The Scien)fic Revolu)on Another Revolu)on? 1543: The Copernician Revolu)on The demise of Aristotle? The Scien)fic/Copernician Revolu)on •  Thomas Samuel Kuhn (1922 – 1996) was an American historian and philosopher who wrote extensively on the history of science •  In The Structure of Scien.fic Revolu.ons (1962), Kuhn argued that science does not progress via a linear accumula)on of new knowledge, but undergoes periodic revolu)ons, also called "paradigm shi+s in which the nature of scien)fic inquiry within a par)cular field is abruptly transformed. The three stages of science? •  Prescience, which lacks a central paradigm, comes first. •  This is followed by "normal science : scien)sts aTempt to enlarge the central paradigm by "puzzle-­‐solving". Thus, the failure of a result to conform to the paradigm is seen not as refu)ng the paradigm, but as the mistake of the researcher. •  As anomalous results build up, science reaches a crisis, at which point a new paradigm, which subsumes the old results along with the anomalous results into one framework, is accepted. This is termed revolu)onary science. Speaking of Revolu)ons... A fundamental transforma)on in scien)fic ideas in physics, astronomy, and biology, in ins)tu)ons suppor)ng scien)fic inves)ga)on, and in the more widely held picture of the universe. As a result, the scien)fic revolu)on is commonly viewed as a founda)on and origin of modern science. But also, a new status for Mathema)cs and a divide between Sciences and Humani)es Ques)ons •  The Prin)ng Revolu)on, the Reforma)on, the Scien)fic Revolu)on? Coincidences? •  The "Con)nuity Thesis" is the opposing view that there was no radical discon)nuity between the development of science in the Middle Ages and later developments in the Renaissance and early modern period. 1543 •  Nicolaus Copernicus (1473-­‐1543) De revolu.onibus orbium coeles.um •  Andreas Vesalius (1514 -­‐ 1564) De Humani Corporis Fabrica Andreas Vesalius 1514-­‐1564 •  Gabriele Fallopio 1523-­‐1562 •  Epitome •  De Fabrica •  Defiance of Galen, of the accepted authority •  Valoriza)on of dissec)on over readings Why, I pray, should we not say those anatomists are rough and untrained who have passed on to posterity Galenic descrip.ons that are false in some respects and in most cases apply to apes and dogs but not humans, as if they had observed them in man, and were in no way afraid, like scribes, to enumerate things they never saw even in a dream, and oFen misunderstood in Galen's books? Rembrandt, The Lesson of Anatomy Nicolaus Copernicus The first astronomer to formulate a scien.fically-­‐
based heliocentric cosmology that displaced the Earth from the center of the universe: the star)ng point of modern astronomy, the defining epiphany that began the Scien)fic Revolu)on. New Science? Greek, Indian and Muslim savants had published heliocentric hypotheses centuries before Copernicus His scien)fic theory of heliocentrism, demonstrates that the mo)ons of celes)al objects can be explained without pucng the Earth at rest in the center of the universe A humanist and polymath Copernicus was a mathema)cian, astronomer, physician, classical scholar, translator, ar)st, Catholic cleric, jurist, governor, military leader, diplomat and economist. Astronomy figured as liTle more than an avoca)on A bishop, a ci)zen of Europe, a student •  Studies in law and medicine at the universi)es of Bologna and Padua. Copernicus, while studying canon and civil law at Bologna, met the famous astronomer, Domenico Maria Novara da Ferrara. Copernicus aTended Novara's lectures and became his disciple and assistant. The first observa)ons that Copernicus made in 1497, together with Novara, are recorded in the De revolu.onibus orbium coeles.um. •  In 1497 Copernicus' uncle was ordained Bishop of Warmia, and Copernicus was named a canon at Frombork Cathedral. But Copernicus remained in Italy, where he aTended the great Jubilee of 1500. He also went to Rome, where he observed a lunar eclipse and gave some lectures in astronomy and mathema)cs. A great idea •  1503: doctorate in Canon law •  In 1514 Copernicus made available to friends his Commentariolus (LiTle Commentary), a six page hand-­‐wriTen text describing his ideas about the heliocentric hypothesis. It contained seven basic assump)ons. Thereaier he con)nued gathering data for a more detailed work. Shyness, modesty or prudence? On 1 November 1536, Archbishop of Capua Nicholas Schönberg wrote to Copernicus from Rome: Some years ago word reached me concerning your proficiency, of which everybody constantly spoke. At that )me I began to have a very high regard for you... For I had learned that you had not merely mastered the discoveries of the ancient astronomers uncommonly well but had also formulated a new cosmology. In it you maintain that the earth moves; that the sun occupies the lowest, and thus the central, place in the universe... Therefore with the utmost earnestness I entreat you, most learned sir, unless I inconvenience you, to communicate this discovery of yours to scholars, and at the earliest possible moment to send me your wri)ngs on the sphere of the universe together with the tables and whatever else you have that is relevant to this subject Encounter with a Mathema)cian Copernicus was s)ll working on De revolu.onibus orbium coeles.um (even if not convinced that he wanted to publish it) when in 1539 Georg Joachim Rhe)cus, a WiTenberg mathema)cian, arrived in Frombork. Philipp Melanchthon had arranged for Rhe)cus to visit several astronomers and study with them. Rhe)cus Rhe)cus became Copernicus' pupil, staying with him for two years and wri)ng a book, Narra.o prima (First Account), outlining the essence of Copernicus' theory. In 1542 Rhe)cus published a trea)se on trigonometry by Copernicus (later included in the second book of De revolu.onibus). Galileo and Copernicus At original publica)on, Copernicus book caused only mild controversy, and provoked no fierce sermons about contradic)ng Holy Scripture. It was only three years later, in 1546, that a Dominican, Giovanni Maria Tolosani, denounced the theory in an appendix to a work defending the absolute truth of Scripture A late (modern?) condemna)on In March 1616, in connec)on with the Galileo affair, the Roman Catholic Church's Congrega)on of the Index issued a decree suspending De revolu.onibus un)l it could be "corrected," on the grounds that the supposedly Pythagorean doctrine that the Earth moves and the Sun doesn't was "false and altogether opposed to Holy Scripture." Galileo Galilei 1564-­‐1642 •  A Tuscan physicist, mathema)cian, astronomer, and philosopher: his achievements include improvements to the telescope and consequent astronomical observa)ons, and support for Copernicanism. •  The "father of modern observa)onal astronomy" A new status for Mathema)cs •  Galileo made original contribu)ons to the science of mo)on through an innova)ve combina)on of experiment and mathema)cs. •  Galileo is perhaps the first to clearly state that the laws of nature are mathema)cal. In The Assayer he wrote "Philosophy is wriTen in this grand book, the universe ... It is wriTen in the language of mathema)cs, and its characters are triangles, circles, and other geometric figures; ..." Feyerabend, Against Method, 1975 'Aristotelians ... demanded strong empirical support while the Galileans were content with far-­‐reaching, unsupported and par)ally refuted theories. I do not cri)cize them for that; on the contrary, I favour Niels Bohr's "this is not crazy enough."' And yet it moves... •  Galileo was ordered to stand trial on suspicion of heresy in 1633. The sentence of the Inquisi)on was in three essen)al parts: •  Galileo was found "vehemently suspect of heresy", namely of having held the opinions that the Sun lies mo)onless at the centre of the universe, that the Earth is not at its centre and moves, and that one may hold and defend an opinion as probable aier it has been declared contrary to Holy Scripture. He was required to "abjure, curse and detest" those opinions. •  He was ordered imprisoned; the sentence was later commuted to house arrest. •  His offending Dialogue on the two systems was banned; and in an ac)on not announced at the trial, publica)on of any of his works was forbidden, including any he might write in the future Observa)ons... •  Based only on uncertain descrip)ons of the first prac)cal telescope, invented by Hans Lippershey in the Netherlands in 1608, Galileo, in the following year, made a telescope with about 3x magnifica)on, and later made others with up to about 30x magnifica)on. •  With this improved device he could see magnified, upright images on the earth – it was what is now known as a terrestrial telescope, or spyglass. He could also use it to observe the sky; for a )me he was one of those who could construct telescopes good enough for that purpose. ... and applied Mathema)cs •  Galileo produced one piece of original work in mathema)cs: Galileo's paradox, which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares (problem solved 250 years later by Georg Cantor). •  Generally, Galileo's applica)on of mathema)cs to experimental physics was innova)ve, his mathema)cal methods were the standard ones of the day. Johannes Kepler 1572-­‐1630 A German mathema)cian, astronomer and astrologer, best known for his laws of planetary mo)on, codified by later astronomers based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astrononomy. They also provided one of the founda)ons for Isaac Newton's theory of universal gravita)on. Mathema)cs teacher at a seminary school in Graz, Austria Assistant to astronomer Tycho Brahe, the court mathema)cian to Emperor Rudolf II Mathema)cs teacher in Linz, Austria, and an adviser to General Wallenstein. Fundamental work in the field of op)cs, inven)on an improvement of the refrac)ng telescope (the Keplerian Telescope), Demonstra)on of the telescopic discoveries of his contemporary Galileo Galilei A new and meaningful world Religious convic)on that God had created the world according to an intelligible plan that is accessible through the natural light of reason. Kepler described his new astronomy as "celes)al physics , as "an excursion into Aristotle's Metaphysics , and as "a supplement to Aristotle's On the Heavens Transforma)on of the ancient tradi)on of physical cosmology by trea)ng astronomy as part of a universal mathema)cal physics A change in disciplines •  There was no clear dis)nc)on between astronomy and astrology, but there was a strong division between astronomy (a branch of mathema)cs within the liberal arts) and physics (a branch of natural philosophy) •  A change in ques)ons... Platonic solids? •  Mysterium Cosmographicum (The Cosmographic Mystery), 1595 •  Teaching about the periodic conjunc)on of Saturn and Jupiter in the zodiac, he realized that regular polygons bound one inscribed and one circumscribed circle at definite ra)os, which, he reasoned, might be the geometrical basis of the universe. •  Aier failing to find a unique arrangement of polygons that fit known astronomical observa)ons (even with extra planets added to the system), Kepler began experimen)ng with 3-­‐
dimensional polyhedra. He found that each of the five Platonic solids could be uniquely inscribed and circumscribed by spherical orbs Mysteries... Nes)ng these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets—Mercury, Venus, Earth, Mars, Jupiter, and Saturn. By ordering the solids—
octahedron, icosahedron, dodecahedron, tetrahedron, cube—
Kepler found that the spheres could be placed at intervals corresponding (within the accuracy limits of available astronomical observa)ons) to the rela)ve sizes of each planet s path, assuming the planets circle the Sun. Kepler also found a formula rela)ng the size of each planet s orb to the length of its orbital period ... and laws •  The extended line of research that culminated in Astronomia nova (A New Astronomy, 1609) — including the first two laws of planetary mo)on — began with the analysis, under Tycho's direc)on, of Mars' orbit. Kepler calculated and recalculated various approxima)ons of Mars' orbit using an equant (the mathema)cal tool that Copernicus had eliminated with his system), eventually crea)ng a model that generally agreed with Tycho's observa)ons to within two arcminutes (the average measurement error). Equant •  mathema)cal concept developed by Claudius Ptolemy in the 2nd century BCE to account for the observed mo)on of heavenly bodies. •  The equant point, indicated in the diagram by the • , is placed so that it is directly opposite the Earth from the center of the deferent. A planet or the center of an epicycle (a smaller circle carrying the planet) was conceived to move with a uniform speed with respect to the equant. •  To a hypothe)cal observer placed at the equant point, the center of the epicycle would appear to move at a steady speed. This concept solved the problem of accoun)ng for the anomalis)c mo)on of the planets but was believed by some to compromise the goals of the ancient astronomer, namely uniform circular mo)on. Epitome of Copernican Astronomy, 1615-­‐1621 Kepler's laws of planetary mo)on are three mathema)cal laws that describe the mo)on of planets in the Solar System. A Mathema)cal adjustment and a philosophical one First Law "The orbit of every planet is an ellipse with the sun at a focus." Second law "A line joining a planet and the sun sweeps out equal areas during equal intervals of )me. The planet moves faster near the Sun, so the same area is swept out in a given )me as at larger distances, where the planet moves more slowly. Third law Planets distant from the sun have longer orbital periods than close planets. Kepler's third law describes this fact quan)ta)vely. "The square of the orbital period of a planet is directly propor)onal to the cube of the semi-­‐
major axis of its orbit." A new status for Mathema)cs... and for the self •  René Descartes, 1596-­‐1650 •  French philosopher, mathema)cian, scien)st, and writer who spent most of his life in the Dutch Republic. •  Cogito ergo sum •  Descartes' influence in mathema)cs is apparent, the Cartesian coordinate system allowing geometric shapes to be expressed in algebraic equa)ons being named for him. He is accredited as the father of analy)cal geometry Medita)ng... •  And so something which I thought I was seeing with my eyes is in fact grasped solely by the faculty of judgment which is in my mind. •  The Cartesian theory of Fallacies: "This statement is a lie." Some Cartesian Musts 1637. Discours de la méthode (Discourse on the Method). An introduc)on to the Essais, which include the Dioptrique, the Météores and the Géométrie. 1641. Medita.ones de prima philosophia (Medita)ons on First Philosophy), also known as Metaphysical Medita)ons. In La)n; a French transla)on, probably done without Descartes' supervision, was published in 1647. Includes six Objec)ons and Replies. 1644 Principia philosophiae (Principles of Philosophy), a La)n textbook at first intended by Descartes to replace the Aristotelian textbooks then used in universi)es. The end of a tradi)on? •  Defiance against scholarship and authori)es •  Divorce from the Church •  The angular proof of Mathema)cs and the valoriza)on of laboratory Observa)on •  The cons)tu)on of scien)fic observa)on: tools of measurement, reproduc)on of the experiment, transcrip)on of the results, mathema)za)on Harmonices Mundi, 1619 •  The geometrical things have provided the Creator with the model for decora)ng the whole world.