Science in the Seventeenth Century

Bacon and the English

The first quarter of the seventeenth century belonged to Bacon and his development of rules for inductive thinking—for empiricism or knowledge from experience. The second quarter belonged to Descartes, deduction, and the primacy of knowledge from the mind.

Bacon was born in London to Nicholas Bacon and his second wife. Like Descartes and Newton, he was a sickly child and was mostly educated at home in his early years. He went up to Trinity College, Cambridge at age 12 where his tutor was Dr. John Whitgift who would later become Archbishop of Canterbury. He later (like Descartes) attended the University of Poitiers.

Early on he decided that the Aristotelian philosophy was an intellectual dead end. Between 1576 and 1579 he travelled with the English ambassador through France and occasionally acted as a diplomatic courier. When his father died in 1579, Bacon’s inheritance was confused and he was forced to take up law to support himself. He practiced law and was elected to Parliament in 1584 and also began to dabble in Puritanism. In 1586 he was one of the members of Parliament that called for the execution of Mary Queen of Scots. He did become advisor to Robert Devereux Earl of Essex who was Queen Elizabeth’s favorite after 1591. When Devereux was arrested for treason, Bacon turned on him and participated in the prosecution that resulted in Essex’s beheading.

He rattled around a series of minor government offices and missed appointments to several more important ones and stayed in more or less constant financial distress. In 1598 he was arrested for his debts. When James I came to the throne, Bacon’s status rose and he was knighted in 1603. In 1608 his uncle, Lord Burghley, finally got him a government post (Clerk of Star Chamber) that carried a magnificent salary of £16,000 a year. He was made attorney general in 1613 and prosecuted Somerset in 1616. In 1617 he got his father’s former office of Lord Keeper of the Royal Seal and, in 1618, he was made Lord Chancellor.

He remained in financial difficulty and, in 1621, was accused of 23 counts of corruption (especially taking bribes) to which he confessed and which resulted in his being briefly held in the Tower of London and being permanently barred from Parliament. He barely missed being stripped of his titles and retired to spend his last five years revising and improving essays he had written earlier.

His private life has been the subject of a good deal of speculation. It is widely believed that he favored young boys and he ultimately disowned his wife (whom he had married when she was 14) when he found out she was having an affair.

He died in Highgate. The story is that he wanted to try the experiment of preserving a fowl by stuffing it with snow and caught pneumonia in the process.

As early as 1592 in a letter to his uncle Lord Burghley, Bacon announced that he would reorganize all of learning. With that he started on the project that would result in the Magna Instauratio or Great Instauration that would summarize all his thoughts on logic, epistemology, and natural philosophy. He

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actually only finished two of a planned six parts. The second of the six was the Novum Organum (the name from Aristotle’s Organum. In the first book he declared that learning in Europe, under the persistent and pervasive influence of Aristotle, had ossified. It was polluted by charlatans and occultists practicing astrology, magic, and alchemy none of which had anything to do with science. Beyond those were the Scholastics who spent their time quibbling and splitting hairs (How many angels and so forth) and contributing nothing new. And then there were those who occupied themselves trying to recover every last fragment of ancient knowledge (the humanists) and were contributing nothing new.

Bacon thought that new knowledge led to new inventions and techniques which translated into power. None of the above faulty models got you to that. There was no progress. Actually, the idea that knowledge could progress at all was the key Baconian insight and was entirely at odds with the scholastics (and Aristotle as well who thought history moved in cycles and not in a ramp). That idea of progress in history—of things getting better—would be at the heart of the Enlightenment. Remember back at the beginning of this journey we talked about the fact that scientific knowledge was different than theology and the arts in that we expect it to progress whereas the others do not.

For that to work the importance of science had to increase and the importance of history and literature had to decrease. And the tool toward progress and more important science was the subject of part two, the New Organon. That new instrument was inductive logic freed from the failings of poor logic.

Bacon’s philosophy centered on induction; that is knowledge proceeded from fact to axiom to law. The idea was to accumulate enough facts to see the pattern that would take you to the causes behind nature’s behavior. This is really the scientific method. His major work was the Novum Organum (New Instrument) of 1620 in which he discusses the three inventions that he believed changed the world: “Printing, gunpowder and the compass: These three have changed the whole face and state of things throughout the world; the first in literature, the second in warfare, the third in navigation; whence have followed innumerable changes, in so much that no empire, no sect, no star seems to have exerted greater power and influence in human affairs than these mechanical discoveries.” It is interesting that he arrived at scientific induction backwards starting with technical advances. The frontis shows a galleon sailing through the Pillars of Hercules and symbolizes both the new world of exploration and the departure of knowledge from the restrictions of Aristotelian cosmology. The Latin at the bottom is from Daniel 12:4 and says “Many will travel and knowledge will be increased.”

The language is florid (Johnson said “A dictionary of the English language might be compiled from Bacon’s works alone”) in spite of the fact that he argued in favor of spare, concise, clear speech. King James said of the New Organon that it was “like the peace of God, which passeth all understanding.”

Anyone who wanted knowledge had to free himself from false notions that distorted the ability to arrive at truth. He called these the idols and divided them into four categories:

Idols of the tribe which are common to human nature. They are innate and can only be recognized, not avoided. The example would be the senses which are easily deceived. Another example would be the natural human tendency to see order where there is none and to see what we believe will be true.

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Idols of the cave which are peculiar to an individual. These are the result of our culture, family background, education, religion, gender, class, experience.

Idols of the marketplace which come from associations with others. The prime example is error caused by language and its vagueness, especially the tendency for words to carry hidden meanings and implications.

Idols of the theatre which come from abuse of authority. This is the condemnation of scholastic philosophy which comes from logic chopping but not from experience. He also includes religion and superstition in this category and was particularly critical of attempts to explain nature based on reference to the Old Testament.

His idea of induction proceeds “at once from . . . sense and particulars up to the most general propositions.” Once you have a generalization that is true “All Olympians are great athletes” you can go to the particular cases “All Olympic swimmers are great athletes” or “All Olympic runners are great athletes.” But that requires that you examine every special case because if there is one swimmer who is not a great athlete the whole thing falls apart. This will reappear when we get to Kuhn and his anomalies. Bacon forbade the leaps of intuition that actually change paradigms. He was a plodder and did not allow for imagination and imaginative hypotheses.

That said one of the ironies is that he assumed that the number of facts and interpretations was, in fact, limited. “The particular phenomena of the arts and sciences are in reality but as a handful, the invention of all causes and sciences would be the labour of but a few years.” Cited in Butterfield 116.

Descartes and the French

Descartes might legitimately be called the “Father of Modern Philosophy” because it was he who really precipitated the western European break from the stranglehold of Aristotelian cosmology and the medieval scholastics who had preserved it and passed it from generation to generation like a family heirloom. Descartes had problems in two areas. First, he doubted sensation as the source for all knowledge. He believed there was an innate sense of truth in all men. Second (ironically) he was suspicious of the Aristotelian fall back to “first causes” when their ability to come up with natural explanations hit a wall. He wanted to explain all natural phenomena as the mechanical interaction of basic (small) bodies or corpuscles.

Descartes was born into a middle class family (his father was a lawyer and member of the provincial parliament and a number of his relatives were physicians) in the small town of La Haye near Tours in 1596. His mother died shortly after his birth and he spent the next four years with his maternal grandmother. His father remarried when he was four. Descartes was chronically ill until he was sent to a Jesuit college in 1607 where he spent the next seven years. He was trained in the classical trivium (grammar, rhetoric, and logic) and quadrivium (arithmetic, music, geometry, and astronomy). He also was taught metaphysics, natural philosophy (science), and ethics, but his natural preference was for

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mathematics. In 1616, he received a law degree and was licensed to practice both civil and canon law at the University of Poitiers. What happened the next two years is not certain, but there have been suggestions that he had a spell of mental illness.

In 1618, he joined the army of Maurice of Nassau as a “gentleman volunteer” in the Netherlands where he met Isaac Beekman who tutored him in mathematics and introduced him to the problems of mechanics and whom he would later accuse of plagiarizing his work. In 1619 he went to Germany to join the army of Maximilian of Bavaria with whom he fought in the Battle of White Mountain in 1620. While at Ulm he had some sort of mystical experience—possibly a dream—in which he “realized” that the world operated on mathematical principles. Sounds a little Pythagorean. He was 23 and it was November 10, 1619 and he remembered the experience all his life. He began to think about a new method of scientific inquiry and a unified system of science.

He dabbled in optics and may have discovered the law of refraction. He also started what would be a lifelong correspondence with Father Marin Mersenne. This was almost exactly coincident with Galileo’s publication that would ultimately land him in house arrest and with Thomas Hobbes’s discovery of geometry. The minds of Western Europe were awakening to the mathematical universe and numbers as the language of understanding that universe (or science in another word). The thing here is that Aristotelian science had been almost entirely (geometry excluded) categorical. It was based entirely on words which are subject to shades of meaning. Descartes, Galileo, and Hobbes were toying with the idea that the only real knowledge of nature was that which could be reduced to numbers that had no shades of meaning. He would get led astray here.

He returned to La Haye in 1623 and invested in bonds that made him financially independent for the rest of his life. He was also with Richelieu at the siege of La Rochelle in 1627.

Descartes took up residence in the Netherlands in 1628 and stayed there until Queen Christina of Sweden invited him there in 1649. While in the Netherlands, he studied mathematics at Leiden University and astronomy the same place and taught at Utrecht University. Between 1629 and 1632 he wrote his first major treatise (The World) that supported the heliocentric vision of the world and that also proposed mechanistic physics as a replacement for Aristotelian “first causes.” At that time, the Church condemned Galileo and Descartes suppressed publication of his book. Between 1634 and 1636 he wrote Dioptique and Meteors with a preface that became Discours sur la Methode. All three were published in 1637. This was also the time that he fathered a daughter by the maid of the family that housed him although the child died early.

The Discours is clearly one of the most important and influential books in the history of science (and probably in the history of western thought). It is built around four rules of logic:

My first rule was to accept nothing as true which I did not clearly recognize to be so; to accept nothing more than what was presented to my mind so clearly and distinctly that I could have no occasion to doubt it.

The second rule was to divide each problem or difficulty into as many parts as possible.

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The third rule was to commence my reflections with objects which were the simplest and easiest to understand, and rise, thence, little by little, to knowledge of the most complex.

The fourth rule was to make enumerations so complete, and reviews so general, that I should be certain to have omitted nothing.

Note that the first rule assumes the innate sense of “truthfulness” that is at the center of Cartesian ontology. This said another way, makes the assumptions and definitions that are the foundation of Euclidean deduction something innate in the human mind. There is a good deal of religion here as well. Descartes was a devout Catholic and the basis of the innateness for him was that God put it there.

The second and third are the basis of the scientific method. The fourth restates mathematics as the language of science.

When he published Meditations on First Philosophy in 1639 he was threatened by the Church for questioning Aristotle and presumably Christianity as well. The ensuing row led to threats to expel him from Utrecht and to publically burn his books. Descartes fled to Protestant Hague and the protection of the Prince of Orange.

In 1644 he published Principles of Philosophy with four books: The Principles of Human Knowledge, The Principles of Material Things, The Visible Universe, and The Earth. He subsequently added The Passions of the Soul, and the lot were translated into vernacular French in 1647.

Christina invited him to Sweden in 1649 where he was expected to be up at 5:00 AM to discuss philosophy with her. Either the schedule or the climate treated him badly and he died February 11, 1650 of pneumonia. Since he was Catholic living in a Protestant country, he was buried in a graveyard used for unbaptized infants in Stockholm. His remains were later transferred to the Abbey of Saint-Germain-des-Pres on the Left Bank. The Pope put his works on the Index of Prohibited Books in 1663.

Descartes’ break with Aristotle was especially significant because the Greek had been so widely accepted by the educated (who were all churchmen) through the Middle Ages that Aristotelianism, scholasticism, and Christianity were in many ways one and the same. The problem with Scholasticism was that its reliance on first causes was tautological. For instance, a fish swims because it is the nature of a fish to swim. The fish’s final goal in life is to swim and it swims so it can be a fish. The religious thought behind that is that God created the fish to swim and gave it that essence and the form necessary to fulfill that mission. In physics, a stone fell to the ground because it was the natural state of a stone to be at the center of the earth and it was merely seeking its natural position. To Descartes, that seemed no explanation at all. He argued that the behavior of things (including animals and even man) could be understood as a function of the interactions between their basic parts.

Besides, how can a stone know it wants to get to the center of the earth if it cannot think? And that led Descartes to separate mind from body with the ultimate reasoning being that actual existence is defined by the ability to think. And, by extension, the only true knowledge comes from thinking and the mind not from experiment and perception.

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Descartes also took issue with the idea that all knowledge comes from sensory input. After all, an object in the distance appears smaller than it really is. The assumption behind that is that the mind starts as a tabula rasa. Descartes argued that perceptions are often faulty and that any truth obtained from sensation was subject to faulty perception and could only be probable, never absolute. He argued for the presence of absolute truth and certain knowledge as innate to the mind.

He also believed that the soul was in the pineal gland because he (incorrectly) believed that only humans had that organ and it was at the center of the body and was not duplicated like other parts of the brain and that was where the mind interacted with the body. The pineal was bathed in CSF which communicated through the nerves to control the body. He performed dissections on live animals with the belief that only humans could feel pain. The animals distressed cries were just reflex. Later, he realized that animals also had pineals and he could not figure out how an immaterial mind would actually interact with a material body and he abandoned the pineal as a connection.

Descartes used a tree as a metaphor for his philosophy. The roots were the metaphysics or the absolute truths. The trunk was physics and the branches were the other sciences (for him, medicine, mechanics, and morals) and the fruits that were useful came from the branches and the “sciences” that were closer to solving problems than to understanding actual truth.

Descartes’ philosophy was grounded in geometric deduction. He believed that there were a set of axioms and definitions that were undeniably true. From those, theorems could be deduced that led to absolute knowledge—universal, necessary, and certain. No probability allowed. No doubt allowed. And, if it can be reduced to mathematics, it is beyond doubt. 2+2 is ever and always 2+2 and is not subject to the uncertainties of perception. He went off the rails a bit, probably as a result of his success in creating analytic geometry where he combined Euclidean deduction with algebra in what we call Cartesian coordinates. The problem was that he went from that to the idea of a universe that ran by solid geometry.

Descartes needed one axiom that was undeniably true that he could use as the Euclidean foundation for everything else. That axiom was Cogito ergo sum. If one is capable of asserting that he or she exists, then he or she must be thinking. Anyone thinking must also exist. Actually, a bit circular. A person is “A thing that doubts, understands, affirms, denies, is willing, is unwilling, and also imagines and has sense perceptions.” Imagination and perception may be distorted by the interaction between sensation and the body, but ideas and volition are pure products of the mind with no interaction with the body. Of course, neurochemists would strenuously argue with that.

Descartes did mathematical investigation that was the basis of Newton’s geometric approach to calculus. He also created analytic geometry and his Cartesian geometry used algebra to describe geometry. He was the first to use superscripts to denote exponents.

Descartes devised a non-atomistic, mechanistic physics in which all physical phenomena were to be explain by the configuration and motion of a body’s miniscule parts.

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This mechanistic physics is also a point of fundamental difference between the Cartesian and Scholastic-Aristotelian schools of thought. For the latter (as Descartes understood them), the regular behavior of inanimate bodies was explained by certain ends towards which those bodies strive. Descartes, on the other hand, thought human effort is better directed toward the discovery of the mechanistic causes of things given the uselessness of final causal explanations and how it is vain to seek God’s purposes. Furthermore, Descartes maintained that the geometric method should also be applied to physics so that results are deduced from the clear and distinct perceptions of the geometrical or quantifiable properties found in bodies, that is, size, shape, motion, determination (or direction), quantity, and so forth. But then he got into the problem we mentioned above. What was it that made the bodies move? He imagined two sorts of matter. The fine, basic matter that was indivisible and continuous and moved about in vortices that attracted and repelled one another and the larger sort of matter that we can sense that is moved by the vortices. Descartes imagined a universe full of invisible toilet bowls with vortices whirling about that drove all the bodies, both small and large, toward their inevitable point at the bottom of the swirling cone. Unfortunately, he had absolutely no physical evidence for the vortices and it would be up to Newton to dispose of them. Of course, that is not so much more unbelievable than to think that matter is distortions in the warped fabric of space-time.

Since the matter constituting the physical universe and its divisibility were previously discussed, a brief explanation of the circular motion of bodies and the preservation of motion is in order. The first thesis is derived from God’s immutability and implies that no quantity of motion is ever added to or subtracted from the universe, but rather quantities of motion are merely passed from one body to another. God’s immutability is also used to support the first law of motion, which is that “each and everything, in so far as it can, always continues in the same state; and thus what is once in motion always continues in motion” (AT VIIIA 62-63: CSM I 241). This principle indicates that something will remain in a given state as long as it is not being affected by some external cause. So a body moving at a certain speed will continue to move at that speed indefinitely unless something comes along to change it. The second thesis about the circular motion of bodies is discussed at Principles, part II, section 33. This claim is based on the earlier thesis that the physical universe is a plenum of contiguous bodies. On this account, one moving body must collide with and replace another body, which, in turn, is set in motion and collides with another body, replacing it and so on. But, at the end of this series of collisions and replacements, the last body moved must then collide with and replace the first body in the sequence. To illustrate: suppose that body A collides with and replaces body B, B replaces C, C replaces D, and then D replaces A. This is known as a Cartesian vortex.

Descartes’ second law of motion is that “all motion is in itself rectilinear; and hence any body moving in a circle always tends to move away from the center of the circle which it describes” (AT VIIIA 63-64: CSM I 241-242). This is justified by God’s immutability and simplicity in that he will preserve a quantity of motion in the exact form in which it is occurring until some created things comes along to change it. The principle expressed here is that any body considered all by itself tends to move in a straight line unless it collides with another body, which deflects it. Notice that this is a thesis about any body left all by itself, and so only lone bodies will continue to move in a straight line. However, since the physical world is a

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plenum, bodies are not all by themselves but constantly colliding with one another, which gives rise to Cartesian vortices as explained above.

The third general law of motion, in turn, governs the collision and deflection of bodies in motion. This third law is that “if a body collides with another body that is stronger than itself, it loses none of its motion; but if it collides with a weaker body, it loses a quantity of motion” (AT VIIIA 65: CSM I 242). This law expresses the principle that if a body’s movement in a straight line is less resistant than a stronger body with which it collides, then it won’t lose any of its motion but its direction will be changed. But if the body collides with a weaker body, then the first body loses a quantity of motion equal to that given in the second. Notice that all three of these principles doe not employ the goals or purposes (that is, final causes) utilized in Scholastic-Aristotelian physics as Descartes understood it but only the most general laws of the mechanisms of bodies by means of their contact and motion.

In part five of the Discourse on Method, Descartes examines the nature of animals and how they are to be distinguished from human beings. Here Descartes argues that if a machine were made with the outward appearance of some animal lacking reason, like a monkey, it would be indistinguishable from a real specimen of that animal found in nature. But if such a machine of a human being were made, it would be readily distinguishable from a real human being due to its inability to use language. Descartes’ point is that the use of language is a sign of rationality and only things endowed with minds or souls are rational. Hence, it follows that no animal has an immaterial mind or soul. For Descartes this also means that animals do not, strictly speaking, have sensations like hunger, thirst and pain. Rather, squeals of pain, for instance, are mere mechanical reactions to external stimuli without any sensation of pain. In other words, hitting a dog with a stick, for example, is a kind of input and the squeal that follows would be merely output, but the dog did not feel anything at all and could not feel pain unless it was endowed with a mind. Humans, however, are endowed with minds or rational souls, and therefore they can use language and feel sensations like hunger, thirst, and pain. Indeed, this Cartesian “fact” is at the heart of Descartes’ argument for the union of the mind with the body summarized near the end of part five of the Discourse and laid out in full in the Sixth Meditation.

Yet Descartes still admits that both animal and human bodies can be best understood to be “machine[s] made of earth, which God forms.” (AT XI 120: CSM I 99). The point is that just as the workings of a clock can be best understood by means of the configuration and motion of its parts so also with animal and human bodies. Indeed, the heart of an animal and that of a human being are so much alike that he advises the reader unversed in anatomy “to have the heart of some large animal with lungs dissected before him (for such a heart is in all respects sufficiently like that of a man), and be shown the two chambers or cavities which are present in it” (AT VI 47: CSM I 134). He then goes on to describe in some detail the motion of the blood through the heart in order to explain that when the heart hardens it is not contracting but really swelling in such a way as to allow more blood into a given cavity. Although this account goes contrary to the (more correct) observation made by William Harvey, an Englishman who published a book on the circulation of the blood in 1628, Descartes argues that his explanation has the force of geometrical demonstration. Accordingly, the physiology and biology of human bodies, considered without regard for those functions requiring the soul to operate, should be conducted in the

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same way as the physiology and biology of animal bodies, namely via the application of the geometrical method to the configuration and motion of parts.

Descartes’ religion was problematic. He went to great lengths to prove the existence of God, but his Catholicism was always questioned. Pascal said, “I cannot forgive Descartes; in all his philosophy, Descartes did his best to dispense with God. But Descartes could not avoid prodding god to set the world in motion with a snap of his lordly fingers; after that, he had no more use for God.”

Newton and Inertial Physics

Newton was the most important and influential figure in science between Aristotle and Einstein. He actually came at the right time. In the 13C, Roger Bacon had tried to study the nature of light and the rainbow and had been accused of black magic and had been prohibited from teaching experimentation in European universities and had even been imprisoned for “suspected novelties.” Christopher Marlowe had said that audiences loved Dr. Faustus for being damned when he tried to understand the laws of nature. But Newton came in a time when those adventures were part of the popular ethos. It was the time of the Royal Society of which Newton would be president for a quarter of a century. Descartes had popularized the idea that there was nothing in nature that was beyond the potential understanding of man (and he, in fact, thought that he had already deciphered most of it.) Newton would drop to mathematics and express a considerable amount of disdain for unfounded “hypotheses” such as those expounded by Descartes, but he would fully subscribe to the mechanistic dogma that said there was no difference between a man and a watch except the degree of complexity.

Newton was born approximately 11-15 weeks premature in the Lincolnshire village of Woolsthorpe-by-Colsterworth. By the Julian calendar still used in England at that time, he was born on Christmas day of 1642 (although his birth has subsequently been re-done in the Gregorian calendar as January 4, 1643.) His mother later said he was so small that he would fit in a quart sized mug. His father, a prosperous but illiterate farmer also named Isaac, died three months before he was born. His mother re-married when Isaac was three to Reverend Barnabus Smith and Isaac was left with his maternal grandmother. He disliked his stepfather so much that he later confessed to having threatened to burn the house with his stepfather and mother in it. He was an odd child given to inventing strange things like a kite with a candle that he could fly at night and convince the neighbors was an apparition. His mother thought he would never be good for much.

At 12 he was sent to the King’s School in Grantham where he stayed until he was 16, by which time his stepfather had died and his mother tried to get him to run the family farm. He hated it and managed to get sent back to school when he convinced his mother he was hopeless for anything else. In 1661 he went up to Trinity College, Cambridge as a combination student and servant to wealthier students. While a student he began work on what would become the calculus.

He received his degree in 1665 just in time for the university to close as a precaution against plague. He went back to Woolsthorpe for two years during which he did most of the thinking that resulted in the calculus, his work on optics, and his law of gravitation.

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“In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of colours & in the May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to the orb of the Moon, & having found out how to estimate the force with wch a globe revolving within a sphere presses the surface of the sphere: from Kepler’s Rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centres of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must be reciprocally as the squares of their distances from the centres about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, and found them answer pretty nearly. All this was in the plague years of 1665 and 1666 For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more than at any time since.”

He went back to Trinity as a fellow in 1667 and, in spite of an undistinguished career as an undergraduate, became Lucasian Professor of Mathematics in 1669, probably mostly from the influence of Isaac Barrow who left the post to become a royal chaplain. As professor, he taught rarely but published enough to satisfy the rather modest demands of the post.

Deciphering the nature of white light was the first experiment. Previously it had been generally accepted that the various colors were different from one another and from white light in a qualitative way—that is they had innate properties that differentiated them, although what those qualities might be as undefined. It is the essence of Newton’s thinking that he studiously avoided undefined qualities (with one notable exception) and tried to replace them with numbers. By breaking white light into a spectrum with each color refracted a different and measurable amount, light was broken quantitatively into its parts. That was the essence of his method. Newton made mathematics the language of physical science.

He published the Principia on July 5, 1687. The book was recognized as unique and generated a good deal of comment, much of it critical.

The Principia is one of the landmarks (maybe one of two) in the history of physics. And Newton (along with Gottfried Wilhelm Leibniz) invented differential and integral calculus—the language of physics. And he created the science of optics by showing that white light could be divided into colors each of which has a unique refractive index—and showed how to construct a reflecting telescope to get around the aberrations introduced by ground lenses. The telescope was important because all previous ones had been refractors. The problem here was that magnification is a function of the size of the lens and the lens can only be supported on its edges. As the lenses get big, their weight distorts them and leads to poor optics. A mirror can be supported from behind and can be much larger. Newton actually made his own tools and his own lenses since he didn’t trust anyone else to do it. He submitted the description to the Royal Society (of which more in a moment) and they were so impressed that they advised him to keep it secret and took measures to do so themselves lest it be copied by “forreiners,” in particular the

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French. They elected him Fellow the following week. He would become president in 1703 and serve in that office for the next 25 years.

He was roundly criticized for postulating gravity as a force that acted at very great distances. This appeared to be the introduction of magic into science since it could not be proven or explained. His response (Hypotheses non fingo) was that it was enough that the data implied the presence of gravitational attraction. He did not have to explain it or come up with a cause for it. The data spoke for themselves.

“Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power. . . . But I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. An 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.”

All of that is somewhat ironic considering the fact that he spent most of his later years writing religious tracts justifying a literal interpretation of the Bible and looking for the philosopher’s stone. He would write 650,000 words on alchemy and another 1.3 million on theology and the Bible. Actually, Newton was a committed Anglican and, in this one case, he fell back on the deity as an explanation. Something had to start a revolving body in motion before it could orbit and something had to create the gravitational force and constant. Neither could be explained by experiment. And they still can’t.

What must be understood about Newton’s arriving at a concept of gravity is that no one previously had made any satisfactory attempt to explain why planets should move around the sun. Copernicus had avoided the question altogether. Kepler had dreamed up a force (anima motrix) emanating from the sun that drove the planets in a circle that was deformed into an ellipse by magnetism between the various bodies. What that force was or how it might operate was left to mystery. London in the 1600s was a hotbed of scientific speculation and the brightest of the English thinkers had gotten together to try out various theories on one another, including Robert Hooke, Edmund Halley, and Sir Christopher Wren. They all believed that something must make the planets move in Kepler’s elliptical orbit and that his anima motrix was a poor, cobbled explanation. Moreover, they also knew that the intensity of light decreased in direct proportion to the square of the distance from the source and had a hunch that the force the sun must exert should follow something like the same law but they had no idea how to prove that. In January 1684, Halley had published the F=1/D2 formula (although with no supporting evidence) and Hooke claimed that “upon that principle all the laws of the celestial motions were to be demonstrated” and moreover claimed that he had done just that. When offered a sizeable amount of money (by Wren) he could not come up with the numbers.

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But they all knew that Newton had a talent for mathematics. In August 1684, Halley went to Cambridge to talk with Newton. “Without mentioning either his own speculation, or those of Hooke and Wren, he at once indicated the object of his visit by asking Newton what would be the curve described by the planets on the supposition that gravity diminished as the square of the distance. Newton immediately answered, an Ellipse. Struck with joy and amazement, Halley asked him how he knew it. “Why” replied he, “I have calculated it;” and being asked for the calculation, he could not find it, but promised to send it to him. After Halley left Cambridge, Newton endeavored to reproduce the calculation, but did not succeed in obtaining the same result. Upon examining carefully his diagram and calculations, he found that in describing an ellipse coarsely with his own hand, he had drawn the two axes of the curve instead of two conjugate diameters somewhat inclined to one another. When this mistake was corrected he obtained the result which he had announced to Halley.” Quoted in Cohen Birth of a New Physics 155-6.

The Royal Society started as a group of approximately 12 scientists, known as the Invisible College, which met at a variety of locations, including the houses of their members and Gresham College. Members at particular times were John Wilkins, Jonathan Goddard, George Ent, Samuel Foster, Theodore Haak, Samuel Hartlib, John Wallis, Robert Hooke, Christopher Wren, William Petty, Cheney Culpeper, John Evelyn, Robert Boyle and Benjamin Owsley. The group discussed the "new science", as promoted by Francis Bacon in his New Atlantis, from approximately 1645 onwards.[2] It initially had no rules or methods, and the primary goals were to organize and view experiments and communicate their discoveries to each other.[3] The group varied over time, eventually splitting into two distinct factions in 1638 due to travel distances; the London Society and the Oxford Society. The Oxford Society was more active owing to the fact that many members of the overall College lived there, and was established as The Philosophical Society of Oxford, run under a set of rules still retained by the Bodleian Library.[4]

The London group continued to meet at Gresham College, primarily after lectures hosted by Christopher Wren. The membership expanded at this time, growing to include Lord Brouncker and Timothy Clarke.[5] It was forced to disband in 1658 during the English Civil War after soldiers invaded their rooms; after the English Restoration, they returned to meeting at Gresham College.[6] It is widely held that these groups were the inspiration for the foundation of the Royal Society.[4]

An alternate view of the founding, held at the time, was that it was due to the influence of French scientists and the Montmor Academy in 1657, reports of which were sent back to England by English scientists attending. This view was held by Jean-Baptiste du Hamel, Giovanni Domenico Cassini, Bernard le Bovier de Fontenelle and Melchisédech Thévenot at the time, and has some grounding in that Henry Oldenburg, the Society's first Secretary, had attended the Montmor Academy meeting.[7] Robert Hooke, however, disputed this, writing that:

"[Cassini] makes, then, Mr Oldenburg to have been the instrument, who inspired the English with a desire to imitate the French, in having Philosophical Clubs, or Meetings; and that this was the occasion of founding the Royal Society, and making the French the first. I will not say, that Mr Oldenburg did rather inspire the French to follow the English, or, at least, did help them, and hinder us. But 'tis well known who were the principal men that began and promoted that design, both in this city and in Oxford; and that a long while before Mr Olden, burg came into England. And not only these Philosophic Meetings were before Mr Oldenburg came from Paris; but the Society itself was begun before he came hither; and those who then knew Mr Oldenburg, understood well enough how little he himself knew of philosophic matter"[8]

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On 28 November 1660, a group of scientists from and influenced by the Invisible College met at Gresham College and announced the formation of a "College for the Promoting of Physico-Mathematical Experimental Learning", which would meet weekly to discuss science and run experiments. At the second meeting, Sir Robert Moray announced that the King approved of the gatherings, and a Royal Charter was signed on 15 July 1662 which created the "Royal Society of London", with Lord Brouncker serving as the first President. A second Royal Charter was signed on 23 April 1663, with the King noted as the Founder and with the name of "The Royal Society of London for the Improvement of Natural Knowledge"; Robert Hooke was appointed as Curator of Experiments in November. This initial royal favor has continued, and since then every monarch has been the patron of the Society.[9]

The Society's early meetings consisted almost entirely of experiments, demonstrated first by Hooke and then by Denis Papin, who was appointed in 1684. The Society also published an English translation of Essays of Natural Experiments Made in the Accademia del Cimento, under the Protection of the Most Serene Prince Leopold of Tuscany in 1884, an Italian book documenting experiments at the Accademia del Cimento.[10] The early experiments varied in their subject area, and were both important in some cases and trivial in others.[11] Although meeting at Gresham College, the Society temporarily relocated to Arundel House in 1666 after the Great Fire of London, which did not harm Gresham but did lead to its appropriation by the Lord Mayor. The Society returned to Gresham in 1673.[12]

There had been an attempt in 1667 to establish a permanent "College" for the society. Michael Hunter argues that this was influenced by "Solomon's House" in Bacon's New Atlantis, and to a lesser extent by J.V. Andreae's Christianopolis, dedicated research institutes, rather than the colleges at Oxford and Cambridge, since the founders only intended for the Society to act as a location for research and discussion. The first proposal was given by John Evelyn to Robert Boyle in a letter dated 3 September 1659; he suggested a far grander scheme, with apartments for members and a central research institute. Similar schemes were expounded by Bengt Skytte and later Abraham Cowley, who wrote in his Proposition for the Advancement of Experimental Philosophy in 1661 of a "'Philosophical College", with houses, a library and a chapel. The Society's ideas contained none of this complexity, and only included residences for a handful of staff, but Hunter maintains that they probably drew inspiration from Cowley and Sktyye's ideas.[13] Henry Oldenburg and Thomas Sprat put forward ideas in 1667, and Oldenburg's co-Secretary John Wilkins moved in a Council meeting on 30 September 1667 to appoint a Committee "for raising contributions among the members of the society, in order to build a college".[14] These plans were progressing by November 1667, but never reached fruition due to the lack of contributions from members and the "unrealised - perhaps unrealistic -" aspirations of the Society.[15]

Henry Oldenburg, the secretary of the Royal Society, had devised a clever way of assigning priority to discoveries. “When any Fellow have any philosophical notion or invention not yet made out, and desired the same, sealed in a box, to be deposited with one of the secretaries till perfected, this might be allowed, for better securing inventions to their authors.” Those claiming a new bit of knowledge were requested to write reports and submit them to the society. That allowed priority to be assigned and also guaranteed a steady flow of material that the Society could publish. Halley convinced Newton to put his calculations into a nine page report (De Motu) which the Society could record in its annals. It was far from complete but good enough to demonstrate that the inverse square law could account for Kepler’s elliptical orbits. It only took a bit more to demonstrate the law of inertia and that the rate of change of motion is proportional to the force applied to a body—the first and second laws.

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This was an interesting educational situation. Prior to the 17C, it had been the job of universities to transmit the body of knowledge inherited from the ancients. Now it was the province of academia to amass new knowledge, assign priority for its discovery (with the attendant rewards), and transmit that information to the general public. As dense as Newton’s work was, it became the subject of popular discussion as in Madame de Chatellet’s salons in Paris.

Newton then went back to work he had started in his twenties when he was also doing Opticks and creating calculus. He expanded the work into a 9 page series of lectures that formed the basis of the Principia. When the Principia was published, Hooke claimed that Newton had stolen the idea of gravity from him. Newton acknowledged that Hooke (among a number of others) had posed the inverse square law of gravity but went on "yet am I not beholden to him for any light into that business but only for the diversion he gave me from my other studies to think on these things & for his dogmaticalness in writing as if he had found the motion in the Ellipsis, which inclined me to try it ..."

The Principia is divided into three parts. The two most interesting are Book 1 in which he lays out the general principles of motion of bodies and Book 3 in which he applies those rules to celestial bodies.

Book 1 starts with a series of definitions and axioms. Perhaps the key assumption—and one that Newton regarded as vitally important and counter to Cartesian relativism—was that space, time, and motion are absolute. Space and time are fixed and independent of the material universe that functions within them. In fact, Newton, being a religious man, viewed the fixed nature of space and time as direct reflections of the fixed and constant Creator.

The first Law says every body at rest stays at rest unless a force acts on it and every body in motion continues in a straight line unless a force acts to change its direction. The second Law says that the change in either motion is directly proportional to the force applied and is in the same direction as the force.

The first law is actually a complete opposite of what Aristotle had convinced people was the truth for millennia. He said that an object would continue to move only if a force continued to be applied. But Newton said it would continue to move unless a force made it stop. Two very different things.

And the second law explained a problem that had vexed scientists a great deal. If Copernicus and Galileo were right and the earth was really going around at 24,000 miles an hour, how come when one threw a ball in the air it came back to the same spot? Shouldn’t it come down a few feet away since the earth had rotated out from under it? The second law says a force (in this case the force of gravity) will only affect motion in the direction in which it acts. But gravity is at right angles to motion tangent to the circle (i.e. motion on the surface of the sphere) and force at a right angle will not change the forward motion. The ball is in forward motion when it is thrown up and continues to be in forward motion all the way up and all the way down. The only change is the negligible force of air friction. Illustration from Cohen Birth.

The tendency of the body go either remain at rest or continue moving in a straight line is also known as inertia. And once you get that, you can understand how the planets and other celestial bodies move in

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their orbits. He had refuted Aristotle and had also generalized what happens to bodies on earth to the cosmos which had always been assumed to operate by a different set of rules. It is interesting that he called his Book Three a “System of the World.” And Newtonian mechanics seemed to explain everything and he follow on assumption was that, if one knew all the starting conditions perfectly, one could apply the laws and predict the future perfectly. It isn’t hard to see where the Enlightenment came from.

It wasn’t all so certain. Newton did manage to reduce the elliptical orbits of comets to mathematics. That was a great accomplishment since they had previously been generally considered ill omens. Then he proceeded to state that they were a necessary part of the planetary ecology since the constant growth and decay of living organisms on earth used up the vital spirit of the planet and he surmised that the vaporized material in the tail of the comets replenished that spirit.

Newton was also a religious man. Remember, the planets move in ellipses. If they were subject only to the force of gravity from the sun, they would fall directly into it. They don’t because something has pushed them in a straight line and that motion is turned into a curve by the second force of gravity. But what pushed them forward to begin with? Newton used that as an argument for the existence of God because it must have been he that gave the initial push. Now we would view that as foolish. Of course the push came from something like the Big Bang.

But maybe we aren’t all that smart. For the bodies to continue to move in a near circle some force has to be continuously applied or they would fly off into space. Gravity, right? But what keeps gravity going? And how in the world would Newton prove that the force that kept planets going around the sun was identical to that which kept Jupiter’s moons in place or that caused a thrown ball to describe a parabola as it fell to the ground (and even caused the tides)? The formula is F=G (mm’/D2) where F=force, m and m’ are the masses of any two bodies and D is the distance between them. G is the universal gravitational constant and is the unexplained part in all of this. And this is one of those very few “constants” that define how our universe works and for which we have no real explanation.

How in the world did Newton figure that out? The explanation is a pure exercise in mathematics and is in Cohen pages 172-174. In brief, he was able to compute the rate of fall (acceleration) that would be necessary to keep the moon in orbit around the earth since he knew its distance from the earth’s center and its rate of rotation and compare it to the acceleration that caused an object to fall to the ground and the numbers (32ft/sec2) were essentially the same. If that was the case, the force acting on them must be the same. Ergo G is universal. Now here is something really amazing. A constant discovered from objects first on earth and then in the solar system can be shown to apply equally well to the paths of binary stars light years away. It does appear to be truly universal—at least in our universe.

The Principia was very much a paradigm shift in the Kuhnian sense. It drew on a series of anomalies of Aristotelian cosmology that had been identified and discussed by Copernicus, Galileo, and Huygens. The 17C efforts to create a consistent system that would apply to all of nature and that would obey rules that could be reduced to mathematical formulae seemed to have been achieved (and would lead to extension to all sorts of areas of human endeavor culminating in the politics, economics, and social theory of the Enlightenment). Like a good paradigm, Newton’s left a vast arena for future scientists to

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study in fleshing out the system. Its rules provided good explanation and accurate prediction not just on earth but also for the celestial bodies. It was also created by a young and active mind in a relative outsider. He had been an indifferent student and would not be Lucasian professor (the post currently held by Stephen Hawking) until 1669.

Newton is said to have been superseded by Einstein but that is really only true in the special cases where an objects velocity becomes significant in relation to the speed of light. For most purposes (including aiming satellites and lunar explorers) his mechanics work perfectly well. A more basic problem is that he made the underlying assumption that both space and time were absolute and they clearly are not. So he really created a special case in which space and time were absolute. The general case in which they are a function of motion relative to other systems is Einsteinian.

He spent much of his life in fights with his peers—first with Hooke over who was responsible for the idea of gravity and then with Leibniz over who invented the calculus. As president of the Royal Society, he badgered royal astronomer John Flamsteed into giving him his life’s work of observations and then publishing them himself. Flamsteed later bought up 300 or the 400 published copies and burned them.

He got the sinecure as warden of the Royal Mint through the good offices of Charles Montagu, 1 st Earl of Halifax who was Chancellor of the Exchequer. He became president of the Royal Society in 1703 and was knighted by Queen Anne in 1705. He served in Parliament twice but was said to have only opened his mouth to complain about the drafts in the chamber. He had no children and never married and died being taken care of by a niece and her husband in London. He was buried at Westminster. He may have died of mercury poisoning from his experiments trying to turn base metals into gold (he had mercury in his body at autopsy).

Still, he died widely respected and relatively well off (when he was knighted by Queen Anne in 1705, he was the first even to receive that honor for being a scientist—although the term had not yet been invented—and he had been collecting a huge salary as warden of the mint) although almost alone. One assistant who worked with him for thirty years said he had laughed only once in the whole time and that was when someone asked what the point was in studying Euclid.

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