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…
The Northern Stellar Hemisphere of Antiquity
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.
“Oh, there you are Peter”*…
The missing links between galaxies have finally been found. This is the first detection of the roughly half of the normal matter in our universe – protons, neutrons and electrons – unaccounted for by previous observations of stars, galaxies and other bright objects in space.
You have probably heard about the hunt for dark matter, a mysterious substance thought to permeate the universe, the effects of which we can see through its gravitational pull. But our models of the universe also say there should be about twice as much ordinary matter out there, compared with what we have observed so far.
Two separate teams found the missing matter – made of particles called baryons rather than dark matter – linking galaxies together through filaments of hot, diffuse gas…
Get galactic at: “Half the universe’s missing matter has just been finally found.”
* meme
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As we heed E.M. Forster, 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.
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