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The Crime Of Galileo Galilei - Biography

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Author Topic: The Crime Of Galileo Galilei - Biography  (Read 1795 times)
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« Reply #15 on: April 02, 2008, 04:19:24 pm »


Galileo was born in Pisa (then part of the Grand Duchy of Tuscany), the first of six children of
Vincenzo Galilei, a famous lutenist and music theorist, and Giulia Ammannati. At the age of 8,
his family moved to Florence, but he was left with Jacopo Borghini for two years. He then was educated in the Camaldolese Monastery at Vallombrosa, 33 km southeast of Florence.

Although he seriously considered the priesthood as a young man, he enrolled for a medical degree
at the University of Pisa at his father's urging. He did not complete this degree, but instead studied mathematics.

In 1589, he was appointed to the chair of mathematics in Pisa. In 1591 his father died and he was entrusted with the care of his younger brother Michelagnolo. In 1592, he moved to the University of Padua, teaching Geometry, Mechanics, and Astronomy until 1610. During this period Galileo made significant discoveries in both pure science (for example, Kinematics of Motion, and Astronomy) and applied science (for example, strength of materials, improvement of the telescope). His multiple interests included the study of Astrology, which in pre-modern disciplinary practice was seen as correlated to the studies of Mathematics and Astronomy.

Although a devout Roman Catholic, Galileo fathered three children out of wedlock with Marina Gamba. They had two daughters (Virginia in 1600 and Livia in 1601) and one son (Vincenzio, in 1606).

Because of their illegitimate birth, their father considered the girls unmarriageable. Their only worthy alternative was the religious life. Both girls were sent to the convent of San Matteo in Arcetri and remained there for the rest of their lives. Virginia (b. 1600) took the name Maria Celeste upon entering the convent. She died on April 2, 1634, and is buried with Galileo at the Basilica di Santa Croce di Firenze. Livia (b. 1601) took the name Suor Arcangela and was ill for most of her life. Vincenzio (b. 1606) was later legitimized and married Sestilia Bocchineri.

In 1610 Galileo published an account of his telescopic observations of the moons of Jupiter, using
this observation to argue in favor of the sun-centered, Copernican theory of the universe against
the dominant earth-centered Ptolemaic and Aristotelian theories.

The next year Galileo visited Rome in order to demonstrate his telescope to the influential philosophers and mathematicians of the Jesuit Collegio Romano, and to let them see with their own eyes the reality of the four moons of Jupiter. While in Rome he was also made a member of the Accademia dei Lincei.

In 1612, opposition arose to the Sun-centered solar system which Galileo supported. In 1614, from the pulpit of Santa Maria Novella, Father Tommaso Caccini (1574–1648) denounced Galileo's opinions on the motion of the Earth, judging them dangerous and close to heresy.

Galileo went to Rome to defend himself against these accusations, but, in 1616, Cardinal Roberto Bellarmino personally handed Galileo an admonition enjoining him neither to advocate nor teach Copernican astronomy.

During 1621 and 1622 Galileo wrote his first book, The Assayer (Il Saggiatore), which was approved and published in 1623. In 1630, he returned to Rome to apply for a license to print the Dialogue Concerning the Two Chief World Systems, published in Florence in 1632. In October of that year, however, he was ordered to appear before the Holy Office in Rome.
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« Reply #16 on: April 02, 2008, 04:26:58 pm »

Scientific methods

Galileo Galilei pioneered the use of quantitative experiments whose results could be analyzed with mathematical precision (More typical of science at the time were the qualitative studies of William Gilbert, on magnetism and electricity). Galileo's father, Vincenzo Galilei, a lutenist and music theorist, had performed experiments establishing perhaps the oldest known non-linear relation in physics: for a stretched string, the pitch varies as the square root of the tension. These observations lay within the framework of the Pythagorean tradition of music, well-known to instrument makers, which included the fact that subdividing a string by a whole number produces a harmonious scale.

Thus, a limited amount of mathematics had long related music and physical science, and young Galileo could see his own father's observations expand on that tradition. Galileo is perhaps the first to clearly state that the laws of nature are mathematical.

In The Assayer he wrote

"Philosophy is written in this grand book, the universe ... It is written in the language of mathematics,

and its characters are triangles, circles, and other geometric figures; ...".

His mathematical analyses are a further development of a tradition employed by late scholastic natural philosophers, which Galileo learned when he studied philosophy.

Although he tried to remain loyal to the Catholic Church, his adherence to experimental results, and their most honest interpretation, led to a rejection of blind allegiance to authority, both philosophical and religious, in matters of science. In broader terms, this aided to separate science from both philosophy and religion;

                                      a major development in human thought.

By the standards of his time, Galileo was often willing to change his views in accordance with observation.

Philosopher of science Paul Feyerabend also noted the supposedly improper aspects of Galileo's methodology, but he argued that Galileo's methods could be justified retroactively by their results.
The bulk of Feyerabend's major work, Against Method (1975), was devoted to an analysis of Galileo, using his astronomical research as a case study to support Feyerabend's own anarchistic theory of scientific method. As he put it:

"Aristotelians ... demanded strong empirical support while the Galileans were content with far-reaching, unsupported and partially refuted theories. I do not criticize them for that; on the contrary, I favour Niels Bohr's "this is not crazy enough.   In order to perform his experiments, Galileo had to set up standards of length and time, so that measurements made on different days and in different laboratories could be compared in a reproducible fashion.

Galileo showed a remarkably modern appreciation for the proper relationship between mathematics, theoretical physics, and experimental physics.

He understood the parabola, both in terms of conic sections and in terms of the ordinate (y) varying as the square of the abscissa (x). Galilei further asserted that the parabola was the theoretically-ideal trajectory for uniformly accelerated motion, in the absence of friction and other disturbances. He also noted that there are limits to the validity of this theory, stating that it was appropriate only for laboratory-scale and battlefield-scale trajectories, and noting on theoretical grounds that the parabola could not possibly apply to a trajectory so large as to be comparable to the size of the planet.

Thirdly, Galilei recognized that his experimental data would never agree exactly with any theoretical or mathematical form, because of the imprecision of measurement, irreducible friction, and other factors."

According to Stephen Hawking, Galileo probably bears more of the responsibility for the birth of
Modern Science than anybody else, and Albert Einstein called him the father of Modern Science.
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« Reply #17 on: April 02, 2008, 04:28:19 pm »

It was on this page that Galileo first noted an observation
of the moons of Jupiter.

This observation upset the notion that all celestial bodies
must revolve around the Earth.

Galileo published a full description in Sidereus Nuncius in
March 1610
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« Reply #18 on: April 02, 2008, 04:37:18 pm »

                                                         A S T R O N O M Y



Based only on uncertain descriptions of the telescope, invented in the Netherlands in 1608, Galileo,
in that same year, made a telescope with about 3x magnification, and later made others with up to about 32x magnification.

With this improved device he could see magnified, upright images on the earth - it was what is now known as a terrestrial telescope, or spyglass. He could also use it to observe the sky; for a time he was one of very few who could construct telescopes good enough for that purpose. On 25 August 1609, he demonstrated his first telescope to Venetian lawmakers.

His work on the device made for a profitable sideline with merchants who found it useful for their shipping businesses and trading issues. He published his initial telescopic astronomical observations
in March 1610 in a short treatise entitled Sidereus Nuncius (Starry Messenger).

On January 7, 1610 Galileo observed with his telescope what he described at the time as

                            "three fixed stars, totally invisible by their smallness",

all within a short distance of Jupiter, and lying on a straight line through it.  Observations on subsequent nights showed that the positions of these "stars" relative to Jupiter were changing in a way that would have been inexplicable if they had really been fixed stars.

On January 10 Galileo noted that one of them had disappeared, an observation which he attributed to its being hidden behind Jupiter. Within a few days he concluded that they were orbiting Jupiter: he had discovered three of Jupiter's four largest satellites (moons):

                                                       Io, Europa, and Callisto.

He discovered the fourth, Ganymede, on January 13.

Galileo named the four satellites he had discovered Medicean stars, in honour of his future patron, Cosimo II de' Medici, Grand Duke of Tuscany, and Cosimo's three brothers. Later astronomers, however, renamed them Galilean satellites in honour of Galileo himself.

A planet with smaller planets orbiting it was problematic for the orderly, comprehensive picture of the geocentric model of the universe, in which everything was supposed to circle around the Earth. As a consequence, many astronomers and philosophers initially refused to believe that Galileo could have discovered such a thing.

Galileo continued to observe the satellites over the next eighteen months, and by mid 1611 he had obtained remarkably accurate estimates for their periods—a feat which Kepler had believed impossible.
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« Reply #19 on: April 02, 2008, 04:39:57 pm »

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« Reply #20 on: April 02, 2008, 04:46:16 pm »

From September 1610, Galileo observed that Venus exhibited a full set of phases similar to that
of the Moon.

The heliocentric model of the solar system developed by Nicolaus Copernicus predicted that all
phases would be visible since the orbit of Venus around the Sun would cause its illuminated hemi-
sphere to face the Earth when it was on the opposite side of the Sun and to face away from the
Earth when it was on the Earth-side of the Sun.

In contrast, the geocentric model of Ptolemy predicted that only crescent and new phases would
be seen, since Venus was thought to remain between the Sun and Earth during its orbit around the Earth.

Galileo's observations of the phases of Venus proved that it orbited the Sun and lent support to
(but did not prove) the heliocentric model.

Galileo also observed the planet Saturn, and at first mistook its rings for planets, thinking it was a three-bodied system. When he observed the planet later, Saturn's rings were directly oriented at Earth, causing him to think that two of the bodies had disappeared. The rings reappeared when he observed the planet in 1616, further confusing him.

Galileo was one of the first Europeans to observe sunspots. He also reinterpreted a sunspot observation from the time of Charlemagne, which formerly had been attributed (impossibly) to a
transit of Mercury. The very existence of sunspots showed another difficulty with the unchanging perfection of the heavens as assumed in the older philosophy. And the annual variations in their motions, first noticed by Francesco Sizzi, presented great difficulties for both the geocentric system and that of Tycho Brahe.

A dispute over priority in the discovery of sunspots, and in their interpretation, led Galileo to a long
and bitter feud with the Jesuit Christoph Scheiner; in fact, there is little doubt that both of them
were beaten by David Fabricius and his son Johannes. Scheiner quickly adopted Kepler's 1615 pro-
posal of the modern telescope design, which gave larger magnification at the cost of inverted images; Galileo apparently never changed to Kepler's design.

Galileo was the first to report lunar mountains and craters, whose existence he deduced from the patterns of light and shadow on the Moon's surface. He even estimated the mountains' heights from these observations. This led him to the conclusion that the Moon was

                          "rough and uneven, and just like the surface of the Earth itself,"

rather than a perfect sphere as Aristotle had claimed.

Galileo observed the Milky Way, previously believed to be nebulous, and found it to be a multitude
of stars packed so densely that they appeared to be clouds from Earth.

He located many other stars too distant to be visible with the naked eye.

Galileo also observed the planet Neptune in 1612, but did not realize that it was a planet and took
no particular notice of it. It appears in his notebooks as one of many unremarkable dim stars.
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« Reply #21 on: April 02, 2008, 04:51:38 pm »

                                     Controversy over comets and The Assayer

The Assayer

In 1619 Galileo became embroiled in a controversy with Father Horatio Grassi, the professor of mathematics at the Jesuit Collegio Romano.

It began as a dispute over the nature of comets, but by the time Galileo had published The Assayer
(Il Saggiatore) in 1623, his last salvo in the dispute, it had become a much wider argument over the very nature of Science itself. Because The Assayer contains such a wealth of Galileo's ideas on how Science should be practised, it has been referred to as his Scientific Manifesto.

Early in 1619 Father Grassi had anonymously published a pamphlet, An Astronomical Disputation on the Three Comets of the Year 1618, which discussed the nature of a comet that had appeared late in November of the previous year. Grassi concluded that the comet was a fiery body which had moved along a segment of a great circle at a constant distance from the earth, and that it had been located well beyond the moon.

Grassi's arguments and conclusions were criticised in a subsequent article, Discourse on the Comets,published under the name of one of Galileo's disciples, a Florentine lawyer named Mario Guiducci, although it had been largely written by Galileo himself. Galileo and Guiducci offered no definitive theory of their own on the nature of comets, although they did present some tentative conjectures which we now know to be mistaken.

In its opening passage, Galileo and Guiducci's Discourse gratuitously insulted the Jesuit Christopher Scheiner, and various uncomplimentary remarks about the professors of the Collegio Romano were scattered throughout the work.

The Jesuits were offended, and Grassi soon replied with a polemical tract of his own, The Astrono-
mical and Philosophical Balance, under the pseudonym Lothario Sarsi, purporting to be one of his
own pupils.

The Assayer, was Galileo's devastating reply to the Astronomical Balance.

It has been widely regarded as a masterpiece of polemical literature, in which "Sarsi's" arguments
are subjected to withering scorn.  It was greeted with wide acclaim, and particularly pleased the
new pope, Urban VIII, to whom it had been dedicated.

Galileo's dispute with Grassi permanently alienated many of the Jesuits who had previously been sympathetic to his ideas, and Galileo and his friends were convinced that these Jesuits were responsible for bringing about his later condemnation. 

The evidence for this is at best equivocal, however.
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« Reply #22 on: April 02, 2008, 04:53:30 pm »

Galileo  Galileo Magnifico oh oh oh...

mama mia mama mia

Beelzebub has a devil for a disciple...

oh me oh me oh me...........

[ guitar solo ]

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« Reply #23 on: April 02, 2008, 04:57:30 pm »

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« Reply #24 on: April 02, 2008, 05:03:24 pm »


Galileo made a number of contributions to what is now known as technology, as distinct from pure physics, and suggested others.

This is not the same distinction as made by Aristotle, who would have considered all Galileo's physics as techne or useful knowledge, as opposed to episteme, or philosophical investigation into the causes of things.

Between 1595–1598, Galileo devised and improved a Geometric and Military Compass suitable for use
by gunners and surveyors. This expanded on earlier instruments designed by Niccolò Tartaglia and Guidobaldo del Monte. For gunners, it offered, in addition to a new and safer way of elevating cannons accurately, a way of quickly computing the charge of gunpowder for cannonballs of different sizes and materials. As a geometric instrument, it enabled the construction of any regular polygon, computation of the area of any polygon or circular sector, and a variety of other calculations. About 1593, Galileo constructed a thermometer, using the expansion and contraction of air in a bulb to move water in an attached tube.

In 1609, Galileo was among the first to use a refracting telescope as an instrument to observe stars, planets or moons. Galileo's telescope was the first instrument given that name by an unidentified Greek poet/theologian, present at a banquet held in 1611 by Prince Federico Cesi to make Galileo a member of his Accademia dei Lincei.

The name was derived from the Greek tele = 'far' and skopein = 'to look or see'. In 1610, he used a telescope at close range to magnify the parts of insects. By 1624 he had perfected a compound microscope.

He gave one of these instruments to Cardinal Zollern in May of that year for presentation to the Duke of Bavaria, and in September he sent another to Prince Cesi.The Linceans played a role again in naming the "microscope" a year later when fellow academy member Giovanni Faber coined the word for Galileo's invention from the Greek words μικρόν (micron) meaning "small", and σκοπεῖν (skopein) meaning "to look at". The word was meant to be analogous with "telescope".

Illustrations of insects made using one of Galileo's microscopes, and published in 1625, appear to
have been the first clear documentation of the use of a compound microscope.

In 1612, having determined the orbital periods of Jupiter's satellites, Galileo proposed that with sufficiently accurate knowledge of their orbits one could use their positions as a universal clock,
and this would make possible the determination of longitude. He worked on this problem from time to time during the remainder of his life; but the practical problems were severe.

The method was first successfully applied by Giovanni Domenico Cassini in 1681 and was later used extensively for large land surveys; this method, for example, was used by Lewis and Clark.

For sea navigation, where delicate telescopic observations were more difficult, the longitude problem eventually required development of a practical portable marine chronometer, such as that of John Harrison.

In his last year, when totally blind, he designed an escapement mechanism for a pendulum clock, a vectorial model of which may be seen here. The first fully operational pendulum clock was made by Christiaan Huygens in the 1650s. Galilei created sketches of various inventions, such as a candle and mirror combination to reflect light throughout a building, an automatic tomato picker, a pocket comb that doubled as an eating utensil, and what appears to be a ballpoint pen.
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« Reply #25 on: April 02, 2008, 05:04:51 pm »


Classical mechanics

Newton's second law

History of ... [show]Fundamental concepts
Space · Time · Mass · Force
Energy · Momentum


Newtonian mechanics 

Lagrangian mechanics

Hamiltonian mechanics


Applied mechanics

Celestial mechanics

Continuum mechanics

Geometric optics

Statistical mechanics


Galileo · Kepler · Newton

Laplace · Hamilton · d'Alembert

Cauchy · Lagrange · Euler

Galileo's theoretical and experimental work on the motions of bodies, along with the largely inde-
pendent work of Kepler and René Descartes, was a precursor of the classical mechanics develop-
ed by Sir Isaac Newton. He was a pioneer, at least in the European tradition, in performing rigorous experiments and insisting on a mathematical description of the laws of nature.

A biography by Galileo's pupil Vincenzo Viviani stated that Galileo had dropped balls of the same material, but different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass. This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight.

While this story has been retold in popular accounts, it is generally accepted by historians that there
is no account by Galileo himself of such an experiment, and that it was at most a thought experiment which did not actually take place.

Moreover, Giambattista Benedetti had reached the same scientific conclusion years before, in 1553.  However, Galileo did perform experiments which proved the same thing by rolling balls down inclined planes: falling or rolling objects (rolling is a slower version of falling, as long as the distribution of mass in the objects is the same) are accelerated independently of their mass.

Galileo was the first person to demonstrate this via experiment, but he was not—contrary to popular belief—the first to argue that it was true.

A number of scholars prior to Galileo wrote -- or showed by experiment -- that in a vacuum, bodies which are composed of the same substance but which have different masses, fall through equal distances in equal times:

Lucretius (ca. 99 - ca. 55 B.C.E., Roman poet)[,

John Philoponus (ca. 490 - ca. 570 C.E., Greek philosopher in Alexandria, Egypt),

Thomas Bradwardine (ca. 1290 - 1349, scholar at Merton College of Oxford University),

Albert of Saxony (1316 - 1390, German cleric and philosopher),

Pietro Monte (a.k.a. Petrus Montius, ca. 1457 - 1530, Spanish master at arms who resided
in N. Italy),

Benedetto Varchi (1502/3 - 1565, Italian historian and poet),

Domingo de Soto (1494 - 1560, Spanish cleric and theologian),

Giambattista Benedetti (1530 - 1590, Venetian mathematician),

Giuseppe Moletti (1531 - 1588, Italian mathematician), and

Simon Stevin (1548/9 - 1620, Flemish engineer and mathematician).
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« Reply #26 on: April 02, 2008, 05:16:25 pm »

Galileo arrived at the correct mathematical law for uniform acceleration: the total distance covered, starting from rest, is proportional to the square of the time (), already discovered by Domingo de Soto in the 16th century. He expressed this law using geometrical constructions and mathematically-precise words, adhering to the standards of the day. (It remained for others to re-express the law in algebraic terms).

But he erroneously claimed gravitational free-fall universally is uniformly accelerated as thefundamental law of motion of his cosmology and cosmogony, a claim that was never generally accepted and soon refuted by the 1660s discovery that it is exponentially increasingly accelerated (a difform motion in scholastic terms) and inversely proportional to distance from its gravitational centre.

He also concluded that objects retain their velocity unless a force—often friction—acts upon them, refuting the generally accepted Aristotelian hypothesis that objects "naturally" slow down and stop unless a force acts upon them (philosophical ideas relating to inertia had been proposed by Ibn al-Haytham centuries earlier, as had Jean Buridan, and according to Joseph Needham, Mo Tzu had proposed it centuries before either of them, but this was the first time that it had been mathematically expressed, verified experimentally, and introduced the idea of frictional force, the key breakthrough in validating inertia). Galileo's Principle of Inertia stated:

"A body moving on a level surface will continue in the same direction at constant speed unless disturbed."

This principle was incorporated into Newton's laws of motion (first law).

Galileo also noted that a pendulum's swings always take the same amount of time, independently of
the amplitude. The story goes that he came to this conclusion by watching the swings of the bronze chandelier in the cathedral of Pisa, using his pulse to time it. While Galileo believed this equality of period to be exact, it is only an approximation appropriate to small amplitudes. It is good enough to regulate a clock, however, as Galileo may have been the first to realize. (See Technology above)
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« Reply #27 on: April 02, 2008, 05:18:28 pm »


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« Reply #28 on: April 02, 2008, 05:30:25 pm »

In 1638 Galileo described an experimental method to measure the speed of light by arranging that
two observers, each having lanterns equipped with shutters, observe each other's lanterns at some distance. The first observer opens the shutter of his lamp, and, the second, upon seeing the light, immediately opens the shutter of his own lantern. The time between the first observer's opening his shutter and seeing the light from the second observer's lamp indicates the time it takes light to travel back and forth between the two observers. Galileo reported that when he tried this at a distance of less than a mile, he was unable to determine whether or not the light appeared instantaneously.

Sometime between Galileo's death and 1667, the members of the Florentine Accademia del Cimento repeated the experiment over a distance of about a mile and obtained a similarly inconclusive result.

Galileo is lesser known for, yet still credited with, being one of the first to understand sound frequency. By scraping a chisel at different speeds, he linked the pitch of the sound produced to the spacing of the chisel's skips, a measure of frequency.

In his 1632 Dialogue Galileo presented a physical theory to account for tides, based on the motion of the Earth. If correct, this would have been a strong argument for the reality of the Earth's motion. In fact, the original title for the book described it as a dialogue on the tides; the reference to tides was removed by order of the Inquisition. His theory gave the first insight into the importance of the shapes of ocean basins in the size and timing of tides; he correctly accounted, for instance, for the negligible tides halfway along the Adriatic Sea compared to those at the ends. As a general account of the cause of tides, however, his theory was a failure. Kepler and others correctly associated the Moon with an influence over the tides, based on empirical data; a proper physical theory of the tides, however, was not available until Newton.

Galileo also put forward the basic principle of relativity, that the laws of physics are the same in any system that is moving at a constant speed in a straight line, regardless of its particular speed or direction. Hence, there is no absolute motion or absolute rest. This principle provided the basic framework for Newton's laws of motion and is central to Einstein's special Theory of Relativity.
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« Reply #29 on: April 02, 2008, 05:31:39 pm »


While Galileo's application of mathematics to experimental physics was innovative, his mathematical methods were the standard ones of the day. The analysis and proofs relied heavily on the Eudoxian theory of proportion, as set forth in the fifth book of Euclid's Elements. This theory had become available only a century before, thanks to accurate translations by Tartaglia and others; but by the end of Galileo's life it was being superseded by the algebraic methods of Descartes.

Galileo produced one piece of original and even prophetic work in mathematics: Galileo's paradox, which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares.

Such seeming contradictions were brought under control 250 years later in the work of Georg Cantor.
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