User:Daniel Drake/Galileo sandbox

Galileo Galilei (1564 – 1642) was an Italian scientist who was a major figure in the Scientific Revolution. He was a pioneer in the modern combination of mathematical theory with systematic experiment in science.

His work in physics included experimentation to establish the behavior of falling bodies, as well as the first modern theoretical work on inertia (for which he was given credit by Newton) and relativity of motion (for which he was credited by Einstein).

He was one of the first astronomers to use a telescope, and the discoverer or co-discoverer of several phenomena that contradicted the accepted ideas of the heavens. His support of the Copernican idea that the Earth rotates around the Sun led to a trial before the Inquisiton on a suspicion of heresy.

Experimental science

2004-01-13 00.38

Experimental science

In the pantheon of the scientific revolution Galileo occupies a high position because of his pioneering use of quantitative experiments with results analyzed mathematically. There was no tradition of such methods in European thought at that time; the great experimentalist who immediately preceded Galileo, William Gilbert, did not use a quantitative approach. (However, Galileo's father, Vincenzo Galilei, had performed experiments in which he discovered what may be the oldest known non-linear relation in physics, between the tension and the pitch of a stretched string.)

In the 20th century the reality of Galileo's experiments was challenged by some authorities, in particular the distinguished French historian of science Alexandre Koyré. The experiments reported in Two New Sciences to determine the law of acceleration of falling bodies, for instance, required accurate measurements of time, which appeared to have been impossible with the technology of 1600. According to Koyré, the law was arrived at deductively, and the experiments were merely illustrative thought experiments.

Later research, however, has validated the experiments. The experiments on falling bodies (actually rolling balls) were replicated using the methods described by Galileo (Settle, 1961), and the precision of the results was consistent with Galileo's report. Later research into Galileo's unpublished working papers from as early as 1604 clearly showed the reality of the experiments and even indicated the particular results that led to the time-squared law (Drake, 1973).

Astronomy

2003-07-19 15:06

In 1610 Galileo discovered Jupiter's four largest [[natural satellite|satellite]]s (moons): Io, [[Europa (moon)|Europa]], Ganymede, and [[Callisto (moon)|Callisto]]. He determined that these moons were orbiting the planet since they would occasionally disappear; something he attributed to their movement behind Jupiter. He made additional observations of them in 1620. (Later astronomers overruled Galileo's naming of these objects, changing his Medicean stars to Galilean satellites.) The demonstration that a planet had smaller planets orbiting it was problematic for the orderly, comprehensive picture of the geocentric model of the universe, in which everything circled around the Earth.

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Galileo noted that Venus exhibited a full set of phases like the Moon. Because the apparent brightness of Venus is nearly constant, Galileo reasoned that Venus could not be circling the Earth at a constant distance. By contrast, the [[heliocentric model]] of the solar system developed by Copernicus would neatly account for the steady brightness by reason of the much greater distance from the Earth at the time of "full Venus".

Galileo made the first European observations of sunspots, although there is evidence that Chinese astronomers had done so before him. The very existence of sunspots showed another difficulty with the 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 either the geocentric system or that of Tycho Brahe.

Mathematics

While Galileo's application of mathematics to experimental physics was innovative, his mathematical methods were the standard ones of the day. The analyses 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, which a modern finds incomparably easier to follow.

Galileo produced one piece of original and even prophetic work in mathematics: Galileo's paradox, which shows that there are as many odd numbers as there are whole numbers including both even and odd. Such seeming contradictions were brought under control 250 years later in the work of Georg Cantor.

Conflict with the Church

2003-07-16 18.03

When Galileo was tried in 1633, the Inquisition was proceeding on the premise that he had been ordered not to teach it at all, based on a paper in the records from 1616; but Galileo produced a letter from Cardinal Bellarmine that showed only the "hold or defend" order. The latter is in Bellarmine's own hand and of unquestioned authenticity; the former is unsigned, violating the Inquisition's own rule that the record of such an admonition had to be signed by all parties and notarized. Leaving aside technical rules of evidence, what can one conclude as to the real events? There are two schools: according to Stillman Drake, the order not to teach was delivered unofficially and improperly; Bellarmine would not allow a formal record to be made, and assured Galileo in writing that the only order in effect was not to "defend or hold". According to Giorgio di Santillana, however, the unsigned minute was simply a fabrication by the Inquisition.

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After the release of this report, the Pope said further that "... Galileo, a sincere believer, showed himself to be more perceptive in this regard [the relation of scientific and Biblical truths] than the theologians who opposed him."