Tag Archives: Tycho Brahe

Geometry and the Cosmos (1) : Kepler, from polyhedra to ellipses


The regularity of so much celestial activity has led many cultures to base their models of the universe on concepts of order and harmony. Around the Mediterranean it was the Pythagoreans who first expressed the idea that the universe is characterised by proportion, rhythm and numerical patterns. Plato’s hypothesis was of an organised cosmos whose laws could be deciphered, explained in geometric terms.

The history of physics is nothing other than the story of man’s desire to uncover the hidden order and harmony of things. The most ambitious physicists have attempted to unify apparently discrete phenomena: Galileo with terrestrial and celestial laws; Newton with gravity and the movement of celestial bodies; Maxwell with magnetism and electricity; Einstein with space and time; today’s physists with gravitation and microphysics.

But, as Heraclitus said as long ago as 500 BC, “Nature loves to hide.” Indeed advances in geometry and mathematics have led to new theories of the cosmos which we are unable to comprehend. They provide only abstract images, which do not allow us to visualise the structure of atoms or the dynamics of space-time or the topology of the universe in any direct sense.

It is this fundamental belief in celestial harmony – for which successive generations have found various elaborate expressions: just proportion, equation of the part and the whole, symmetry, constancy, resonance, group theory, strings -that has underlain the development of physics for the past 2,500 years.

Melancholy, or the Spirit of Man in Search of the Secret of the Universe. This etching, dating from 1514 according to the numbers in the square in the top right corner, depicts man contemplating the nature of the world in a state of melancholy, which in medieval times was associated with black bile and with the planet Saturn. The winged man prefigures Johannes Kepler’s interrogations as he calculates how to express the underlying harmony of the cosmos using spheres and polyhedra. The bright light in the sky is the great comet that was observed in the winter of 1513-14. As it shines on the scales (depicting the astronomical sign Libra) it symbolises the end of an earthly cycle, if not the end of time itself. The ladder with seven rungs represents the belief held by the Byzantines that the world would not exist for more than seven thousand years. It is the end of the Middle Ages; Diirer (1471-1528) is to be one of the prime movers of the Renaissance.


Geometry and the Cosmos

“Geometry, which before the origin of things was coeternal with the divine mind and is God himself […], supplied God with patterns for the creation of the world.”
Johannes Kepler, The Harmony of the World, 1619.

The 17th century German astronomer Johannes Kepler was undoubtedly the first to integrate man’s fascination with harmony into an overall vision of the world which can properly be called scientific. For Kepler, as for the natural philosophers of ancient Greece, the cosmos was an organised system comprising the earth and the visible stars. His avowed intention was to investigate the reasons for the number and sizes of the planets and why they moved as they did. He believed that those reasons, and consequently the secret of universal order, could be found in geometry. Kepler wanted to do more than create a simple model or describe the results of his experiments and observations; he wanted to explain the causes of what he saw. This makes him one of the greatest innovators in the history of science and it led him in particular to formulate laws of planetary motion which are still valid today.

Despite his innovative methods, Kepler wrote two studies of the cosmos in the style of the ancient Greeks: Mysterium Cosmographicum (The Secret of the Cosmos) in 1596 and Harmonices Mundi (The Harmony of the World) in 1619. At this turning point between ancient and modern thinking Kepler was steeped in a tradition which connected cosmology explicitly with the notion of divine harmony. But what Kepler sought to express was not the numerical mysticism of the Pythagoreans; his starting point was geometric patterns, which he saw as “logical elements”. His profound desire to devise a rational explanation for the cosmos led him to establish procedures which resembled those of modern science. Continue reading

Willem Blaeu, a prolific cartographer and globemaker

Detail of a geographic map by W. Blaeu
A portrait of W. Blaeu by Jeremias Falck, engraving from the Digitale bibliootheek voor de Nederlandse letteren.

Willem Janszoon Blaeu (1571-1638) founded one of history’s greatest cartographic publishing firms in 1599. Mostly renowned as a cartographer, he also made terrestrial and celestial globes, various instruments such as quadrants, a planetarium and a tellurium. He invented mechanical devices for improving the technics of printing. As an astronomer, a former student of Tycho Brahe, Willem Blaeu made careful observations of a moon eclipse, he discovered a variable star now known as P Cygni, and carried out a measurement of a degree on the surface of the earth (as his countryman Snell did in 1617).


The Blaeu family has its origin in the island of Wieringen, where about 1490, Willem Jacobszoon Blauwe – the grandfather of Willem – was born. From his marriage with Anna Jansdochter sprang six children. The second son, Jan Willemsz. (1527- before 1589) was the father of Willem Blaeu, and continued the family tradition by practicing the prosperous trade of herring packer. From his second marriage with Stijntge, Willem Jansz. Blaeu was born at Alkmaar or Uitgeest.

At an early age, Willem Blaeu went to Amsterdam in order to learn the herring trade, in which he was destined to succeed his father. But Willem did not like this work very much, being more inclined to Mathematics and Astronomy. He did not attend a university and worked first as a carpenter and a clerk in the Amsterdam mercantile office of his cousin Hooft.

Tycho Brahe and assistants making an astronomical observation at Uraniborg

However, in 1595 he became a student of Tycho Brahe (1546-1601). The celebrated Danish astronomer demanded a high standard of his pupils. Some were invited by him, others were undoubtedly taken on special recommendation. We may therefore presume that young Blaeu had reached a good standard of education and technical skill, since he was considered worthy to become a student of the great astronomer. Blaeu lived on the Island of Hven over the winter of 1595/1596, at Brahe’s famous observatory in Uraniborg. Thanks to this exact knowledge acquired from Brahe, Blaeu was able to make tables for sun declination ; especially he also learned from Brahe to make globes and instruments like the quadrants.

As it is well-known, Tycho Brahe had his own cosmic system, a sort of compromise between the Ptolemaic and Copernican. Willem Blaeu, although a supporter of the Copernican system, remained cautious during the rest of his career. In his books he mentioned the Copernican model as one of the existing theories, besides the Ptolemaic and Tychonic. It will not only save him for confrontations with religious people, but this attitude was also beneficial for his sales.

The Tychonic system of the world depicted in Andreas Cellarius atlas “Harmonia macrocosmica” (1660).

 After his return from Hven in 1596, Blaeu settled in Alkmaar. Very little is known of his stay here. He married, probably in 1597, Marretie or Maertgen, daughter of Cornelis from Uitgeest. Here too, his eldest son Joan was born. Continue reading