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Social distancing and calculus.
Social distancing and calculus.
Isaac Newton was in his early 20s when the Great Plague of London struck. He was just another college student at Trinity College, Cambridge. As a form of social distancing, Cambridge sent all students home to continue their studies. For Newton, that meant Woolsthorpe Manor, the family estate about 60 miles northwest of Cambridge. The year-plus he spent away was later referred to as his annus mirabilis, the “year of wonders.” During this enforced leave of absence, it was said that he developed calculus at a rate in which a college student would learn calculus.
Principia Mathematica
Principia Mathematica
... is the greatest scientific publication of all centuries.
The book to read is not one that thinks for you
but one that makes you think.
(Harper Lee, author of "To kill a Mockingbird")
The book to read is not one that thinks for you
but one that makes you think.
(Harper Lee, author of "To kill a Mockingbird")
One must not confuse Isaac Newton's Principia Mathematica with the Principia Mathematica written by the famous philosophers Alfred North Whitehead and Bertrand Russell published in 1910. Whitehead and Russell's publication is a three-volume work on the foundations of mathematics and formal logic.
Sir Isaac Newton's Principia published in 1687
Isaac Newton's Principia was originally titled PHILOSOPHIAE NATURALIS PRINCIPIA MATHEMATICA and the title was translated into English as MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY. The term natural philosophy is to distinguish it as philosophy of the natural sciences as opposed to philosophy of the humanities.
The original Principia published in 1687 was in Latin. Andrew Motte translated Newton's Principia into English and published it in 1728. It remained the best known version in the English language. Motte version has a definitive and detail section on the life and time of Isaac Newton. This section although long is quite readable. You can download a free copy of Principia here from Academia.edu.
Edmond Halley of the famed Halley's comet went, to cambridge to see Newton about publishing his work. As son of a prosperous soapmaker and property owner, Edmond Halley offered to fund Newton's publication.
Newton showed that astronomical observations has proven the inverse square law of gravitation (to an accuracy that was high by the standards of Newton's time). Newton proposed for the first time that a body stays in constant motion unless acted on by an external force.
Since the time of Aristotle 5 thousand years earlier it has been accepted that a body eventually stops moving because it gets "tired". Newton's insight of a body staying in constant motion unless acted on by an external force, is monumental. The greatness of this scientific publication lies in Newton's laws of motion and theory of gravity underpin much of today's modern physics and engineering.
The beauty of Principia is that the thesis is based on a series of axioms. Each axioms is derived from elementary geometry. So if you have high school geometry you should be able to read and comprehend the Principia. Here is an excerpt from a page in Principia.
The thesis of Principia is based on a series of axioms. Each axioms is elementary geometry.
If you have high school geometry you should be able to read and comprehend the Principia. Here is an excerpt from a page in Principia.
The fastest trajectory going from A to a lower point B is not as one would intuitively think of as a straight line from A to B but a cycloid as indicated by the red line. This fastest trajectory is regardless of the mass of the body or the strength of the local gravitational pull. The trajectory is called the Brachistochrone curve. Watch the animation above.
This problem was first proposed by Johann Bernoulli. Yes, Johann is the brother of Daniel Bernoulli, the famed mathematician of the Bernoulli equation for fluid dynamics. Bernoulli initially allowed six months for the solutions with no takers even from most famous mathematicians. At the request of Leibniz, the time was later extended to a year and a half
On 29 January 1697 Newton returned at 4pm from working at the Royal Mint and found in his post the problems that Bernoulli had sent to him directly. Newton stayed up till 4am before arriving at a solution; on the following day he sent the solution to the Royal Society for anonymous publication. Although Newton's solution was anonymous, he was recognized by Bernoulli as its author; and Bernou came up with the famous phrase "tanquam ex ungue leonem" (we recognize the lion by his claw).
The brachistochrone curve is a cycloid. The problem can be solved using tools from the calculus of variations and optimal control.
Newton's Scientific Papers
Newton's Scientific Papers
When Newton died at age 84, he left no will. He left his enormous stack of scientific papers to John Conduitt – the husband of one of Newton’s half-nieces. These papers were inherited over generations. Eventually the papers ended up at Cambridge University Library and now available online at Cambridge Digital Library.
Here is an excerpt of a page from the Principia.
Here is an excerpt of a page from the Principia.
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