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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
I know Lucas isn't the most popular round here at the moment, but I still like this line by Sir Alec Guiness: "In my experience, there's no such thing as luck"
Iran has endorsed
I agree completely, I gave up on university-level calculus and felt ashamed. How could someone "invent" this such a long time ago. Of course we (/.-ers) all read Neal Stephansons trilogy "The Baroque Cycle" so we know a bit about Newton and the likes. It wasn't just Newton, it was the atmosfere surrounding the Royal Society (assuming that part of the trilogy is not fiction). Still, a relatively small group of people accomplishing this is amazing...
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"
...he died a virgin and studied alchemy.
This wasn't just plain terrible, this was fancy terrible. This was terrible with raisins in it. - Dorothy Parker
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)
I went to the same boys school as Newton originally went to, called the 'Kings School' in Grantham, Lincolnshire, England where Newton scratched his name into the wall of the old library. As was the custom at the time, many other students scratched and carved their names. His looks considerably less impressive than others. We were all taught that he attended the school and about his subsequent accomplishments. There is a garden named after him with a single apple tree in the middle, although it's not one he ever sat under. One of the various 'houses' in the school is also named after him. The town has a statue of him in front of the guildhall (equivalent to a town hall). However, in their rush to name things after him they have named a travisty of a shopping mall after him, which is awful, it's called the 'Isaac Newton Shopping Centre' and is particularlly down market with a big plastic apple hanging high near one of the entrances. Growing up asa kid I saw Newton's name and face everywhere as he adorned the back of the one pound note, the equivalent of a $1 bill. Sadly that was replaced by a coin with nobody on the reverse of the queens 'head' side. Even worse my home town is now remembered more for 'Maggie Thatcher' than Newton. I hope that one day the place will be associated more for Newton than Thatcher, but it is unlikely as he wasn't born there (he was born in Colsterworth nearby), only attending school there for a while when he was young. Lastly, I hope that Apple Computer bring back their Newton as it was a fantastic machine which deserved to bear the name of such an amazing man.
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.
That's because they don't teach it the way it was developed. What you learn is a santised version and you learn it in the wrong order (compared to order of discovery and development).
These posts express my own personal views, not those of my employer
While some of Newtons ideas were later proven to be incorrect by Einstein
Without the imperfect (but functional) model developed by Newton (which we still use today with some refinements! very few situations require a more complex model of forces and effects) it seems unlikley that Einstein would have been able to develop relativity, indeed many other advances would not have been made until someone else replicated Newton's work.
Newton himself said "If I have seen further, it is because I stand on the shoulders of giants" (which is etched onto the Brish pound coin) - and he is definatly one of the giants upon which later physists stood. Science is a process, not a product, and viewing it in terms of right and wrong is foolish - it's a series of advances leading to a more and more accurate understanding of the universe. No step towards that goal is any less worthy than another.
Beep beep.
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'
The model doesn't work at the atomic level, and that's where the relativistic model enters. Both are true in a sense.
You are confusing Relativity and Quantum Theory, Classical physics and Modern.
Relativity is a classical theory of gravitational, i.e. macro, masses.
KFG
You are weirder - you can't go five words without a spelling mistake.
Although a work of fiction, Neal Stephenson's "Quicksilver" mentions the needles-in-eyes incident and covers many other episodes in Newton's life (and much more besides, I should add) - I'm sure by now most SlashDot readers have either loved it or loathed it, but if you haven't tried, give it a whirl....
Neal Stephenson is fond of using odd spellings in the book, so you should be right at home...
The author of the site is (or at least was) highly reputed. It was also him who first pointed out that the so-called gravitational anomaly, found by Pioneer spacecrafts, probably has a simple (Newtonian) explanation: dust in the Kuiper Belt--and this explanation has been entirely ignored by most physicists.
Some physicists seem to prefer complicated explanations over simple ones.
The story about him and Robert Hooke is quite and interesting one and makes you think about how much he actually did do. Robert Hooke did infact accuse Newton of plagiarism but the charge was dropped because Hooke didn't have proof of his own theory and made some assumptions on intuitive grounds.
Makes one think that if someone would now proof Einsteins theory of relativity, if they would then discredit Einstein for the discovery.
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.
When he said that he was referring almost exclusively to Gallileo who formulated the laws of motion in a slightly different fasion many years before Newton did. That doesn't take anything away from the man's genius mind you. He did most of his work when he was 22 years old. Just slightly older then I am. Pretty amazing.
The darkness... controls the music. The music... controls the soul.
Both classical mechanics and general relativity are incomplete; they are approximations of the physical reality we observe, both excellent for some applications but useless for others.
Newton's classical mechanics is amazingly accurate when familiar scales and speeds are involved, but breaks down when large speeds are involved. Relativity fixes this; however, both theories break down at the subatomic scale, where we need quantum mechanics instead. (Unfortunately, though, quantum mechanics ONLY holds for the subatomic scale.)
You're right about Einstein "getting it right", however, since in addition to working out relativity he was one of those physicists who developed the quantum theory. On the other hand he never really accepted quantum mechanics...
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 think it's fair to say that both Euler and Gauss surpass Newton as mathematicians, as well as some others. But you're right; as a jack of all trades, he is non pareil. In my humble opinion as a physicist and a mathematician :)
To follow knowledge like a sinking star, / Beyond the utmost bound of human thought. ("Ulysses", Tennyson)
Hawking claims that this was a caustic remark on the shortness of physical build of Robert Hooke.
As far as I know, it is not about his work on Mechanics that Newton said this, but about his work on Optics.
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
Descartes invented co-ordinate geometry Euclid gave us quite possibly the greatest base for mathematics of anyone, ever There are plenty of mathematical greats. Which is a good thing! :)
I remember a documentary on Newton in which it was stated that he came up with the phrase as a put down to Robert Hooke who disagreed with Newton's position on optics.
Hooke was a hunchback and sensetive about his height. It was in a letter sent by Newton to his rival that he said:
" If I have seen a little further it is by standing on the shoulders of giants"
Or, as is the case for me and most others, "if I have failed to see further, it is because giants are standing on my shoulders".
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.
That's three posts now claiming the "shoulders of giants" remark was a dig at Hooke. The context doesn't really bear it out. Newton sent the letter to diffuse a dispute over attribution, really a simple apology, with this remark as a "no hard feelings" conclusion.
They did have a serious row shortly before the publication of Principia Mathematica when Hooke provoked another argument in a more obnoxious way, and Newton responded by deleting all the (originally generous) citations to Hooke. From this point, we can assume bad faith on both sides. However, the idea that Newton was slipping ad hominem remarks into his earlier letters is a bit fanciful.
I believe he gave credit to others:
If I have seen farther than others, it is because I have stood on the shoulders of giants.
--Isaac Newton
And let us not forget the greatest one-liner in the history of science:
If I have not seen as far as others, it is because there were giants standing on my shoulders.
--Hal Abelson
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.
> Pretty amazing.
/. didn't existed at that time, so he didn't waste his time like you and I do :-)
Not at all !
Votez ecolo : Chiez dans l'urne !
Welcome to the point sherlock. I'm not henpecking, I'm just stating a fact. They're not perfect, knowone is. People seem to be under the impression that they are 100% responcible for calculus as we know it. They certainly deserve credit for the bulk of it, but they had help along the way.
The darkness... controls the music. The music... controls the soul.
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.
You omit his greatest contribution to science, which was establishing that the laws of nature are universal. He saw that the force of gravity which makes things fall to the ground is exactly the same force, obeying the same law, as the force of gravity between celestial bodies. It seems obvious today, but it was not at all obvious in the seventeenth century. Most people took it for granted that the celestial bodies were ruled by quite different laws from those we experienced in our daily lives.
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.
[I]t's quite difficult to spend time in Cambridge, England without encountering Newton.
Well, hard to not encounter anyone who has a King Kong sized statue in his old college's chapel.
I wonder whether the discovery of the Turing Machine, the machine that can be all machines, at the very same place might not be an equally impressive achievement.
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Did you read Principia?
No, but I saw the movie. I thought it was pretty good. Definitely one of Tor Johnson's better roles. I also liked how Bela Lugosi keeps a cape over his face in most of his scenes - it gives him a real aura of mystery.
Please keep your platonic beliefs to yourself; mathematics is not necessarily discovered. The philosophical reasons for this are numerous, and to say categorically that it must be discovered is naive at best.
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.
MATH BRAWL !
Everybody duck!
young nerds, pay attention to this thread and learn. This is teh bottom of the well, the dregs of the coffee, the vapors in the gas tank. It does not get any nerdier than this.
Perhaps. But mathematical definitions are not necessarily rigorous. Try to formulate a rigorous definition of a set.
Another interesting case of the non-rigorous use of mathematics was by Dirac. He used the delta-function comfortably for a while, while the mathematicians cried foul (IIRC, the great von Neumann was one of them). Eventually they realized that, while not rigorous, he was right. Of course, he knew he had to be.
I don't discount the worth of rigor--far from it. An attempt at a rigorous argument often exposes implicit assumptions and possible caveats. But those who believe that mathematics is (or is even capable of being) an absolute, water-tight framework are living in a fantasy world (as the great Bertrand Russell unfortunately discovered).