Galileo Galilei

Galileo Galilei

Italian mathematician, astronomer, and physicist Galilei (1564-1642) is considered to be the founder of the modern scientific method. He pioneered verifi­cation by experimentation and critical analysis of phenomena. Galileo was the first person to use a telescope to make and interpret systematic astro­nomical observations and made many discoveries regarding the solar system. Galileo’s observations of the eclipses of Jupiter’s moons led to his discov­ery of a cosmic clock that, in effect, recorded abso­lute time. The Galilean transformations of space and time variables led to the development of the Newtonian laws of mechanics. His theore­tical work in physics laid the groundwork for the future exploration of relativity and the laws of motion. Although Galileo himself did not invent the pendulum-regulated clock, his initial designs inspired others to do so. His preliminary research and design of an escapement mechanism led to the development of the first pendulum-regulated time­piece. Galileo’s quest to measure very small quanti­ties of time accurately paved the way for discoveries about sound and light waves that eventually led to modern investigations of quantum physics.

Galileo was born in Pisa, Italy, on February 15, 1564. He was the first of six, possibly seven children born to Vincenzo Galilei, a musician, composer, and wool trader; their mother was Giulia Ammannati of Pesscia. Three days later the famous artist Michelangelo died. Leonardo da Vinci had passed away 45 years prior to Galileo’s birth. Nicholas Copernicus had been dead for 21 years. William Shakespeare would be born 2 months later. This was the time of the Renaissance. A new awakening had arrived for philosophy, music, art, the sciences, literature, and discovery.

Early Life

At age 7, Galileo was sent off to a monastery to prepare to study medicine. Galileo enjoyed life at the monastery and soon decided he wanted to become a monk. His father did not agree and, complaining about his son’s untreated eye infection, removed Galileo from the monastery. Back at home young Galileo was strongly influ­enced by his father’s experiments on the nonlin­ear relationship between the tension and pitch of stretched lute strings. Working with his father, Galileo learned how to experiment and gather data. By attaching carefully measured weights to a range of strings of different lengths and thicknesses, the Galileis listened to the tones produced. Each modification altered the frequency of the vibration, producing a differ­ent note. The length of the string altered the pitch, or cycles per second of the vibrating string, in much the same way the rate of the swinging of a pendulum was related to the length of its cord. This led to the discovery that the interval between two notes was related to the inverse squares of the length of the string, when the same weight was attached and the same interval observed. For a vibrating string, the frequency or sound heard is inversely pro­portional to the square root of the string’s weight per unit of length, so thicker, heavier strings produce lower notes. This mathematical law contradicted traditional musical theory. Galileo learned from his father that it was fool­ish to accept anything as truth without examin­ing the evidence in support of it. He was taught in the tradition of Plato’s student Aristotle that theory must follow facts. It has been argued that Galileo’s devotion to the Catholic Church inspired him to seek evidence about the world in order to protect the church from disseminating misinformation.

Contributions to Medicine

In 1582, at age 18, Galileo began his study of medicine at the University of Pisa. Years later, Galileo wrote about the state of medical education by describing an anatomical dissection. The topic was the origin of the nervous system. According to Aristotle, the heart was the source of the nerves, but the anatomist clearly demonstrated the brain was the true source of the nerves. The Aristotelian philosopher replied that the evidence before his eyes would clearly indicate the brain as the origin of the nerves and he would believe it to be so, if it were not for the words of Aristotle!

While attending services at Pisa’s cathedral, Galileo noticed a swinging lamp and, using his resting heart rate as a timepiece, he observed that each swing of the lamp appeared to take the same number of pulses in his wrist and therefore approximately the same amount of time, regard­less of the length of the swing. One could imag­ine him reminiscing about weights hanging from lute strings at home. His observations and dis­cussions of this isochronicity of the pendulum led a friend of his, Santorre Santorio, a physician in Venice, to design a small pendulum that could be used to calibrate the human heartbeat rate. This device, called the pulsilogium, could be used to get an objective measurement of the heart rate of a medical patient. By observing changes in the pulse rate, physicians could now obtain data on the vitality of their patients and the efficacy of their treatments. In addition, Galileo was the first to invent a device to measure changes in tem­perature. With Santorio, Galileo worked to improve the of experimental medicine, including the study of human metabolism. Although Galileo chose not to complete his study of medicine, his research led to major contribu­tions to the scientific study of human anatomy and physiology.

Physical and Mathematical Investigations

Leaving the study of the medical arts behind, Galileo embarked on a lifelong journey in mathe­matics. Galileo’s exploration of the geometry of Euclid of Alexandria and the physics of Archimedes of Syracuse and of Aristarchus of Samos inspired his creative genius. Stimulated by exploration of the foundations of astronomy from Hipparchus of Samos and Claudius Ptolemaeus, Galileo’s mind was preparing to wrangle with ideas of cosmic proportions. Here Galileo cultivated a philosophy of scientific realism and a belief that there were explanations for natural phenomena that are revealed through observation and reason.

Inspired by the story of Archimedes and the golden crown of suspect purity, Galileo experi­mented with floating objects and developed a precise balance scale he called the hydrostatic balance, which could compare the weight of an object to an equal volume of water. He described this invention in a book he titled The Sensitive Balance (La Bilancetta) in 1586. He would later use measured volumes of water to cali­brate elapsed time precisely in his acceleration experiments.

In 1587, Galileo was asked to cast a horoscope for Francesco de Medici, the Grand Duke of Tuscany. Galileo had disdain for astrology, which he considered to be heretical, but felt it was unwise to thwart the wishes of this generous bene­factor. Drawing up a chart for the 46-year-old Grand Duke, Galileo announced that it indicated a long and fruitful life. Within a week the Duke was dead. In January of 2007, an analysis of the Duke’s remains revealed an extremely elevated level of arsenic that was indicative of deliberate poisoning.

By 1593, Galileo had moved to the University of Padua where he taught mathematics and mili­tary engineering. It was here that he met and fell in love with Maria Gamba. While never married, they did have three children. His two daughters entered the convent and his son Vincenzo was by his side when he died. Galileo worked on many inventions, including a device that used horses to raise water from aquifers. In 1604, a “New Star,” as it was called then, appeared in the constellation Sagittarius. Here was evidence for all to see that the heavens were not fixed and permanent, as Aristotle had decreed. If the great philosopher Aristotle could be wrong about this fundamental quality of the heavens, what else could he be in error about? We now know that what Galileo had witnessed was not a new (Nova) star, but rather a very old star in its last stages of stellar evolution.

Financial success came from Galileo’s invention of a military compass that could be used to calcu­late the ideal firing angle for cannons as well as the gunpowder charge and projectile weight for maximum effect and accuracy. A civilian compass model that could be used for land surveying fol­lowed. This invention is considered by many to be the world’s first pocket calculator. His text describ­ing the use of the compass, titled Operations of the Geometric and Military Compass (Le Operazioni del Compasso Geometrico e Militare) was published in 1606. This invention also intro­duced Galileo to the unpleasant world of patent infringement, as he eventually had to prove that others had copied his work.

Galileo’s lecture series on the location, shape, and dimensions of Dante’s Inferno helped to earn him a 3-year appointment at the University of Pisa to teach mathematics. It was there, according to legend, that Galileo demonstrated that falling bodies of varying sizes and weights fell the 54 meters from the top of the Leaning Tower of Pisa at the same rate. By disproving one of Aristotle’s alleged laws of nature, Galileo showed that blind acceptance of doctrine must yield to scientific experimentation. Galileo was adept at thought experiments. He reasoned that if two weights, one heavier than the other, were supposed to fall at different speeds, then why did hailstones of a wide range of weights fall together? He also pondered the question of whether, if a lighter and heavier weight were tied together, their rate of descent would change. Galileo asked whether, if the two were tied together, would the lesser one subtract velocity from the fall or would the two weights added together increase the rate of fall? If the lighter one subtracted velocity from the heavier one, then they should fall more slowly. Or, if the two together now weighed more than the original, would they fall all the faster? His conflicting results led inevitably to the conclusion that they must fall at the same rate regardless of their weight. Galileo used these kinds of thought experiments to help others to visualize the fundamental elements of motion.

When the objection was raised that a feather did indeed fall much more slowly than a cannonball, Galileo realized that air resistance accounted for the difference and that if this variable could be con­trolled, the two objects would fall at the same rate. Galileo experimented with resistance in different media such as water and oil. He was not able to perform the experiment in a vacuum, the produc­tion of which was then technically unattainable. In July of 1971, 365 years later, Apollo 15 astronaut David Scott dropped a falcon feather weighing 0.03 kilograms and a geological hammer weighing 1.32 kilograms from a height of 1.6 meters on the moon. With no air resistance, they landed simultaneously, and Commander Scott duly noted that Galileo had been right.

Galileo sought an accurate way to measure the change in the speed of a falling object over time. Galileo, a talented musician and composer, had a well-developed internal rhythm and would be able count off beats in his head quite accurately to measure seconds. The tools available to measure time in those days were extremely limited in accu­racy and reliability. Sundials and hourglasses would be useless to measure the brief intervals that Galileo sought to investigate. Mechanical clocks had appeared in Western Europe around 1330. A few years later a clock was built by Giovanni de’Dondi in Padua, Italy, that displayed the posi­tion of the sun, moon, planets, and the timing of eclipses. It was beautiful to behold, but its accu­racy was limited. The timepieces available to Galileo could measure hours with reasonable accuracy; however, the quantities of time involved in calibrating acceleration would require accuracy not just to the minute, but to the “second min­ute,” which we now know as the “second.” It appeared to be virtually impossible to calculate events occurring in fractions of seconds.

Galileo needed a way to quantify time objec­tively. He tackled this daunting problem from two directions. First he devised a way to slow the fall­ing object’s rate of speed. By building a diagonal ramp he, in effect, diluted gravity. Now he could study acceleration at a more leisurely pace by roll­ing a ball down the highly polished inclined plane. Using his military compass, he could carefully determine the angle of descent of the plane. The second part of the problem involved measuring very small intervals of time. His familiarity with the lute would most likely lead him to include frets or slightly raised ridges on some of his inclined planes. By doing so, he could hear the ball striking the frets as it descended. By spacing the frets in a way that the time interval between each sound was identical, Galileo would have a mea­surable unit of distance to indicate acceleration. He had previously measured the isochronicity of a pendulum’s swing using his own resting pulse rate; but from his observations with the pulsilo- gium, he knew that the pulse rate was too variable and therefore not a reliable enough clock to gauge acceleration. Added to this was another element arguing against using his own pulse as a clock. As his experiments began to reveal the laws of motion, his excitement would no doubt raise his pulse rate, rendering the measurement useless.

Another of his inventions, the hydrostatic bal­ance scale, would provide the inspiration for a quantifiable unit of acceleration. Galileo designed a water clock to measure velocity indirectly. By starting the ball down the ramp and beginning the release of water simultaneously, and stopping the flow of water when the ball reached the end of the ramp, he could weigh the amount of water released in a given time. In this fashion Galileo was able to make an accurate comparison of the amount of time a rolling object spent in each por­tion of its descent down the ramp. He found that the distance the ball rolled down the plane was proportional to the square of the elapsed time. Galileo observed that balls of different weights increased their speed at the same rate. The devel­opment of modern science is based on the idea of mathematically measurable sequences. One such measure, a unit of acceleration, is known as a “Galileo.” Galileo’s struggle with the accurate measurement of time laid the foundation for those who followed. His calculations would be used in 1687 by Sir Isaac Newton to formalize the laws of motion in Principia Mathematica.

Another observation of nature that stimulated Galileo’s inquisitive mind was the apparent dif­ference between the speed of light and the speed of sound. Since lightning precedes thunder and the cannon’s flash precedes the boom, Galileo knew that here was another mystery that could be solved mathematically. He attempted to design an experiment using lanterns spaced miles apart but could report only that light traveled so much faster than sound that light speed could not be measured with the instruments available at the time. Today, scientists can measure time to the attosecond, which is one quintillionth of a second!

Optics and Astronomy

While visiting Venice in 1609, Galileo first heard of the spyglass that a Dutch spectacle maker had invented. Galileo realized that a device that made distant objects appear closer had obvious military and potential financial value. His prior experience with the military compass and artillery inspired him to improve and capitalize on this invention. By experimenting with various combinations of concave and convex lenses he was able to improve on the original design by increasing its magnifying ability and righting the image. Without the proper combination and spacing of lenses, images appeared upside-down. Viewing an upside­down ship with the sea above and the sky below was disconcerting and detracted from the general usefulness of the spyglass. Galileo presented his improved 10-power telescope to the senate of Venice and demonstrated how ships at sea could be identified as friend or foe hours before a look­out without such a device could make such an identification. He was proclaimed a genius and given a generous salary increase and lifetime ten­ure. This granting of tenure, along with the appear­ance shortly thereafter of a large influx of cheap spyglasses from Northern Europe, angered some and may have contributed to problems he would face later in life.

Galileo continued to improve his telescope. With higher magnifying power and improved lens shaping and polishing techniques, he began his observations of the heavens. His preliminary investigations of the moon immediately revealed that it was uneven, rough, and full of cavities, craters, and prominences. It was not the smooth, polished, perfect heavenly body everyone believed it to be. By carefully observing the shadows cast by lunar mountains, he was able to make estimates of their altitudes. To those who insisted that the moon was covered with a smooth transparent crystal, he replied that they should grant him the equal courtesy of con­structing with that same crystal mountains, valleys, and craters.

Galileo’s explorations of the night sky brought new discoveries every clear evening. The Milky Way, which was considered to be a pale vapor of light, revealed itself to be an uncountable number of stars vast distances away. The Seven Sisters, a star cluster also known as the Pleiades, in the con­stellation Taurus the Bull, when magnified became hundreds of stars. The Great Sword of Orion, when closely examined displayed a marvelous cloud embedded with tiny newborn stars. Galileo’s examination of Ursa Major, the Great Bear or Big Dipper or Plough, revealed an amazing double star that he observed during a failed attempt to measure parallax and therefore demonstrate Earth’s revolution around the Sun.

In January 1610 Galileo turned his new and improved telescope on Jupiter. With modifica­tions to the lenses, Galileo was now able to magnify the apparent diameter of an image 30 times. He noted a star to the left of Jupiter and two on the right, all in a straight line. One could only imagine Galileo’s amazement when on the next evening he saw that all three of the stars were now on the left and still in a straight line. Weeks of observations and further improve­ments that widened the field of view of his tele­scope revealed a fourth star that circled around Jupiter. Galileo realized that these were moons that orbited Jupiter just as our moon orbited Earth. Here was evidence that not everything revolved around the earth. Seeing Jupiter’s moons revolve around Jupiter also discredited the idea that if the earth revolved around the sun it would leave its moon behind. Additional cali­bration of the orbits of Jupiter’s moons inspired Galileo to consider that their regular orbital periods could serve as a cosmic clock for ships at sea. This could aid in the accurate timekeeping that was essential for the determination of longi­tude. Galileo continued his telescopic observa­tions and developed a table of the eclipses of Jupiter’s moons to be used by ship’s captains as a cosmic timepiece to determine longitude while out of sight of land. He even developed a tele­scopic device one could wear like a hat to observe Jupiter while keeping the hands free to pilot the ship. Apparently it was difficult to use and was abandoned. Galileo did notice a slight abnor­mality in the timing of eclipses of Jupiter’s moons. It was not until 66 years later, in 1676, that the Danish astronomer Oleaus Romer was able to calculate that the 10-minute systematic error of Jupiter’s observed synodic period was because light does not travel instantaneously. Years later it would be understood as a function of the varying distance between Earth and Jupiter. This parallax effect is a manifestation of our changing viewpoint as we revolve around the sun. Galileo named Jupiter’s moons the “Medician Moons” in honor of his benefactors. Simon Mayr created the names we use today—Io, Europa, Ganemede, and Callisto—in 1614.

Galileo observed the planet Mars and saw that its apparent diameter increased when it was closer and diminished significantly when it was farther away from Earth. This was additional evidence that Mars revolved around the sun. When Mars and Earth were on the same side of the sun, Mars appeared twice as big as it did when Mars was on the far side of its orbit around the sun. This could not be clearly seen with the unaided eye, but was readily apparent when viewed through the tele­scope. In his honor, there is a crater on Mars called Galilaei as well as an asteroid named Galilea.

Another important observation first made by Galileo was that the planet Venus showed phases like the moon. When it was at its greatest distance from Earth, and more directly illuminated by the sun, it appeared as a small sphere. As its orbit took it around the sun and closer to Earth, it appeared as a progressively larger waning cres­cent. These observations lent credence to the Copernican idea that the sun was at the center of the solar system. Countless hours of watching the planets convinced Galileo of the validity of the Copernican heliocentric view. Seeing sunspots parading across the solar disc clearly demon­strated that our star, the sun, was not the perfect heavenly object described by the ancients.

Galileo was fascinated and perplexed by his observations of Saturn. The limited resolving abil­ity of his telescope rendered a tiny, blurry image of Saturn and its ring system that was not a sphere like Jupiter but looked rather elongated or shaped like an American football. Could this be more evidence against the Aristotelian belief in perfectly spherical heavenly bodies? Galileo assumed that he was seeing three separate bodies. It is interest­ing to note that Galileo’s observations of the planet Saturn led to an ironic cryptic message. In a coded letter, Galileo wrote that the last planet was triune or three-mooned. In the year 2005, the Hubble space telescope revealed that Pluto, which was considered at the time to be the last planet in our solar system, had three moons, which were named Charon, Hydra, and Nix. A contemporary analysis of Galileo’s notes indicates that he prob­ably was the first person to observe the planet Neptune, in the year 1612.

Galileo described his astronomical observa­tions made using a telescope in a small book he called The Starry Messenger (Siderius Nuncius) in March of 1610. It received a great deal of atten­tion and generated much heated discussion. In it, Galileo explained his view of scientific realism. He was certain that there were explanations of natural phenomena that would be revealed through observation and reasoning. There were those who felt that some of Galileo’s findings contradicted the teachings of the Catholic Church. Objections were raised that certain passages in the Bible appeared to indicate that the sun went around the earth and that to believe otherwise was heresy. Galileo responded that while the Bible could never be wrong, it was not meant to be taken literally and that mistakes of interpreta­tion could lead to confusion. This led others to complain that only the clergy could interpret the Bible and that Galileo had to be stopped. With the Protestant Reformation of Martin Luther and John Calvin and The Thirty Years War to con­tend with, the Catholic Church had little toler­ance for dissension within the ranks. Galileo had met Giordano Bruno, who in 1600 was found guilty of heresy and burned to death. He knew others who had suffered at the hands of the Inquisition and was aware that he had better tread lightly. An investigation of the charges against Galileo found him innocent of heresy, but he was cautioned not to teach the Copernican system as a proven fact.

In 1618, three comets were visible over Europe. A Jesuit mathematician, Father Horiatio (Orazio) Grassi, who wrote using the pseudonym Lotario Sarsi, argued that the highly elliptical orbit of the comets argued against Copernicanism, which postulated circular orbits. Galileo replied in an essay titled The Assayer (Il Saggiatore), published in 1623. Here Galileo established norms and rules for the investigation of nature. It is consid­ered to be one of the great works of scientific literature. In it, Galileo describes how the grand book of the universe is written in the language of mathematics.

Geocentrism, Heliocentrism, and Conflict With Established Authority

Galileo’s attraction to the sea and things nautical led him to a contemplation of the causes of the tides. He believed that here he would develop the strongest evidence for Earth’s motion around its axis and around the sun. As it turned out, he was wrong in discounting the moon’s influence on the tides, which is much greater than the influ­ence of the sun. Galileo sought permission from Pope Urban VIII to write a book about the motions of the solar system. The pope agreed, provided that the book gave a balanced view of the two conflicting theories of geocentrism and heliocentrism. The pope also requested that Galileo mention the pope’s personal views that the heavenly bodies may move in ways that man cannot comprehend. Instead of writing his find­ings in the form of a scientific report, Galileo choose to present his ideas as a conversation among three individuals. His “: Ptolemaic and Copernican” (Dialogo sopra i due massimi sistemi del mundo, tolemaico e copernicano) was pub­lished in 1632. The December 2006 issue of Discover magazine listed Galileo’s Dialogue as the fourth greatest scientific book of all time. This dialogue featured a character named Salviati, a proponent of Galileo’s ideas. Salviati’s helio­centric or sun-centered views were presented as witty, intelligent, and well informed. Sagredo, the bystander, who served as the mediator, was usually persuaded by Sagredo. Simplicio, the proponent of geocentrism or an Earth-centered solar system, was portrayed as somewhat slow- witted and easily befuddled. As an expert on Aristotelian thought, Simplicio represented those who ignored evidence and preferred to cling to dogma rather than explore new ideas. The dialogue on the two great systems of the world presented Copernican theory as the logical and intelligent man’s preference. It was considered by many to be a literary and philosophical mas­terpiece. It was considered by Pope Urban VIII to be a grievous insult to have his views pre­sented by the dim-witted character Simplicio, the simpleton.

Word reached Rome that Galileo was teaching Copernicanism; and worse, it was suggested that he had modeled the fool in his dialogue after the pope. Some said that The Dialogue made a mockery of the pope’s intellectual authority and undermined his temporal power. Galileo had, in effect, challenged the Catholic Church’s authority in the interpretation of scientific knowledge. He was ordered to appear before the Holy Office of the Inquisition to face charges of heresy. Aware of the potential for torture and death, Galileo confessed that he had been wrong to say that the earth moved around the sun. Galileo was found guilty of suspicion of heresy and forced to recant his heliocentric beliefs. He was sentenced to life imprisonment, later commuted to house arrest, and forbidden to discuss his views with anyone. Publication of anything he had written or would write in the future was forbidden. It is interesting to note that Copernicus had never been accused of heresy and that his book, De Revolutionibus, was not banned but rather withdrawn for corrections. In his 2001 book, Galileo’s Mistake, author Wade Roland argues that the church’s main problem with Galileo was not his belief in the Copernican system but rather in Galileo’s belief in a mechanistic, materialistic philosophy that seeing is believing.

While confined to his home, Galileo continued to investigate other areas of science. He applied mathematics to a variety of problems. He explored geometry and went from the study of lengths, areas, and volumes to the contemplation of motion, mass, and time. For his last, and some consider his greatest, literary masterpiece he returned to the literary device of three gentlemen discussing a wide variety of issues and arguing their points of view. Here, Galileo developed the fundamentals of relativity. He went into great detail regarding the nature of matter. Galileo was able to have his notes smuggled out of Italy and published in 1638 by a Dutch publisher named Luis Elzevir as Discourses About (Discorsi e dimostrazioni matematiche intorno a due nuove scienze). This work proved to be the foundation for the modern science of physics.

Galileo’s last astronomical discovery was the lunar librations. Galileo discovered that the moon’s equator is inclined to its orbital plane. This causes a slight wobble in the moon’s axis and allows us to see a bit of the far side of the moon periodically. A lunar crater 15 kilometers in diameter is named in honor of Galileo. It is located just west of the one named for Copernicus.

Galileo and Modernity

At the end of his life, Galileo, who had seen far­ther than any man before him, became completely blind. He passed away on January 8, 1642, with his son and students by his side. Isaac Newton was born 11 months later. Newton referred to Galileo when he said that the reason he had seen farther was because he had stood on the shoulders of a giant. Stephen Hawking, the Lucasian Professor of Mathematics at Cambridge University and author of A Brief History of Time, describes Galileo as the single individual most responsible for the birth of modern science. He notes that Galileo was one of the first to argue that man can understand how the world works by observing the real world.

It was not until 99 years after Galileo’s death, in the year 1741, that Pope Benedict XIV lifted the ban on Galileo’s scientific works. In 1979 Pope John Paul II asked the Pontifical Academy of Sciences to conduct an in-depth study of the Galileo case. In 1992, the church formally and publicly cleared Galileo of any wrongdoing, 350 years after his death. Pope John Paul II expressed regret for how the had been handled. In his summary of the conclusions he noted that Galileo showed himself to be more perceptive of the crite­ria for scriptural interpretation than the theolo­gians who opposed him. The pontiff paraphrased Saint Augustine’s words that truth can never con­tradict truth, and that where the Holy Scriptures appear to contradict the natural world, it is the error of interpretation that must be resolved.

Edward J. Mahoney

See also Aristotle; Bruno, Giordano; Clocks, Mechanical; Copernicus, Nicolaus; Einstein, Albert; Hawking, Stephen; Kuhn, Thomas S.; Newton, Isaac; Nicholas of Cusa (Cusanus); Telescopes; Time, Measurements of

Further Readings

Bixby, W. (1964). The universe of Galileo and Newton. New York: American Heritage.

Drake, S. (1978). Galileo at work: His scientific biography. Chicago: University of Chicago Press.

Frova, A., & Marenzana, M. (2006). Thus spoke Galileo. Oxford, UK: Oxford University Press. Hilliam, R. (2005). , father of modern science. New York: Rosen.

Reston, J., Jr. (1994). Galileo, a life. New York: HarperCollins.

Rowland, W. (2001). Galileo’s mistake. New York: Arcade.

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George Gamow

George Gamow