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The Greatest And The Luckiest Of Mortals
sgant writes "So says the 18th-century French mathematician Joseph-Louis Lagrange about Sir Isaac Newton. The New York Times has a piece on 'The Newtonian Moment: Science and the Making of Modern Culture' which is a new exhibit at the NY Public Library. It includes a number of Newton's manuscripts from the Cambridge University Library, including a first edition of his most famous work, "Principia," bearing the author's corrections and additions for the next printing, have never before been shown in the United States."
not invented, discovered
also, Leibniz also independantly devised the system of calculus at the same time
Well, Archimedes discovered quite a few calculus-esque ideas such as adding up infinite slices to determine the area of something in a cube. This was of course quite some time ago. Although these different calculuses (calculii) vary quite a bit I think that some credit should also go to Archimedes.
( o ) one could say I'm rather baked
Newton didn't get it 'wrong' it is just that his theories are less accurate at extremes - Einstein's theories of relativity produce answers that are the same as Newton's theories of motion at 'non-relativistic' speeds (hence the term non-relativistic).
These speeds (or more properly velocities perhaps) are those anything less than a significant fraction of the speed of light (or very close to a massive object for gravitational calculations). So, you only need Newton's equations for almost all practical applications.
"Plague is sweeping across England, and a young Isaac Newton retreats to the isolation of Lincolnshire. Sitting in the family garden he watches an apple fall, and unlocks the secrets of gravity - or does he? Adam explores the truth behind this famous moment in the history of science, and discovers that Newton wrote his own account over forty years after the supposed event."
Listen to it here (starts 1 min 50 secs in)
To learn it the other way around, as mentioned above, pick up Tom Apostol's Calculus (2 vols).
Keep in mind that calculus as we know it has been modified somewhat from their original formulation. For instance, both Newton and Leibinitz incorrectly used infintesimals in their definitions. It wasn't until the 1800's that Karl Weierstrass formulated the limit definition that we use today.
The darkness... controls the music. The music... controls the soul.
It's pretty well known that Einstein didn't come up with relativity on his own. The equations and some of the analysis had already been done by Lorentz. Unfortunately Lorentz didn't want to fully accept the conclusions and he had a far narrower view of the effects. Einstein came along and formulated a diffrent derrivation of all the formulas and a far far wider interpretation.
The darkness... controls the music. The music... controls the soul.
I have also read that Newton's phrase "standing on the shoulders of giants" was a veiled insult to Robert Hooke, who was apparently not the tallest of people.
flossie
Write now. Defend liberty
Certain aspects of calculus were developed two centuries prior to Newton in India by Madhava of Sangamagrama. This seems to be widely accepted now. A few links to Madhava and other Keralese mathematicians are also present here.
That was the old view. There were some problems with their use of infinitesimals, but those problems have been cleared up more recently. The modern version of calculus via infinitesimals is known as nonstandard analysis. The landmark work on the subject is Robinson's 1966 book "Non-standard analysis".
Moreover, that sort of hen-pecking at Newton and Leibniz is not really productive. No one cares more about precision and correctness in definitions than mathematicians, and yet mathematicians still assign credit to those two.
Have you read the Principia? I have only read portions, but Newton does some pretty amazing stuff in there, besides just the use of calculus and the derivation of the inverse square law for gravity. For example, he proves that there is no closed form for elliptic integrals of a certain kind.
Newton's phrase "standing on the shoulders of giants" was a veiled insult to Robert Hooke...
This allegation is made almost every time Newton is mentioned on Slashdot but it has no historical basis.
As this analysis points out, when Newton uses the phrase he is refering to both Descarte and Hook. The most obvious interpretation is that he is complementing Hook by comparing him to Descarte and referring to them both as giants.
Furthermore, Hook was not especially short and in other cases where Newton engaged in scientific debate he specifically avoided what he called "oblique and glancing expressions".
There is thus every reason to suppose that when Newton said he stood on the shoulders of giants, he was acknowledging his debt to Copernicus, Kepler, Galileo, Descartes and Hook, who was at the time England's most eminent scientist.