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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
That was Leibnitz, you insensitive clod!
(and thus, the science's oldest flame war is brought into the 21st century!)
It's said that he died a virgin... so in at least one respect Newton was not, and did not get, "lucky".
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
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I'm enduring college level calculus right now, and to think that one man, more or less invented a major area of mathematics that we use in a vast array of situations, is simply, incredible.
Boy is that ever true, I remember when going through all my calc classes that I found it hard to conceive that someone could ever figure out all this stuff on their own. It's hard enough to remember/learn even now (unless you're really talened at math) after hundreds of years and countless refinement.It's not just Newton though. I had to take a math history class as part of my "capstone" courses to get my CS degree. It was a fascinating course and we learned of so many people who developed different areas of math. One thing I remember well because it was funny is that pretty much everyone who's done significant work on set theory has spent time in mental hospitals, most after they did the work. :)
And of course, Archimedes pretty much a cat's whisker away from discovering the integral around 200 BC, as described in the nearly lost work "The Method"
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.
He did not "invent" or "discover" the thing by himself. It's like all research: people put brick after brick, and then someone puts the last one and says "here is a building", and gets all the credit. And many years later (30 for Albert, 300 for Isaac) some geeks put posters of the guy in their rooms and suddenly feel illuminated. :)
"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).
Newton himself said of his work that he was only "standing on the shoulders of giants" meaning that if he had discovered new knowledge, it was from the ideas put down by euclid, archimedes etc before him.
(This phrase is engraved round the edge of £2 coins in the UK, since Newton also invented milling the edges of coins to prevent people from clipping them.)
However, he was probably being too modest. It wasn't just calc: this guy basically went away at some point in his life and came up with:
His laws of motion, which explained pretty much every physical phenomenom then studied.
His theory of gravity, which relates the movement of celestial bodies back to the laws of motion.
and
The differential calculus, which provided the maths necessary to apply all this.
He also did work in optics and other fields, and invented the catflap.
If anyone surpasses him as a physicist, it must be Einstein.
If anyone surpasses him both as a physicist and a mathematician, it's news to me.
Respect is due.
my password really is 'stinkypants'
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.
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.
As an engineer, I frequently use Newton's laws of motion. I can't say that I have ever had the need to consider bodies travelling at a significant fraction of the speed of light in my work.
flossie
Write now. Defend liberty
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.
I do agree that Newton discovered/invented a large part of our mathematics
No he didn't! Elementary calculus may be useful but it's only a teardrop in the ocean of mathematics. Compare to Gauss who contributed to nearly everything mathematics was studying in his time and most of which is still relevant, while Newton's formulations have long since been surpassed by more modern constructions.
And Latin. We now know Latin to be a dead language. What real scientist uses Latin?
And the English system of weights and measures. He didn't even use the Metric system, or bother to convert the values!
How the great learned history critics and scientists of the future will scoff at our inaccurate decimal system, our clunky wire-based infosystems, and our use of BASIC.
We use the tools we have. The best of us modify them to fit our own needs. Every once in a while, someone comes up with a mod that everyone agrees is really cool. On that measure, Isaac Newton is the greatest hacker of all time. OK, maybe Edison was greater, or the woman who invented the stick.
I picking on your fine post (a bit unfairly, to be sure) because if someone comes up with a mod, how does that make everything that went before it "incorrect"?
sigs, as if you care.
Amazing how Newton's status has changed. In the early 70s the Cambridge Union Society actually sold off a copy of the Principia cheap (as the guy who beat me to it gloated at me at considerable length). They wouldn't do that nowadays when virtually every Latin edition is worth a great deal of money.
Just as it's extremely difficult to spend any time in Florence without becoming aware of the Dante connection, it's quite difficult to spend time in Cambridge, England without encountering Newton. Whatever his faults - and he was clearly not an easy person to get on with - he made major contributions to optics, pure physics, chemistry, mathematics and the running of the Royal Mint. Other people around at the time did remarkable work - Hooke, Boyle, Liebniz - but Newton surpassed them al for sheer output, breadth and depth. Logically, nowadays, with a much larger and better educated population we should be throwing up lots of Newtons. Why aren't we? Is it because all the relatively easy science and maths has now been done and it takes large organisations and computing power to make any advance at all? Or is it because clever people get pulled off into business or celebrity before they really have a chance to do any work that will really endure?
Panurge has posted for the last time. Thanks for the positive moderations.
but what do i know, i'm just a model.
Incorrect might not be the right word, it was not mathematically rigorous. There were instances when he treated an infintesimal as a zero and discarded it, there were instances where he treated it as a non-zero and divided it. Math is rigorous. You need a set of rules that hold in all situations. [Emphasis added]
A set of rules that hold in all situations means that there are no paradoxes.
There is nothing non-rigorous about infintesimals which behave in some cases identically with zero when added to something and in other cases behave like non-zeros when dividing two of them. What is non-rigorous and non-defensible is the attempted distinction between zero and non-zero. Not everything mathematical is a number. In fact most mathematical things are not numbers. It all has to do with functions from spaces to spaces that preserve interesting properties.