By: Galileo Galilei, read in 2012
xxiii "A man is here revealed who possesses the passionate will, the intelligence, and the courage to stand up as the representative of rational thinking against the host of those who, relying on the ignorance of the people and the indolence of teachers in priest's and scholar's garb, maintain and defend their positions of authority. His unusual literary gift enables him to address the educated men of his age in such clear and impressive language as to overcome the anthropocentric and mythical thinking of his contemporaries and to lead them back to an objective and causal attitude toward the cosmos, an attitude which had become lost to humanity with the decline of Greek culture." - Albert Einstein (Seems to describe Greylorn Ell)
xxvii "...the "true orbits" of the planets—a problem of almost insurmountable difficulty, which, however, was solved by Kepler (during Galileo's lifetime) in a truly ingenious fashion. But this decisive progress did not leave any traces in Galileo's life work—a grotesque illustration of the fact that creative individuals are often not receptive." – Albert Einstein
xxviii "To put into sharp contrast the empirical and the deductive attitude is misleading, and was entirely foreign to Galileo. Actually it was not until the nineteenth century that logical (mathematical) systems whose structures were completely independent of any empirical content had been cleanly extracted." - Albert Einstein
xxix "Galileo himself makes considerable use of logical deduction. His endeavors are not so much directed at "factual knowledge" as at "comprehension." But to comprehend is essentially to draw conclusions from an already accepted logical system." - Albert Einstein
10 "You have all this doctrine in the second text. Afterwards, in the third we read ad pleniorem scientiam, that All, and Whole, and Perfect are formally one and the same, and that therefore among figures only the solid is complete. For it alone is determined by three, which is All, and, being divisible in three ways, it is divisible in every possible way. Of the other figures, one is divisible in one way, and the other in two, because they have their divisibility and their continuity according to the number of dimensions allotted to them. Thus one figure is continuous in one way, the other in two, but the third, namely the solid, is so in every way."
11 "Do you not think that in all these places he has sufficiently proved that there is no passing beyond the three dimensions, length, breadth, and thickness, and that therefore the body, or solid, which has them all, is perfect?"
11 "Plato's opinion that the human mind partakes of divinity because it comprehends numbers"
15 Aristotle's argument for, and derivation of, God. E.g. perfection, immutability, etc.
21 Interesting discussion of primordial order and disorder
43 Aristotle's argument for the perfection, incorruptibility, eternality, etc. of God
55 The Mediterranean inundation was known to Galileo
65 "There is no danger that such a multitude of great, subtle, and wise philosophers will allow themselves to be overcome by one or two who bluster a bit. Rather without even directing their pens against them, by means of silence alone, they place them in universal scorn and derision."
131 "...it is not proper that those who never philosophize should usurp the honorable title of philosopher."
188 Galileo explains why digressions are sometimes OK
206 Shooting birds in flight
233 Shouldn't "CA" be "BA"?
236 "...it must be admitted that trying to deal with physical problems without geometry is attempting the impossible."
240 Abstract spheres and material spheres are different
241 "...I assure you that things are in no less agreement than arithmetical computations. The errors then, lie not in the abstractness or concreteness, not in geometry or physics, but in a calculator who does not know how to make a true accounting. Hence if you had a perfect sphere and a perfect plane, even though they were material, you would have no doubt that they touched in one point, and if it is impossible to have these, then it was quite beside the purpose to say sphaera aenea non tangit in puncto."
243 How to make a sphere
265 I couldn't follow this argument
291 "...since proceeding by interrogations seems to me to shed much light upon things, in addition to the pleasure one may get out of pumping ones companion and making things drop from his lips which he never knew that he knew, I shall make use of that artifice." The Socratic method
291 Using a telescope at the top of a mast vs. at the foot of the mast
294 "It must therefore be admitted that the use of the telescope at the top of the mast is no more difficult than at the foot, for the changes of angle are the same in both places."
345 Math error
382 "I think it is very difficult for some people, simple though they may be, to recognize and admit that they are simple just because they know themselves to be so regarded."
472 "To apply oneself to great inventions, starting from the smallest beginnings, and to judge that wonderful arts lie hidden behind trivial and childish things is not for ordinary minds, these are concepts and ideas for superhuman souls."
523 Balls rolling down arcs and chords
535 "...I am much astonished that among men of sublime intellect, of whom there have been plenty, none have been struck by the incompatibility between the reciprocating motion of the contained waters and the immobility of the containing vessels, a contradiction which now seems so obvious to me."
536 "In the conversations of these four days we have, then, strong evidences in favor of the Copernican system, among which three have been shown to be very convincing—those taken from the stoppings and retrograde motions of the planets, and their approaches toward and recessions from the earth; second, from the revolution of the sun upon itself, and from what is to be observed in the sunspots; and third, from the ebbing and flowing of the ocean tides."
©2013 Paul R. Martin, All rights reserved.