Speaker 1: You see, something's going to happen. What's going to happen?
Speaker 1: What I help? On a winter night in sixteen oh four,
Speaker 1: a new star burned through the velvet of the sky
Speaker 1: in Prague, A thin, nearsighted mathematician stood at a window
Speaker 1: and took notes by kindlelight. That man Johannes Kepler believed
Speaker 1: the heavens were legible, that number and harmony were the
Speaker 1: alphabet of creation. I made this episode because Keppler sits
Speaker 1: exactly where our show loves to work, at the scene
Speaker 1: where mysticism meets measurement, where sacred geometry becomes celestial mechanics,
Speaker 1: and we're an astrologer, school teacher, refugee, and court mathematician
Speaker 1: chisel law out of wonder. Kepler's life is a parable
Speaker 1: for anyone trying to keep faith and reason in the
Speaker 1: same room. He cast horoscopes to pay rent and scrapped
Speaker 1: circles for eclipses because the data said so. He wrote
Speaker 1: prayers into his proofs. He defended his mother in a
Speaker 1: witchcraft trial and still found the patients to compute mars
Speaker 1: for years. His voice, equal parts devout and defiant, tells
Speaker 1: us that truth is the daughter of time, and in
Speaker 1: his time, we let him speak tonight. We follow him
Speaker 1: step by step, from Wilderstadt to the lecture halls of Tubingan,
Speaker 1: from the platonic dreams of Mysterium Cosmographicum to the hard,
Speaker 1: stubborn numbers of Estronomia Nova, from the music of the
Speaker 1: spheres and Harmonisius Mundi to the glass and light of Diopters.
Speaker 1: From Graz to Prague to Linn's to Ulm, carrying tables,
Speaker 1: depths and a vision of order that outlived the Thirty
Speaker 1: Years War. We're here to read Kepler in his own words,
Speaker 1: to place him in the world. He walked mud streets,
Speaker 1: church bells, printing presses, played cards, and to ask what
Speaker 1: his laws, his optics, his reformed astrology, and his lunar
Speaker 1: dream mean for art, ritual and the modern imagination. If
Speaker 1: you ever looked up and felt that hush, the sense
Speaker 1: the sky isn't just scenery but syntax, this is your episode.
Speaker 1: Johannes Kepler lived from fifteen seventy one to sixteen thirty
Speaker 1: and he lived in an age of religious turmoil and
Speaker 1: scientific rebirth. He was a German astronomer, mathematician, astrologer and
Speaker 1: natural philosopher, a visionary who helped transform Renaissance s mysticism
Speaker 1: into empirical science of the Scientific Revolution. Kepler is best
Speaker 1: known for discovering the laws of planetary motion, foundational principles
Speaker 1: that guided later scientists like Isaac Newton towards the theory
Speaker 1: of gravity. But Kepler was more than a mathematician. He
Speaker 1: was a man of deep faith and imagination, convinced that
Speaker 1: the cosmos was an orderly creation imbued with meaning. Those
Speaker 1: laws of nature are within the grasp of the human mind.
Speaker 1: God wanted us to recognize by creating us after his
Speaker 1: own image, so that we could share in his own thoughts.
Speaker 1: Kepler wrote expressing the belief that deciphering the heavens was
Speaker 1: a way to think God's thoughts after him. His life's
Speaker 1: work was driven by this almost spiritual quest for cosmic
Speaker 1: harmony and truth. And telling Kepler's story one finds a
Speaker 1: narrative as dramatic as the times in which he lived.
Speaker 1: He witnessed the fading of old certainties, the geocentric Earth,
Speaker 1: Earth centered universe, and the sharp divide between science and superstition,
Speaker 1: and he helped usher in new understanding, grounding, and observation
Speaker 1: geometry and physics. Yet Kepler's path was not easy. He
Speaker 1: endured war, religious persecution, personal tragedies, and even a witchcraft
Speaker 1: trial against his own mother. Through it all, he remained
Speaker 1: scrupulously honest to the data and to his convictions. The
Speaker 1: result was a legacy that spans astronomy and optics, music
Speaker 1: and mysticism, religion and philosoph This episode follows Kepler's journey
Speaker 1: chronologically from his humble beginnings and education, through his wanderings
Speaker 1: across Europe in search of intellectual refuge, to his scientific triumphs,
Speaker 1: while also exploring the rich tapestry of influences, ideas, and
Speaker 1: historical events that shaped his work. As we shall see,
Speaker 1: Kepler much preferred the sharpest criticism of a single intelligent
Speaker 1: man to the thoughtless approval of the masses, forging a
Speaker 1: unique path that married rigorous science with a profound sense
Speaker 1: of wonder. Johannes Kepler was born on December twenty seventh,
Speaker 1: fifteen seventy one, and the small Swabian town of Weilderstadt
Speaker 1: in the Holy Roman Empire in modern Germany. He came
Speaker 1: from a modest and tumultuous family background. His father, Heinrich
Speaker 1: Keppler was a mercenary soldier who left home when Johannes
Speaker 1: was young and likely died abroad by fifteen seventy seven,
Speaker 1: and his mother, Katharina Goldenman, was the daughter of an
Speaker 1: innkeeper known for her herbal remedies and folkilling. The Kepler
Speaker 1: family had been respected in earlier generations. Johannas's grandfather, Sebald Kepler,
Speaker 1: had even served as mayor of their city, but by
Speaker 1: the time of Johanna's birth, their fortunes had dwindled. Born
Speaker 1: prematurely and frequently ill in childhood, Keppler was a frail
Speaker 1: boy with weak vision. A bout of smallpox left his
Speaker 1: eyes damaged and his hands crippled, Yet he showed early
Speaker 1: intellectual gifts and in an almost mystical awe for the heavens.
Speaker 1: In fifteen seventy seven, at just six years old, Johannes's
Speaker 1: mother took him to a high place to witness the
Speaker 1: Great Comet of fifteen seventy seven, a spectacle that captivated
Speaker 1: astronomers across Europe. He later recalled being entranced by the
Speaker 1: bright comet hanging in the sky. Two years later, in
Speaker 1: fifteen eighty, he was called outside at night to see
Speaker 1: a lunar eclipse, noting how the moon appeared quite red,
Speaker 1: another formative experience for the young stargazer. These childhood events
Speaker 1: kindled a passion for astronomy that would last his entire
Speaker 1: even though his poor eyesight meant he would never be
Speaker 1: known from making telescopic discoveries like Alileo, Kepler himself joked
Speaker 1: that although his mind was sky bound, the shadow of
Speaker 1: his body lies here on earth, a poignant reflection he
Speaker 1: will later choose for his epitheph. Encouraged by his family's
Speaker 1: Lutheran faith and by his own evident intellect, Kepler pursued
Speaker 1: an education that combined classical learning with religious training. He
Speaker 1: attended local Latin schools, and in fifteen eighty four, at
Speaker 1: age thirteen, he entered the Protestant seminary at Eldenburg. He
Speaker 1: proved to be a brilliant student. By fifteen eighty nine,
Speaker 1: Kepler earned a scholarship to the University of Tubajin, a
Speaker 1: leading Protestant university, to study theology and prepare for the
Speaker 1: Lutheran ministry. At Tubingan's Tubingerstiff Seminary, Kepler received a thorough
Speaker 1: grounding in classical philosophy, mathematics, and astronomy. His mentor in
Speaker 1: mathematics and astronomy was Michael Maslin, one of the few
Speaker 1: academics of the time who embraced the Copernican heliocentric model,
Speaker 1: though cautiously and only in private lectures. Under Maslin's guidance,
Speaker 1: Kepler learned both the traditional Polemaic Earth centered system and
Speaker 1: the revolutionary Copernican Sun centered system of planetary motion. Kepler
Speaker 1: was quickly won over to Copernican's vision. He later wrote
Speaker 1: that it was a tubingin that he became a Copernican
Speaker 1: for what he called physical or if you prefer metaphysical reasons.
Speaker 1: In other words, he sensed that a sun centered cosmos
Speaker 1: had a deeper natural truth and harmony to it. Indeed,
Speaker 1: Kepler's faith in a rational God created order predisposed him
Speaker 1: to favor a system where the Sun, symbol of God's light,
Speaker 1: sat at the center. As a student, he even engaged
Speaker 1: in a public disputation defending heliocentrism on both scientific and
Speaker 1: theological grounds, arguing that the Sun is the principal source
Speaker 1: of motion to the universe. This was bold given that
Speaker 1: Lutheran and Catholic authorities alike still regarded heliocentrism with suspicion.
Speaker 1: Kepler's subtle deviations from strict Lutheran doctrine already began causing friction.
Speaker 1: He refused to fully subscribe to the formula of Concord
Speaker 1: in fifteen seventy seven, a Lutheran confession of faith, because
Speaker 1: he had private doubts on points of theology. Because of
Speaker 1: these scruples, Kepler's hopes of becoming a pastor dimmed. Nevertheless,
Speaker 1: he saw no conflict between faith and science. I wanted
Speaker 1: to become a theologian. For a long time. I was unhappy.
Speaker 1: Now behold, God is praised by my work, even in astronomy.
Speaker 1: Kepler later reflected to him uncovering the mathematical laws of
Speaker 1: creation was a form of devotion. This conviction set the
Speaker 1: stage for his life's work. In fifteen ninety four, at
Speaker 1: the age of twenty two, Johannes Kepler left academia to
Speaker 1: begin a career in teaching and incidentally, in government service
Speaker 1: as an astrologer. He was recommended for and accepted a
Speaker 1: post as professor of mathematics at the Protestant Seminary in
Speaker 1: Gratz in the US Austrian province of Steria. In this role,
Speaker 1: he taught arithmetic, geometry, and sometimes Greek and rhetoric to
Speaker 1: the school students. He also carried the title of district mathematician,
Speaker 1: which meant he was responsible for issuing official calendars in
Speaker 1: astrological almanacs, a lucrative and respected task at the time.
Speaker 1: In the late sixteenth century, there was no firm separation
Speaker 1: between astronomy and astrology. The two were considered two sides
Speaker 1: of the same coin. Like other learned astronomers, even Tycho
Speaker 1: Brahe and Galileo, Kepler practiced astrology to earn his keep.
Speaker 1: He cast horoscopes for wealthy patrons and local nobility, and
Speaker 1: made weather and political predictions in annual calendars. Though he
Speaker 1: privately disdained the more superstitious aspects of astrology, he conceded
Speaker 1: that mother astronomy would surely have to suffer hunger if
Speaker 1: the daughter astrology did not earn their bread. In other words,
Speaker 1: it was astrology that paid the bills, allowing him to
Speaker 1: pursue pure astronomy. Kepler spent a huge amount of time
Speaker 1: trying to reform astrology on a sounder footing, composing over
Speaker 1: eight hundred horoscopes and several treaties on the subject. He
Speaker 1: aimed to distill whatever he thought scientifically plausible, for instance,
Speaker 1: effects of the sun, moon, and planets mediated through an
Speaker 1: Earth's soul via harmonies or light from what he called
Speaker 1: the Swinnish rashness of fortune tellers. In sixteen oh one,
Speaker 1: he even wrote a short work on giving astrology sounder
Speaker 1: foundations to accompany one of his almanacs, and in sixteen ten,
Speaker 1: when two other authors feuded over astrology merits, Kepler intervened
Speaker 1: with attract third party intervening, cautioning that while much astrological
Speaker 1: superstition deserves rejection, one must not throw the baby out
Speaker 1: with the bath water by dismissing real cosmic influences. This
Speaker 1: balanced approach typified Kepler's unque blend of mysticism and empiricism
Speaker 1: during his grazzias. Even while he fulfilled his public duties,
Speaker 1: Kepler was pursuing an arditious private research program, an attempt
Speaker 1: to decipher the geometrical plan of the cosmos. Shortly after
Speaker 1: arriving at Grotz, he experienced what he described as a
Speaker 1: moment of illumination. On July nineteenth, fifteen ninety five, while
Speaker 1: teaching a class, Kepler was explaining the periodic conjunctions of
Speaker 1: Saturn and Jupiter and the Zodiac when he had an epiphany.
Speaker 1: He realized that the intervals between planets might be explained
Speaker 1: by pure geometry. Initially, Kepler tried inscribing and circumscribing one
Speaker 1: circle between another using regular polygons, seeking a unique geometric
Speaker 1: spacing for the six known planets, but this approach failed
Speaker 1: to much observations. He then contemplated three dimensional shapes. In
Speaker 1: a breakthrough, Kepler imagined nesting the five periodic platonic solids
Speaker 1: one inside another, each separated by circumscribed and inscribed sphere.
Speaker 1: There were only five such polyhedra, and placing them in
Speaker 1: the proper order produced six layers, which he identified with
Speaker 1: the six planets Mercury, Venus, Earth, Mars, Jupiter, Saturn. To
Speaker 1: Kepler's delight, the model roughly matched the relative sizes of
Speaker 1: the planet's orbits as known from Copernicus's data, Especially for
Speaker 1: planets beyond Mercury. He believed he had glimpsed the very
Speaker 1: geometric blueprint of God. Geometry is co eternal with God,
Speaker 1: and God used it in laying out the world Keppelo
Speaker 1: would write later reflecting his neoplatonic conviction that geometrical forms
Speaker 1: give structure to creation. With almost evangelical zeal, the young
Speaker 1: astronomer set out to share his revelation. In fifteen ninety six,
Speaker 1: at just twenty five years old, Keppela published his first book,
Speaker 1: Pisterium Cosmographicum Mystery of the Cosmos. This was his first
Speaker 1: bold attempt to decipher the divine geometric plan of the universe.
Speaker 1: Kepplo was a deeply religious thinker who believe that God,
Speaker 1: the great mathematician, had built the cosmos with mathematical harmony.
Speaker 1: Inspired by quasi mystical revelation while teaching in Gods, he
Speaker 1: became convinced that the spacing of the six known planets
Speaker 1: was no accident. It must be patterned after the five
Speaker 1: perfect platonic solids of antiquity. Kepler set out to prove
Speaker 1: that each planetary orbit is separated by a nested polyhedron,
Speaker 1: inscribed and circumscribed by spheres matching the orbit of one
Speaker 1: planet to the next. This elegant model, he thought, explained
Speaker 1: why there were exactly six planets and provided a compelling
Speaker 1: geometric rationale for Copernicus's son's censored system. Keppler's Mysterium was
Speaker 1: the first published defense of copernicant heliocentrism since Copernicus himself,
Speaker 1: and it was strikingly unusual for the blending rigorous astronomy
Speaker 1: with neoplatonic mysticism. In the book's preface, he declared his
Speaker 1: mission to show that God, in creating the universe and
Speaker 1: regulating the order of the cosmos, had in view the
Speaker 1: fire irregular bodies of geometry, and that he has fixed,
Speaker 1: according to those geometric dimensions, the number of the heavens,
Speaker 1: their proportions, and relations of their movements. The Mysterium did
Speaker 1: more than propose a poetic model. It insisted that astronomy
Speaker 1: must explain the actual spacing of planetary orbits in three
Speaker 1: dimensional space, not just their abstract order. To Kepler, Copernicus's
Speaker 1: system implied a physical reality in which nothing could be
Speaker 1: altered without upsetting the harmony of the whole. This mindset
Speaker 1: led him to consider the Sun's force as it caused
Speaker 1: a planetary motion weakening with distance, oppressing, and insight that
Speaker 1: nudged astronomy away from purely kinematic models towards physics. Although
Speaker 1: the platonic solid model itself was not quantitatively accurate, its
Speaker 1: beauty and haunting strangeness captivated Kepler and set him on
Speaker 1: a path of asking deeper questions. He even published a
Speaker 1: second edition twenty five years later, unwilling to aband and
Speaker 1: in the idea that some fundamental harmonies underlies the cosmos.
Speaker 1: With hindsight, we see Mysterium Cosmographicum as an important stepping
Speaker 1: stone and empirically inaccurate but esthetically beautiful hypothesis that nevertheless
Speaker 1: prompted Kepler to seek physical causes and would ultimately lead
Speaker 1: to his monumental Laws of planetary motion. While in Grotz,
Speaker 1: Kepler also began side studies in chronology and astrology, even
Speaker 1: trying to link planetary positions to weather and earthly events.
Speaker 1: He speculated about the Earth having a soul that responds
Speaker 1: to the positions of the planets. This was part of
Speaker 1: a grand plan that he had sketched out to write
Speaker 1: several books on the stationary sun and fixed stars, on
Speaker 1: planetary motions, on the physical nature of planets, and on
Speaker 1: the influences of the heavens on Earth. The Mysterium was
Speaker 1: only the first installment of this ambitious program. However, events
Speaker 1: in Grots would soon disrupt Kepler's work and force him
Speaker 1: to flee. Our Reformation was gathering steam under Archduke Shun
Speaker 1: Emperor Ferdinand the second, a staunch Catholic, determined to root
Speaker 1: out Protestantism in his realms. Tensions in Steria mounted in
Speaker 1: September fifteen ninety eight, and decree expelled all Protestant teachers
Speaker 1: and preachers from Gratz. Initially, Keppel was exempted from expulsion
Speaker 1: because of his valuable status as district mathematician. The authorities
Speaker 1: did not want to lose the calendar maker, but Kepler
Speaker 1: felt far from safe. That year, he wrote to a
Speaker 1: friend that he foresore dark times ahead. Sure enough, by
Speaker 1: fifteen ninety nine his position was untenable. Meanwhile, in Prague,
Speaker 1: Tycho brahe had been appointed Imperial mathematician to Emperor Rudolph
Speaker 1: the second. Ticho, the Great Danish astronomer, was eager for
Speaker 1: a skilled assistant to help make sense of his vast
Speaker 1: treasury of planetary observations. He had heard of Kepler's talent
Speaker 1: for theoretical insight. In December fifteen ninety nine, Tycho intended
Speaker 1: an invitation to Kepler to join him in Prague. Kepler
Speaker 1: leapt at the opportunity, without even waiting for the formal
Speaker 1: letter to arrive. He set off from Gratz on January first,
Speaker 1: sixteen hundred, heading north to Bohemia in hopes that Tycho's
Speaker 1: patronage could solve both his scientific quandaries and his precarious
Speaker 1: political situation. Kepler's departure from Grotz was abrupt. He left
Speaker 1: behind his post and the home that he had established there,
Speaker 1: and it must be noted he left in the company
Speaker 1: of some emotional turmoil. During his Grotz years, Keppler had
Speaker 1: fallen in love and married. In December fifteen ninety five,
Speaker 1: he met Barbara Muller, a twenty three year old, twice
Speaker 1: widowed young woman with a small daughter. Barbara came from
Speaker 1: a prosperous family, for Falla was a successful mill owner,
Speaker 1: whereas Keppler was an impecuineous scholar. Her Falla was initially
Speaker 1: opposed to the match, considering Kepler's poverty unacceptable despite his
Speaker 1: noble ancestry. Only after Kepler finished Mysterium Cosmographicum, perhaps proving
Speaker 1: his potential, did her family rely, and Barbara and Johannes
Speaker 1: married on April twenty seventh, fifteen ninety seven. The marriage
Speaker 1: in its early years was reportedly strained by financial worries
Speaker 1: and by Kepler's single minded focus on his studies. They
Speaker 1: had two children in Grotz in fifteen ninety eight and
Speaker 1: fifteen ninety nine, but tragically both infants, a son, Heinrich
Speaker 1: and a daughter, Susannah, died in infancy. It was amid
Speaker 1: these personal trials that Kepler abandoned Grotz. By September sixteen hundred,
Speaker 1: after a final edict demanded that all Protestants convert to
Speaker 1: Catholicism or leave Steria. Kepler and Barbara, pregnant again, packed
Speaker 1: their belongings and fled grots for Prague, effectively as religious refugees.
Speaker 1: Keppeler did not know it yet, but he would never
Speaker 1: return into the life of a provincial school teacher, ahead
Speaker 1: lay his most productive scientific years under the patronage of
Speaker 1: the Holy Roman Emperor. When Keppeler arrived in Prague in
Speaker 1: early sixteen hundred, he entered an environment that must have
Speaker 1: seemed like the Promised Land to a man obsessed with astronomy.
Speaker 1: Tycho Brahe welcomed him to the Imperial Observatory and soon
Speaker 1: put Keplar to work analyzing observations of Mars. Mars was
Speaker 1: famously the most troublesome planet for astronomers. Its apparent backward
Speaker 1: retrograde motions and changes in brightness had defied simple explanation
Speaker 1: in circular orbit models. Tycho possessed the most precise Mars
Speaker 1: data ever obtained, measured without telescopes using giant citing instruments.
Speaker 1: His measurements were accurate within a arc minute or two.
Speaker 1: For the first time, Kepler had the accurate empirical foundation
Speaker 1: he needed. However, Tycho was protective of his data. He
Speaker 1: did not initially allow Kepler unlimited access or copies of
Speaker 1: his observations. Kepler estimated it might take him up to
Speaker 1: two years of hard work to test his geometric theories
Speaker 1: against Tycho's Mars data, since he would have to perform
Speaker 1: calculations on site. He and Tycho had a brief falling
Speaker 1: out in the spring of sixteen hundred over for more
Speaker 1: employment terms and salary that led Kepler to leave for
Speaker 1: a short time. Fortunately, the reconciled quickly and reached an agreement.
Speaker 1: Tycho recognized Keppler's value and secured him a position as
Speaker 1: an imperial collaborator. By summer of sixteen hundred, after returning
Speaker 1: to Gratz briefly to collect his family, Kepler settled in
Speaker 1: Prague for good. Tragically, Kepler's direct collaboration with the illustrious
Speaker 1: Tycho would be short lived. In October sixteen oh one,
Speaker 1: only about a year after Kepler arrived, Tycho Brahe died suddenly.
Speaker 1: Tycho's death threatened to leave Kepler stranded, but the Emperor
Speaker 1: Rudolph the Second promptly appointed Kepler as Tycho's successor Imperial Mathematician.
Speaker 1: This was the most prestigious post for a mathematician in Europe,
Speaker 1: essentially making Kepler the court astronomer. It also gave him
Speaker 1: custody of Tycho's precious astronomical data. After some wrangling with
Speaker 1: Tycho's heirs, who tried to claim that data was private property,
Speaker 1: Kepler gained access to the observations he needed. He was
Speaker 1: keenly aware of the importance of this moment. He had
Speaker 1: in his hands the raw material to revolutionize astronomy, to
Speaker 1: us on whom divine benevolence has bestowed the most diligent
Speaker 1: of observers, Tycho Brahe, from whose observations this eight minute
Speaker 1: error in the orbit of Mars is deduced. It is
Speaker 1: fitting that we accept with grateful minds this gift from
Speaker 1: God and both acknowledge and build upon it. Referring to
Speaker 1: a tiny discrepancy Tycho had found in Mars's orbit that
Speaker 1: hinted the ancient models were wrong, Kepla would indeed build
Speaker 1: upon Tycho's legacy, and in doing so he changed our
Speaker 1: view of the cosmos. As imperial mathematician and Prague, Keppler's
Speaker 1: duties were twofold, for example, providing astrological forecasts and calendars
Speaker 1: to the Emperor, and to conduct astronomical research, including the
Speaker 1: completion of the new Rudolphine Tables, an updated set of
Speaker 1: astronomical tables, planetary positions, star catalogs, et cetera, using tycho
Speaker 1: superior observations and per Rudolph the second was an enlightened
Speaker 1: and eccentric patron of the sciences, interested in astronomy, alchemy,
Speaker 1: and all matter of esoteric knowledge. He tolerated Keppler's Lutheran faith,
Speaker 1: despite Prague being officially Catholic. In practice, Kepler had a
Speaker 1: fair degree of intellectual freedom at Ruolph's court, even as
Speaker 1: he struggled with intermittent salary payments from the cash strapped
Speaker 1: Imperial Treasury. It was an invigorating situation. Kepler rubbed shoulders
Speaker 1: with other learned men in Prague from Jeweler's turned mathematicians
Speaker 1: like Josh Bergee, tou scalars like Johannes Mathaus, Whacker and
Speaker 1: David Fabricius. This collegial atmosphere, combined with Keppler's own single
Speaker 1: minded determination, led to an explosion of productivity. The eleven
Speaker 1: years Kepler spent in Prague sixteen oh one to sixteen
Speaker 1: twelve would be the most scientifically fruitful time of his life.
Speaker 1: One of Kepler's first targets of study was the orbit
Speaker 1: of Mars. Continuing the work Tycho had assigned him, Kepeler
Speaker 1: approached the problem with a novel mindset. He was willing
Speaker 1: to abandon the ancient insumption that planetary motions must be
Speaker 1: combinations of uniform circular paths. Instead, he sought a single,
Speaker 1: unified orbit from Mars, shaped by a physical cause, what
Speaker 1: he called a celestial physics. He suspected the Sun was
Speaker 1: the source of a force that drove the planets, an
Speaker 1: idea inspired by his belief that the son symbolized God
Speaker 1: the Father, and likely influenced by William Gilbert's sixteen hundred
Speaker 1: book d Magneti, which posited a magnetic soul in the Earth.
Speaker 1: Keppler theorized that a force emanating from the Sun weakened
Speaker 1: with distance, causing planets further out to move more slowly,
Speaker 1: a remarkable prescient intuition we can recognize in it an
Speaker 1: early notion of a gravitational or magnetic inverse square law.
Speaker 1: Armed with Tycho's precise measurements of Mars positions at various
Speaker 1: points in its orbits, Kepler attacked the data with tireless calculations.
Speaker 1: He tried one geometric model after another, measuring the error
Speaker 1: each time. Initially, he attempted to use a small oval
Speaker 1: like path, and even tried incorporating the old equon a
Speaker 1: mathematical point that Copernicus had eliminated to see if he
Speaker 1: could fit the data, but nothing gave a perfect match.
Speaker 1: Mars observed positions differed by as much as eight arc
Speaker 1: minutes eight sixtieth of a degree from the best circular
Speaker 1: or oval models Kepler could construct. Instead of dismissing this
Speaker 1: tiny discrepancy, Kepler famously said that the commander of eight minutes.
Speaker 1: It the error will lead us to complete reform of astronomy.
Speaker 1: His contemporaries might have swept such a small error under
Speaker 1: the rug, but Kepler trusted the data with Tycho's observations.
Speaker 1: This eight minute discrepancy is a gift of God, he wrote,
Speaker 1: believing that such anomalies were clues to the true theory.
Speaker 1: After numerous failed attempts, Kepler made his greatest discovery in
Speaker 1: late sixteen o four. Hed had what one might call
Speaker 1: his second epiphany, the first being the platonic solids model.
Speaker 1: Having tried over forty different geometrical constructions to fit Mars's orbit,
Speaker 1: he finally considered that the path might be an ellipse
Speaker 1: rather than a circle or arbitrary oval. The ellipses were
Speaker 1: a simple conic section, a familiar shape, Yet no astronomer
Speaker 1: before had dad suggests the planets literally travel on ellipses.
Speaker 1: Kepler had initially thought an ellipse was too simple. Surely,
Speaker 1: he imagined the great minds of antiquity would have tried
Speaker 1: it if it worked. But when he plotted Mars's position
Speaker 1: as an elliptical path with the Sun at once focus
Speaker 1: of the ellipse, the data fit beautifully, the long standing
Speaker 1: mystery of Mars's motion was solved. Mars, and by extension,
Speaker 1: the other planets move around the Sun in ellipses rather
Speaker 1: than perfect circles. Kepler immediately generalized this insight into what
Speaker 1: we now call Kepler's first law, the orbits of the
Speaker 1: planets or ellipses with the Sun at one time focus. Furthermore,
Speaker 1: he had already deduced a rule for how a planet
Speaker 1: speed varies along its orbit. By sixteen oh two. Through
Speaker 1: laborious calculations, Kepler found that the line connecting a planet
Speaker 1: to the Sun sweeps out equal areas in equal times,
Speaker 1: implying that a planet moves faster when nearer the Sun
Speaker 1: and slower when farther. This became Kepler's second law of
Speaker 1: planetary motion, the area law. It was intimately linked to
Speaker 1: his assumption of a solar force. This area law mathematically
Speaker 1: represents a conserved motion consistent with a type influence, though
Speaker 1: he didn't formulate it in those terms. The aerial law
Speaker 1: mathematically represents a conserved motion consistent with a one R
Speaker 1: two type influence, though he didn't formulate it in those terms.
Speaker 1: By combining the aerial law with the elliptical shape. Kepler
Speaker 1: had constructed the first accurate physic based model of planetary motion.
Speaker 1: While still in gross in astronomy, Kepler turned his analytical
Speaker 1: genius to the science of light and vision. In sixteen
Speaker 1: o four he published additions to Matello in which the
Speaker 1: optical part of astronomy is taught. Often known more simply
Speaker 1: as astronomy pars optica, this tone was a truly groundbreaking
Speaker 1: work on optical signs. Kepler built upon the medieval optics
Speaker 1: of al Hahazan and Wtello, but he far surpassed his predecessors,
Speaker 1: earning the title of father of modern optics. An Astronomy
Speaker 1: pars optica, Kepler essentially founded the modern understanding of how
Speaker 1: we see and how light behaves light intensity. He formulated
Speaker 1: the inverse square law of light propagation, recognizing that the
Speaker 1: apparent brightness of a light source decreases with the square
Speaker 1: of the distance. This was a critical insight for astronomy, explaining,
Speaker 1: for example, the dwindling light of distant stars that we
Speaker 1: have reflection and pinhole images. Kepler systematically described the behavior
Speaker 1: of light upon reflection from flat and curved mirrors, laying
Speaker 1: groundwork from mirror optics. He also explained the principles of
Speaker 1: the pinhole camera, showing how a small aperture projects an
Speaker 1: inverted image, an analogy that would prove vital for understanding
Speaker 1: the eye's images. Then we have astronomical optics. Anticipating telescopic astronomy,
Speaker 1: Kepler treated the optical phenomena affecting astronomical observation. He analyzed
Speaker 1: how atmospheric refraction bends light making, for instance, the sun
Speaker 1: appeared distorted near the horizon, and investigated parallax and apparent
Speaker 1: sizes of celestial bodies. By doing so, he made it
Speaker 1: clear that astronomical sightings must account for optical efforts, hence
Speaker 1: the book's subtitle, The Optical Part of Astronomy. He touched
Speaker 1: on the vision of the eye. Most famously, Kepler solved
Speaker 1: the age old riddle of how vision works. Rejecting h
Speaker 1: and ideas that the eye emits visual rays, Kepler proved
Speaker 1: instead that an image of the world is formed inside
Speaker 1: the eye. He was the first to understand that the
Speaker 1: lens of the eye projects an inverted picture of the
Speaker 1: scene into the retina. I say there is vision, Kepler wrote,
Speaker 1: when a representation of the whole hemisphere of the world,
Speaker 1: that is, before the eye fixes itself on the concave
Speaker 1: surface of the retina. He likened the eye to a
Speaker 1: camera obscurre, with the retinal image as its painting. Crucially,
Speaker 1: Kepler acknowledged that although the image is inverted, the mind
Speaker 1: interprets it correctly, effectively kicking off the study of physiological optics.
Speaker 1: Kepler's insights into vision were revolutionary. He explained the operation
Speaker 1: of corrective lenses for the first time, as well describing
Speaker 1: how concave lenses diverge light for the myopic and convex
Speaker 1: lenses converge light for the far sighted. This was not
Speaker 1: an invention of eyeglasses, they predated him by centuries, but
Speaker 1: it was the first scientific explanation of why lenses work
Speaker 1: to remedy vision. For all these contributions, Kepler's sixteen oh
Speaker 1: four Optica is considered a major turning point in the
Speaker 1: dea development of the discipline of optics. A modern historian
Speaker 1: notes that the book contains the first statement that the
Speaker 1: image is created in the eye on the retina and
Speaker 1: not in the crystal lens. Kepler's contemporaries were astonished his
Speaker 1: work on optics was truly ahead of its time, so
Speaker 1: much that Galileo, who built telescopes around the same years,
Speaker 1: largely ignored these new optical insights. Nonetheless, Kepler's blend of
Speaker 1: theory and practical explanation, he even delved into the phyrix
Speaker 1: of camera obscurers and the nature of lenses, justifies his
Speaker 1: reputation as the founder of modern optics and Kepler's own
Speaker 1: delighted words. Through understanding light and vision were standing on
Speaker 1: the shoulders of giants, uncovering nature's secrets with new found clarity.
Speaker 1: Kepler spent the next few years preparing a major treatise
Speaker 1: to announce these discoveries to the world. In sixteen oh
Speaker 1: five he completed the manuscript, which, by imperial privilege he
Speaker 1: taught Astronomia Nova the New Astronomy. Due to delays, including
Speaker 1: legal disputes with Tycho's family over data ownership, the book
Speaker 1: was not published until sixteen o nine. When it finally appeared,
Speaker 1: it was nothing short of revolutionary. In it, Kepler narrates
Speaker 1: in the first person the long saga of his analysis
Speaker 1: of Mars, giving a candid account of false starts and
Speaker 1: failed hypothesis on the weight of the truth. This was
Speaker 1: the first published account wherein a scientist documents how he
Speaker 1: has copied with a multitude of imperfect data to forge
Speaker 1: a theory of surpassing accuracy. As historian Owen Jingerich noted
Speaker 1: in essence, Kepler was practicing a modern scientific method. He
Speaker 1: led observations guy theory, and he was willing to abandon
Speaker 1: beautiful ideas like nested polyhedra or combinations of circles when
Speaker 1: the data disproved them. He also firmly introduced physics in
Speaker 1: to astronomy. In the very preface of Astronomia Nova, Keppler
Speaker 1: described his work as celestial physics, an excursion into Aristotle's
Speaker 1: metaphysics of motion applied to the heavens. He even likened
Speaker 1: the celestial machine not to a divine living being, but
Speaker 1: to a mechanical clock. My aim is to show that
Speaker 1: the celestial machine is to be likened not to a
Speaker 1: divine organism, but rather to a clockwork. In it, almost
Speaker 1: all the varied motions are carried out by means of
Speaker 1: a single, quite simple magnetic force, as in a clock,
Speaker 1: all motions derived from a simple weight. He wrote this
Speaker 1: metaphor of the clockwork universe driven by physical force was
Speaker 1: a radical departure from the traditional view of heavenly spheres
Speaker 1: moved by guided intelligences or angels. Kepler had paved the
Speaker 1: way for understanding planetary motion as governed by natural law.
Speaker 1: While Mars in the Astronomya nova occupied much of Kepler's
Speaker 1: time in Prague, other remarkable events and works also came
Speaker 1: during this period. In October sixteen oh four, a bright
Speaker 1: new star appeared in the constellation of Fucus, a supernova
Speaker 1: now known as Kepler's supernova. Initially skeptical of the rumors,
Speaker 1: Keppeler observed it himself and began a meticulous study. This
Speaker 1: new star shone for over a year before fading, and
Speaker 1: it stirred fevered astrological speculation. Coincided with a great conjunction year,
Speaker 1: which some took as an omen. Keppeler published a book
Speaker 1: in sixteen oh six on the new star in Opfucus.
Speaker 1: Analyzing the phenomenon, he demonstrated, via the lack of measurable parallax,
Speaker 1: that the star was far beyond the planets in the
Speaker 1: realm of the fixed stars. This provided more evidence against
Speaker 1: the old Aristolian doctrine of an unchanging celestial realm. The
Speaker 1: heavens could change, new stars could appear, and then vanish.
Speaker 1: Keppler also cautiously addressed the astrological frenzy while cataloging others interpretations,
Speaker 1: He himself remained scared reptical that the supernova herald anything
Speaker 1: specific beyond the general observation that nature occasionally produces rare events. Interestingly,
Speaker 1: Kepler appended to this book an essay on the Star
Speaker 1: of Bethlehem, prompted by a chronology study by Laurentius Sousilia.
Speaker 1: Soslieger argued that the calendar of Christ's birth was off
Speaker 1: by several years, placing the Nativity around four or five BC. Kepler,
Speaker 1: connecting the dots, noted that a series of great conjunctions
Speaker 1: of Jupiter and Saturn occurred around seven BC. He speculated
Speaker 1: that the Star of Bethlehem might have been such a conjunction,
Speaker 1: possibly with a nova analogoust to the new Star of
Speaker 1: sixteen oh four. This was an early example of Kepler's
Speaker 1: habit of blending scientific inquiry with religious and historical questions,
Speaker 1: an approach he expanded in other works on chronology. Kepler
Speaker 1: also made fundamental contributions to the field of optics during
Speaker 1: his produce in sixteen o nine to sixteen ten. The
Speaker 1: invention of the telescope by Galileo and other opened a
Speaker 1: new frontier in astronomy. Galileo's startling telescope discoveries mountains on
Speaker 1: the Moon, moons around Jupiter, phases of Venus, and so on,
Speaker 1: were published in March sixteen ten Insiderius Nunsius the Starry Messenger, Galileo,
Speaker 1: facing skepticism, short Kepler's endorsement. Kepler responded eagerly. In April
Speaker 1: sixteen ten, he wrote an open letter of support conversation
Speaker 1: with Starry Messenger, in which he praised Galileo's findings and
Speaker 1: speculated on what they meant for cosmology. He enthusiastically confirmed
Speaker 1: that Galileo's reported phenomena were a plausible and argued readers
Speaker 1: to trust the observations. Later that year, Kepler obtained a
Speaker 1: telescope himself, courtesy of Duke Ernst of Cologne, and trained
Speaker 1: it on Jupiter. By August sixteen ten, he had independently
Speaker 1: observed Jupiter's four largest moons, and in sixteen eleven he
Speaker 1: published narrative about four satellites of Jupiter observed, further validating
Speaker 1: Galileo's discoveries. It was Keppler who first coined the term
Speaker 1: satellite for these secondary bodies, a term still used today.
Speaker 1: Kepler support was immensely valuable to Galileo, who never publicly
Speaker 1: acknowledged Astronomya Nova, but certainly appreciated Kepler's championship of the
Speaker 1: Copernican cause onm With Brahees unpresentedly precise observation of the planets,
Speaker 1: especially Mars, Kepler spent the next decade in a tireless
Speaker 1: war with Mars, an intensive battle to reconcile theory with observation.
Speaker 1: The outcome was Astronomya Nova new astronomy. Kepler did not
Speaker 1: stop at observations. He turned his formidable analytical skills to
Speaker 1: the theory of telescopes. By late sixteen ten, he had
Speaker 1: completed a manuscript on the optic of lenses and telescopic combinations.
Speaker 1: In sixteen eleven, he published this work as Diaptress. In Diaptriss,
Speaker 1: Kepler explained how convex and concave lenses converge a diverged light,
Speaker 1: and he presented the design of a new improved telescope,
Speaker 1: the Kepileririan telescope, also known as the astronomical telescope. It
Speaker 1: used two convex lenses, an objective and an eyepiece, resulting
Speaker 1: in a higher magnification and wider field of view than
Speaker 1: Galileo's original design, which used a concave eyepiece. The trade
Speaker 1: off was that the kepplerin telescope produced an inverted image,
Speaker 1: but astronomers readily accepted that for the sake of the
Speaker 1: better performance. Essentially, all later refracting telescopes followed Kepler's design.
Speaker 1: The Optris also discussed the phenomenon of total internal reflection
Speaker 1: and the optics of the human eye, making it a
Speaker 1: foundational text in optical physics. By the end of his
Speaker 1: Progue period, Kepler had laid out groundwork not only in
Speaker 1: astronomy but in optics as well, showcasing his extraordinary broad
Speaker 1: scientific reach. Now a little bit more about this book.
Speaker 1: In sixteen ten, Galileo's telescope had unveiled the moons of
Speaker 1: Jupiter and mountains on the Moon. This new instrument worked
Speaker 1: was a mystery to most. Kepler, with his deep knowledge
Speaker 1: of optics, took up the challenge. In sixteen eleven, he
Speaker 1: published Diopterris, the first theoretical Treatise on the Optics of Telescopes.
Speaker 1: Dioptriss Is a slim volume, but its impact was enormous.
Speaker 1: It laid the theoretical foundation for the modern telescope, introducing
Speaker 1: even the very term dioptrics the study of refraction that
Speaker 1: we still use today. Keppeler's diopters systematically explained how lenses
Speaker 1: bend in focus light to produce magnified images, something never
Speaker 1: before clarified. He began by giving the first correct explanation
Speaker 1: of the Dutch refracting telescope, the type invented in sixteen
Speaker 1: oh eight and used by Galileo. A convex objective lens
Speaker 1: gathers light from a distant object, and a concave eyepiece
Speaker 1: lens spreads it into a large virtual image. More importantly,
Speaker 1: Kepler didn't stop there. He imagined new designs. In a
Speaker 1: stroke of genius, Dioptris proposed a telescope with two convex lenses,
Speaker 1: a convex objective and a convex eyepiece. This configuration would
Speaker 1: produce an inverted image, but Kepler showed it would allow
Speaker 1: a much wider field of view and higher magnification the
Speaker 1: Galileo's design. This Kepleriian telescope, also called the astronomical telescope,
Speaker 1: is a direct ancestor of the refracting telescopes used in
Speaker 1: observatories to this day. He even explored more complex arrangements,
Speaker 1: for instance, adding a third convex lens to reinvert the image,
Speaker 1: creating an erecting telescope for terrestrial viewing, and a rudimentary
Speaker 1: version of a telephoto lens system for greater focused distance.
Speaker 1: All of this was purely theoretical. Kepler himself did not
Speaker 1: build these telescopes, but the designs he published were soon
Speaker 1: realized by others, validating his ideas. Within a few decades,
Speaker 1: the Keplerian telescope became the standard astronomical tool once lens
Speaker 1: makers learned to mitigate the inverted image and lens imperfections.
Speaker 1: It is remarkable that diapts also extended Kepler's investing gations
Speaker 1: of vision. He revisited the problem of how lenses form images,
Speaker 1: reinforcing the explanation that real inverted images or formed whether
Speaker 1: in a camera or inside the eye, a concept directly
Speaker 1: building on his sixteen or four optical work. In fact,
Speaker 1: Kepler included an appendix responding to Galileo's reports, the narrative
Speaker 1: on Galileo's Serial Messenger, in which he enthusiastically endorsed Galileo's
Speaker 1: discoveries and discussed how his own optical principles could explain
Speaker 1: the telescope's function. Thanks to Dioptrius, what had been a
Speaker 1: magical device was put on firm scientific footing. Kepler was
Speaker 1: the first to explain how lenses could be combined to
Speaker 1: magnify distant objects, a theory still relevant in today's optical sciences.
Speaker 1: For this, Kepler is often credited with inventing the improved
Speaker 1: refracting telescope, and indeed the design he outlined is known
Speaker 1: by his name. Historically, a Jesuit astronomer built the first
Speaker 1: working Keplerian telescope a few years later, corroborating Kepler's design.
Speaker 1: In some dioptrist transformed the telescope from a curious gadget
Speaker 1: into a subject of science. It completed Kepler's trilogy of
Speaker 1: optical works with the sixteen oh four Optica in sixteen
Speaker 1: ten Optical part of Astronomy Supplement, securing his legacy as
Speaker 1: a pioneer in both astronomy and optics. As a twenty
Speaker 1: twenty five reissue of the Optus aptly noted. Kepler's work
Speaker 1: introduced the design of the Keplerian telescope and coined the
Speaker 1: term dioptrics, still in use today. The death of Emperor
Speaker 1: Rudolph the Second in sixteen twelve and the succession of
Speaker 1: Matthias marked the end of Kepler's relatively secure tenure in Prague.
Speaker 1: Political and religious tensions, which had been brewing and would
Speaker 1: soon ignite the Thirty Years War in sixteen eighteen, made
Speaker 1: Prague increasingly inhospitable for a Protestant scientist. Furthermore, Kepler had
Speaker 1: just undergone personal heartbreak. In sixteen eleven, an epidemic of
Speaker 1: Hungarian spotted fever struck Prague, and Kepler's wife, Barbara fell
Speaker 1: gravely ill with seizures. Though she recovered initially. That autumn,
Speaker 1: all three of their children court smallpox. Six year old Frederick,
Speaker 1: Kepler's oldest son, died and the other two, Susanna and Ludwig,
Speaker 1: were very sick. As if these blows were not enough,
Speaker 1: Keppler found himself entangled in a legal dispute over his
Speaker 1: late wife's modest estate. She had a small inheritance from
Speaker 1: her family. Worn out by these trials, Keppler sought to
Speaker 1: leave Prague. He attempted to return to Tubingan. The Lutheran
Speaker 1: authorities still there viewed him with suspicion for his theological
Speaker 1: non conformity. They dubbed him too Calvinist leaning. Since Kepler
Speaker 1: advocated for intercommunion between Lutherans and Calvinists, even the Duke
Speaker 1: of Woodemberg turned him down on the advice of churchmen. Interestingly,
Speaker 1: the University of Padawa in Italy, where Galileo had taught,
Speaker 1: reached out to Kepler in sixteen eleven. Galileo himself departing
Speaker 1: Padawa for Florence, had recommended Kepler as his successor. Kepler
Speaker 1: considered the pristigious Padowit chair, but ultimately declined, preferring to
Speaker 1: keep his family in a German Protestant region and perhaps
Speaker 1: sensing that as a Protestant he might not thrive under
Speaker 1: Venice's Catholic oversight. Instead, Kepler secured an appointment as a
Speaker 1: provincial mathematician, similar to his old role in Gratz, in
Speaker 1: the Upper Austrian city of Linz, and per Mathaeus permitted
Speaker 1: Kepler to leave Prague for Lynz in sixteen twelve. While
Speaker 1: technically retaining his title and Mega salary as an Imperial mathematician,
Speaker 1: and would remain based there for the next fourteen years.
Speaker 1: This period was marked by further personal turbulence, but also
Speaker 1: major scientific achievements. In Linz, Kepler's official tasks included teaching
Speaker 1: at the local gymnasium school and continuing to provide astrological
Speaker 1: and astronomical services such as calendars for the province. Compared
Speaker 1: to Prague, Linz offered more religious freedom at first. Matthias's
Speaker 1: regime was less actively repressive in Austria, and Kepler initially
Speaker 1: enjoyed the ability to practice his Lutheran faith openly. However,
Speaker 1: Kepler's stubborn individualism in matters of doctrine soon caused friction
Speaker 1: with the Lutheran establishment because Kepela would not affirm the
Speaker 1: orthodox Lutheran view of the Eucharist. He rejected the idea
Speaker 1: of Christ's physical ubiquity in the Bread and Wine, and
Speaker 1: he refused to sign the strict formula of concord. The
Speaker 1: Lutheran clergy excommunicated him forbidding him from the Lord's Supper
Speaker 1: in sixteen thirteen. In their eyes, Kepler was a heretic
Speaker 1: leaning toward Calvinism. Thus, ironically, this devout Christian found himself
Speaker 1: alienated by both Protestant and Catholic authorities. Christ the Lord
Speaker 1: neither is Lutheran, nor Calvinist, nor papist. Kepler once remarked,
Speaker 1: urging more tolerance, his religious isolation and lens was a
Speaker 1: heavy blow, but he bore it as the price of
Speaker 1: intellectual honesty. Some historians see the harsh treatment Kepler received
Speaker 1: from Lutheran pastors, his excommunication, and a few years later
Speaker 1: the targeting of his mother as a witch in the
Speaker 1: Lutheran town as indicative of the counter attack he faced
Speaker 1: from his own camp for being so unorthodox. Despite these difficulties,
Speaker 1: Keppela found happiness again in his personal life. His first wife, Barbara,
Speaker 1: had died in Prague in sixteen eleven during the tumultuous times,
Speaker 1: leaving Keppelo a widower with two surviving young children in Linz.
Speaker 1: Keppler decided to remarry. His approach to finding his second
Speaker 1: wife was characteristically analytical. He considered no fewer than eleven
Speaker 1: potential matches, evaluating their qualities and even making a ranked list,
Speaker 1: a process often cited as an early example of the
Speaker 1: optimal marriage problem in decision theory. His first several choices
Speaker 1: fell through. Some candidates rejected him, others redeemed unsuitable, But
Speaker 1: eventually Kepler returned to one of the earliest prospects, a
Speaker 1: twenty four year old named Susanna Rudinger. Susannah was not wealthy,
Speaker 1: but Kepler wrote that she won me over with love,
Speaker 1: humble loyalty, the economy of household diligence, and the love
Speaker 1: she gave to step children. The married on October thirtieth,
Speaker 1: sixteen thirteen. By all accounts, the second marriage was a
Speaker 1: much happier and more stable union than Kepler's first. Susanna
Speaker 1: and Joannis had six children together. Tragically, the first three, Margaretta, Regina, Catharina,
Speaker 1: and Sebald, died in childhood, but the younger three, Cordula, Fridmar,
Speaker 1: and Hidelbert, survived to adulthood. Through these family ups and downs,
Speaker 1: Susanna provided a loving home life that sustained Kepler through
Speaker 1: his later travails. Kepler resumed his scientific work with the
Speaker 1: vigorant Lynds. One of his early publications there was Di
Speaker 1: Vero Anno sixteen thirteen, a treatise on pinpointing the year
Speaker 1: of Christ's birth. Using historical records and astronomy, the sighting
Speaker 1: of Herod's death and the Star of Bethlehem calculations, Kepler
Speaker 1: concluded that Jesus was born in four BC, a result
Speaker 1: which is now standard in historical scholarship. He has also
Speaker 1: became involved in a project to persuade the Protestant German
Speaker 1: states to adopt the improved Gregorian calendar, which had been
Speaker 1: introduced by the Catholic Church in fifteen eighty two. Many
Speaker 1: Protestant regions were hesitant to accept a papal reform. Kepler,
Speaker 1: pragmatic as ever, participated in deliberations in sixteen fifteen to
Speaker 1: sixteen sixteen to show that the Gregorian calendar was scientifically
Speaker 1: sound and not a tool of povery. Protestant states did
Speaker 1: eventually adopt it in Germany by seventeen hundred, thanks in
Speaker 1: part to such efforts. Even as Kepler published these works,
Speaker 1: a dark cloud was forming on his horizon the witchcraft
Speaker 1: trial of his mother Katharina. In sixteen fifteen, back in
Speaker 1: Kepler's native Werdeenberg, an ugly series of accusations led to
Speaker 1: Katharina Kepler, then in her seventies, being charged with practicing witchcraft.
Speaker 1: The charges arose from local feuds. A woman had claimed
Speaker 1: Katherina bewitched her with a potion, but in the fevered
Speaker 1: atmosphere of the time, the threat was deadly serious. Dozens
Speaker 1: of the lead witches were being executed in the region.
Speaker 1: Kepler was horrified. In sixteen sixteen, he traveled to Wittenberg
Speaker 1: to intervene on his mother's behalf. For the next several years,
Speaker 1: amid his own work, he fought a legal battle to
Speaker 1: save her. The trial dragged on, with Katherina imprisoned in
Speaker 1: atrocious conditions from sixteen twenty to sixteen twenty one. Kepler
Speaker 1: prepared an exhaustive legal defense, drawing on his scientific mind
Speaker 1: to refute the ridiculous claims point by point. He even
Speaker 1: invoked his knowledge of astronomy to explain that a certain
Speaker 1: herb wolfbane she gathered was for legitimate medicinal use, not sorcery,
Speaker 1: and the reported apparitions could be explained naturally. His efforts succeeded.
Speaker 1: In late sixteen twenty, Katherina was acquitted and released, narrowly
Speaker 1: escaping a possible death sentence. Kepler's de during this crisis
Speaker 1: showed a very personal side of the scientist, a loving
Speaker 1: son who applied reason and eloquence to combat superstition. Some
Speaker 1: scholars have speculated that this episode also influenced Kepler's literary side.
Speaker 1: For years, since around sixteen oh nine, Kepler had been
Speaker 1: tinkering with a manuscript called Somnium the Dream, a fanciful
Speaker 1: story about a voyage to the moon framed as a
Speaker 1: dream narrated by a student of Tychos. In the story,
Speaker 1: a which and a demon helped transport the protagonist to
Speaker 1: observe Earth from the lunar surface. The Somnium was partly
Speaker 1: an allegory defending Copernican astronomy by showing how the sky
Speaker 1: would look from another world, thus normalizing the idea the
Speaker 1: Earth as a planet, but it also contained autobiographical elements.
Speaker 1: The mother of the protagonists was a wise woman clearly
Speaker 1: inspired by Catherina. A distorted version of some Nium's manuscripts
Speaker 1: circulated during the trial, and some have argued it might
Speaker 1: have fueled the witchcraft accusations, as ignorant folk took Kepler's
Speaker 1: f fictional demonology as evidence of his family dealings with
Speaker 1: the occult. After Catherina's ordeal, Kepler added extensive footnotes to
Speaker 1: the Somnium two hundred and twenty three, footnotes much larger
Speaker 1: than the story itself, explaining the scientific content and clarifying
Speaker 1: the allegory. This work, often called the first piece of
Speaker 1: science fiction, was only published in sixteen thirty four, but
Speaker 1: it stands today as a testament to Kepler's imaginative and
Speaker 1: humanistic side. Amid these personal battles, Kepler pushed toward the
Speaker 1: frontiers of astronomy. In sixteen seventeen, he began publishing parts
Speaker 1: of a long promised textbook, The Epitome of Copernican Astrology.
Speaker 1: The Epitome, published in three volumes between sixteen seventeen and
Speaker 1: sixteen twenty one, was intended as a comprehensive guide to
Speaker 1: heliocentric astronomy for the uninitiated, modeled after Maslin's old geocentric textbook. However,
Speaker 1: as Kepler wrote it, it became much more than a
Speaker 1: beginner's guide, the summation of his own astronomical system, including
Speaker 1: all three of his planetary laws, and his attempts to
Speaker 1: explain celestial motion by physical causes. The epitomey was written
Speaker 1: in question and answer dialog form and was quite accessible
Speaker 1: by the standards of the day. It explicitly extended Kepler's
Speaker 1: first two laws previously shown from Mars, to all the planets,
Speaker 1: and even to the moon and Jupiter's moons. It did
Speaker 1: not mathematically derive elliptical orbits from observations, something that was
Speaker 1: too complex for a handbook, but it taught readers how
Speaker 1: the planets move and encouraged them to accept the Copernican
Speaker 1: worldview free of ptomomaic crutches. Initially, Volume one, books through
Speaker 1: one to three, was printed in sixteen seventeen, then Volume two,
Speaker 1: Book four in sixteen twenty, and Volume three, Books five
Speaker 1: through seven in sixteen twenty one. This staggering publication was
Speaker 1: partly due to disruptions. In sixteen sixteen, the Catholic Church
Speaker 1: placed all copernicuan book looks on the index of prohibited
Speaker 1: books pending correction, making it dangerous to publish on Heliocentrism
Speaker 1: under Catholic rule. Kepler was in Protestant territory, but he
Speaker 1: still took care. After sixteen eighteen, as the Thirty Years
Speaker 1: War began, even Protestant publishers grew anxious to avoid religious censure.
Speaker 1: Kepler pitched the later volumes of Epittomey to more specialist readers.
Speaker 1: He made the arguments more rigorous and mathematical, and even
Speaker 1: left Copernican out of the titles of some parts so
Speaker 1: as not to draw overt attention. Nevertheless, that Epotomy became
Speaker 1: the most widely used astronomy textbook in Europe and the
Speaker 1: decades after Kepler's death. Between sixteen thirty and sixteen fifty,
Speaker 1: it effectively spread Kepler's ellipse based astronomy to the next
Speaker 1: generation of astronomers. Many who were initially unconvinced by Kepler's
Speaker 1: sixteen or nine new astronomy came to accept his models
Speaker 1: through the didactic Epotomy. Thus, even if Kepler himself did
Speaker 1: not converts stalwarts like Galileo, his ideas steadily permeated the
Speaker 1: scientific community via this work. Kepler's other towering achievement in
Speaker 1: the Linz Error was the completion of Tycho's legacy, the
Speaker 1: Ridolphine Tables. These were new planetary tables and star catalog
Speaker 1: named after Emperor Rudolph the Second. Since sixteen oh one,
Speaker 1: Kepler had been obligated to produce them, but only in
Speaker 1: Lens did he have the piece to finish the laborious calculations.
Speaker 1: The project was huge, required computing the positions of the
Speaker 1: planets over time, using Kepler's laws and Tycho's data, now
Speaker 1: employing the latest aid logarithms. John Napier had published the
Speaker 1: invention of logarithms in sixteen fourteen, and Kepler soon grasped
Speaker 1: their value for reducing calculation drudgery. He even published a
Speaker 1: book of logarithm tables in sixteen twenty four and developed
Speaker 1: some of the underlying theory independently. By sixteen twenty three,
Speaker 1: Kepler had finished the manuscript of the Ridolphine Tables. However,
Speaker 1: the calamities of war delayed their printing. In sixteen twenty
Speaker 1: five to twenty six, a bitter peasant uprising and the
Speaker 1: invasion of imperial forces turned Upper Austria into a battleground.
Speaker 1: In sixteen twenty six, rebels actually beseized Linz, and during
Speaker 1: the chaos a fire broke out that burned down the
Speaker 1: printing house where Kepler's tables were in press, destroying a
Speaker 1: large portion of the work in progress. Keppela had to
Speaker 1: start over with a new publisher and the Free City
Speaker 1: of Ohm. He left Lins in late sixteen twenty six
Speaker 1: as the war made it impossible to stay. Soldiers have
Speaker 1: even been courted in his home, and by sixteen twenty
Speaker 1: seven he succeeded in publishing the finished Radolphine Tables in
Speaker 1: om These tables were a triumph four more accurate than
Speaker 1: any previous. They allowed astronomers and navigators to calculate planetary
Speaker 1: positions with unprecedented precision. To illustrate the power of his tables,
Speaker 1: keppel U used them to predict a transit of Mercury
Speaker 1: across the Sun on November seventh, sixteen thirty one, and
Speaker 1: a transit of Venus in December of sixteen thirty one,
Speaker 1: rare events. He sent out words to astronomers to watch. Indeed,
Speaker 1: the first prediction was vindicated when the French astronomer Pierre
Speaker 1: Gassendi observed Mercury's transit on the predicted date. Kepeler's table
Speaker 1: slightly missed Venus transit. It happened, but was not visible
Speaker 1: in most of Europe, which Gassende didn't realize. The young
Speaker 1: English astronomer Jeremiah Horrocks corrected the parameters and successfully observed
Speaker 1: the transit of Venus in sixteen thirty nine, further confirming
Speaker 1: Kepler's system. The Adolphine tables remained the principal reference for
Speaker 1: planetary motion for many decades until su planted by Newtonian
Speaker 1: tables in the eighteenth century. The star catalog portion of
Speaker 1: the tables contained one thousand and five stars, far more
Speaker 1: than any other previous catalog, each with updated coordinates. Title's
Speaker 1: original catalog had seven hundred and seventy seven stars. Kepler
Speaker 1: increased it by incorporating additional observations and even some Aptolemy's
Speaker 1: and Johann Bayer's entries for southern stars. It was the
Speaker 1: first pre telescopic star catalog ever compiled. The positions were
Speaker 1: calibrated to Tycho's precise naked eye measurements and refined by
Speaker 1: Kepler's calculations, achieving accuracies of one arcminut or better from
Speaker 1: many stars. Alongside the fixed stars, the Rudolphine tables provided
Speaker 1: planetary tables, essentially almanac data in formulas by which one
Speaker 1: to determine each planet's position on any date. These planetary
Speaker 1: tables were rooted in Kepler's model heliocentric with elliptical orbits
Speaker 1: and area law motion. Because of this, they dramatically outperformed
Speaker 1: all the tables based on circular or geocentric models. For example,
Speaker 1: the widely used Brutenic tables of the fifteen hundreds based
Speaker 1: on Copernicus's circular orbits, could err by many degrees for Mars.
Speaker 1: Kepler's tables using ellipses hit much closer to the mark.
Speaker 1: As University of Rostock's history summary notes, the Radolphine tables
Speaker 1: were considerably more precise than earli as such tables, and
Speaker 1: finally made heliocentric calculations practical and trusted. In a way,
Speaker 1: these tables were the proof of the pudding. If Copernicus
Speaker 1: and Kepler were right, the tables would predict celestial events correctly,
Speaker 1: and they did. Kepler meticulous as ever included in the
Speaker 1: tables all the tools in astronomer would need. He added
Speaker 1: corrections for atmospheric refraction so that users could adjust apparent
Speaker 1: star and planet altitudes to true values. This was the
Speaker 1: first time refraction was accounted for in such tables. He
Speaker 1: also incorporated the new aid of logarithms, recently invented by
Speaker 1: John Dappier, providing a table of logarithms and anti logarithms
Speaker 1: to facilitate computations. This made the calculations far quicker and
Speaker 1: less error prone, a very modern touch. The Redulphin Tables
Speaker 1: even came with a set of instructions and examples on
Speaker 1: how to use the data to determine things like planetary
Speaker 1: longitudes and latitudes. Kepler included a world map with this book,
Speaker 1: illustrating how one might find longitude by using lunar eclipses
Speaker 1: and the tabulated positions of the moon. The road to
Speaker 1: publishing the Rudolphine Tables were long and fraud Kepler inherited
Speaker 1: Tycho's observational data in sixteen oh one when Tycho died,
Speaker 1: under the condition that he produced the tables and credit Tycho.
Speaker 1: He started the work in Prague, but soon came turmoil.
Speaker 1: Emperor Rudolph the Second, who had supported the project, was deposed.
Speaker 1: By sixteen twelve, Kepler lost his position in Prague and
Speaker 1: had to move to Linz. The outbreak of the war
Speaker 1: and personal hardships, including the witch trial of his mother
Speaker 1: and the deaths of his children, delayed his progress. Moreova,
Speaker 1: tycho brahes heirs hounded Kepler attempting to claim Tycho's data
Speaker 1: and the profits of the tables. In letters, Kepler sometimes
Speaker 1: expressed weariness at the sheer drudgery of number crunching required.
Speaker 1: I beseech thee my friends do not sentenced me entirely
Speaker 1: to the treadmill of mathematical computations and leave me time
Speaker 1: for philosophical speculations, which are my only delight. He pleaded
Speaker 1: to one impatient correspondent who pressed him for the tables. Indeed,
Speaker 1: calculating and checking hundred subplanetary positions by hand was a
Speaker 1: mammoth task in an error before mechanical calculators, and Kepler
Speaker 1: was understandably reluctant, but his sense of duty in Tycho's
Speaker 1: dying wish compelled him to finish. By sixteen twenty three,
Speaker 1: he had completed the manuscript. Securing funds to publish, however,
Speaker 1: was another challenge. Keppler literally chased down back pay and
Speaker 1: stipends across Central Europe to finance the printing. He finally
Speaker 1: gathered enough money for paper and paid the printer, largely
Speaker 1: out of his own pocket. Initially, he hoped to print
Speaker 1: and lens, but the city became engulfed in the chaos
Speaker 1: of the Thirty Years War, so Kepler moved the operation
Speaker 1: to the Free City of Ohm. There After, quarrels with
Speaker 1: the printer about accuracy. The first edition of one thousand
Speaker 1: copies rolled off the press in September sixteen twenty seven,
Speaker 1: just in time for the Autumn Frankfurt book Fair. The
Speaker 1: Radolphine Tables were immediately recognized as a monumental achievement. Astronomers
Speaker 1: and navigators everywhere adopted them. For the first time, one
Speaker 1: could make reliable predictions of astronomical events. Within a decade.
Speaker 1: Johannes Shrek and others brought them to China, where in
Speaker 1: sixteen thirty five they helped Jesuit astronomer Adam Shawl van
Speaker 1: Bell reform the Chinese calendar. In essence, the Radolphine Tables
Speaker 1: did more to further the acceptance of a heliosectric model
Speaker 1: of the cosmos than any argument alone could. Their accuracy
Speaker 1: was convincing. They remained the premier reference until mid century,
Speaker 1: when newer data and eventually Newtonian theory produced better tables.
Speaker 1: Kepler dedicated the work to Rudolph's successor, Emperor Ferdinand the Second,
Speaker 1: since Rudolph the Second had died in sixteen twelve, but
Speaker 1: he kept Rudolph's name on the title in homage. The
Speaker 1: front piece of the publish book is rich in symbolism.
Speaker 1: It depicts the great astronomers Hipparchus, Ptolemy, Copernicus, and Tycho
Speaker 1: gathered in a grand temple of Urania views of astronomy,
Speaker 1: with Kepler himself modestly represented among them. In the center,
Speaker 1: Copernicus and Tycho appeared to debate, while nearby a depiction
Speaker 1: of Tycho's island observatory in Kepler's model of the Solar
Speaker 1: System are shown. It's essentially a monument in print celebrating
Speaker 1: the triumph of precise astronomy over the skies. In triumph,
Speaker 1: it was the Ridolphine Tables encapsulated Kepler's legacy. They enentrined
Speaker 1: his three laws. All the calculations in the tables assumed
Speaker 1: the elliptical orbits and area law timing, and they implicitly confirmed
Speaker 1: the harmonic law across the planets. They proved that the
Speaker 1: heliocentric cosmos was not only philosophically pleasing, but emperodically superior,
Speaker 1: in a way when Newton later said, if I had
Speaker 1: seen further, it is by standing on the shoulders of giants.
Speaker 1: One of those giants was Kepler, and works like Rudolphine
Speaker 1: tables formed the very platform in which Newton stood. Kepler,
Speaker 1: through incredible perseverance, gave humanity a parting gift. The sky
Speaker 1: mapped and tabulated, ready for future explorers to navigate, both
Speaker 1: in reality and theory. By sixteen twenty seven, Kepler's scientific
Speaker 1: work was essentially completed, but his personal journey was entering
Speaker 1: a desperate phase. The Thirty Years War had engulfed Germany
Speaker 1: and Kepler's patron, Emperor Ferdinand the Second, who had succeeded Matthaeus,
Speaker 1: who had little interest in supporting a Protestant mathematician. Kepler
Speaker 1: had also lost his position in Lins when he left.
Speaker 1: Now effectively unemployed with a family to support, Kepler wandered
Speaker 1: in search of a new patron. He found temporary refuge
Speaker 1: at the court of Albert von Wallenstein, the famous and
Speaker 1: infamous general of the Imperial Armies. Lollenstein was a cultured
Speaker 1: man with an interest in astrology. He believed importance and
Speaker 1: sought advice from astrologers. In sixteen twenty eight, Wallenstein invented
Speaker 1: Kepler to his estate and Saggin. Kepler spent some time
Speaker 1: as an adviser in Wallenstein's service, casting horoscopes and providing
Speaker 1: astronomical Council, yet this was not a long term solution.
Speaker 1: In sixteen thirty, hearing that an Imperial diet Assembly would
Speaker 1: meet at Regensburg, Kepler decided to attend, hoping to petition
Speaker 1: for the payment of back salary still owed to him
Speaker 1: from his imperial post years before. It was a risky
Speaker 1: journey given the wartime conditions, but Kepler was determined he
Speaker 1: had endured financial struggles for too long. He arrived at
Speaker 1: Regensburg in Bavaria in October sixteen thirty. There, exhausted from
Speaker 1: travel and the distresses of previous years, Kepler fell ill
Speaker 1: with the fever, possibly a tropical fever or simply a
Speaker 1: feverish cold that turned deadly. On November fifteenth, sixteen thirty,
Speaker 1: at the age of fifty eight, Johannes Kepler died in Regensburg.
Speaker 1: I used to measure the heavens now. I measure the
Speaker 1: shit shadows of the earth. Although my mind was sky bound.
Speaker 1: The shadow of my body lies here, reads the epithaph
Speaker 1: Kepler composed for himself. Because of ongoing conflict, Kepler's grave
Speaker 1: in Regionsburg was neglected and within a few years was destroyed.
Speaker 1: The churchyard was ravaged during the war. Thus no physical
Speaker 1: monument remained at his burial site. But Kepler's true monument
Speaker 1: was his scientific legacy, which soon spread across Europe and
Speaker 1: stands to this day. Kepler's contributions to knowledge were vest
Speaker 1: and varied. He is most celebrated for the three laws
Speaker 1: of planetary motion, which can be summarized as follows. One
Speaker 1: planets move in ellipses with the Sun at one focus. Two,
Speaker 1: a planet sweeps out equal areas in equal times. Its
Speaker 1: speed varies such that it covers the same area segment
Speaker 1: of its orbit in a given time. And three, the
Speaker 1: square of a planet's orbital period is proportional to the
Speaker 1: cube of its average distance from the Sun. These laws
Speaker 1: emperiodically to arrived by Kepler from Tycho's data, with the
Speaker 1: first natural laws of astronomy, universal precise and expressed in
Speaker 1: mathematical form. Kepler published the first two laws in Astromy
Speaker 1: and Nova in sixteen o nine, and the third low
Speaker 1: a decade later, in Harmonix Monday in sixteen nineteen. It
Speaker 1: is hard to overstate how revolutionary they were. They swept
Speaker 1: away the complicated epicycles of ptolemaic astronomy and even the
Speaker 1: circular orbits of Copernicus, replacing them with a simple, elegant
Speaker 1: geometric description that actually matched the heavens. By introducing physical
Speaker 1: causality into celestial motions, Kepler also bridged the gap between
Speaker 1: astronomy and physics, which had been separate disciplines. This was
Speaker 1: considered impious or at least rash by some of his contemporaries.
Speaker 1: Kepler's own teacher, Maslin, objected to the idea that the
Speaker 1: heavens were mechanical rather than ruled by divine spheres, but
Speaker 1: in hindsight, Kepler's approach was a critical step toward the
Speaker 1: modern scientific method. Later physicists like Newton would build directly
Speaker 1: on Keppler's laws. Famously, Newton proved in sixteen eighty seven
Speaker 1: that if gravity poll's planets towards the Sun with an
Speaker 1: inverse square force, then Kepler's laws necessarily follow. Kepler's work
Speaker 1: thus provided one of the key foundations for the concept
Speaker 1: of universal gravitation. Beyond the planetary laws, Kepler achieved many
Speaker 1: firsts and science in the field of optics. He was
Speaker 1: the first to explain how a telescope works and to
Speaker 1: design the improved keppellarian telescope with two convex lenses that
Speaker 1: became the standard for astronomical refractors. He was the first
Speaker 1: to correctly describe the formation of real, virtual, upright and
Speaker 1: inverted images by lenses. He elucidated the role of the
Speaker 1: retina envision, recognizing that the eyes lens projects an inverted
Speaker 1: image on it. He investigated pinhole cameras and mirror reflections,
Speaker 1: laying the groundwork from modern optics so much that Ashroomapar's
Speaker 1: optica had been called the foundation of modern optics. In mathematics,
Speaker 1: Kepler's sixteen fifteen book New Stereometry of Wine Barrels was
Speaker 1: a study in measuring the volume of barrels by thinking
Speaker 1: of them as stacks of cross sectional discs, an approach
Speaker 1: that anticipated the development of integral calculus. Kepler's work on
Speaker 1: volume in the method of indivisibles would later inspire Cavaliery
Speaker 1: and indirectly Libyans in the creation of calculus. Now a
Speaker 1: little bit more about this book of measuring wine barrels.
Speaker 1: Amid his astronomical endeavors, Keppler also produced a gem in mathematics,
Speaker 1: one born from a practical problem that literally rolled into
Speaker 1: his life. In sixteen thirteen, while living in Linz, Kepler remarried.
Speaker 1: As the story goes, he purchased a large barrel of
Speaker 1: local wine for the wedding festivities, But the wine merchant's
Speaker 1: method of gauging the barrel's volume struck Kepler as crude
Speaker 1: and likely inaccurate. The merchant had simply inserted a rod
Speaker 1: through the whole and measured the phil height to set
Speaker 1: the price, and irked Kepler suspected the gaging stick method
Speaker 1: did not properly account for the barrel's shape. Could a
Speaker 1: short squad barrel and a toll skinny barrel of equal
Speaker 1: rod measurement really hold the same volume? Rather than shrug
Speaker 1: it off, the ever curious mathematicians saw a challenge. This
Speaker 1: wine barrel incident inspired Kepler to delve into the mathematics
Speaker 1: of volumes and led him to write this book. In
Speaker 1: doing so, Kepler made one of the earliest contributions to
Speaker 1: what would later be known as integral calculus. Despite its origin,
Speaker 1: this book is a serious work of mathematics. In it,
Speaker 1: Kepler develops a systematic method for calculating areas and volumes
Speaker 1: by an approach that foreshadows the use of infinite tesimals.
Speaker 1: He essentially resurrects and extends the methods of Archimedes, imagining
Speaker 1: shapes to be divided into an infinite number of very
Speaker 1: thin cross sections or indivisibles that can be summed to
Speaker 1: find volume. Kepler begins with simple cases, like the area
Speaker 1: of a circle, which he conceies as made of infinitely
Speaker 1: many triangular wedges, yielding the classic area of formula, and
Speaker 1: then tackles more complex three D solids. A large portion
Speaker 1: of the book is devoted to solids of revolution shapes
Speaker 1: like barrels, which can be generated by rotating a curve
Speaker 1: around an axis. Kepler computed or estimated the volumes of
Speaker 1: over ninety different such solids, ranging from cylinders and spheres
Speaker 1: to ellipsoids and toroids. In each case, he conceptually sliced
Speaker 1: the solid into infinitesimal disks or washes, summed their volumes,
Speaker 1: and arrived at results that are equivalent to what integral
Speaker 1: calculus would give, though he lacked our notion. For example,
Speaker 1: he found the volume of his sphere by summing the
Speaker 1: volumes of an infinite number of thin cones covering it,
Speaker 1: reaching the correct formula. Such reasoning was revolutionary for the time.
Speaker 1: Mathematicians would only much later formalize it. As historians C. H.
Speaker 1: Edwards noted, Kepela's approach in his stereometry was to dissect
Speaker 1: a given solid into an infinite number of infinite tesimal
Speaker 1: pieces convenient to the problem, then add them up. In
Speaker 1: other words, Kepler was doing calculus beforecklace had been invented.
Speaker 1: Little wondered that this work is regarded as one of
Speaker 1: the most significant works in the prehistory of calculus, and
Speaker 1: Kepler is counted among the forerunners of Newton and Libens
Speaker 1: in this domain. This book did not stop a theory.
Speaker 1: Returning to the wine barrels, Kepler applied his methods to
Speaker 1: find out how to accurately measure their volume. He introduced
Speaker 1: the concept of a measuring rod calibrated not just by length,
Speaker 1: but by the barrel's geometry. He computed volumes for different
Speaker 1: barrel shapes, and even posed an optimization problem. Given a
Speaker 1: certain amount of wood a fixed barrel, diagonal or circumference,
Speaker 1: what barrel shape like the ratio of height to diameter
Speaker 1: yields the maximum volume. This was essentially a problem with
Speaker 1: differential calculus, finding a maximum of a continuous function. Kepler
Speaker 1: approached it by intelligent trial. He determined that a barrel
Speaker 1: of a certain squad proportion held the most wine for
Speaker 1: its size. He discovered, in fact, that the merchant's preferred
Speaker 1: barrel design was nearly optimal, which, despite minor differences, vindicated
Speaker 1: the merchant's practice in a way much to Kepler's amusement. Thus,
Speaker 1: Kepler's annoyance turned into insight. He showed the merchant's method
Speaker 1: was not widely wrong, but he offered a far more
Speaker 1: rigorous way to get it right. In the process, he
Speaker 1: essentially formulated what later became known as Kepler's rule for volume,
Speaker 1: an early numerical integration scheme for solids of revolution. To
Speaker 1: share the practical benefits, Kepler even published a short German
Speaker 1: pamphlet in sixteen sixteen explaining the new measuring rules for
Speaker 1: artisans and wine cellars. In summary, this book stands out
Speaker 1: as a brilliant example of Kepler's versatility. Known primarily as
Speaker 1: an astronomer, here Kepler behaves as a true mathematician and
Speaker 1: even an innovator in engineering. He brings the abstract to
Speaker 1: the every day. From calculating a circle's area to determine
Speaker 1: how much wine is in a barrel, all with unprecedented thoroughness.
Speaker 1: As one article puts it, Kepler's work is a systematic
Speaker 1: work the calculation of areas and volumes by infinitesimal techniques.
Speaker 1: Today we use integral calculus to solve these kinds of problems.
Speaker 1: In bridging the gap between Archimedes and modern calculus, Keppel
Speaker 1: once again showed his conviction that nature, whether in the
Speaker 1: heavens or the Cooper's workshop, runs by noble mathematical rules,
Speaker 1: and in doing so he made even the measurement of
Speaker 1: wine an episode in the story of scientific progress. Keppel
Speaker 1: also independently devised a system of logarithms. After Napia's invention,
Speaker 1: Keblisch published his own table of logarithms and contributed to
Speaker 1: their theoretical basis. Keppel published his own table of logarithms
Speaker 1: and contributed to their theoretical basis. In geometrical crystallography, Kepler
Speaker 1: wrote the first scientific essay on snowflakes, A New Year's
Speaker 1: Gift of Hexagonal Snow, in sixteen eleven. In this charming booklet,
Speaker 1: he asked why snowflakes always formed six cornered hexagonal symmetry.
Speaker 1: He mused that nature must arrange small spherical particles in
Speaker 1: the most efficient way, and conjecture that the densest weight
Speaker 1: to pack equals spheres is in a pyramidal lattice, essentially
Speaker 1: stating that kepler conjecture about sphere packing. This conjecture remained
Speaker 1: unproven until nineteen ninety eight. Over three hundred and seventy
Speaker 1: eight years later, an astronomy proper Kepler made the first
Speaker 1: scientific attempt to measure the distance to the stars using parallax.
Speaker 1: He reasoned that if Earth's orbit produces no detectable parallax
Speaker 1: shift in star's positions, the stars must be extremely far away.
Speaker 1: He correctly attributed the tides mainly to the Moon's influence,
Speaker 1: a notion Galileo actually ridiculed at the time, and he
Speaker 1: was the first to realize that the Sun itself rotates
Speaker 1: on an axis, noticing that sun spots, whose discovery by
Speaker 1: others in sixteen ten to sixteen eleven he followed closely
Speaker 1: must imply the Sun's spins. He even coined the words satellite.
Speaker 1: In a sixteen eleven pamphlet, he introduced a term for
Speaker 1: Jupiter's moons, drawing on the idea of attendant followers of
Speaker 1: a planet. So many modern concepts and turn hormonologies can
Speaker 1: be traced to Kepler's fertile mind. So many modern concepts
Speaker 1: and terminologies can be traced back to Kepler. Little wonder
Speaker 1: that he is regarded as one of the founding figures
Speaker 1: of modern astronomy, physics, and science. Yet Keppler was not
Speaker 1: a modern scientist in the narrow sense of excluding metaphysics
Speaker 1: or spirituality. He was a man of the Late Renaissance,
Speaker 1: steeped in Neoplatonism, biblical theory, and even a dose of mysticism.
Speaker 1: Understanding Keppler's philosophy and mysticism is essential to understanding the man.
Speaker 1: He saw mathematics, particularly geometry, as holy. Geometry is one
Speaker 1: an eternal a reflection of the mind of God. That
Speaker 1: share in it accorded to humans is one of the
Speaker 1: reasons that humanity is the image of God. Kepler wrote
Speaker 1: this almost mystical reverence for geometry drove him to the
Speaker 1: platonic solids model and related to the harmonies of the
Speaker 1: planetary motions. Keppeler earnestly believed that the universe is built
Speaker 1: on harmonic principles, a cosmic music. In his magnum Opus
Speaker 1: Harmony of the World. In sixteen nineteen, Kepler delved into
Speaker 1: his Pythagorean dream. He had spent years since the God
Speaker 1: Stays exploring how geometrical ratios, musical intervals, and the structure
Speaker 1: of nature might all be unified, and finally, in book five,
Speaker 1: he examines the harmony in planetary motions. There he articulates
Speaker 1: the third law in a musical context. The ratio of
Speaker 1: the square of planets periods to the cubes of their
Speaker 1: distance is the same for all planets. A silent harmony.
Speaker 1: Kepler imagined that each planet, in its swift and slow motion,
Speaker 1: analogous to high and low notes, emits a tone. At
Speaker 1: different points in their orbits. Planets sing different notes. For example, Earth,
Speaker 1: with its slightly varying speed, sings me fa me, and
Speaker 1: Kepler couldn't resist a word play. The Earth sings me
Speaker 1: fa me. So we can gather from this that misery
Speaker 1: and famine reign in our Habitat this dismal pon his side,
Speaker 1: Keppelo truly thought the celestial motions found a grand pola.
Speaker 1: This dismal ponicide. Keppelo truly thought the celestial motions formed
Speaker 1: a grand polyphony, the music of the spheres that philosophers
Speaker 1: had long hypothesized. He even identified specific musical intervals for
Speaker 1: planetary velocity ranges. For instance, Venus's speed range formed a
Speaker 1: nearly perfect fifth, Earth, a minor third, and so on.
Speaker 1: He had some rivalry with the English neoplatonist Robert Flood
Speaker 1: on these matters. Flood published his own harmonic theory around
Speaker 1: the same time, and Kepler sharply criticized Flood for being
Speaker 1: speculative and numerological. But whereas Flood's harmonies were tied to
Speaker 1: astrological mysticism, Kepler's were anchored in data. He quantified the
Speaker 1: angles and speeds. In the end, this book gave the
Speaker 1: world the Third Law. But it also stands as a
Speaker 1: testament to Kepler's metaphysical vision, a universe where mathematical beauty
Speaker 1: is not just aesthetic but real, where the celestial machine
Speaker 1: is not a kind of divine organism but a kind
Speaker 1: of clockwork created by God, and yet that clockwork produces
Speaker 1: a wondrous harmony perceptible to the intellect. Some say this
Speaker 1: book often reads like a hymn. Kepler's joy and reverence
Speaker 1: burst forth in the final pages as he addresses the divine.
Speaker 1: The heavenly bodies are nothing but a continuous song for
Speaker 1: several voices, perceived not by the year, but by the intellect,
Speaker 1: a music which sets landmarks in the immeasurable flow of time.
Speaker 1: It is no longer surprising that man, an imitation of
Speaker 1: his creator, has at last discovered the art of figured song.
Speaker 1: And even in more feverent prayer, he writes, the wisdom
Speaker 1: of the Lord is infinite. Ye heavens sing his praise, sun, moon,
Speaker 1: and planets. Glorify him in your ineffable language. Praise him
Speaker 1: celestial harmonies and all ye who can comprehend them. These
Speaker 1: poetic lines show Kepler saw his scientific work as profoundly spiritual.
Speaker 1: He felt he was thinking God's thoughts after him. With
Speaker 1: the Third Law, the Copernian cosmos had a new harmonious
Speaker 1: order that only a divinely inspired geometrical mind could have arranged.
Speaker 1: Kepler's religious faith was absolutely central to his life, albeit
Speaker 1: an unorthodox one, and frequently spoke of God in his works.
Speaker 1: He saw scientific vocation as a priesthood of sorts. I
Speaker 1: am merely thinking God's thoughts after him. He is often
Speaker 1: quoted a paraphrase of his own words, He believed God
Speaker 1: has designed the cosmos according to an intelligible plan accessible
Speaker 1: through reason, since humans are made of God's image with
Speaker 1: the capacity for understanding. This theological optimism fueled Kepler's dog
Speaker 1: perseverance through years of calculation and frustration. He was convinced
Speaker 1: the underlying patterns would be simple and elegant, because a
Speaker 1: perfect God would choose a perfect geometry. His faith also
Speaker 1: made him unafraid of upevil By placing the Son at
Speaker 1: the center and Earth the moondong the planets, Keppela felt
Speaker 1: he was glorifying God's work rather than demoting Earth. In
Speaker 1: one of the beautiful passages at the end of Astronomy
Speaker 1: and Nova, after working out Mars's orbit, Keppelo offers a
Speaker 1: prayer of thanks. I feel carried away and possessed by
Speaker 1: an unutterable rapture over the divine spectacle of heavenly harmony.
Speaker 1: He exults. He expresses gratitude that God permitted him to
Speaker 1: discover truths hidden for ages. Such spiritual language runs through
Speaker 1: many of Kepler's writings. At the same time, Keppler had
Speaker 1: an eerie humanist side to his religion, Living amidst the
Speaker 1: Catholic Protestant conflict, he longed for reconciliation. As noted, Keppelo
Speaker 1: was condemned by Lutheran authorities for being soft on Calvinists.
Speaker 1: He openly argued for toleration among Christian sects. Christ the
Speaker 1: Law was neither Lutheran, nor Calvinist, nor papist, he wrote,
Speaker 1: childing partisans on all sides. This spirit won him no
Speaker 1: friends in Orthodoxy, but it speaks to Kepler's independent mind
Speaker 1: and moral courage. He managed remarkably to maintain patriots under
Speaker 1: Catholic emperors and friendships with Jesuit scientists like those who
Speaker 1: vetted his mother's trial, even as he personally remained Protestant.
Speaker 1: His ultimate loyalty was to truth as he saw it,
Speaker 1: whether in science or faith. Keppel's blend of occult and
Speaker 1: rational thinking is best illustrated by his stance on astrology
Speaker 1: and witches. As we described, Keppler practiced astrology, but sought
Speaker 1: to reform it by stripping out superstition and basing it
Speaker 1: on empirical correlations. For example, he believed the weather might
Speaker 1: be influenced by planetary aspects, and he thought the human
Speaker 1: soul could resonate with cosmic harmonies, but he mocked the
Speaker 1: simplistic horoscope predictions of quacks and his Turtius intervenians. He
Speaker 1: calls out both the thick headed band of fat bellied
Speaker 1: astrologers and those who dismiss astrology entirely, urging a middle way.
Speaker 1: To him, astrology was the vestige of an older mode
Speaker 1: of thought that could be modernized or at least used
Speaker 1: carefully regarding the occult, Keppler showed deep personal bravery in
Speaker 1: saving his mother from a witchtrial, effectively pitting scientific reasoning
Speaker 1: against fear and ignorance. After that, in the Somnium's extensive footnotes,
Speaker 1: he explained at length that what appeared as demons and
Speaker 1: spirits in his story were actually astronomical allegories or natural phenomena.
Speaker 1: For instance, he detailed the physical conditions of the moon
Speaker 1: and described how one might experience weightlessness. There all couched
Speaker 1: in a fantastical narrative as a clever literary device. It
Speaker 1: is a little wonder that some Niam earned Kepler recognition
Speaker 1: as a pregenitor of science fiction. The novel strained mixture
Speaker 1: of witchcraft in space travel mirrors Kepler's own life, striving
Speaker 1: as superstitious pass and a scientific future. Some astronomers accepted
Speaker 1: elliptical orbits but not the area law. For example, some
Speaker 1: astronomers accepted elliptical orbits but not the area law. Others,
Speaker 1: like seth Ward, tweaked Keppler's model to fit their comfort.
Speaker 1: Giants of science, such as Galileo or Renee Discards, paid
Speaker 1: surprisingly little public attention to Kepler's eschero mia nova. Galileo,
Speaker 1: though a friend and ally of Kepler in the Compernican cause,
Speaker 1: never explicitly endorsed the elliptical orbits. He stuck to circular
Speaker 1: orbits in his writings, possibly because he lacked the physics
Speaker 1: to justify ellipses. Descartes, too, formulated a cosmology of vortices
Speaker 1: that ignored Kepler's laws. It would take time and new
Speaker 1: observational proofs like the transit of mercury in sixteen thirty one,
Speaker 1: observed right on schedule by Gascinde, using Kepler's prediction, to
Speaker 1: convince the broader scientific community that Kepler's system was truly superior.
Speaker 1: The turning point arguably came with Isaac Newton. By the
Speaker 1: late seventeenth century, thinkers like Robert Hook and Giovanni Borelli
Speaker 1: were incorporating Kepler's idea of attractive forces into their theories.
Speaker 1: Newton's Percipia Mathematica in sixteen eighty seven then provided the
Speaker 1: master synthesis. It derived Kepler's three laws from a single
Speaker 1: universal law of gravitation. This not only validated Keppler's laws
Speaker 1: beyond doubt, but elevated them to the status of necessary
Speaker 1: consequences of physical principles. The problem of why planets move
Speaker 1: as they do, which Kepler could only answer with a
Speaker 1: vague motive soul or magnetic force from the Sun, was
Speaker 1: finally answered by Newton with gravity and mechanics. Newton famuously
Speaker 1: acknowledged his depth to Kepler's work, saying that by standing
Speaker 1: on the soldiers of giants like Kepler and Galileo, he
Speaker 1: could see further in solving the Kepler problem, as it
Speaker 1: came to be known, finding the forced law that gives
Speaker 1: rise to Keppeler's orbits. Newton cemented Kepler's place as a
Speaker 1: central figure in the scientific revolution. In the history and
Speaker 1: philosophy of science, Kepler's legacy has also been richly examined.
Speaker 1: Enlightenment era historians sometimes downplayed Keppler's mystical side. By contrast,
Speaker 1: nineteenth century Romantic scholars like E. F. Eppelt, who studied
Speaker 1: Kepler's unpublished manuscripts in detail, celebrated the unity of Kepler's
Speaker 1: scientific and spiritual vision. A. Pelt in eighteen forty nine
Speaker 1: wrote the first full biography of Kepler, portraying him as
Speaker 1: a hero of the revolution of the sciences who fused
Speaker 1: mathematical rigor with esthetic and religious insight. In the twentieth century,
Speaker 1: Alexandre Kore's influential studies of Kepler in the nineteen thirties
Speaker 1: further highlighted Kepper's role in transforming our worldview from an
Speaker 1: ancient closed cosmos to a modern infinite universe. Krey emphasized
Speaker 1: Keppler's platonic and mystical motivations as positive driving forces in
Speaker 1: his scientific breakthroughs. Philosophers of science have repeatedly used Kepler
Speaker 1: as a case study. For instance, Carl Popper pointed to
Speaker 1: Kepler's bold conjectures and attempts at falsification. Kepler tested dozens
Speaker 1: of hypotheses against data, discarding those that didn't work as
Speaker 1: exemplary of the scientific method. Keppler's confrontation with the competing
Speaker 1: world view of flood even got the attention of psychologist
Speaker 1: Wolfgang Poli, who wrote about it in the context of
Speaker 1: conflict between rational analysis and archae type of symbolism. In short,
Speaker 1: Kepler's work has been a treasure trove for scholars examining
Speaker 1: how science evolves and how human creativity bridges the gap
Speaker 1: between mysticism and empiricism. Culturally, Kepler's influence has extended into literature, music,
Speaker 1: and the arts. His life and ideas have inspired novels, operas,
Speaker 1: and artworks. For example, the Irish novelist John Bainville wrote
Speaker 1: Kepler in nineteen eighty one, a lyrical fictionalized biography that
Speaker 1: won the James Tate Black Memorial Prize. Banville's novel explores
Speaker 1: Kepler's in a world, his dreams, his anxieties, his spiritual
Speaker 1: musings against the backdrop of the chaotic seventeenth century, bridging
Speaker 1: the distant figure of life from modern readers. In music,
Speaker 1: the American composed of Philip Glass premiered and opera titled
Speaker 1: Kepler in two thousand and nine. This opera portrays episodes
Speaker 1: of Keppler's life in his series of theatrical scenes set
Speaker 1: to Glass's signature minimalistic but emotionally charged score. Glass was
Speaker 1: fascinated by Kepler's quest for order and juxtaposition of scientific
Speaker 1: and mystical themes. The city of Lenz, where Kepla lived,
Speaker 1: commissioned the opera as part of a celebration of science
Speaker 1: and art. Even in film, Keppler's cosmological ideas have made appearances.
Speaker 1: The twenty twelve science fiction film Mars et Avril opens
Speaker 1: with imagery based on Kepler's model for Harmonius Munday, illustrating
Speaker 1: a universe whose harmony is determined by celestial motion. The
Speaker 1: film's music score, composed by Benir Chorus, was even crafted
Speaker 1: according to Kepler's harmonic theory, translating the planet's orbital ratios
Speaker 1: into musical cues. In the visual arts, Keppeler's own drawings,
Speaker 1: such as his diagram of the nested platonic solids, often
Speaker 1: reproduced as a striking image of his sphere within a
Speaker 1: cube within a sphere and so on, or his sketches
Speaker 1: of Mars orbit are frequently celebrated for their esthetic beauty.
Speaker 1: Modern artists and poets seeing Keppler a figure of the
Speaker 1: contemplative scientists, someone whose sense of wonder and poetic description
Speaker 1: of nature. His writings are full of metaphors in sometimes
Speaker 1: lapses into poetic language, bridges the two cultures of science
Speaker 1: and art. The most famous poem historically associated with Kepler
Speaker 1: is actually one he didn't write, but inspired. The Latin
Speaker 1: verses on the front piece of the Radulphing Tables, written
Speaker 1: by an unknown poet, praised the unity of God's creation
Speaker 1: in the astronomer's task in measuring the stars. Those verses
Speaker 1: call on astronomers to serve eternity by joining the divine
Speaker 1: order of the heavens with human inquiry and apt summation
Speaker 1: of Kepler's ethos. Keppeler's name today adorns many honors and science.
Speaker 1: The Kepler Space Telescope, launched by NASA in two thousand
Speaker 1: and nine, has discovered thousands of exoplanets, truly continuing Keppler's
Speaker 1: legacy of planetary discovery. The mission was named in tribute
Speaker 1: to him. Appropriately. One of its great successes is finding
Speaker 1: planetary systems that confirm that Kepler's laws are universal. Even
Speaker 1: solar systems around other stars follow the same rules. The
Speaker 1: lunar creator Kepler and the asteroid eleven thirty four Kepler
Speaker 1: also bear his name, ensuing he is literally inscribed among
Speaker 1: the heavens. He studied. In Kepler's hometown Wioldstadt and other cities.
Speaker 1: He lived in Lenz, Prague Gratz, there are museums and
Speaker 1: monuments honoring him. A statue of Lens depicts him thoughtfully
Speaker 1: holding a model of orbits, and in Prague, a joint
Speaker 1: monument to Kepler and Tycho Brahe stands as a symbol
Speaker 1: of their cooperation. Kepler's life has also served as an
Speaker 1: inspiration in reflections on the relationship between science and religion.
Speaker 1: The MIT Independent Activities Period once ran a series on
Speaker 1: faith of scientists featuring Kepler, noting how his belief and
Speaker 1: cosmic order powered his science in the realm of a
Speaker 1: cult and esoteric Kepler's influence is more indirect, but still notable.
Speaker 1: While Kepler helped discredit traditional astrology among scientists, after his time,
Speaker 1: the two fields decisively split. By the eighteenth century, no
Speaker 1: serious astronomer practiced astrology. There remains an astrological Kepler in
Speaker 1: the sense that some astrologists today view him as a
Speaker 1: reformer of their art. Kepler College in Seattle, an astrology school,
Speaker 1: is named after him. Somewhat paradoxically giving Kepler's own mixed
Speaker 1: feelings about astrology. Additionally, Kepler's emphasis on geometric harmony influenced
Speaker 1: later mystics in New Age thinkers who romanticize sacred geometry.
Speaker 1: The image of the five platonic solids governing the cosmos,
Speaker 1: for example, resurfaces in esoteric literature as a symbol of
Speaker 1: hidden order. Kepler's successful blending of mystical intuition and empirical
Speaker 1: rigor stands as a challenge and model to anyone, even today,
Speaker 1: who seeks to reconcile holistic or spiritual perspectives with scientific method.
Speaker 1: Johannes Kepler's life was a tapestry woven with threads of genius, faith, hardship,
Speaker 1: and perseverance. He was born into a world defined by
Speaker 1: rigansphers and divine immutability. Yet he imagined a new world
Speaker 1: and lived to see it start to take hold, a
Speaker 1: world where planets soar along ellipses in an infinite universe
Speaker 1: governed by mathematical law. It is hard to picture the
Speaker 1: courage it took for Kepler to pursue his vision. He
Speaker 1: labored for years virtually alone, calculating by hand, often under
Speaker 1: financial duress and personal anguish. Guided only by a fierce
Speaker 1: conviction that the cosmos had a rational order, he could discern.
Speaker 1: Truth is the daughter of Time, and I feel no
Speaker 1: shame in being her midwife, Kepler wrote, expressing his willingness
Speaker 1: to endure doubt and ridicule in order to eventually birth
Speaker 1: the truth. Indeed, time has vindicated him. The treasures hidden
Speaker 1: in the heavens proved richer than anyone knew, and Kepler
Speaker 1: opened those treasure trolls with keys of geometry and physics.
Speaker 1: Through his laws, we launched satellites to Mars and predict eclipses.
Speaker 1: Through his optics, we peered to the edge of the
Speaker 1: universe with giant telescopes. Every time a spacecraft uses an
Speaker 1: orbital transfer or a transit method and finds a new exoplanet,
Speaker 1: Kepler's legacy is alive, and yet, beyond the technical triumphs,
Speaker 1: there is something profouling, human and heartfelt in Kepler's story.
Speaker 1: He was, as he said, moved by the geometry of
Speaker 1: the universe, by the shapes of the stars and the planets,
Speaker 1: and by the perfection of the forms of nature. In
Speaker 1: an era of war and witch hunts, Keppela held fast
Speaker 1: to the belief that the world is intelligible and beautiful.
Speaker 1: He never lost his sense of wonder. At the end
Speaker 1: of the harmony of the world, upon discovering the Third Law,
Speaker 1: Kepler broke into a prayer of gratitude and awe. I
Speaker 1: feel carried away and possessed by an unutterable rapture over
Speaker 1: the divine spectacle of the heavenly harmony. He gushed, Lord,
Speaker 1: I thank you that you have allowed me to see
Speaker 1: the beauty in your work. Such words remind us that science,
Speaker 1: for Keppla was not merely about cold numbers, but a
Speaker 1: passionate quest to touch the mind of God. After a
Speaker 1: lifetime of struggle, Keppla died far from home, without wealth
Speaker 1: or high rank. But he left us the very equations
Speaker 1: that described the dance of the planets. On his humble grave.
Speaker 1: Before it vanished, a friend recorded Kepler's own self composed epitaph.
Speaker 1: I used to measure the heavens now, I measure the
Speaker 1: shadows of earth, although my mind was skybound. The shadow
Speaker 1: of my body lies here In those lines, speaks a
Speaker 1: man who knew his place in the grand scheme, a
Speaker 1: child of Earth who reached for the stars Johannes Kepler's
Speaker 1: legacy lives on in every orbit calculated, every harmony found
Speaker 1: in nature, and every soul who looks up at the
Speaker 1: night sky and even for a moment, feels carried away
Speaker 1: by the unutterable rapture of its beauty. His life show
Speaker 1: the show of a fearless intellect lighting a candle in
Speaker 1: the dark cosmos, who continues to inspire and resonate, a
Speaker 1: rich and heartfelt testament to the unity of science and wonder.