Newton, Four Letters from Sir Isaac Newton to Doctor Bentley. Containing some Arguments in Proof of a Deity & Principia

Las Four Letters from Sir Isaac Newton to Doctor Bentley. Containing some Arguments in Proof of a Deity fueron escritas en 1692-1693[1] y publicadas en Londres póstumamente en 1756. Según Pask, “these private letters … reveal some of Newton’s most important concerns about his system of dynamics[2]. Richard Bentley (1662-1742) fue un clérigo, profesor, crítico y teólogo inglés, el cual, según Koyré, no sabía mucho de física[4]. Bentley era 20 años más joven que Newton. Newton nació el año en que Galileo murió (1642) y murió en 1727.

En la Carta III, Newton recurre a un agente[6] para explicar la atracción de los cuerpos (la fuerza de la gravedad). Newton declara que para él la idea de que la gravedad sea inherente y esencial a la materia es absurda[7]. Koyré escribe: “Bentley … interpreted Newton in the way that became common in the eighteenth century, namely as asserting that physical reality of attraction and of attractive force as inherent to matter[8].La gravedad tiene que ser causada, según Newton, por un agente que actúa según ciertas leyes. Newton no responde si este agente es material o inmaterial, sino que prefiere dejar que los lectores decidan[9]. Como muy bien apunta Koyré[10], en la Carta II, Newton había declarado que, aunque defendiera que la causa de la gravedad no es algo esencial e inherente a la materia, él desconocía la causa: “You sometimes speak of gravity as essential and inherent to matter. Pray, do not ascribe that notion from me; for the cause of gravity is what I do not pretend to know and therefore would take more time to consider of it[11]. En la Carta III, sin embargo, “Newton does not pretend any longer not to know the cause of gravity; he only informs us that he left this question unanswered, leaving it to his readers to find out themselves the solution[12]. En el universo newtoniano, es más coherente que este agente sea inmaterial: “the ‘agent’ which ’causes’ gravity cannot be material, but must be a spirit, that is, either the spirit of nature of his colleague Henry More, or, simply, God”[13].

En la Carta I, Newton declara que cuando escribió los Principia[14] tuvo en mente compaginar sus principios matemáticos con la idea de una divinidad[15]: “When I wrote my treatise about our system, I had an eye upon such principles as might work with considering men for the belief of a Deity[16]. Al final de la Carta I, escribe: “There is yet another argument for a Deity, which I take to be a very strong one; but till the principles on which it is grounded are better received, I think it [is] more advisable to let it sleep”[17]. Aquí parece referirse a la causa de la gravedad, idea que trata en la Carta III. En la Carta II, Newton, aunque confiese no conocer la causa de la gravedad, habla de un poder divino y un agente inteligente: “gravity may put planets into motion, but, without the divine power, it could never put them into such a circulating motion as they have about the sun; and therefore, for this, as well as other reasons, I am compelled to ascribe the frame of this system to an intelligent Agent[18]. En la Carta IV, Newton habla de una divinidad: “the hypothesis of matter’s being at first evenly spread through the heavens, is, in my opinion, inconsistent with the hypothesis of innate gravity, without a supernatural power to reconcile them; and therefore it infers a Deity[19]. Newton, pues, recurre a un dios (un poder divino, un agente inteligente) para explicar el universo. Susskind escribe que Newton era un ferviente creyente, y que escribió más sobre teología[20] (y ocultismo[21]) que sobre ciencia y matemáticas: “For Newton … the existence of an intelligent Creator must have been an intellectual necessity”[22]. Según Newton, el hombre sólo puede tener un conocimiento limitado de Dios, y puede conocerlo a través de la naturaleza y las causas finales: “We know him only by his most wise and excellent contrivances of things, and final causes (…) All the diversity of natural things … arise from nothing but the ideas and will of a Being necessarily existing[23]. En los siglos XX y XXI, en cambio, para muchos hombres de ciencia, Dios es superfluo y la naturaleza es suficiente. Hawking declara: “We are each free to believe what we want and it’s my view that the simplest explanation is[:] there is no God. No one created the universe and no one directs our fate[24]. Referente a la idea de Dios en Newton, Pask escribe: “Some three hundred years later, we still debate this view of God, his relevance for science, and whether a scientist may also be a religious person. Much has been written on this topic[25].

Aunque Newton fuera muy religioso, sólo habla de Dios en los Principia en el “General Scholium”[26]: “This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being (…) This Being governs all things, not as the soul of the world, but as Lord over all (…) The Supreme God is a Being eternal, infinite, absolutely perfect (…) for we say, my God, your God, the God of Israel, the God of Gods, and Lord of Lords (…) He is eternal and infinite, omnipotent and omniscient[27]. Pask escribe: “Newton believes that God is the ‘intelligent designer’ … of the solar system. The suggestion is that only God could make such a system and set it in motion in such a beautiful way”[28]. Newton declara en el “General Scholium” (al igual que en la Carta II a Bentley) que no conoce ni ha podido descubrir la causa de la fuerza de la gravedad, pero que lo importante es que la gravedad existe y que actúa según las leyes que Newton describe en los Principia: “we have explained the phaenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power (…) I have not been able to discover the cause of those properties of gravity from phaenomena, and I frame no hypotheses (…) to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea[29]. Kragh escribe: “While the law of gravitation governed Newton’s cosmos, the true governor was God, who was never absent from the mind of Newton and his contemporaries”[30].Schaffer afirma: “Newton himself wanted to design a Universe where God was absolutely present and absolutely powerful”[31].North escribe:”[according to Newton] if the Universe is in equilibrium, it is God who keeps it so[32].Según Kragh, Newton nunca concibió el universo como una máquina perfecta o un reloj: “It needs to be emphasized that Newton’s cosmos was far from a perfect machine or a clockwork universe. The clockwork metaphor was popular in the seventeenth century and frequently employed by Leibniz, among others, but Newton never mentioned the image of the clock[33].

En el Libro III[34] de los Principia, Newton habla extensamente de la fuerza de la gravedad: describe la fuerza de la gravedad de la luna: “That the force by which the moon is retained in its orbit tends to the earth; and is reciprocally as the square of the distance of its place from the earth’s centre[35]; describe la fuerza de la gravedad de los planetas: “All the planets do mutually gravitate towards one another[36]; describe la fuerza de la gravedad de los cuerpos hacia los planetas: “That all bodies gravitate towards every planet[37]; describe la fuerza de la gravedad de todos los cuerpos: “That there is a power of gravity tending to all bodies, proportional to the several quantities of matter which they contain[38]. La ley de la gravitación universal “predicts the orbits of the earth, the moon, and the planets with great accuracy[39]. En los Principia, Newton no usa “su” famosa ecuación de la fuerza de la gravedad[40] sino que usa proporciones y comparaciones. Newton tampoco introduce la constante G[41]. Newton establece 4 puntos: “(1) gravity is an attractive centripetral … force, (2) it depends inversely on the square of the distance between two bodies, (3) it depends on the product of the masses of the bodies, and (4) it operates for any two bodies … it is a universal force[42]. Hawking escribe: “Newton postulated a law of universal gravitation according to which each body in the universe was attracted toward every other body by a force that was stronger the more massive the bodies and the closer they were to each other[43]. Para encontrar la ley de la gravitación universal fue necesario inventar el cálculo infinitesimal[44]. Según Singh, la ley de la gravitación de Newton resume todo lo que Copérnico, Kleper y Galileo habían intentado explicar sobre el Sistema Solar: “the fact that an apple falls towards the ground is not because it wants to get to the centre of the universe, but simply because the Earth and the apple both have mass, and so are naturally attracted towards each other by the force of gravity[45]. Sellés escribe: “[Para] Galileo … el peso era … una tendencia a ir hacia abajo, al centro de la Tierra. Descartes … atribuyó el peso a la tendencia centrífuga de la materia en rotación dentro de un torbellino (…) [Según] Hooke … los planetas seguían una trayectoria inercial … desviada por una fuerza inversamente proporcional al cuadrado de la distancia al centro y dirigida al mismo”[46]. La ley de la gravedad de Newton explica por qué la Tierra orbita alrededor del Sol: “because both bodies have a mass and therefore there is a mutual attraction between them … the Earth orbits the Sun and not vice versa because the Earth is much less massive than the Sun[47]. Según Kaku[48], todo lo que se mueve en la Tierra se mueve según las leyes de gravedad y el cálculo de Newton. Las ecuaciones de Einstein sólo se utilizan cuando nos acercamos a la velocidad de la luz o a un agujero negro. De las cuatro fuerzas fundamentales[49], la fuerza gravitatoria es la más débil.

La famosa historia de la caída de la manzana de Newton fue contada por Voltaire al mundo en Lettres philosophiques (1734) y Éléments de la Philosophie de Newton[50] (1738). La fuerza que hace caer la manzana es la misma fuerza que hace que la luna “caiga”, es decir, que orbite alrededor de la Tierra[51]. Con la ley de la gravitación universal, Newton unificó los mundos aristotélicos sublunar y supralunar: “the physical effects and laws of physics that we observe on Earth should be taken as valid everywhere in the universe. This is a major change from Aristotle and his theory of perfect heavens; it forms the basis for everything we do in astronomy and astrophysics[52].

Newton fue al parecer una persona reservada y arisca[53]. Tuvo una infancia difícil[54] y nunca formó una familia. Fue amigo de Locke[55]. En 1703 Newton fue nombrado presidente de la Royal Society of London[56]; y en 1705 fue nombrado caballero. North escribe: “[Newton] died … a national figure with an unrivalled international scientific reputation[57]. Según Einstein, Newton fue “[a] brilliant genius, who determined the course of western thought, research, and practice like no one else before or since[58]. Kuhn escribe: “Examples of Newtonianism’s fruitfulness in astronomy could be multiplied almost endlessly, and astronomy was not the only science affected[59]. Jacob afirma: “Of all the great thinkers of the Scientific Revolution there is no doubt … that Isaac Newton is the most important[60].

Según Hawking, los Principia es “probably the most important single work ever published in the physical sciences”[61]. North escribe:”Newton’s Principia is often described as the most important work ever published in the physical sciences[62]. Según Kaku, los Principia es una de las obras más importantes de la humanidad:”Believe it or not, [the Principia] is perhaps one of the most important works ever written by a human being in the 100.000 years since we evolved from Africa”[63].Pask escribe: “The publication of the Principia was one of mankind’s greatest steps … The Principia laid the foundations for the science of mechanics[64]. Kragh afirma: “From a cosmological point of view, Principia is important mainly because it offered the first mathematically formulated explanation of all known celestial phenomena based on a single set of physical laws[65].

Newton y Einstein han sido las dos bombas centrales en la historia de la física, las matemáticas y la astronomía. Newton, junto con Copérnico[66], Tycho[67], Galileo[68], Kepler[69], Huygens[70], Leibniz[71] y Halley[72], entre otros, produjo la llamada Revolución Científica[73]. Según Koyré, “Newton’s natural philosophy stands or falls with the concepts of absolute time and absolute space[74]. Los conceptos de tiempo y espacio absolutos desaparecerán con la Teoría Especial de la Relatividad de Einstein (1905) y la Teoría General de la Relatividad (1907), una teoría de la gravedad completamente nueva: “If Einstein was right, then physicists would be forced to question the work of Isaac Newton, one of the icons of physics”[75]. Según Einstein, tanto el espacio como el tiempo son flexibles y no absolutos: “time is flexible, as are the three dimensions of space (…) the flexibility of both space and time are inextricably linked, which led Einstein to consider a single flexible entity known as spacetime (…) Spacetime consists of four dimensions, three os space and one of time, which is unimaginable for most mortals[76]. Según Newton, la gravedad es una fuerza que atrae a los cuerpos; según Einstein, la gravedad es una curvatura en el espacio-tiempo: “[According to] Newton … an apple fell to Earth because there was a mutual force of gravitational attraction, but [according to] Einstein … the apple fell to Earth because it was falling into the deep hollow in spacetime caused by the mass of the Earth[77]. Susskind hace un comentario interesante: “Surprisingly, in many ways the laws of physics are simpler in curved space-time than they are in Newtonian physics”[78].

Antonia Tejeda Barros, Viena, noviembre 2013

newton-apple

Bibliografía

Hawking, Stephen, A Brief History of Time. From the Big Bang to the Black Holes, Bantam Books, London, 1989 (1988), pp. vi – 211

Koyré, Alexandre, From the Closed World to the Infinite Universe, GB, Forgotten Books, 2008 (1957), pp. iii – 233

Kragh, Helge S., Conceptions of Cosmos. From Myths to the Accelerating Universe. A History of Cosmology, Oxford (UK), Oxford University Press, 2013 (2007), pp. 1 – 276

Kuhn, Thomas S., The Copernican Revolution. Planetary Astronomy in the Development of Western Thought, USA, Harvard University Press, 2003 (1957), pp. vii – 297

Newton, Isaac, Four Letters from Sir Isaac Newton to Doctor Bentley (pp. 203 – 215) en Bentley, Richard, Sermons preached at Boyle’s Lecture; remarks upon a Discourse of Free-Thinking; Proposals for an Edition of the Greek Testament; etc. etc. by Richard Bentley, D. D. Edited, with Notes, by Rev. Alexander Dyce, Francis Macpherson, London, 1838

Newton, Isaac, The Principia (Translated by Andrew Motte), New York, Prometheus Books, 1995 (1729), pp. vii – 455

North, John, The Fontana History of Astronomy and Cosmology, Fontana Press (HarperCollinsPublishers), London, 1994, pp. vii – 697

Sellés, Manuel, Introducción a la historia de la cosmología, UNED, Madrid, 2007, pp. 7 – 301

Singh, Simon, Big Bang. The most important scientific discovery of all time and why you need to know about it, Harper Perennial (HarperCollinsPublishers), London, 2005 (2004), pp. 3-532

Susskind, Leonard, The Black Hole War. My Battle with Stephen Hawking to make the World safe for Quantum Mechanics, 2009 (2008), New York, Back Bay Books / Little, Brown & Company, pp. 3 – 470

Webs & Links

NASA (“The National Aeronautics and Space Administration”)

The Newton Project

Kaku, Michio, “The Universe in a Nutshell”, The Floating University, New York, 2011

The Scientific Revolution. Part I

The Scientific Revolution. Part II

Newton’s Dark Secrets (Dir. Chris Oxley)

Isaac Newton. The Last Magician, BBC, 2013

Hawking, Stephen, “Discovery Channel Curiosity”, S1E1, USA, 2011

NOTAS

[1]La Carta I está fechada el 10 de diciembre de 1692; la Carta II, el 17 de enero de 1692-3; la Carta III, el 25 de febrero de 1692-3; y la Carta IV, el 11 de febrero de 1693 (los años y las relaciones de las fechas son extraños, pero así figuran en el manuscrito)

[2]Pask, Magnificent Principia. Exploring Isaac Newton’s Masterpiece, p. 27

[4] “Richard Bentley … who did not know much physics”, Koyré, From the Closed World to the Infinite Universe, p. 132

[6]It is inconceivable that inanimate brute matter should, without mediation of something else which is not material, operate upon and affect other matter without mutual contact“, Newton, Carta III a Bentley

[7]That gravity should be innate inherent & {essential} to matter so that one body may act upon another at a distance through a vacuum without the mediation of any thing else by & through which their action or force {may} be conveyed from one to another is to me so great an absurdity that I believe no man who has in philosophical matters any competent faculty of thinking can ever fall into it”, Newton, Carta III a Bentley

[8]Koyré, From the Closed World to the Infinite Universe, p. 131

[9]Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial I have left to the consideration of my readers”, Newton, Carta III a Bentley

[10]En From the Closed World to the Infinite Universe

[11] Newton, Four Letters from Sir Isaac Newton to Doctor Bentley, p. 210

[12] Koyré, From the Closed World to the Infinite Universe, p. 132

[13] Ibid.

[14] Aunque las cantidades de las copias de Principia (escrito en latín, la lengua científica de la época) parezcan hoy en día minúsculas, para la época fueron enormes. Pask explica que en la 1ª edición (1687) se imprimieron 300 ejemplares; en la segunda (1713), 750 ejemplares; y en la 3ª (1726), 1.200 ejemplares: “At that time, apparently, 240 was a large printing, so the Principia must have been wanted by many people“, Pask, Magnificent Principia, p. 476. En Inglaterra, los Principia fueron un éxito, pero en la Europa continental “[it] raised opposition and many doubts“, Pask, op. cit, p. 476. La traducción inglesa de Motte apareció en 1729. La base de la mecánica clásica se halla en las tres famosas leyes de los Principia: “la primera recoge el principio de la inercia (…) la segunda … establece la proporcionalidad entre la fuerza y la aceleración (…) la tercera el principio de acción y reacción”, Sellés, Introducción a la historia de la cosmología, p. 169

[15]Para Newton, religión y ciencia eran inseparables

[16] Newton, Four Letters from Sir Isaac Newton to Doctor Bentley, p. 203

[17] Ibid., p. 207

[18] Ibid., p. 210

[19] Ibid., p. 215

[20]Newton llegó a afirmar que en el 2060 se produciría el final del mundo: “We find it surprising that Newton sounds like a tele-evangelist talking about the end of time. We only find it shocking because we’ve made Newton something that he is not“, Force, “Newton’s Dark Secrets”. Newton creía que Jesús era el hijo de Dios, pero negaba la Trinidad: “Because Newton was so convinced that God is extremely powerful and unique, Newton … begins to … deny the divinity of Christ“, Schaffer, “Newton’s Dark Secrets”

[21]Newton era, en secreto, un gran alquimista. En la Inglaterra de los siglos XVII y XVIII, la alquimia era penada con la muerte. Keynes (1883 – 1946) dijo en 1942: “Newton was not the first of the age of reason, he was the last of the magicians”

[22]Susskind, The Black Hole War. My Battle with Stephen Hawking to make the World safe for Quantum Mechanics, p. 277

[23]Newton, The Principia, p. 442, “General Scholium”

[24]Hawking, “Discovery Channel Curiosity”

[25]Pask, Magnificent Principia, p. 465

[26] El “General Scholium” sólo tiene 4 páginas pero es de gran importancia para entender la visión de Newton sobre Dios. “[Newton] wrote the General Scholium for the second edition, and it remained, after a few small changes, in the final, third edition. It takes up only about four pages“, Pask, op. cit.,p. 460

[27] Newton, The Principia, pp. 440, 441, “General Scholium”

[28] Pask, op. cit., p. 462

[29] Newton, op. cit., pp. 442, 443, “General Scholium”

[30] Kragh, Conceptions of Cosmos. From Myths to the Accelerating Universe: A History of Cosmology, p. 67

[31] Schaffer, “Newton’s Dark Secrets”

[32]North, The Fontana History of Astronomy and Cosmology, p. 375

[33]Kragh, op. cit., p. 71

[34] Titulado “The System of the World”. Los Principia contiene tres libros. En el Libro III, “the motions of the planets and their satellites, of the comets, of the Earth and the tides and its seas -all are explained in terms of a universal gravitation. The planet attracts the Sun as the Sun attracts the planet. All matter attracts all other matter, and the force is independent of the type of matter. Only the ‘quantity of matter’ and the separation were significant (…) Newton did not mention Kepler’s name in his Principia until the third book”, North, The Fontana History of Astronomy and Cosmology, p. 369

[35] Newton, op. cit., p. 326, “Proposition III. Theorem III”

[36] Newton, op. cit., p. 329, “Proposition V. Theorem V. Cor. 3”

[37] Newton, op. cit., p. 330, “Proposition VI. Theorem VI”

[38] Newton, The Principia, p. 333, “Proposition VII. Theorem VII”

[39]Hawking, A Brief History of Time. From the Big Bang to the Black Holes, p. 17

[40] Hawking escribe: “Newton’s theory of gravity was based on [a] model, in which bodies attracted each other with a force that was proportional to a quantity called their mass and inversely proportional to the square of the distance between them”, op. cit., p. 11

[41] G representa la constante de la gravitación universal (la fuerza de la gravedad entre dos cuerpos). Es una de las constantes más imprecisas: “…it is extremely difficult to measure G, and of all the fundamental constants, it is one of the most poorly known”, Pask, Magnificent Principia, p. 407

[42]Pask, op. cit., p. 394

[43]Hawking, op. cit., p. 5

[44]“… un nuevo y poderoso procedimiento matemático que fue puesto a punto independientemente en dos versiones distintas denominadas cálculo fluxional y cálculo diferencial, desarrolladas respectivamente por Newton y por Leibniz”, Sellés, Introducción a la historia de la cosmología, p. 175. “Both Leibniz and Newton had independently developed … calculus, which underlies most of modern physics. Although we now know that Newton discovered calculus years before Leibniz, he published his work much later“, Hawking, A Brief History of Time, p. 192. “The whole way of looking at the world changed because of calculus”, Lewin, “Newton’s Dark Secrets”. El cálculo es el estudio del cambio: “For the first time it was possible to calculate quantities that are constantly changing like the speed of a falling apple in any particular moment or our planet’s position changes over time”, Narrator, “Newton’s Dark Secrets”

[45] Singh, Big Bang, p. 119

[46]Sellés, Introducción a la historia de la cosmología, pp. 173, 174

[47] Singh, op. cit., p. 119. Pask escribe: “The center of gravity is always close to the center of the Sun because it is so massive when compared with all the planets“, Magnificent Principia, p. 415

[48]Kaku, “The Universe in a Nutshell”

[49]Las cuatro fuerzas fundamentales (llamadas también fuerzas interactivas o interacciones fundamentales) son: la fuerza gravitatoria, la fuerza electromagnética, la fuerza nuclear fuerte y la fuerza nuclear débil. La fuerza gravitatoria, aunque sea la más débil, siempre atrae, nunca repela, y es la única que actúa en todas las partículas que poseen masa

[50]Voltaire introdujo el newtonismo en Francia (hasta 1738, la ciencia en Francia era cartesiana)

[51] “the same force is responsible for the Moon’s ‘fall’ and a body’s fall on Earth“, Pask, Magnificent Principia, p. 400. Newton escribe: “That the moon gravitates towards the earth, and by the force of gravity is continually drawn off from its recitilinear motion, and retained in its orbit“, The Principia, p. 327, “Proposition IV. Theorem IV”

[52]Pask, op. cit., p. 395

[53]Newton was a complex, difficult and secretive man“, Narrator, “Isaac Newton. The Last Magician”

[54]Su padre murió tres meses antes de que Newton naciera, y su madre lo dejó son su abuela a los tres años, al casarse de nuevo

[55] John Locke (1632 – 1704). Pask escribe: “Newton is most kindly mentioned in Locke’s major work An Essay concerning Human Understanding”, op. cit., p. 27

[56]Fundada en 1662

[57]North, The Fontana History of Astronomy and Cosmology, p. 366

[58]Escrito en 1927, en el 200 aniversario de la muerte de Newton. Citado por Pask, Magnificent Principia, p. 23. La cita de Einstein se halla en su libro Ideas and Opinions (“Mechanics of Newton and Their Influence on the Development of Theoretical Physics”), 1959

[59]Kuhn, The Copernican Revolution. Planetary Astronomy in the Development of Western Thought, p. 262

[60] Jacob, “The Scientific Revolution”

[61]Hawking, A Brief History of Time, p. 5

[62]North, op. cit., p. 372

[63]Kaku, “The Universe in a Nutshell”

[64] Pask, Magnificent Principia, p. 471

[65] Kragh, Conceptions of Cosmos, p. 70

[66] Nicolaus Copernicus (1473 – 1543). Polaco. Obra clave: De revolutionibus orbium coelestium (1543)

[67]Tycho Brahe (1546 – 1601). Danés. Obras clave: De nova stella (1573) y Astronomiæ Instauratæ Progymnasmata (1588)

[68]Galileo Galilei (1564 – 1642). Italiano. Obras clave: Sidereus Nuncius (1610), Lettera … alla gran duchessa … (1615), Discorso del flusso e reflusso del mare (1616), Dialogo dei due massimi sistemi del mondo (1632) y Discorsi e dimostrazioni matematiche, intorno à due nuove scienze (1638)

[69]Johannes Kepler (1571 – 1630). Asistente inglés de Tycho. Obras clave: Astronomia nova (1609), Harmonice mundi (1619) y Mysterium cosmographicum (1621)

[70]Christiaan Huygens (1629 – 1695). Matemático, físico, astrónomo y horólogo holandés; escribió sobre extraterrestres y describió al sol como una estrella más: “In his posthumous Cosmotheoros … -perhaps best known for its detailed description of extraterrestrial life -he severely criticized Kleper’s Sun-centred cosmology and emphasized … that the Sun was just one star among many”, Kragh, Conceptions of Cosmos, p. 69

[71] Gottfried Wilhelm von Leibniz (1646 – 1716). Alemán. Obras clave: Ars combinatoria (1666), Essais de Théodicée sur la bonté de Dieu, la liberté de l’homme et l’origine du mal (1710) y Nouveaux essais sur l’entendement humain (1704 / 1765)

[72] Edmond Halley (1656 – 1742) revisó los Principia de Newton y describió la órbita de 24 cometas. Los “diferentes” cometas de 1531, 1607 y 1682 resultaron ser el mismo cometa con una órbita de 76 años. Halley predijo que el cometa volvería a ser visto en 1758, y así fue (el cometa fue nombrado luego Cometa Halley, el cual fue visto por última vez en 1986)

[73] La Revolución Científica empieza en 1543 con la publicación de De revolutionibus orbium coelestium de Copérnico

[74]Koyré, From the Closed World to the Infinite Universe, p. 118

[75] Singh, Big Bang, p. 117

[76] Singh, op. cit., p. 120

[77] Singh, op. cit., p. 122

[78]Susskind, The Black Hole War, p. 64

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