition viewed as out of touchout of touch

A painting by Pieter Breughel, the Elder, showing alchemists as A painting by Pieter Breughel, the Elder, showing alchemists as irresponsible and oblivious to the outside world.irresponsible and oblivious to the outside world.

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The Magical Tradition in the The Magical Tradition in the Scientific RevolutionScientific Revolution

CopernicusCopernicusThe Sun the centre of the universe and the The Sun the centre of the universe and the source of all lifesource of all lifeMathematics is for mathematicians.Mathematics is for mathematicians.Mathematical harmony trumps common Mathematical harmony trumps common sense.sense.

Giordano BrunoGiordano BrunoThe infinity of worlds.The infinity of worlds.The universe is magical.The universe is magical.


The Magical Tradition in the The Magical Tradition in the Scientific Revolution, 2Scientific Revolution, 2

William GilbertWilliam GilbertOn the Magnet.On the Magnet.Action at a distance.Action at a distance.

ParacelsusParacelsusThe human body as a microcosmThe human body as a microcosmIatrochemistry.Iatrochemistry.

Johannes KeplerJohannes KeplerMathematical relationships are the ultimate Mathematical relationships are the ultimate secrets of the universe.secrets of the universe.


The Mechanist ViewpointThe Mechanist ViewpointThe world is (like) a The world is (like) a machine.machine.Understand the world Understand the world through analogies to through analogies to machines.machines.Everything to be explained Everything to be explained by combinations of pushes by combinations of pushes and pulls.and pulls.No hidden forces or No hidden forces or mysterious influences.mysterious influences.Emphasis on Emphasis on ““howhow”” –– not not ““why.why.””

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The Mechanist Tradition in The Mechanist Tradition in Antiquity and the Middle AgesAntiquity and the Middle Ages

ArchimedesArchimedesLevers, pulleys, floating bodies, ingenious Levers, pulleys, floating bodies, ingenious machines.machines.Archimedes asked Archimedes asked howhow does it work?does it work?


The Mechanist Tradition in The Mechanist Tradition in Antiquity and the Middle Ages, 2Antiquity and the Middle Ages, 2In the Middle AgesIn the Middle Ages

Craftsmen, builders of Craftsmen, builders of windmills, windmills, waterwheels, devices waterwheels, devices of all sorts.of all sorts.What later became What later became ““engineers.engineers.””

A water wheel operating a bellows


The Mechanist Tradition in the The Mechanist Tradition in the Scientific RevolutionScientific Revolution

NiccoloNiccolo TartagliaTartagliaCannonball trajectory.Cannonball trajectory.Translated Translated Archimedes and Archimedes and Euclid.Euclid.

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The Mechanist Tradition in the The Mechanist Tradition in the Scientific Revolution, 2Scientific Revolution, 2

GalileoGalileoSimplify problem, Simplify problem, make model, find make model, find mechanism.mechanism.Describe Describe mathematicallymathematicallyAvoid system buildingAvoid system building



RenRenéé DescartesDescartesForces are occultForces are occult



Evangelista Evangelista ToricelliToricelli and and BlaiseBlaise PascalPascalAtmospheric pressure and the barometerAtmospheric pressure and the barometerThe Puy de The Puy de DDômeôme experiment, carrying a experiment, carrying a barometer up the mountain and noting the fall barometer up the mountain and noting the fall in atmospheric pressurein atmospheric pressure——the sea of air.the sea of air.

Robert BoyleRobert BoyleMeasurement in chemistryMeasurement in chemistryBoyleBoyle’’s law, PV=Ks law, PV=K

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The Royal Society of The Royal Society of London for Improving London for Improving Natural KnowledgeNatural Knowledge

Founded in 1662Founded in 1662Patron, Charles IIPatron, Charles IIFounded on Founded on BaconianBaconianprecepts (build knowledge precepts (build knowledge from observation), from observation), members became later members became later committed to the committed to the mechanist viewpoint.mechanist viewpoint.


The Genius of Isaac NewtonThe Genius of Isaac NewtonNewton combined Newton combined the mechanist and the mechanist and the magical the magical viewpoints.viewpoints.The mathematical The mathematical formulation was formulation was the true the true description, description, according to according to Newton.Newton.


The clockwork universeThe clockwork universe——that that needed winding up and resettingneeded winding up and resetting

The world operates as a The world operates as a vast machine vast machine –– the the ““clockwork universe.clockwork universe.””

God (a supernatural and God (a supernatural and definitely definitely notnot mechanical mechanical force) made things work force) made things work when the mechanism when the mechanism failed.failed.The Universe is a riddle.The Universe is a riddle.Gravity is Gravity is action at a action at a distance.distance.

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At the end of the Scientific At the end of the Scientific RevolutionRevolution

Mechanism triumphs.Mechanism triumphs.The Organic viewpoint is in disrepute.The Organic viewpoint is in disrepute.The incompatibility of the Magical and the The incompatibility of the Magical and the Mechanist views are forgotten or ignored.Mechanist views are forgotten or ignored.Mathematics is accepted as the language Mathematics is accepted as the language of science.of science.The mechanical model is accepted as the The mechanical model is accepted as the ultimate explanation.ultimate explanation.


The Newtonian Model for true The Newtonian Model for true knowledgeknowledge

Axiomatic presentation.Axiomatic presentation.Mathematical precision and tight logic.Mathematical precision and tight logic.

With this Euclidean style, Newton showed that With this Euclidean style, Newton showed that he could (in principle) account for all observed he could (in principle) account for all observed phenomena in the physical world, both in the phenomena in the physical world, both in the heavens and on Earth.heavens and on Earth.

Implication: All science should have this Implication: All science should have this format.format.

This became the model for science.This became the model for science.


NewtonianismNewtonianism

The application of the Newtonian model The application of the Newtonian model beyond physics, e.g. in philosophy, beyond physics, e.g. in philosophy, psychology, sociology, economics.psychology, sociology, economics.John Locke, John Locke, Essay on Human Essay on Human UnderstandingUnderstandingBenedict Spinoza, Benedict Spinoza, Tractatus Tractatus TheologiaTheologiaAdam Smith, Adam Smith, Wealth of NationsWealth of Nations

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