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October 12, 2003

The Old Master's last laugh

Johannes Kepler has a good a claim as anyone to be the father of empiricism. He was the first to formulate scientific "laws" based on rigorous observation (e.g. Planets travel in ellipses- based on Brahe's meticulous observations of Mars' orbit).

His first book, the Mysterium Cosmographicum, published at age 25 in 1596, singehandedly makes the transition from ancient metaphysical speculation to modern empirical science.

Kepler first posits the idea that the universe is built around the Platonic solids-which form its invisible skeleton, i.e. the five Platonic solids comprise the five intervals between the then known six planets. Illustrations from the work are here (scroll down).

Kepler noted the exact date this flash of insight came to him (July 9, 1595) and as one biographer states: "it determined the course of life, and remained his main inspiration throughout it."

But that was the ancient metaphysics-Kepler later goes on to state: "If [the observations] do not confirm the thesis, then all our previous efforts have been in vain." And modern empirical science is away and running.

Historians of science have noted the falseness of Kepler's inspiration, which nevertheless paved the way for the formulation of his groundbreaking laws. E.g. Koestler writes in The Sleepwalkers: "For Kepler's misguided belief in the five perfect bodies was not a passing fancy, but remained with him, in a modified version, to the end of his life, showing all the symptoms of a paranoid delusion."

How much we have yet to learn from the old masters.

Catching up on the science news of the week, I note that the October 9 issue of Nature features an article entitled: "Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background."

If you're sort of out to lunch-a dodecahedron is a...yep... a Platonic solid!

The gist of it is that observations by NASA's Wilkinson Microwave Anisotropy Probe (WMAP), launched in 2001 to measure temperature ripples in the afterglow radiation from the big bang, have caused Weeks and his colleagues to posit that "space wraps back on itself in a bizarre way... Effectively, the universe [is] like a hall of mirrors, with the wraparound effect producing multiple images of everything inside... According to Weeks, the WMAP results point to a very specific illusion- that our universe seems like an endlessly repeating set of dodecahedrons, football-like shapes with a surface of 12 identical pentagons...If you exit the football through one pentagon, you re-enter the same region through the opposite face and you keep meeting the same galaxies over and over again."

In other words, one of the galaxies in the Hubble Deep Field may be the Milky Way? weird whacky stuff- anyway, i hope they give a shout out to Johannes.

Could Kepler's flash of insight in 1596 be confirmed (to an extent-I won't get carried away) by a 2001 space probe? And what does that portend for what is really the source of scientific knowledge and discovery?

Posted by martin at 02:15 PM




1) don't forget galileo.

2) and of course, don't forget sextus empiricus-though yeah, he wasn't the father of modern empiricism....

3) a title that often goes to francis bacon.... (in the context of science)

Posted by: razib at October 12, 2003 02:25 PM


As I said Kepler has as good a claim as any of the above. I'm partial to the man, if you couldn't tell.

Posted by: martin at October 12, 2003 02:37 PM


I read something, maybe in the Scientific American, about Kepler's methods. Apparently Kepler's analysis of Brahe's data required hundreds of pages of advanced mathematical calculations. The man was a human computer.

Ulugh Beg, d. 1449, a grandson of Tamerlane, ruler of Samarqand, was highly honored by European astronomers, who relied upon his observations (correcting Ptolemy) for a period; as I understand, Brahe built on his work. He tended to be was a secular and perhaps should be the hero for Green modernists.

Posted by: Zizka at October 12, 2003 06:06 PM


More on Ulugh Beg. He inherited Tamerlane's throne from his father Shah Rukh, but only held it for two years because his son had him beheaded (perhaps for impiety?) His grandson was Babur, the Moghul founder.

Below is from the Wikipedia, which is not necessarily accurate. It seems to be based on the legendary 1911 Encyclopedia Brittanica, however.

http://en.wikipedia.org/wiki/Ulugh_Beg

Posted by: Zizka at October 12, 2003 06:14 PM


This may have been obvious to everyone else, but I was taken aback when dodecahedrons were described as "football shaped". Oh--British article--they're talking about about what I'd call a soccer ball. Of course, even that isn't very accurate, but it's not quite as wrong.

Posted by: Nancy Lebovitz at October 13, 2003 06:35 AM


You're right Nancy. What struck me as odd is that you'd think anyone interested enough to read the article wouldn't require a dodecahedron explanation, much less an inexact one.

Posted by: martin at October 13, 2003 08:38 AM


So now, instead of gravity waves, or wormholes, or hyperspace, our heroes will pass thru Keplerian dodies to get to where the action is.

Posted by: triticale at October 13, 2003 09:48 AM


The popular articles are a little misleading, because it's not the universe is "dodecahedron shaped" or anything like that, it's that *any* finite 3-dimensional space without a boundary can be described topologically in terms of some polyhedron with its faces identified with each other. In a similar way, any finite 2-dimensional surface can be described topologically as a polygon with its edges connected...here's an article that shows this representation for two different 2-D surfaces, a torus and a Klein bottle:

http://www.jcu.edu/math/vignettes/Mobius.htm

And this article talks more about how the same idea can be used with the faces of a polyhedron to identify the topology of a finite 3-D space:

http://www.mathsci.appstate.edu/~sjg/class/1010/wc/geom/universe2a.html

Anyway, the key is that this is just a mathematical technique for identifying topology, people shouldn't be surprised that the universe is described as being made up of dodecahedrons rather that some curvier or more irregular shape.

Posted by: Jesse at October 13, 2003 10:35 AM