Digital Rare Book :
Newton's Principia - The Mathematical Principles of Natural Philosophy
By Sir Isaac Newton
Translated into English by Andrew Motte
Published by Daniel Adee, New York - 1846
I consider Newton to be the greatest scientist of all times. It is difficult to understand how he spent a large part of his scientific career on experiments on Alchemy trying to discover the ultimate material. Although he failed find anything his great experience with metals earned him the post of the master of the mint which was the highest paid job in England. Surprisingly Voltaire supported Newton in his feud with Leibnitz though the latter was based at Paris. He jokingly wrote that Newton's fame was not due to his own talents but due to the great beauty and charm of his niece who managed his house. He was also involved in a bitter dispute with Young.
Scientists are no different than historians. They do exhibit irrational behavior off and on and ignore evidence which is inconvenient to their pet hypothesis. The both believe in God and ghosts from the past!Voltaire supported Newton not only because of the irrefutable logic of his theories, but also because Voltaire spent his best years in England. I doubt if one can actually call him a Frenchman. Greatness in Sciences or in History does not guaranty absence of pusillanimity and petty jealosies in personal life. History of Science (and also mathematics) abounds in such stories.
Newton was certainly a flawed individual. He also argued with Hooke, at that time a major figure in science and the new Royal Society. Someone has suggested that Newton's comment about standing on the shoulders of giants was a reference to Hooke who was apparently 'not tall'. Newton also had some odd and for those times, dangerous views of religion. But his science was another matter, we all stand on his shoulders.
Ranajit, regarding Newton's alchemy, we must remember that at that time, the nature of science itself as still being debated and the existing practices were still deemed relevant. There was a shift in paradigm occurring and newton et al had feet in both sides of it. Besides we shouldn't be too harsh on alchemy, I understand that its practitioners weren't all fools and charlatans, and it did metamorphose into chemistry.
@Allen Copsey I am sorry, I should have mentioned Hooke. Yes. Newton was a flawed individual and we all are flawed individuals but I would have liked to be a flawed individual like Newton. Recently I was reading Stephen Hawking's (he sits on the same Lucasian chair that was once adorned by Newton) comments on Newton's flaws but Hawkings come and go but Newton, in my opinion, stands unsurpassed. I had the good fortune to work under a Physicist who had worked under P.A. M. Dirac who was the Lucasian Professor before Hawking. Dirac belonged to Newton class and he has now replaced the Newton's equations with Dirac's equation. Dirac had the highest opinion about Newton. When I was a college student I was thrilled to see the rings which go by his name. But I am aware that this was first observed by Hooke and also that the inverse square law was known to Hooke and possibly also Halley before Newton. I feel Newton would have been less of a flawed individual had he acknowledged Hooke's contribution. It is also probably correct that Newton may have been behind the destruction of Hooke's portrait in the Royal Society. But to discover a mathematical structure and then solve problems with that in the manner Newton did is something few mortals have achieved. Remember Einstein wrote a set of non-linear differential equations of General theory of relativity but could not rigourously solve it himself. The first two men who solved them were Alexander Friedman and Lemaitre (whose student was also my teacher). My supervisor Prof. S. Dattamajumdar gave the seventh rigourous solution of Einstein's equations and has universes named after him. Hooke was also less generous and did not want to give credit to Newton for his discovery of the reflecting telescope. Hooke did not know mathematics. Yes, you are right that in Newton's time Alchemy had a different status. Think of a man of Newton's caliber spending sleepless nights for thirty years ! He failed in Alchemy but he was not a failed scientist. Thanks for your thoughts.
@ Allen Copsey I had also some experience of Newton's method of approximation and was awed by it. Such a simple method but it was Newton who first discovered it. We now have better methods. Leibnitz cannot be said to be equal to Newton though he may stand taller as a philosopher. Even Bertrand Russell who was a great admirer of Leibnitz had to admit that differential calculus was discovered by Newton before Leibnitz but he did not publish it in time. But for Halley's prodding even the Principia Mathematica would not have been published. And the Taylor's theorem which is a pillar in analysis can be called Newton's theorem. And his greatest discoveries were all made within a very short span of about four years when there was a plague in Cambridge.
I am not surprised that Stephen Hawking, who is a media creature, should criticize Newton, but Isaac Barrow who was the Lucasian Professor before newton vacated the chair to make room for young Newton. Einstein also paid his tributes to Newton during the bicentenary celebrations of Newton.
Waiting to read Newton's Biography written by James Gleick.
@Ranajit: That's quite a pedigree you have :)
Your Prof has universes named after him? There's not many that can claim that, and I'd be satisfied with just one being named after me.
Your comments have driven home just how important Newton was, and is, and I'm also struck my how little that is appreciated.
These are theoretical structures that follow from his static model and are called Papapetrou-Dattamajumdar universes.
In my opinion Newton can be compared with Brahmagupta about whom we do not know enough. Al-beruni who was the greatest scholar of his day showers praises on the Indian mathematicians. But did Brahmagupta make any experimental discovery like Newton? We do not know.
Milton's 'Paradise Lost' was published in 1667 which was also the year of discoveries for Newton. Both were from Cambridge and there are faint echoes of Milton in Newton's writings. Though politically they were on opposite sides they must have known each other. When Milton went to Italy he met Galileo which shows his interest in Physics and he must have been aware of Newton's work. Newton's step-father was a clever man who kept equal distance from the royalists and the revolutionaries and prospered even during the worst years. Newton hated him intensely, for his mother left him and the young Newton grew up almost uncared for. But he not only depended on the money and property that he got from him, his scholarly nature was also in a way due to his step-father whose books he inherited. Newton's father was nearly illiterate and my hunch is that Newton hated his step-father but wanted to surpass him in learning.
Mr. Pal flits between centuries with the ease of a spaceship. Newton and Hawkins were seperated by three and a half centuries. To compare Barrow's deference with Hawking's irreverence over Newton is irrelevant. The Lukasian chair was created for Mathematics and "natural sciences" came to be a part in the following decades after much deliberations over disputes over the statute of the Lucasian fellowship. Newton saved himself from getting ordained (as was required of Cambridge fellows) by interpreting the Statute in a different way.
Likewise, it is ridiculous to compare Newton with Brahmagupt. Mr. Pal admits we know very little about Brahmagupt. Then how can one compare him with some about who we know so much more?
Mr. Pal, you meant to mention Einstein's remarks during the tricentenary celebrations of course. One great thing about Newton's life and work is that every year we may have to celebrate tercentanry of his this or that proposition. Einstein called Newton a great "systematizer".
Mr. Pal I can't understand your statement "Newton's father was nearly illiterate and my hunch is that Newton hated his step-father but wanted to surpass him in learning." How would Newton want to surpass his illiterate father in learning?
@Sekhar Sathe Yes! Newton was indeed a great systematizer. His father died when he was very young and he was not a lerned man. His mother's line was different and his maternal uncle was a M.A. from Cambridge who loved Newton very much. Newton's step-father and his uncles were all priests and Newton also first enrolled at Cambridge for religious studies. Brahmagupta first treated zero as an entity and must be seen as one of the greatest mathematicians of history.
'Zero' was a great invention of the human mind.
@Asad Ahmed: WE cannot say with certainty whether it was an invention or a discovery!
The concept of 'zero' was completely original and its placement after every nine numerals was brilliant. It was a true invention. The other numerals (1 - 9) were simple but the addition of '0' next to them must have required deep thinking. We use such ideas in our everyday lives without ever stopping to think about their greatness. Before the introduction of Indic numerals, the Romans used to use those awkward letters like L, V. X, I etc to count. Likewise, the great works on Euclids, or Socratic dialectics etc, are some of the greatest treasures mankind has inherited from the ancients.
I am amazed by the level of mathematical knowledge in Sumer during Ram-Sin's (or Rim-Sin) rule. One tablet clearly shows the knowledge of the Pythagorean theorem. Needless to say the rigorous proof was beyond them at this very early stage. The Nobel Laureate Prof. P.A.M. Dirac's view ( reported by my supervisor Prof. S. Dattamajumdar who worked with him) was that the Indians excelled in arithmetic but were behind others in Geometry.
One of my classmates said a few days back...Physics would have been much simpler if Jackfruit had fallen on newton's head :P !!
Zero as a number is different from the placement of the symbol for zero after 9 to signify ten and its subsequent recurrence. There is no doubt that the use of the symbol in the algorithm was brilliant. In that sense it was an invention. But the moment you look at zero as a "number" like other numbers 1,2,3,..... can one call it an invention? The use of the symbol in representing number 10 is dramatically different from zero as a number. It is doubtful if zero as a number with consequent operations involving zero as number such as multiplication, division, power can be attributed to Indian mathematicians, especially to Brahmagupt decisively. They may have grappled with the concept but may not have resolved all operations with zero. As for the question whether numbers are an invention or discovery presupposes resolution of a more fundamental question whether numbers "exist" or they are merely a construct of the human mind like our language.
It seems strange that Milton went out of the way to meet Galileo the heretic and did not meet Newton who was next door.
Yes Shekhar, the numeral '0' has two functions: (i) to signify nothing - a null value, and (ii) an added numeral after 7,8,9 ... etc to denote 70,80,90 etc. At first sight, the two functions have nothing in common, yet it works out so nicely that we take it for granted and don't even pause to think about it. To connect the two was a stroke of genius. Also to assign a numeral to nothing was interesting in itself. It simply makes me wonder how smart our ancestors were.
I was not aware that Milton went out to meet Galileo, but not Newton. It may simply be because Galileo (but not Newton) was facing the death sentence from the Inquisition. To think it over, does it really matter whether the Sun goes around the Earth, or the Earth goes around the Sun when one's life is at stake?
Asadbhai, yes if you mean by "our ancestors" our forefathers from all continents who were brilliant and allowed their faith to leap from one abstraction to another.
In this respect, the philosophical contributions of the Greek masters are unmatched.
Read Book Online : http://www.archive.org/stream/newtonspmathema00newtrich#page/n7/mode/2up
Download pdf Book : http://ia600300.us.archive.org/8/items/newtonspmathema00newtrich/newtonspmathema00newtrich.pdf
I consider Newton to be the greatest scientist of all times. It is difficult to understand how he spent a large part of his scientific career on experiments on Alchemy trying to discover the ultimate material. Although he failed find anything his great experience with metals earned him the post of the master of the mint which was the highest paid job in England. Surprisingly Voltaire supported Newton in his feud with Leibnitz though the latter was based at Paris. He jokingly wrote that Newton's fame was not due to his own talents but due to the great beauty and charm of his niece who managed his house. He was also involved in a bitter dispute with Young.
Scientists are no different than historians. They do exhibit irrational behavior off and on and ignore evidence which is inconvenient to their pet hypothesis. The both believe in God and ghosts from the past!Voltaire supported Newton not only because of the irrefutable logic of his theories, but also because Voltaire spent his best years in England. I doubt if one can actually call him a Frenchman. Greatness in Sciences or in History does not guaranty absence of pusillanimity and petty jealosies in personal life. History of Science (and also mathematics) abounds in such stories.
Newton was certainly a flawed individual. He also argued with Hooke, at that time a major figure in science and the new Royal Society. Someone has suggested that Newton's comment about standing on the shoulders of giants was a reference to Hooke who was apparently 'not tall'. Newton also had some odd and for those times, dangerous views of religion. But his science was another matter, we all stand on his shoulders. Ranajit, regarding Newton's alchemy, we must remember that at that time, the nature of science itself as still being debated and the existing practices were still deemed relevant. There was a shift in paradigm occurring and newton et al had feet in both sides of it. Besides we shouldn't be too harsh on alchemy, I understand that its practitioners weren't all fools and charlatans, and it did metamorphose into chemistry.
@Allen Copsey I am sorry, I should have mentioned Hooke. Yes. Newton was a flawed individual and we all are flawed individuals but I would have liked to be a flawed individual like Newton. Recently I was reading Stephen Hawking's (he sits on the same Lucasian chair that was once adorned by Newton) comments on Newton's flaws but Hawkings come and go but Newton, in my opinion, stands unsurpassed. I had the good fortune to work under a Physicist who had worked under P.A. M. Dirac who was the Lucasian Professor before Hawking. Dirac belonged to Newton class and he has now replaced the Newton's equations with Dirac's equation. Dirac had the highest opinion about Newton. When I was a college student I was thrilled to see the rings which go by his name. But I am aware that this was first observed by Hooke and also that the inverse square law was known to Hooke and possibly also Halley before Newton. I feel Newton would have been less of a flawed individual had he acknowledged Hooke's contribution. It is also probably correct that Newton may have been behind the destruction of Hooke's portrait in the Royal Society. But to discover a mathematical structure and then solve problems with that in the manner Newton did is something few mortals have achieved. Remember Einstein wrote a set of non-linear differential equations of General theory of relativity but could not rigourously solve it himself. The first two men who solved them were Alexander Friedman and Lemaitre (whose student was also my teacher). My supervisor Prof. S. Dattamajumdar gave the seventh rigourous solution of Einstein's equations and has universes named after him. Hooke was also less generous and did not want to give credit to Newton for his discovery of the reflecting telescope. Hooke did not know mathematics. Yes, you are right that in Newton's time Alchemy had a different status. Think of a man of Newton's caliber spending sleepless nights for thirty years ! He failed in Alchemy but he was not a failed scientist. Thanks for your thoughts.
@ Allen Copsey I had also some experience of Newton's method of approximation and was awed by it. Such a simple method but it was Newton who first discovered it. We now have better methods. Leibnitz cannot be said to be equal to Newton though he may stand taller as a philosopher. Even Bertrand Russell who was a great admirer of Leibnitz had to admit that differential calculus was discovered by Newton before Leibnitz but he did not publish it in time. But for Halley's prodding even the Principia Mathematica would not have been published. And the Taylor's theorem which is a pillar in analysis can be called Newton's theorem. And his greatest discoveries were all made within a very short span of about four years when there was a plague in Cambridge.
I am not surprised that Stephen Hawking, who is a media creature, should criticize Newton, but Isaac Barrow who was the Lucasian Professor before newton vacated the chair to make room for young Newton. Einstein also paid his tributes to Newton during the bicentenary celebrations of Newton.
Waiting to read Newton's Biography written by James Gleick.
@Ranajit: That's quite a pedigree you have :) Your Prof has universes named after him? There's not many that can claim that, and I'd be satisfied with just one being named after me. Your comments have driven home just how important Newton was, and is, and I'm also struck my how little that is appreciated.
These are theoretical structures that follow from his static model and are called Papapetrou-Dattamajumdar universes.
In my opinion Newton can be compared with Brahmagupta about whom we do not know enough. Al-beruni who was the greatest scholar of his day showers praises on the Indian mathematicians. But did Brahmagupta make any experimental discovery like Newton? We do not know.
Milton's 'Paradise Lost' was published in 1667 which was also the year of discoveries for Newton. Both were from Cambridge and there are faint echoes of Milton in Newton's writings. Though politically they were on opposite sides they must have known each other. When Milton went to Italy he met Galileo which shows his interest in Physics and he must have been aware of Newton's work. Newton's step-father was a clever man who kept equal distance from the royalists and the revolutionaries and prospered even during the worst years. Newton hated him intensely, for his mother left him and the young Newton grew up almost uncared for. But he not only depended on the money and property that he got from him, his scholarly nature was also in a way due to his step-father whose books he inherited. Newton's father was nearly illiterate and my hunch is that Newton hated his step-father but wanted to surpass him in learning.
Mr. Pal flits between centuries with the ease of a spaceship. Newton and Hawkins were seperated by three and a half centuries. To compare Barrow's deference with Hawking's irreverence over Newton is irrelevant. The Lukasian chair was created for Mathematics and "natural sciences" came to be a part in the following decades after much deliberations over disputes over the statute of the Lucasian fellowship. Newton saved himself from getting ordained (as was required of Cambridge fellows) by interpreting the Statute in a different way.
Likewise, it is ridiculous to compare Newton with Brahmagupt. Mr. Pal admits we know very little about Brahmagupt. Then how can one compare him with some about who we know so much more?
Mr. Pal, you meant to mention Einstein's remarks during the tricentenary celebrations of course. One great thing about Newton's life and work is that every year we may have to celebrate tercentanry of his this or that proposition. Einstein called Newton a great "systematizer".
Mr. Pal I can't understand your statement "Newton's father was nearly illiterate and my hunch is that Newton hated his step-father but wanted to surpass him in learning." How would Newton want to surpass his illiterate father in learning?
@Sekhar Sathe Yes! Newton was indeed a great systematizer. His father died when he was very young and he was not a lerned man. His mother's line was different and his maternal uncle was a M.A. from Cambridge who loved Newton very much. Newton's step-father and his uncles were all priests and Newton also first enrolled at Cambridge for religious studies. Brahmagupta first treated zero as an entity and must be seen as one of the greatest mathematicians of history.
'Zero' was a great invention of the human mind.
@Asad Ahmed: WE cannot say with certainty whether it was an invention or a discovery!
The concept of 'zero' was completely original and its placement after every nine numerals was brilliant. It was a true invention. The other numerals (1 - 9) were simple but the addition of '0' next to them must have required deep thinking. We use such ideas in our everyday lives without ever stopping to think about their greatness. Before the introduction of Indic numerals, the Romans used to use those awkward letters like L, V. X, I etc to count. Likewise, the great works on Euclids, or Socratic dialectics etc, are some of the greatest treasures mankind has inherited from the ancients.
I am amazed by the level of mathematical knowledge in Sumer during Ram-Sin's (or Rim-Sin) rule. One tablet clearly shows the knowledge of the Pythagorean theorem. Needless to say the rigorous proof was beyond them at this very early stage. The Nobel Laureate Prof. P.A.M. Dirac's view ( reported by my supervisor Prof. S. Dattamajumdar who worked with him) was that the Indians excelled in arithmetic but were behind others in Geometry.
One of my classmates said a few days back...Physics would have been much simpler if Jackfruit had fallen on newton's head :P !!
Zero as a number is different from the placement of the symbol for zero after 9 to signify ten and its subsequent recurrence. There is no doubt that the use of the symbol in the algorithm was brilliant. In that sense it was an invention. But the moment you look at zero as a "number" like other numbers 1,2,3,..... can one call it an invention? The use of the symbol in representing number 10 is dramatically different from zero as a number. It is doubtful if zero as a number with consequent operations involving zero as number such as multiplication, division, power can be attributed to Indian mathematicians, especially to Brahmagupt decisively. They may have grappled with the concept but may not have resolved all operations with zero. As for the question whether numbers are an invention or discovery presupposes resolution of a more fundamental question whether numbers "exist" or they are merely a construct of the human mind like our language.
It seems strange that Milton went out of the way to meet Galileo the heretic and did not meet Newton who was next door.
Yes Shekhar, the numeral '0' has two functions: (i) to signify nothing - a null value, and (ii) an added numeral after 7,8,9 ... etc to denote 70,80,90 etc. At first sight, the two functions have nothing in common, yet it works out so nicely that we take it for granted and don't even pause to think about it. To connect the two was a stroke of genius. Also to assign a numeral to nothing was interesting in itself. It simply makes me wonder how smart our ancestors were. I was not aware that Milton went out to meet Galileo, but not Newton. It may simply be because Galileo (but not Newton) was facing the death sentence from the Inquisition. To think it over, does it really matter whether the Sun goes around the Earth, or the Earth goes around the Sun when one's life is at stake?
Asadbhai, yes if you mean by "our ancestors" our forefathers from all continents who were brilliant and allowed their faith to leap from one abstraction to another.
In this respect, the philosophical contributions of the Greek masters are unmatched.