## Posts Tagged ‘**quaternions**’

## “The Bible shows the way to go to heaven, not the way the heavens go”*…

Harmonia Macrocosmica(1660), an atlas of the stars from the Dutch Golden Age of cartography, maps the structure of the heavens in twenty-nine extraordinary double-folio spreads. We are presented with the motions of the celestial bodies, the stellar constellations of the northern hemisphere, the old geocentric universe of Ptolemy, the newish heliocentric one of Copernicus [as above], and Tycho Brahe’s eccentric combination of the two — in which the Moon orbits the Earth, and the planets orbit the Sun, but the Sun still orbits the Earth. The marginal area of each brightly coloured map is a hive of activity: astronomers bent over charts debate their findings, eager youngsters direct their quadrants skywards, and cherubs fly about with pet birds in tow…

More marvelous maps of the heavens at “The Celestial Atlas of Andreas Cellarius (1660)”

* Galileo (quoting a librarian at the Vatican)

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**As we look to the stars,** we might recall that it was on this date in 1843 that Sir William Rowan Hamilton conceived the theory of quaternions. A physicist, astronomer, and mathematician who made important contributions to classical mechanics, optics, and algebra, he had been working since the late 1830s on the basic principles of algebra, resulting in a theory of conjugate functions, or algebraic couples, in which complex numbers are expressed as ordered pairs of real numbers. But he hadn’t succeeded in developing a theory of triplets that could be applied to three-dimensional geometric problems. Walking with his wife along the Royal Canal in Dublin, Hamilton realized that the theory should involve quadruplets, not triplets– at which point he stopped to carve carve the underlying equations in a nearby bridge lest he forget them.