3 ms·

It's too bad Newton wasn't as succinct.

by mbm 16y ago

korch 16y ago
While that seems like a bad idea now, there's a very necessary reason for Newton doing it that way. Newton presented Calculus exclusively in the more complex language of Euclidean geometry in order for it to be taken seriously by the intelligentsia, the royalty, and clergy of the era, as well as to make a bold statement about the historical magnitude of his discovery. In that era, Euclid and Newton were the book ends bounding all that was known of mathematics and natural philosophy(proto-science). So of course he had to write it the same way way Euclid would. Euclid's manner of logic and geometrical reasoning was lauded and unchallenged by both the church and the king, so there would be no way to refute a proof built upon the same language. I think there are two levels of refutations which Newton was guarding against. First, it's the typical peculiar trait of mathematicians to achieve perfectionism in a proof. The margin for error is zero-it's either all right or it's all wrong. Everything you are working on is either the most important thing in the world, or utterly worthless folly. So it's a point of immense personal pride to present a work that is complete, irrefutable, and entirely self-consistent. Second, considering the political & religious climate of the time, had Newton shown calculus without Euclid, the religious implications could have easily blown up into a scandal because his physics starts the ball rolling in formally challenging several major foundations of Christian theology. If you consider that Newton and all professors of the era at Cambridge had to be approved as official clergy in the Church of England, so his job and his future career success would depend highly on not outraging his superiors. Many men who spark revolutions by challenging ancient power structures end up tragic martyrs. But Newton navigated that problem with equal mastery. He ended up the Master of the Mint, was elected to parliament, grew immensely wealthy, had the ear of the Queen, and became so famous that visiting foreign celebrities would mark him as the first person to visit upon arriving-even before the Queen! For many decades after the publication of the Principia, Newton in fact concealed the derivation of the calculus using mathematical terminology we would now easily recognize as being similar to our own. But he did write it all down, he just never published it. There's an interesting story about this manuscript. Newton's friend, the secretary of the Royal Society kept this paper in safekeeping and private. Leibniz once visited England before he was famous and influential, and Leibniz knew Newton's secretary and visited him in London. The secretary allowed Leibniz to read Newton's private manuscript, describing the derivation of calculus, which no other people had ever seen. Not too much later, after Leibniz returned to the continent, he published his own book demonstrating calculus. Newton recognized the plagiarism, Leibniz denied it, and they maintained an intense personal feud for the next 40 years.
nitrogen 16y ago
There is another post in response to this comment containing four full paragraphs explaining why Newton wasn't succinct, but the post is now marked as dead. If anyone familiar with the Leibniz vs Newton history wants to turn showdead on in their HN settings and read the post, I'd appreciate commentary on its accuracy and origins (and, perhaps, an explanation of why it was killed).
- riffraff 16y ago
  I'll taks a stab at guessing the killing: parent^2 was being facetious and a lengty serious answer was not considered appropriate. I am mostly guessing though, and I don't think it should have been killed.
- mhartl 16y ago
  Based on my reading of Jim Gleick's biography Isaac Newton and my background as a theoretical physicist, I believe your comment is essentially accurate. In particular, Newton's desire to connect calculus with Euclidean geometry is certainly correct. As you note, the Principia eschews calculus in favor of geometric arguments: Newton used calculus for his private calculations and then translated the results into more conventional geometry to meet his audience's expectations. I'm not sure about the religious aspect, but Newton was privately a heretic (he believed in a unitary god—an awkward belief for a professor at Trinity College), so he definitely knew how to placate the religious authorities. Finally, the Leibniz anecdote is new to me, but it sounds plausible. In any case, I don't think your comment should have been killed.
  - nitrogen 16y ago
    I believe your comment is essentially accurate. I can't take credit for the comment. It was posted by HN user korch. I only wanted to know if it was correct.

It's too bad Newton wasn't as succinct.

by mbm 16y ago

It's too bad Newton wasn't as succinct.

korch 16y ago

While that seems like a bad idea now, there's a very necessary reason for Newton doing it that way. Newton presented Calculus exclusively in the more complex language of Euclidean geometry in order for it to be taken seriously by the intelligentsia, the royalty, and clergy of the era, as well as to make a bold statement about the historical magnitude of his discovery. In that era, Euclid and Newton were the book ends bounding all that was known of mathematics and natural philosophy(proto-science). So of course he had to write it the same way way Euclid would. Euclid's manner of logic and geometrical reasoning was lauded and unchallenged by both the church and the king, so there would be no way to refute a proof built upon the same language. I think there are two levels of refutations which Newton was guarding against. First, it's the typical peculiar trait of mathematicians to achieve perfectionism in a proof. The margin for error is zero-it's either all right or it's all wrong. Everything you are working on is either the most important thing in the world, or utterly worthless folly. So it's a point of immense personal pride to present a work that is complete, irrefutable, and entirely self-consistent. Second, considering the political & religious climate of the time, had Newton shown calculus without Euclid, the religious implications could have easily blown up into a scandal because his physics starts the ball rolling in formally challenging several major foundations of Christian theology. If you consider that Newton and all professors of the era at Cambridge had to be approved as official clergy in the Church of England, so his job and his future career success would depend highly on not outraging his superiors. Many men who spark revolutions by challenging ancient power structures end up tragic martyrs. But Newton navigated that problem with equal mastery. He ended up the Master of the Mint, was elected to parliament, grew immensely wealthy, had the ear of the Queen, and became so famous that visiting foreign celebrities would mark him as the first person to visit upon arriving-even before the Queen! For many decades after the publication of the Principia, Newton in fact concealed the derivation of the calculus using mathematical terminology we would now easily recognize as being similar to our own. But he did write it all down, he just never published it. There's an interesting story about this manuscript. Newton's friend, the secretary of the Royal Society kept this paper in safekeeping and private. Leibniz once visited England before he was famous and influential, and Leibniz knew Newton's secretary and visited him in London. The secretary allowed Leibniz to read Newton's private manuscript, describing the derivation of calculus, which no other people had ever seen. Not too much later, after Leibniz returned to the continent, he published his own book demonstrating calculus. Newton recognized the plagiarism, Leibniz denied it, and they maintained an intense personal feud for the next 40 years.

nitrogen 16y ago

There is another post in response to this comment containing four full paragraphs explaining why Newton wasn't succinct, but the post is now marked as dead. If anyone familiar with the Leibniz vs Newton history wants to turn showdead on in their HN settings and read the post, I'd appreciate commentary on its accuracy and origins (and, perhaps, an explanation of why it was killed).

riffraff 16y ago
I'll taks a stab at guessing the killing: parent^2 was being facetious and a lengty serious answer was not considered appropriate. I am mostly guessing though, and I don't think it should have been killed.
mhartl 16y ago
Based on my reading of Jim Gleick's biography Isaac Newton and my background as a theoretical physicist, I believe your comment is essentially accurate. In particular, Newton's desire to connect calculus with Euclidean geometry is certainly correct. As you note, the Principia eschews calculus in favor of geometric arguments: Newton used calculus for his private calculations and then translated the results into more conventional geometry to meet his audience's expectations. I'm not sure about the religious aspect, but Newton was privately a heretic (he believed in a unitary god—an awkward belief for a professor at Trinity College), so he definitely knew how to placate the religious authorities. Finally, the Leibniz anecdote is new to me, but it sounds plausible. In any case, I don't think your comment should have been killed.
- nitrogen 16y ago
  I believe your comment is essentially accurate. I can't take credit for the comment. It was posted by HN user korch. I only wanted to know if it was correct.