foreign media [Music] [Applause] [Music] [Applause] thank you thank you thank you today we come to the end of this part of our journey and I'd like to celebrate by playing some music for you but this is no ordinary music this is something quite extraordinary of course Johannes Kepler was the one who found out how the universe works and what he found out was that it's very complicated the orbits of the planets are eccentric the sun is off center the planets speed up and slow down as they go around and so on Kepler couldn't help asking himself why the Creator hadn't chosen a simpler design and when he thought he found the answer this is what he wrote he said the Heavenly motions are nothing but a continuous song for several voices a music witch through discordant tensions through syncopations and cadenzas progressives towards certain pre-designed six voice cadences and thereby sets landmarks in the immeasurable flow of time 20 centuries earlier the pythagoreans had thought that the heavens were a perfectly tuned instrument whose music could be heard only by the ear of the master Pythagoras himself but the idea of heavenly music is older than time itself and it was this idea of The Music of the Spheres echoing down through the corridors of history that Kepler had seized upon a simply Universe would have made boring music the Creator had made a subtle and complex composition that could go on almost forever without repeating itself Kepler thought that he had seen into the mind of the Creator in fact he often thought that and he wrote down what he had seen in this book Johannes Kepler the harmony of the universe published in 1619. and he put down in this book the music of the songs of each of the planets and he challenged the musicians of his own time to play the celestial music oh apparently the musicians of his time thought they had better things to do and so keplin never got to hear his own music but in our time two men John Rogers and Willie Ruff of Yale University have synthesized Kepler's music on a computer so that we can hear it and that's the music I'm going to play for you so we have the Music of the Spheres synthesized on a computer every single one of you is waiting for me to say that this is far out but I'm not going to say it instead I'll just play the music for you [Music] Mercury nearest planet to the Sun Venus and Earth the sister planets second and third Mars the Striking red planet Jupiter largest planet in the solar system Saturn until recently ringed with mystery Uranus the first planet discovered in modern times Neptune the eighth planet from the Sun Pluto the ninth and most distant planet from the Sun before the written word there were metaphysical connections between music and the heavenly bodies now the sights and the sounds of the cosmos are linked for all to see and hear inspired by hindemith's grand opera about Kepler day Harmony develt Ruffin Rogers created a full nine-part Harmony the harmony of the universe listen carefully and hear the six tonal voices Mercury the highest pitched Venus and Earth constantly changing from major to minor chords Mars most distinctive easy to pick out in the full Harmony Jupiter saw deeper baser baritone and much slower Saturn hardly more than a growl in the heavens and as far as Kepler saw and heard but listen to the Rhythm Section the voices of the outer planets Uranus rapidly ticking then Neptune's steady beat and finally Pluto's based drum the foundation of the whole structure this is The Music of the Spheres and in one way or another it's been listened to for a very very long time around 600 years before Christ Pythagoras of Samos walked the Earth in search of our most profound Mysteries [Music] and with his Greek followers the Pythagorean Brotherhood he came across some amazing discoveries mathematical riches as valuable today as they were in the Golden Age a theorem about squares on the sides of right triangles for example that was later used to calculate how far the Moon Falls each second foreign [Music] the pythagoreans also figured out that the odd numbers head up to the perfect squares [Music] above all while listening to the heavens To The Music of the Spheres they discovered the laws of musical Harmony on Earth and for the next few thousand years Western composers based their scores on the Pythagorean harmonies apparently everyone was happy dancing to the same old tomb until in the Renaissance the Florentine musician played Havoc with the status quo this man wrote a book that was very critical of the influence of ancient Greek Concepts on the music of his day his name was Vincenzo Galilei and his nature intellectual and rebellious was inherited by his son Galileo Galilei grew up to be a scientist a revolutionary copernican despite the consequences and in the process he corresponded on the Heavenly nature of things with the like-minded astronomer and mathematical genius named Johannes Kepler much has been made of Kepler's dazzling accomplishments but perhaps his most far-reaching was the harmony of the world in it he not only heard the age-old Music of the Spheres he set down at Space Age sound on paper like his colleague Kepler and his father Vincenzo Galileo himself had a thing or two to say about Harmony that is about harmonic motion discovering that every swing of a pendulum took exactly the same amount of time Galileo found not only the formula for making beautiful music but he unlocked the secret of keeping perfect time foreign [Music] and he didn't stop there when Galileo realized that a small rhythmically applied force could make oscillations grow to the Limit he knew he'd discovered something else about music principle of resonance as an idea resonance wasn't as dangerous as the ones for which Galileo was eventually brought to trial but in its own way resonance did and still does produce some shattering results [Music] the Amplified voice of Ella Fitzgerald shattered this glass [Applause] [Music] if it can be said that Galileo and his father made careers of shattering Greek traditions of Science and music it should be acknowledged that every Western scholar made progress only by climbing those ancient foundations to begin with [Music] by the same token if Galileo was inspired by his father perhaps so too was Pythagoras whose father was a gem cutter even today viewing the geometrical shapes of natural crystals one can see them as facets of the mathematical nature of nature itself looking deeply into the nature of just about everything Greek philosophers perceived that matter is made up of atoms but it would take centuries to discover that the shape of matter would reflect the arrangement of atoms an arrangement in which atoms are bound together by the electrical potential energies that act between them and while interactions between atoms are electrical in nature interactions between members of the human species can be just as complex and highly charged as demonstrated by The Bitter controversy between Baron Gottfried Von leibnitz and Sir Isaac Newton among many other remarkable distinctions Newton was Cambridge University's representative to the British Parliament he was not England's greatest Statesman but when it came to the behavior of masses and forces no one laid down the law better than he did the change of motion he proclaimed is proportional to the force impressed and is made in the direction of the straight line in which the force is impressed in other words and in modern terms Force equals mass times acceleration which is a vector equation [Music] about the derivative of a derivative [Music] foreign with that equation he found a power beyond the scope of politics and a glorious Reason unequaled by any other scientific idea in history in f equals m a Isaac Newton found the means to upset the apple card of the universe and for the first time in several thousand years the way to set it straight again [Music] Newton's second law of motion explains the fall of a sphere in a viscous liquid and The Descent of a penny and a feather in a vacuum Newton's equation f equals m a explains the moon's falling motion through the vacuum called outer space and the falling motion of a star this one caught as a Charged drop of oil in the Inner Space of a scientific Laboratory combined with his law of gravity Newton's second law of motion gives the motion of every projectile on Earth foreign as well as everybody in the heavens in fact when Newton realized that the Falling Moon obeys the same equation as a falling happen [Music] he United the physics of Earth with the physics of the heavens and they were United not only in the realm of equations but also in the sphere of pure geometry the path of any projectile on earth like the orbits of the planets in the heavens is a conic section it can be said without hyperbole that every projectile on Earth follows a parabola and every planet traces out and ellipse the similarity is hardly surprised since all these motions obey the same equations [Music] how in the world can one small equation be as powerful as the universe itself for one thing f equals m a applies to every force in the Mechanical Universe whether it's the force of gravity on a falling body or the magnetic force between electric currents or the force of viscosity on a falling marble or the force of a spring on a bobbing Mass not only does Newton's second law of motion apply to any Force it applies to any Mass no matter what and no matter where [Music] whether it's a bobbing Mass or a pole vaulter [Music] a home run ball or a pool ball but most important of all the incredible power of f equals m a resides in the fact that it doesn't describe where a body is nor how fast it moves it describes how fast it gets faster in other words f equals m a is an equation about derivatives and therein lies Newton's essential power and superiority for example an algebraic equation can give the precise trajectory of one particular Cannonball but f equals m a because it's a differential equation can give the trajectory of every projectile ever thrown or fired [Music] but in the beginning what was it that drove young Isaac Newton to create such a powerful method with which to express himself indeed what set off the Scientific Revolution in the first place as much as anything else it was the Revolutionary passion of an otherwise timid polish monk Nicholas Copernicus unlike ptolemy's Aristotelian solar system the copernican universe no longer placed the Earth in the center of things no longer was the Earth itself fixed and stationary nor for that matter was anything else Copernicus not only set the earth into motion spinning the academic world around and plutonic circles but he set the scientific imagination loose [Music] free to challenge ancient assumptions progress didn't come easily or all at once but after Copernicus the world was an open book of course with Galileo and all that intellectual Freedom came responsibility the responsibility to describe nature as it really is do that required a new mathematics the mathematics of motion [Music] of course the ancient Greeks had found that the area of a circle was as easy as pie and that was a move in the right direction Archimedes found a formula for the area of a parabolic segment and that was progress but the mathematics of motion doesn't merely describe the shape of things to come [Music] sounds that sort of figuring was more or less exhausted in the Golden Age [Music] so rather than describing something in fixed old world terms the new mathematics derives the rate at which something changes whether the rate at which your body falls or the rate at which a hill is on the rise the derivative is a mathematical device that throughout the ever-changing Universe of motion goes to the Limit [Music] but there's almost no limit for the number of functions that can be differentiated once a few simple rules have been stored away [Music] and derivatives serve in another area as well in fact in the area of any region bounded by a smooth curve [Music] indeed after Isaac Newton and Wilhelm leibniz found the connection between integration and differentiation between area and rate of change sky was the limit however the mathematics of change some things are constant as constant as human curiosity about what may or may not exist in outer space then the expanding nature of differential equations the most constant thing is the constant itself [Music] thank you in some cases the constant merely shows how fast the projectile starts its Journey but other constants have a broader and more significant scope for example whether it's a common game of Billiards [Music] or a cosmic game of tag [Music] whenever there's no outside force involved momentum is constant [Music] momentum is mass times velocity and the change of momentum can be expressed by a differential equation force is the rate of change of momentum of course if there are no forces operating the derivative is equal to zero therefore the vector p is constant in other words when force is zero momentum is conserved and if R cross f is zero something else is concerned so what is r cross F the derivative of if R cross f is zero the quantity conserved is called the angular momentum [Music] whether it's the motion of a gyroscope [Music] or the motion of a planet if there's no twisting force angular momentum is constant and energy is constant once the work is done [Music] whether large or small work is forced through distance and it all adds up or in the language of calculus it integrates if work is done lifting a block from one height to another becomes the change in potential energy [Music] oh [Music] If instead work is done to accelerate the block it becomes kinetic energy [Music] foreign [Music] the kinetic energy of a falling object may be transformed into another kind of kinetic energy a form of energy called Heat which spreads from molecule to molecule which dissipates the energy but which never destroys it potential energy you kinetic energy k and Heat Q add them together and the result is total energy and forever constant and its energy potential and kinetic that ultimately determines the orbits of the planets that Symphony of perfect order the harmony of the Spheres [Music] as Johannes Kepler wrote the Heavenly motions are nothing but a continuous song for several voices to be perceived by the intellect not by the ear a music which through discordant tensions through syncopations and cadenzas as it were progresses towards certain pre-designed six voice cadences thereby sets landmarks in the immeasurable flow of time [Music] [Music] well we've been through a lot together we've come from the dawn of History write down the physics as we know it today ladies and gentlemen that's all I have to tell you about classical mechanics foreign um foreign media for information about this and other Annenberg media programs call 1-800 learner and visit us at www.learner.org [Music]