第 4 章
The Mathematical Revolution Begins
In 1664, Newton encountered Isaac Barrow, Cambridge's first mathematics professor, who examined him on Euclid's Elements-a text Newton hadn't previously studied. Driven by curiosity, Newton acquired advanced mathematical texts from continental Europe, including works by Descartes, Oughtred, and Wallis. That winter, a comet appeared, keeping Newton outdoors night after night observing its path.
Soon after, rumors of plague reached England from Holland. As the epidemic spread through London, killing one in six residents, Cambridge colleges shut down. Newton returned to Woolsthorpe, built himself a study, and began filling his "Waste Book" with notes that evolved into groundbreaking original research. In isolation during the plague year, he transformed himself into the world's foremost mathematician, pushing past the frontiers of known mathematics.
As printed books spread across Europe, a new metaphor emerged: the book of nature. Scholars exchanged knowledge through Latin texts spanning tribal divisions, rediscovering ancient wisdom while surpassing it. Galileo declared that philosophy "is written in this grand book-the universe," composed in "the language of mathematics" with characters of "triangles, circles, and other geometrical figures."
For this solitary scholar, mathematics offered particular comfort-when he found answers, he could judge their correctness without public disputation. He absorbed Euclid's geometric theorems but was truly inspired by Descartes's joining of geometry and algebra. Through symbols and equations, Newton explored relations between quantities, generating curves from equations and freeing "strange new bestiaries of curves" beyond the Greeks' elegant conic sections.
No one truly understands mathematical genius-that rare mental faculty where brilliance sometimes borders on savantism. Newton possessed limitless patience, describing truth as "the offspring of silence and meditation." He would "keep the subject constantly before me and wait 'till the first dawnings open slowly." His Waste Book filled with increasingly abstract computations as he worked obsessively, transforming equations across reference frames.
第 5 章
The Infinitesimal and the Birth of Calculus
While Descartes had warned against arguing about infinity, Newton embraced it. He wrestled with the infinitesimal-that impossible quantity smaller than any finite value yet not zero. As he developed his mathematics, he saw ellipses in multiple ways-geometrically as curves drawn with cord and pegs, analytically as quadratic formulas, or as circles with bifurcated centers.
He devised methods for finding tangents to curves by computing relationships between points separated by infinitesimal distances, using "O" as his symbol for these vanishing increments that could be "ever blotted out." Newton recognized the fundamental connection between differentiation and integration-that problems of tangents were the inverse of problems of quadrature. This insight unified seemingly disparate concepts: time and space, speed and area.
In multiple attempts throughout 1665-66, he developed a system "to resolve Problems by motion," creating a mathematical framework based on continuous change rather than discrete atoms. He called changing quantities "fluents" and their rates of change "fluxions." Working alone at age twenty-four, he had created powerful mathematical tools that would enable the measurement of dynamics and the mathematization of nature.
The Scientific Revolution emerged as a self-conscious break with the past, with Newton often viewed as its culmination. This transformation in human knowledge progressed like a relay race from Copernicus to Kepler to Galileo to Newton, gradually dismantling the Aristotelian cosmology. Copernicus had dared to place the sun at the center of the universe in 1543; Kepler discovered planetary orbits were elliptical rather than circular; and Galileo pointed his "spy-glasses" skyward to reveal mountains on the moon, spots on the sun, and moons orbiting Jupiter.
第 6 章
The Experimentalist's Mind and Body
Newton turned his analytical mind inward, exploring the complex relationship between perception and reality with characteristic thoroughness. Through meticulous self-observation, he documented how different conditions affected his mental acuity. He noted that imagination could be enhanced by "good aire fasting moderate wine" but damaged by "drunkenesse, Gluttony, too much study"-the latter potentially leading to madness. His personal notes revealed a deep understanding of the delicate balance required for optimal intellectual performance, including observations about sleep patterns, diet, and environmental conditions that influenced his thinking.
In investigating light's nature, he confronted the philosophical boundary between perception and perceiver that had puzzled thinkers since Aristotle. This investigation led him to question fundamental assumptions about how humans process visual information and the reliability of sensory experience. His approach combined philosophical inquiry with practical experimentation, setting a new standard for scientific investigation.
In a startling and dangerous act of self-experimentation, he inserted a bodkin - a thick needle - between his eyeball and eye socket, methodically pressing until he saw "severall white darke & coloured circles" that faded when he held both eye and instrument still. He meticulously documented these observations, noting how pressure, angle, and duration affected the visual phenomena. He also deliberately stared at the sun's reflection until he saw persistent afterimages of colored circles, discovering he could recreate these effects through mental concentration alone. These experiments, while reckless by modern standards, demonstrated his commitment to first-hand observation. After these experiments threatened his vision, he confined himself to a dark room for three days until his sight recovered, carefully recording his recovery process.
Newton found significant inspiration in Robert Hooke's "Micrographia," a groundbreaking work that championed careful observation of "material and obvious things" over pure theoretical speculation. The book's detailed illustrations and methodical approach to observation aligned with Newton's own empirical inclinations. Hooke, who would later become Newton's rival in bitter disputes over optical theories and calculus, served as Curator of Experiments for the newly formed Royal Society of London, an institution dedicated to promoting "Experimental Philosophy" under the motto "Nullius in verba" (take nobody's word for it).
The Royal Society represented a revolutionary approach to scientific inquiry, embodying a fundamental commitment to open information flow and public science. Rejecting the traditional secrecy of alchemists and natural philosophers, it established global communication networks through correspondence and published transactions. Its founders ambitiously envisioned an "Empire in Learning" where discoveries from around the world would converge in London, with Latin serving as a standardizing language amid Europe's diverse vernacular dialects. They strongly advocated for plain speaking and mathematical language over florid eloquence, recognizing words as "truant things" that required precise definition. This emphasis on clarity and precision in communication would become a hallmark of modern scientific discourse.
第 7 章
Discovering the Nature of Light
From his Trinity College chambers, Newton observed tennis players and noted how spinning balls curved through the air due to uneven air pressure-what he termed "reluctancy and reaction." This everyday observation would later influence his understanding of how forces interact with objects in motion. In February 1672, rather than appearing personally before the Royal Society, Newton sent Henry Oldenburg a detailed letter about his optical experiments, which was quickly published in Philosophical Transactions, marking his first major scientific publication.
Newton described how six years earlier, in 1666, he had directed sunlight through a prism into a darkened room, creating a rainbow spectrum against the wall. He had deliberately darkened his chamber by drilling a small hole in his window shutters, allowing only a thin beam of sunlight to enter. While the phenomenon of prismatic colors was ancient, known since Roman times and discussed by scholars like Roger Bacon, Newton noticed something unexpected: instead of forming a circular image as conventional wisdom suggested, the refracted light created an oblong shape approximately five times longer than it was wide.
This observation led to his crucial experiment (Experimentum Crucis) using two prisms and boards with holes to isolate beams of colored light. He positioned the first prism near his window to create a spectrum, then used a board with a small hole to isolate individual colors. These isolated beams were directed through a second prism, allowing Newton to study each color's properties independently.
Through meticulous experimentation, he discovered that different colors refracted at different angles, with blue light bending more sharply than red, and that a second prism neither created new colors nor altered existing ones. This proved his revolutionary conclusion: white light is not pure but a heterogeneous mixture of differently refrangible rays, and prisms don't create colors but merely separate them. This finding directly challenged Aristotle's long-held theory that colors were modifications of white light.
The publication sparked immediate controversy, particularly with Robert Hooke, who claimed Newton had stolen his ideas about light diffraction. Newton responded by meticulously analyzing what was truly original in Hooke's work versus what Hooke had borrowed from Descartes' earlier writings on optics. Their dispute escalated through Royal Society meetings, with Oldenburg consistently favoring Newton's position. The controversy became so heated that Newton threatened to withdraw from scientific discourse entirely.
Hooke eventually wrote directly to Newton, attempting to reconcile their differences. Newton's famous reply, crafted with calculated politeness, included the now-immortal phrase: "If I have seen further it is by standing on the sholders of Giants." This statement, while appearing humble, was possibly a subtle jab at Hooke's short stature and spinal deformity, demonstrating Newton's skill at combining courtesy with cutting undertones.
第 8 章
The Secret Pursuits of an Alchemist
By his thirties, Newton had become Europe's preeminent alchemist. He conceived of mercury not just as an element but as a principle inherent in all metals, seeking a special "philosophical mercury" with qualities beyond the common form. Mercury's ability to react with and purify other metals fascinated him, though he unknowingly poisoned himself with its toxic effects.
Unlike other experimenters, Newton meticulously weighed chemicals and measured time, while still using his senses to evaluate results. Newton's alchemy sought to understand life's processes-vegetation, putrefaction, corruption and generation. He saw the world as continually dying and being reborn in a great circulation driven by an "active spirit" he identified with light itself, which he connected to God.
His vision of nature was organic rather than mechanical, with alchemical language suffused with sexuality-masculine and feminine principles joining to create new substances. For Newton, alchemy merged with theology as a spiritual quest for purification.
While mechanical philosophers like Descartes sought explanations free of occult qualities, Newton rebelled against this approach. He sought universal causes rather than separate mechanical explanations for each phenomenon, believing God had implanted principles of motion beyond human understanding. Newton created a massive private Index chemicus cataloging alchemical writings across centuries, work that remained hidden long after his death.
Newton approached Christian theology with the same obsessive intensity as his scientific work. He saw himself doing God's work, writing that "Just as the world was created from dark Chaos through the bringing forth of the light... so our work brings forth the beginning out of black chaos and its first matter."
第 9 章
The Birth of Universal Gravitation
In 1680, a comet appeared in the skies. First visible faintly in November's early morning sky, then returning as a dramatic spectacle in December with a tail "broader than the moon" that stretched over King's College Chapel. Newton tracked it almost nightly through early 1681, as did Edmond Halley and Robert Hooke.
John Flamsteed, the newly appointed Astronomer Royal, suspected these might be the same comet and shared his observations with Newton through a mutual friend, speculating about the comet's composition and movement. Newton finally responded, rejecting Flamsteed's magnetism theory but crucially acknowledging: "I can easily allow an attractive power in the sun whereby the Planets are kept in their courses about him from going away in tangent lines."
Meanwhile, Hooke had written Newton seeking reconciliation and asking for feedback on his published idea that planetary motions resulted from a compound of straight-line tangent motion and "an attractive motion towards the centrall body." Their correspondence quickly evolved into a debate about falling objects and orbital mechanics, with Hooke eventually stating the problem precisely, proposing "that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall"-the inverse-square law.
Four years later, in August 1684, Edmond Halley visited Cambridge and asked Newton directly: assuming an inverse-square law of attraction toward the sun, what curve would a planet follow? Newton immediately answered "an ellipse," claiming he had calculated this years before but couldn't locate his proof. He promised to redo it.
Newton transformed his answer to Halley into a comprehensive treatise. Abandoning his alchemical furnaces and theological manuscripts, he worked feverishly, often standing at his desk, eating minimal meals in his room. When venturing outside, he appeared lost in thought, walking erratically before disappearing indoors again.
第 10 章
The Principia: A New System of the World
Newton's Principia opened with three fundamental laws of motion:
Law 1: "Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed." This refined Galileo's principle of inertia, establishing that rest and uniform motion are equivalent states.
Law 2: "A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed." Force generates motion, with both being quantities that follow mathematical rules.
Law 3: "To any action there is always an opposite and equal reaction." Whether a finger pressing a stone or the earth tugging at the moon, interactions are always reciprocal with equal forces in opposite directions.
Newton presented his laws as axioms, calling them "laws" (lex)-a deliberate echo of Descartes while intending to supplant him. These laws formed the bedrock of his system, rules of conduct for every piece of creation to obey. Though he cloaked his work in classical geometric style-axioms, lemmas, corollaries-his approach was revolutionary. Behind the static diagrams lay dynamic processes incorporating infinities and infinitesimals.
In Book III, "The System of the World," Newton gathered astronomical observations with unprecedented precision. He proved that satellites are pulled toward their centers (Jupiter, sun, or earth) by a force varying inversely with the square of distance. "The moon gravitates toward the earth and by the force of gravity is always drawn back from rectilinear motion and kept in its orbit."
Newton declared: "It is now established that this force is gravity, and therefore we shall call it gravity from now on." This universal gravitation meant every particle of matter attracts every other particle throughout the universe. From this principle, he calculated planetary densities, explained Earth's oblate shape, accounted for the precession of Earth's axis, and developed a comprehensive theory of comets and tides.
第 11 章
The Lion in Winter: Newton's Later Years
As the 17th century ended, Newton's published work consisted mainly of the Principia, scarce and valuable at two guineas per copy. His legend spread by word of mouth among a tiny community of scholars. Johann Bernoulli recognized Newton's anonymous solution to a geometry problem "ex ungue leonem"-the lion by his claw. Leibniz told the Queen of Prussia that in mathematics, there was all previous history and then Newton, "the better half."
When England's money faced crisis-worn silver pennies and fluctuating guineas created monetary chaos-Charles Montague appointed Newton as Warden of the Mint in 1696. Newton transformed this traditionally ceremonial position into one of intense industrial management, supervising round-the-clock operations at the Tower of London. In 1700, he became Master, earning both salary and percentage of coinage, growing wealthy while establishing a comfortable London home.
He pursued counterfeiters with righteous fury, personally overseeing prosecutions as Justice of the Peace. William Chaloner, who both counterfeited guineas and accused the Mint itself of making false money, went to the gallows despite his desperate final plea. Newton took the Trial of the Pyx seriously, meticulously preparing for these ceremonial tests of the coinage's weight and purity. His precision brought standardization to unprecedented levels, earning him knighthood from Queen Anne in 1705.
With Hooke's death in 1703, Newton finally returned to the Royal Society, not merely as a member but as President. He attended nearly every meeting, commented on almost every paper, controlled council membership, and displayed the royal mace only when personally presiding. He also published Opticks, his second great work, in English prose rather than Latin mathematics, describing experiments on light, color, reflection, and refraction that he had suppressed since 1675 "to avoid being engaged in Disputes."
第 12 章
A Legacy That Transformed the World
Newton died early Sunday, March 19, 1727, having refused the church's sacrament on his deathbed. Despite amassing a considerable fortune of 31,821-including crimson-furnished rooms, mathematical instruments, thousands of books, and gold bars-he left no will. His papers, sold at auction in 1936, revealed to John Maynard Keynes not the cold rationalist of legend but "the last of the magicians, the last of the Babylonians and Sumerians."
Newton's influence transformed science and culture. His predictions about the earth's oblate shape were confirmed by French expeditions. Halley demonstrated Newtonianism's power by accurately predicting celestial events, including a solar eclipse in 1715 that the Royal Society witnessed. As Newtonianism evolved into orthodoxy, it inspired both followers and critics across disciplines.
The Romantic poets later rebelled against Newton's rational worldview-Keats lamented that he had "unweaved the rainbow," while Blake portrayed him as both demigod and enemy of imagination, blaming him for mechanization and "dark Satanic mills."
Despite claims that Einstein's relativity overthrew Newtonian physics, Einstein himself acknowledged Newton's enduring significance: "His great and lucid ideas will retain their unique significance for all time as the foundation of our whole modern conceptual structure in the sphere of natural philosophy." Newton had actually anticipated aspects of modern physics, questioning whether true rest or equable motion existed, speculating about the convertibility of light and matter, and theorizing about forces at the subatomic level.
His legacy established enduring principles: that a few general laws govern the universe's myriad properties, and that the universe's building blocks and laws are everywhere the same. As Newton himself had written on an abandoned sheet: "To explain all nature is too difficult a task for any one man or even for any one age. Tis much better to do a little with certainty & leave the rest for others that come after you."
