Posts Tagged ‘Newton’
Pictures worth a million words…
In his great opus De Revolutionibus Orbium Coelestium published shortly before his death in 1543, Copernicus takes 405 pages of words, numbers and equations to explain his heliocentric theory. But it is the diagram that he draws at the beginning of the book that captures in a simple image his revolutionary new idea: it is the Sun that is at the centre of the Solar System, not the Earth.
A diagram has the power to create a whole new visual language to navigate a scientific idea. Isaac Newton’s optics diagrams [Opticks, 1704] for example transform light into geometry. By representing light as lines, Newton is able to use mathematics and geometry to predict the behaviour of light. It was a revolutionary idea.
Mathematicians had been struggling with the idea of the square root of minus one. There seemed to be no number on the number line whose square was negative. Experts knew that if such a number existed it would transform their subject. But where was this number? It was a picture drawn independently by three mathematicians at the beginning of the 19th Century that brought these numbers to life. Called the Argand diagram after one of its creators, this picture… was a potent tool in manipulating these new numbers [Imaginary Numbers] since the geometry of the diagram reflected the underlying algebra of the numbers they depicted.
Although better known for her contributions to nursing, Florence Nightingale’s greatest achievements were mathematical. She was the first to use the idea of a pie chart to represent data. Nightingale’s diagrams were designed to highlight deaths in the Crimea. She had discovered that the majority of deaths in the Crimea were due to poor sanitation rather than casualties in battle. She wanted to persuade government of the need for better hygiene in hospitals. She realised though that just looking at the numbers was unlikely to impress ministers. But once those numbers were translated into a picture – her “Diagram of the Causes of Mortality in the Army in the East” – the message could not be ignored.
Read more (and find links to enlarged versions of the images above) at BBC.com, in “Diagrams that Changed the World,” a teaser for new BBC TV series, Marcus du Sautoy’s six-part The Beauty of Diagrams (on air now, and available via iPlayer to readers in the U.K… and readers with VPNs that can terminate in the U.K.)
As we marvel at the power of pictures, we might recall that it was on this date in 1997 that eight planets in our Solar System lined up from West to East– beginning with Pluto, followed by Mercury, Mars, Venus, Uranus, Neptune, Saturn and Jupiter, with a crescent moon alongside– in a rare alignment visible from Earth. Mercury, Mars, Venus, Jupiter and Saturn were visible to the naked eye; the small blue dots that are Uranus and Neptune, with binoculars. Pluto was visible only by telescope (but has subsequently been demoted from “planet” anyway…). The planets also aligned in May 2000, but too close to the sun to be visible from Earth.
Readers who missed it have a long wait for the reprise: it will be at least another 100 years before so many planets will be so close and so visible.
Adventures in the Counterintuitive…
Your correspondent is headed away for a week or so, ranging more then ten times zones from home– the current limit to continuous timely posting of (R)D… So, while regular service will resume on-or-around the 20th, a little something to keep one occupied:
Readers will recall that, on the occasion of an earlier hiatus, your correspondent wheeled out “the Monty Hall Problem” (c.f., “Riddle Me This” and “Birdbrains“). This time, with thanks to Prof. Stan Wagon at Macalester College:
Alice and Bob face three doors marked 1, 2, 3. Behind the doors are placed, randomly, a car, a key, and a goat. The couple wins the car if Bob finds the car and Alice finds the key.
First Bob (with Alice removed from the scene) will open a door; if the car is not behind it he can open a second door. If he fails to find the car, they lose. If he does find the car, then all doors are closed and Alice gets to open a door in the hope of finding the key and, if not, trying again with a second door.
Alice and Bob do not communicate except to make a plan beforehand. What is their best strategy?
Source: A. S. Landsberg (Physics, Claremont Colleges, California), Letters, Spring 2009 issue of The Mathematical Intelligencer.
The answer is here— and more nifty puzzles, here.
As we craft our own strategies, we might solve a memorial problem for Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet, the French mathematician and physicist who is probably better known as Voltaire’s mistress; she died on this date in 1749. Fascinated by the work of Newton and Leibniz, she dressed as a man to frequent the cafes where the scientific discussions of the time were held. Her major work was a translation of Newton’s Principia, for which Voltaire wrote the preface. The work was published a decade after her death, and was for many years the only translation of the Principia into French.
Judge me for my own merits, or lack of them, but do not look upon me as a mere appendage to this great general or that great scholar, this star that shines at the court of France or that famed author. I am in my own right a whole person, responsible to myself alone for all that I am, all that I say, all that I do. it may be that there are metaphysicians and philosophers whose learning is greater than mine, although I have not met them. Yet, they are but frail humans, too, and have their faults; so, when I add the sum total of my graces, I confess I am inferior to no one.
– Mme du Châtelet to Frederick the Great of Prussia
Waldo, found…
©2009 ~sfumato21
(via Daily What)
As we call off the dogs, we might recall that it was reputedly on this date in 1675 that Gottfried Wilhelm von Leibniz first used the “long s” as the integral symbol in calculus:
It was understood to be Leibnitz’s co-option of the Latin “summa.”
When Newton and Leibniz first published their versions of calculus (in the late 1680s), there was tremendous controversy over which mathematician (and therefore which country, England or Germany) deserved credit. Newton derived his results first, but Leibniz published first. The prickly Newton claimed Leibniz had stolen ideas from Newton’s unpublished notes, which Newton had shared with a few members of the Royal Society; a bitter argument ensued, dividing English-speaking mathematicians from continental mathematicians for many years– much to the detriment of English mathematics. A careful examination of the papers of Leibniz and Newton has convinced scholars that the two arrived at their results independently, with Leibniz starting with integration; and Newton, with differentiation. It was the symbolically-gifted Leibniz, however, who gave this new branch of mathematics its name. Newton called his version of calculus the “the science of fluxions”… One shudders to imagine that on one’s textbook (or in the mouths of schoolchildren…)
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