Post #133,920
1/6/04 5:14:45 PM
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Even more interesting "reasonableness"
If the following description of events is correct, I have to ask: if Kepler already had accurate predictive formulae, what drove Newton to look for his, more elegant explanations? I see here an example of true faith in "reasonableness".
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Detailed observation of the movement of planets in the sky didn't yield results that made any sense in terms of the old idea of them being attached to rotating crystal spheres. In fact, given that Mercury and Venus didn't stray far from the Sun, it didn't even quite make sense that the earth was at the center. Copernicus proposed that the Sun was actually the center, causing something of a stir.
A rather unpleasant man named Tycho Brahe spent years making extremely accurate records of the movements of the planets (all without telescopes, I might mention) and when he died all that data was inherited by Kepler, who tried to make sense of it. He finally concluded that Copernicus was right, but also determined that all orbits were actually elliptical rather than circular, with the sun at one focus of the ellipse. Even more astounding, each planet's orbital speed changed in well defined ways, moving fastest when closest to the sun and slowest when furthest away from it. He was able to formulate mathematical descriptions of it all that were very good at predicting future observations of the planets, but did not explain why it might be happening.
It was Newton, "standing on the shoulders of giants", who ultimately figured it out with the formulation of the universal law of gravitation. It was a tremendous achievement, but it also broke through another basic dogma because it seemed to be the same everywhere, as ultimately turned out to be the case with all of Galilean mechanics, and ultimately all of physics and all of science. Movement of objects in the heavens were not different than movement here on earth. In fact, there didn't seem to be any difference at all between the heavens and the earth except that the earth was closer to us.
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(from [link|http://www.denbeste.nu/cd_log_entries/2004/01/Threewaystruggle.shtml|denBeste] - kindly ignore ideology or go to Politics.
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"It\ufffds possible to build a reasonably prosperous society that invests in its people, doesn\ufffdt invade its neighbors, opposes Israel and stands up to America. (Just look at France.)"
-- James Lileks
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Post #133,924
1/6/04 5:27:30 PM
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Info is in the Principia.
[link|http://members.tripod.com/~gravitee/history.htm|Here] is a little history: The birth of the Principia may be traced back to a discussion in 1684 at the Royal Society. Astronomer Edmund Halley and architect Sir Christopher Wren suspected that there was an inverse square relation governing celestial motions based on Kepler's Third Law of elliptical orbits, but no one could prove it. They brought the question before Newton's arch rival Robert Hooke, who claimed that he could prove the inverse square law and all three of Kepler's laws. His claim was met with scepticism, and Wren offered a forty-shilling book as a prize for the correct proof within a two-month limit. Hooke failed to produce the calculation, and Halley travelled to Cambridge to ask for Newton's opinion. Newton responded with a typical lack of interest in work that he had already completed, that he had already solved the problem years before. He could not find the calculation among his papers and promised to send Halley a proof. Halley, suspecting the same bogus claim he had received from Hooke, left frustrated and returned to London. Three months later he received a nine page treatise from Newton, written in Latin, De Motu Corporum, or On the Motions of Bodies in Orbit. In it, Newton offers the correct proof of Kepler's laws in terms of an inverse square law of gravitation and his three laws of motion. Halley suggested publication, but Newton, reluctant to appear in print, refused. At Halley's insistence, Newton finally began writing and, with typical thoroughness, worked for 18 months revising and rewriting the short paper until it grew into three volumes. The Royal Society, having exhausted available funds on an extravagant edition of De Historia Piscium, or The History of Fishes, could not pay for the publication and so it was at Edmund Halley's expense that Philosophi\ufffd Naturalis Principia Mathematica was finally published.
The Mathematical Principles of Natural Philosophy, or The Principia as it came to be commonly known, begins with the solid foundation on which the three books rest. Newton begins by defining the concepts of mass, motion (momentum), and three types of forces: inertial, impressed and centripetal. He also gives his definitions of absolute time, space, and motion, offering evidence for the existence of absolute space and motion in his famous "bucket experiment". These absolute concepts provoked great criticism from philosophers Leibnitz, Berkeley, and others, including Ernst Mach centuries later. The three Laws of Motion are proposed, with consequences derived from them. The remainder of The Principia continues in rigorously logical Euclidean fashion in the form of propositions, lemmas, corollaries and scholia. Book One, Of The Motion of Bodies, applies the laws of motion to the behaviour of bodies in various orbits. Book Two continues with the motion of resisted bodies in fluids, and with the behaviour of fluids themselves. In the Third Book, The System of the World, Newton applies the Law of Universal Gravitation to the motion of planets, moons and comets within the Solar System. He explains a diversity of phenomena from this unifying concept, including the behaviour of Earth's tides, the precession of the equinoxes, and the irregularities in the moon's orbit.
The Principia brought Newton fame, publicity, and financial security. It established him, at the age of 45, as one of the greatest scientists in history. Bless the workaholics. Cheers, Scott.
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Post #134,037
1/7/04 6:41:22 AM
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Re: Info is in the Principia.
I am highly skeptical of this "history".
The idea of "inverse square law" originating in anyone other than Newton is absurd - there were NO dynamical laws of ANY KIND before Newton wrote them, and indeed this is his actual achievement - putting down a distinct, well-defined dynamical theory of matter. The whole idea of force itself was invented by him, and indeed the mathematical method to describe it.
Newton antagonized many of his colleagues, who he must have understood were so far behind him that education was hopeless. Newton did not always behave in the most straightforward manner and let his frustrations get the better of him on occasion. But there is not a shred of doubt that "inverse square law of gravity" is Newton's alone. Halley's speculation about "attraction according to the reciprocal duplicate proportion" cannot be called a force law. Indeed while he was speculating about this problem, the solution was already known to Newton, who had tired of battling with the loudmouth Hooke (the string theorist of his day), had withdrawn and refused to publish his work. Halley deserves great credit for putting up with the nearly paranoic Newton and in getting him to come out of his shell and explain his work. This was the real origin of the Principia, and Halley's actual contribution.
-drl
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Post #134,106
1/7/04 2:47:19 PM
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I'm not
The description exactly matches a decent biography of Newton's that I read recently. Hooke had good intuition and nothing else. He guessed what the right law of gravity was, and knew what he'd have to show to show that it was right. However it was all guesses, Hooke didn't have the mathematical techniques to tackle the problem. He just had good intuition and a big mouth.
Newton had been over the same territory decades earlier, with the right math, and enough elbow grease to back it up. There is no question that Newton had the result long before Hooke's boast. Furthermore Newton seems to have suspected that Hooke couldn't have come up with that guess, and believed that Hooke must have stolen it somehow from Newton.
This took place, of course, after Hooke and Newton had already tangled about optics. That Halley got Newton to admit to having a proof, and further got Newton to publish it is a testament both to Halley's dedication and some luck. It probably helped that Newton tried to prove his point by sending a "challenge" to the Royal Society, one which Newton made a mathematical mistake in his treatment of, and one which Hooke guessed right. (The challenge was that under an inverse square law, when an object is dropped, does it actually fall straight down? Hooke guessed the right answer from Kepler's laws.)
Newton's public embarrassment may have played a role in Newton's decision to produce as comprehensive a work as he did. There is no question that Newton's irritations over Hooke's past quibbling and grandstanding was part of why Newton deliberately made the Principia hard to read. Newton wanted to make sure that anyone who wanted to comment had to READ the blasted thing first. (He says as much in letters to people.)
Cheers,
Ben
"good ideas and bad code build communities, the other three combinations do not"
- [link|http://archives.real-time.com/pipermail/cocoon-devel/2000-October/003023.html|Stefano Mazzocchi]
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Post #133,926
1/6/04 5:39:23 PM
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Several things
First of all there was the question of comets. Comets appeared, and seemed to follow paths like the ones that planets did. Why?
Second there were moon systems. Starting with Galileo, people knew that Jupiter had moons. They were able to see that Jupiter's moons seemed to follow a Keplerian rule of their own around Jupiter with different constants. Coincidence? It was natural to try to generalize. Particularly since we had our own Moon that didn't fit the system.
Third, Kepler's laws were not perfect. While they are fairly accurate, they don't take into account perturbations in the orbits of the planets from other planets.
Fourth, gravity is all around us. It was one thing to say that Venus moved around The Sun. It is quite another to explain why Venus doesn't fall on our heads instead.
And the last reason was the hope that a better theory would explain more phenomena. And it did. Newton fit all of the above together while explaining tides, the precession of the Earth, and various other perturbations.
An interesting side-note. It turns out that if we had a binary star but were far enough away, that The Earth could readily have survived as long as it has. However figuring out orbital mechanics would have been insanely hard. The simple perioodicities which lay behind theories from the Greeks through Kepler only happen when a single gravity source dominates. Arriving at the same conclusion would be far harder with 2 interacting gravity sources acting on everything else.
Cheers,
Ben
"good ideas and bad code build communities, the other three combinations do not"
- [link|http://archives.real-time.com/pipermail/cocoon-devel/2000-October/003023.html|Stefano Mazzocchi]
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Post #134,039
1/7/04 7:00:09 AM
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Re: Even more interesting "reasonableness"
Kepler had what is now known as "kinematics" - a description of motion with an explanation. The "spring law" of Hooke is of the same character. What Newton did was derive the kinematical laws from a 1st principle, that the acceleration of a body is proportional to the impressed force, which in Newton is a primitive concept. So, what Newton did was create a brand new thing, a dynamical theory of matter itself based on the idea of force. Kepler's "laws" are then just a special case for a centripetal (pointing to the center) acceleration that has a strength inversely proportional to the distance.
Today we have theories that are totally kinematic (strings), partially kinematic (gauge theories of weak and strong interactions), almost dynamic (gravitation), and totally dynamic (electrodynamics). The impetus is toward dynamical theories in which everything is reduced to a basic principle.
(Gravitation in Einstein's form fails to be completely dynamic because direction is a localized concept, while length is not.)
-drl
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