Great Astronomers: Laplace
Great Astronomers in Modern English
by Sir Robert S. Ball, 1895 (paraphrased by Leslie Noelani Laurio)
To view the table of contents for the rest of this book, click here.
Pierre-Simon Laplace, 1749-1827
Nebular hypothesis: the solar system formed out of nebulous material spinning outwards.
Pierre-Simon Laplace, known for his 5-volume work in celestial mechanics, was born in Normandy [France] in March, 1749, thirteen years after his famous friend Joseph-Louis Lagrange. His father was a farmer, but had enough means to provide a good education for his promising young son. His father intended him for a church career (although, much later in his life, Laplace held some unorthodox beliefs). He went to the University of Caen to study theology at age 16, but he became more interested in mathematics, and was able to become a mathematics teacher in his hometown at age 18.
But Pierre-Simon Laplace wanted to learn more and seek his fortune in the big city, so he set out for Paris with letters of introduction to the brilliant mathematician and scientist Jean le Rond d'Alembert. D'Alembert was so famous that Catherine the Great asked him to come to Russia and tutor her son for a thousand francs. But D'Alembert turned down this offer. He preferred a quiet life of study at his home in Paris, even though the salary was modest. When he declined, Catherine wrote, 'I understand that you wish to continue your studies in peace, and to be near your friends. Why don't you bring your friends with you? I will provide accommodations for all of you.' But he still refused. Frederick the Great also invited D'Alembert to Berlin, but he declined that offer as well. Thus this respected scholar whose work could only be understood and appreciated by mathematical minds was sought after by Russian and German royalty.
And now Laplace, the son of a farmer, sought to meet D'Alembert. But his letters of introduction were ignored. So Laplace wrote a letter to D'Alembert discussing some point about Dynamics. This got D'Alembert's attention! He recognized Laplace's mathematical talent and invited him to come visit him. So he did, and after they got to know each other, D'Alembert got him a position as professor of mathematics in the Military School in Paris. This was just the kind of opening Laplace had hoped for, and he made the most of it.
[Wikipedia says, "According to d'Alembert's great-great-grandson, d'Alembert received Laplace rather poorly, and to get rid of him gave him a thick mathematics book, saying to come back when he had read it. When Laplace came back a few days later, d'Alembert was even less friendly and did not hide his opinion that it was impossible that Laplace could have read and understood the book. But upon questioning him, he realised that it was true, and from that time he took Laplace under his care. Another account is that Laplace solved overnight a problem that d'Alembert set him for submission the following week, then solved a harder problem the following night. D'Alembert was impressed and recommended him for a teaching place in the Ecole Militaire."]
At twenty three years old, Laplace got his first Memoir [scientific article] published in the Memoirs of the Academy at Turin. Following that one, he wrote many more attacking the difficulties in Newton's theory of gravity as an explanation of the movement of the solar system. Like his contemporary Joseph-Louis Lagrange, he tackled theoretical problems that required great analytical skill. The scientific world was riveted on the discoveries made by Laplace and Lagrange. [Laplace also collaborated with the French chemist Antoine Lavoisier on a Memoir about Heat and molecular motion.]
Pierre-Simon Laplace's most famous work is "Mecanique Celeste." ["Celestial Mechanics" in five volumes; there may be an English translation online at archive.org. Nathaniel Bowditch published an English version with his own annotations!] In this work Laplace laid out a comprehensive attempt to apply Isaac Newton's principles in even more detail than Newton ever did. Once Newton hit upon the idea of gravitation, he had to invent the mathematics to apply it to the way the celestial bodies move. But in the fifty years since Newton had died, mathematics had come a long way. The branch of mathematics that Newton had developed -- called infinitesimal calculus -- had become much more accurate, so that Laplace could calculate more efficiently than Newton had been able to. The geometry that Isaac Newton used did a good job demonstrating general tendencies of forces and explaining things that influence the orbits of celestial bodies -- but it couldn't deal with gravity's more subtle effects. The influence that one planet can have over the orbit of another planet requires much more analytical methods of calculation.
In his "Mecanique Celeste," Laplace tried to unravel the mysteries of the heavens using Newton's mathematics with the improvements from a couple of generations of mathematicians. His book is extremely difficult to understand because the subject is so complex, and it takes a considerable amount of mathematical ability to make sense of his points. His writing style is also difficult to follow and he leaves gaps in his explanations that are hard for readers to fill in. Laplace often writes that it's 'easy to see' how one step follows another -- but it isn't. Even excellent mathematicians have had a hard time grasping his train of logic. They say that there were times when Laplace was giving a lecture, and when he came to a place where his book had said a point was 'easy to see,' even he himself would have to think for an hour or two to remember his train of reasoning! Yet certain parts of his book are enthusiastically admired by mathematicians. He invented entire branches of science, some of which were expanded by later scientists studying nature.
If there's any flaw with Laplace's work, it's a moral oversight rather than an error in data. Laplace and Lagrange made progress at the same rate as they both investigated the mechanics of how celestial bodies move. Sometimes they were even studying the exact same problem at the same time using identical research methods. Sometimes Lagrange found the solution first. Sometimes it was Laplace. It would be difficult to sort out which contributions to astronomy were made by which of them. But Laplace failed to acknowledge Lagrange's contributions, or any of the other mathematicians who advanced our understanding of the heavens -- except Isaac Newton. Anyone reading the "Mecanique Celeste" would have no way of knowing whether the discoveries he read about were made by Pierre-Simon Laplace, or Joseph-Louis Lagrange, or Leonhard Euler, or Alexis Clairaut. If a scientist today published a work that was dependent on the contributions of others and then neglected to acknowledge those others, he would be severely criticized and there would be bitter controversies. Perhaps things were done differently in his time and judging him by our standards is unfair. Or perhaps there's more to it than we're aware of. When two researchers are working on the same problem and constantly publishing their results, it's sometimes difficult for the researchers themselves to know who should be credited for which discoveries. Perhaps Laplace was diligently focused on devoting his time and energy on interpreting the secrets of nature using all the skill and resources available to him, and refused to let any side issues distract him. What if he couldn't bear to waste pages and time discussing who should be credited for each formula or idea? Maybe he was only concerned about providing a complete picture of celestial mechanics, and details about whose mathematics were used seemed so trivial in comparison that he didn't bother to relate them. Perhaps he was thinking, 'If Lagrange thinks I've used his data incorrectly, then he should do just what I did and write his own book. He's certainly talented enough, and he would be welcome to use any data I came up with just as I have used his. I would welcome such a contribution to the library of science. What difference does it make who contributed which mathematical formula?' That may indeed be his reasoning, because he and Lagrange remained the best of friends until death separated them -- and Laplace even gave the oration at Lagrange's funeral.
Laplace's work is too technical to explain in this book. But he did publish one book called 'Systeme du Monde' [The System of the World, you can view it online at archive.org] in which he was able to explain the basic theories of how celestial bodies move and some related discoveries without discussing the mathematics involved. This is the book that made his name known to people who are interested in astronomy but are not mathematicians. This is the book where he explains the Nebular Hypothesis [a model of cosmogony that hypothesizes that the solar system is formed of nebular material -- protosolar clouds that 'cooled and contracted, flattened and spun more rapidly, throwing off a series of gaseous rings of material.' From Wikipedia]. This is the most widely accepted theory among cosmologists.
The Nebular Theory explains how the sun ended up in the middle of the solar system, with the planets and their moons orbiting it. Laplace had noticed that all of the planets revolve in the same direction around the sun. He also noticed that each planet spins on its axis [or pole] in the same direction as its orbit around the sun, and moons circle their planets as satellites in that same direction. Even the sun itself rotates in the same direction, as if it was turning on an axis. Laplace recognized that this was remarkable, and his scientific mind reflected that this consistently uniform movement ought to be investigated. It was too coincidental for there to be no reason for it. To help us consider this idea, let's focus on three celestial bodies: the earth, the sun, and the moon. The earth travels around the sun in a certain direction, and it also rotates on its axis. The earth could have been spinning in the same direction as its orbit, but it could just as likely have been spinning in the opposite direction. But it just so happens that its orbit and its axis rotation are both going in the same direction. The moon orbits around the earth every month in the same direction -- and it turns on its axis in that same direction. So that's four movements, and they all happen to be going in the same direction -- which also happens to be the same direction in which the sun rotates every twenty five days. That's a pretty unlikely coincidence! There must be some physical reason for it. If someone were to toss a coin five times, it's unlikely that it would land on 'heads' five times in a row -- there's only a one in sixteen chance of that happening.
But there are more than three heavenly bodies in the solar system -- there are the great planets, Jupiter, Saturn, Mars, Venus, and Mercury, and their satellite moons. And every one of them orbits and spins on its pole in the same direction! If we just count the five planets Laplace knew about, plus the earth, and the sun, that makes six bodies orbiting, and seven bodies turning on an axis (the sun turns as if on an axis, but it doesn't make an orbit around anything). There are sixteen satellites orbiting their planets in the same direction. We haven't been close enough [in 1895] to see in what direction they're all spinning on their poles, but we can see in which direction they orbit around their planets. That makes thirty orbits and spins that Laplace could confirm -- and all were in the same direction! The chances of that happening randomly are about as unlikely as tossing a coin thirty times, and having it land on 'heads' all thirty times.
Statistically, the chances of that happening are one in five million. Laplace had studied the theory of probabilities, and he recognized that this couldn't be random. There must be some physical reason why everything is turning in the same direction. So he looked for some physical cause. That's how he came up with his Nebular Theory. If his theory was correct, it would explain why everything is turning in the same direction.
Imagine there was a huge mass of cloudy material that was so hot that anything it touched -- such as iron, nickel, oxygen, and other substances that make up the earth and other planets -- was suspended as vapor. That's not actually an unreasonable thing to suppose. In fact, we can see thousands of these kinds of nebulae through our modern telescopes. It's unlikely that this kind of cloudy mass could exist without being in some kind of turning motion. We've seen enough nebulae to confirm that a huge cloudy mass that isn't rotating would be extremely improbable. Imagine that the ages rolled on and the heat from our cloudy nebula mass was radiating away. According to well-known principles of physics, as the suspended vapor got cooler it began to bond together. Much of this material joined into a white hot giant mass with the uncondensed vapors hanging around it. There were also smaller masses forming around the large central mass. In the ages that it took during its cooling off period, the result was one large central mass with a few smaller masses surrounding it. All of them were still rotating, just as the original cloudy mass had been; now, the smaller masses were turning around the larger mass, all of them spinning on their axes and travelling around the main body, all in the same direction. The smaller masses had even smaller masses rotating around them, also rotating and spinning in the same direction.
Ages and ages went by. The heat from these masses gradually dissipated and the smaller masses blended together, first as hot molten globs, and then, as they cooled even more, into solid masses: planets. The huge mass in the center, being so large and taking longer to cool, was still white hot: a sun. In this way, Laplace was able to explain why the rotations of the celestial bodies are all going in the same direction. His account also explains some other things we've observed in the heavens, which seems to confirm his theory. In fact, the more we learn about astronomy, the more certain we are that Laplace's Nebular Hypothesis is the way our solar system came to be.
[Laplace married Marie-Charlotte de Courty de Romanges in 1788. They had two children. The MacTutor Online biography says, "Before the 1793 Reign of Terror Laplace together with his wife and two children left Paris and lived 50 km southeast of Paris. He did not return to Paris until after July 1794. Although Laplace managed to avoid the fate of some of his colleagues during the Revolution, such as Lavoisier who was guillotined in May 1794 while Laplace was out of Paris, he did have some difficult times."]
Pierre-Simon Laplace wanted to be involved in more than science, so he thought he would involve himself in public affairs. Napoleon recognized his genius and wanted him to serve him in his government, so he made him his Minister of the Interior in 1799 [in France, this position is somewhat like the US Attorney General and Secretary of Homeland Security; see more at Wikipedia]. But that didn't work out too well; Laplace was more suited to be a scientist than a statesman. Napoleon was disappointed with his inability at government administration, and decided after only six weeks that Laplace's mathematical mind might be better qualified for business management. So Napoleon made him chancellor of the Senate instead. Laplace accepted the honours Napoleon granted to him, but he wasn't very loyal: when Napoleon was beaten and the Bourbon nobility regained power, Laplace worked for them, too, and was even made a Marquis by King Louis VXIII. Pierre-Simon Laplace spent the last years of his life in the country at Arcueil, 3 miles outside of Paris. He continued to study, and lived a prudent, sober life that helped him avoid many of the infirmities of old age. He died at age 77, in March, 1827. His last words were, 'What we know is very little; what we don't know is immense.'
by Sir Robert S. Ball, 1895 (paraphrased by Leslie Noelani Laurio)
To view the table of contents for the rest of this book, click here.
Pierre-Simon Laplace, 1749-1827
Nebular hypothesis: the solar system formed out of nebulous material spinning outwards.
Pierre-Simon Laplace, known for his 5-volume work in celestial mechanics, was born in Normandy [France] in March, 1749, thirteen years after his famous friend Joseph-Louis Lagrange. His father was a farmer, but had enough means to provide a good education for his promising young son. His father intended him for a church career (although, much later in his life, Laplace held some unorthodox beliefs). He went to the University of Caen to study theology at age 16, but he became more interested in mathematics, and was able to become a mathematics teacher in his hometown at age 18.
But Pierre-Simon Laplace wanted to learn more and seek his fortune in the big city, so he set out for Paris with letters of introduction to the brilliant mathematician and scientist Jean le Rond d'Alembert. D'Alembert was so famous that Catherine the Great asked him to come to Russia and tutor her son for a thousand francs. But D'Alembert turned down this offer. He preferred a quiet life of study at his home in Paris, even though the salary was modest. When he declined, Catherine wrote, 'I understand that you wish to continue your studies in peace, and to be near your friends. Why don't you bring your friends with you? I will provide accommodations for all of you.' But he still refused. Frederick the Great also invited D'Alembert to Berlin, but he declined that offer as well. Thus this respected scholar whose work could only be understood and appreciated by mathematical minds was sought after by Russian and German royalty.
And now Laplace, the son of a farmer, sought to meet D'Alembert. But his letters of introduction were ignored. So Laplace wrote a letter to D'Alembert discussing some point about Dynamics. This got D'Alembert's attention! He recognized Laplace's mathematical talent and invited him to come visit him. So he did, and after they got to know each other, D'Alembert got him a position as professor of mathematics in the Military School in Paris. This was just the kind of opening Laplace had hoped for, and he made the most of it.
[Wikipedia says, "According to d'Alembert's great-great-grandson, d'Alembert received Laplace rather poorly, and to get rid of him gave him a thick mathematics book, saying to come back when he had read it. When Laplace came back a few days later, d'Alembert was even less friendly and did not hide his opinion that it was impossible that Laplace could have read and understood the book. But upon questioning him, he realised that it was true, and from that time he took Laplace under his care. Another account is that Laplace solved overnight a problem that d'Alembert set him for submission the following week, then solved a harder problem the following night. D'Alembert was impressed and recommended him for a teaching place in the Ecole Militaire."]
At twenty three years old, Laplace got his first Memoir [scientific article] published in the Memoirs of the Academy at Turin. Following that one, he wrote many more attacking the difficulties in Newton's theory of gravity as an explanation of the movement of the solar system. Like his contemporary Joseph-Louis Lagrange, he tackled theoretical problems that required great analytical skill. The scientific world was riveted on the discoveries made by Laplace and Lagrange. [Laplace also collaborated with the French chemist Antoine Lavoisier on a Memoir about Heat and molecular motion.]
Pierre-Simon Laplace's most famous work is "Mecanique Celeste." ["Celestial Mechanics" in five volumes; there may be an English translation online at archive.org. Nathaniel Bowditch published an English version with his own annotations!] In this work Laplace laid out a comprehensive attempt to apply Isaac Newton's principles in even more detail than Newton ever did. Once Newton hit upon the idea of gravitation, he had to invent the mathematics to apply it to the way the celestial bodies move. But in the fifty years since Newton had died, mathematics had come a long way. The branch of mathematics that Newton had developed -- called infinitesimal calculus -- had become much more accurate, so that Laplace could calculate more efficiently than Newton had been able to. The geometry that Isaac Newton used did a good job demonstrating general tendencies of forces and explaining things that influence the orbits of celestial bodies -- but it couldn't deal with gravity's more subtle effects. The influence that one planet can have over the orbit of another planet requires much more analytical methods of calculation.
In his "Mecanique Celeste," Laplace tried to unravel the mysteries of the heavens using Newton's mathematics with the improvements from a couple of generations of mathematicians. His book is extremely difficult to understand because the subject is so complex, and it takes a considerable amount of mathematical ability to make sense of his points. His writing style is also difficult to follow and he leaves gaps in his explanations that are hard for readers to fill in. Laplace often writes that it's 'easy to see' how one step follows another -- but it isn't. Even excellent mathematicians have had a hard time grasping his train of logic. They say that there were times when Laplace was giving a lecture, and when he came to a place where his book had said a point was 'easy to see,' even he himself would have to think for an hour or two to remember his train of reasoning! Yet certain parts of his book are enthusiastically admired by mathematicians. He invented entire branches of science, some of which were expanded by later scientists studying nature.
If there's any flaw with Laplace's work, it's a moral oversight rather than an error in data. Laplace and Lagrange made progress at the same rate as they both investigated the mechanics of how celestial bodies move. Sometimes they were even studying the exact same problem at the same time using identical research methods. Sometimes Lagrange found the solution first. Sometimes it was Laplace. It would be difficult to sort out which contributions to astronomy were made by which of them. But Laplace failed to acknowledge Lagrange's contributions, or any of the other mathematicians who advanced our understanding of the heavens -- except Isaac Newton. Anyone reading the "Mecanique Celeste" would have no way of knowing whether the discoveries he read about were made by Pierre-Simon Laplace, or Joseph-Louis Lagrange, or Leonhard Euler, or Alexis Clairaut. If a scientist today published a work that was dependent on the contributions of others and then neglected to acknowledge those others, he would be severely criticized and there would be bitter controversies. Perhaps things were done differently in his time and judging him by our standards is unfair. Or perhaps there's more to it than we're aware of. When two researchers are working on the same problem and constantly publishing their results, it's sometimes difficult for the researchers themselves to know who should be credited for which discoveries. Perhaps Laplace was diligently focused on devoting his time and energy on interpreting the secrets of nature using all the skill and resources available to him, and refused to let any side issues distract him. What if he couldn't bear to waste pages and time discussing who should be credited for each formula or idea? Maybe he was only concerned about providing a complete picture of celestial mechanics, and details about whose mathematics were used seemed so trivial in comparison that he didn't bother to relate them. Perhaps he was thinking, 'If Lagrange thinks I've used his data incorrectly, then he should do just what I did and write his own book. He's certainly talented enough, and he would be welcome to use any data I came up with just as I have used his. I would welcome such a contribution to the library of science. What difference does it make who contributed which mathematical formula?' That may indeed be his reasoning, because he and Lagrange remained the best of friends until death separated them -- and Laplace even gave the oration at Lagrange's funeral.
Laplace's work is too technical to explain in this book. But he did publish one book called 'Systeme du Monde' [The System of the World, you can view it online at archive.org] in which he was able to explain the basic theories of how celestial bodies move and some related discoveries without discussing the mathematics involved. This is the book that made his name known to people who are interested in astronomy but are not mathematicians. This is the book where he explains the Nebular Hypothesis [a model of cosmogony that hypothesizes that the solar system is formed of nebular material -- protosolar clouds that 'cooled and contracted, flattened and spun more rapidly, throwing off a series of gaseous rings of material.' From Wikipedia]. This is the most widely accepted theory among cosmologists.
The Nebular Theory explains how the sun ended up in the middle of the solar system, with the planets and their moons orbiting it. Laplace had noticed that all of the planets revolve in the same direction around the sun. He also noticed that each planet spins on its axis [or pole] in the same direction as its orbit around the sun, and moons circle their planets as satellites in that same direction. Even the sun itself rotates in the same direction, as if it was turning on an axis. Laplace recognized that this was remarkable, and his scientific mind reflected that this consistently uniform movement ought to be investigated. It was too coincidental for there to be no reason for it. To help us consider this idea, let's focus on three celestial bodies: the earth, the sun, and the moon. The earth travels around the sun in a certain direction, and it also rotates on its axis. The earth could have been spinning in the same direction as its orbit, but it could just as likely have been spinning in the opposite direction. But it just so happens that its orbit and its axis rotation are both going in the same direction. The moon orbits around the earth every month in the same direction -- and it turns on its axis in that same direction. So that's four movements, and they all happen to be going in the same direction -- which also happens to be the same direction in which the sun rotates every twenty five days. That's a pretty unlikely coincidence! There must be some physical reason for it. If someone were to toss a coin five times, it's unlikely that it would land on 'heads' five times in a row -- there's only a one in sixteen chance of that happening.
But there are more than three heavenly bodies in the solar system -- there are the great planets, Jupiter, Saturn, Mars, Venus, and Mercury, and their satellite moons. And every one of them orbits and spins on its pole in the same direction! If we just count the five planets Laplace knew about, plus the earth, and the sun, that makes six bodies orbiting, and seven bodies turning on an axis (the sun turns as if on an axis, but it doesn't make an orbit around anything). There are sixteen satellites orbiting their planets in the same direction. We haven't been close enough [in 1895] to see in what direction they're all spinning on their poles, but we can see in which direction they orbit around their planets. That makes thirty orbits and spins that Laplace could confirm -- and all were in the same direction! The chances of that happening randomly are about as unlikely as tossing a coin thirty times, and having it land on 'heads' all thirty times.
Statistically, the chances of that happening are one in five million. Laplace had studied the theory of probabilities, and he recognized that this couldn't be random. There must be some physical reason why everything is turning in the same direction. So he looked for some physical cause. That's how he came up with his Nebular Theory. If his theory was correct, it would explain why everything is turning in the same direction.
Imagine there was a huge mass of cloudy material that was so hot that anything it touched -- such as iron, nickel, oxygen, and other substances that make up the earth and other planets -- was suspended as vapor. That's not actually an unreasonable thing to suppose. In fact, we can see thousands of these kinds of nebulae through our modern telescopes. It's unlikely that this kind of cloudy mass could exist without being in some kind of turning motion. We've seen enough nebulae to confirm that a huge cloudy mass that isn't rotating would be extremely improbable. Imagine that the ages rolled on and the heat from our cloudy nebula mass was radiating away. According to well-known principles of physics, as the suspended vapor got cooler it began to bond together. Much of this material joined into a white hot giant mass with the uncondensed vapors hanging around it. There were also smaller masses forming around the large central mass. In the ages that it took during its cooling off period, the result was one large central mass with a few smaller masses surrounding it. All of them were still rotating, just as the original cloudy mass had been; now, the smaller masses were turning around the larger mass, all of them spinning on their axes and travelling around the main body, all in the same direction. The smaller masses had even smaller masses rotating around them, also rotating and spinning in the same direction.
Ages and ages went by. The heat from these masses gradually dissipated and the smaller masses blended together, first as hot molten globs, and then, as they cooled even more, into solid masses: planets. The huge mass in the center, being so large and taking longer to cool, was still white hot: a sun. In this way, Laplace was able to explain why the rotations of the celestial bodies are all going in the same direction. His account also explains some other things we've observed in the heavens, which seems to confirm his theory. In fact, the more we learn about astronomy, the more certain we are that Laplace's Nebular Hypothesis is the way our solar system came to be.
[Laplace married Marie-Charlotte de Courty de Romanges in 1788. They had two children. The MacTutor Online biography says, "Before the 1793 Reign of Terror Laplace together with his wife and two children left Paris and lived 50 km southeast of Paris. He did not return to Paris until after July 1794. Although Laplace managed to avoid the fate of some of his colleagues during the Revolution, such as Lavoisier who was guillotined in May 1794 while Laplace was out of Paris, he did have some difficult times."]
Pierre-Simon Laplace wanted to be involved in more than science, so he thought he would involve himself in public affairs. Napoleon recognized his genius and wanted him to serve him in his government, so he made him his Minister of the Interior in 1799 [in France, this position is somewhat like the US Attorney General and Secretary of Homeland Security; see more at Wikipedia]. But that didn't work out too well; Laplace was more suited to be a scientist than a statesman. Napoleon was disappointed with his inability at government administration, and decided after only six weeks that Laplace's mathematical mind might be better qualified for business management. So Napoleon made him chancellor of the Senate instead. Laplace accepted the honours Napoleon granted to him, but he wasn't very loyal: when Napoleon was beaten and the Bourbon nobility regained power, Laplace worked for them, too, and was even made a Marquis by King Louis VXIII. Pierre-Simon Laplace spent the last years of his life in the country at Arcueil, 3 miles outside of Paris. He continued to study, and lived a prudent, sober life that helped him avoid many of the infirmities of old age. He died at age 77, in March, 1827. His last words were, 'What we know is very little; what we don't know is immense.'
Comments
Post a Comment