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Posts Tagged ‘square root of minus one

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.


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