Sky's Dark Labyrinth (5 page)

‘Enough Jepp, leave him be,' called Tycho.

After a moment, the dwarf's posture relaxed and he retreated to the edge of the table. But at the last moment, he lunged back in Kepler's direction. Instinctively Kepler pushed himself away. The rear legs of his chair caught on the lip of a flagstone, and Kepler tipped over, cracking his head. Jepp perched on the edge of the table, watching his victim.

The guests roared with laughter. Jepp somersaulted from the table into the middle of the room and bowed, drawing more howls of delight from the onlookers. Shaking with humiliation, Kepler turned towards his host. The great Tycho Brahe was looking back, roaring with laughter.

Each evening, the assistants met to discuss the coming night's work. They stood in a huddle and listened as Tycho informed them of their priorities and the division of labour. Once the programme of work was clear to everyone, they wrapped themselves in heavy capes and set off up the staircase. Their robes bestowed the illusion of priests ascending to worship the heavens.

Kepler stayed on the outskirts of the discussion and was assigned to help Longomontanus. ‘I had not anticipated taking part in the observing,' he whispered to his room-mate. ‘I'm inadequately clothed.'

‘I have a spare cloak you may borrow.' They detached themselves from the procession and headed for their room. Once there, Longomontanus opened a cupboard and handed over a
musty-smelling
garment. Kepler swung it around himself. A clear foot of material pooled on the floor.

‘You will be the warmest of us all,' grinned Longomontanus.

When they arrived on the roof, the great nocturnal beast of the observatory was stirring into action. A dozen shadowy figures moved between the silhouettes of the instruments, preparing them for the night's observing. During the day, the devices had been clamped rigid; now they were set free with the turn of fist-sized screws. Agog, Kepler watched the shadowplay; it was as beautiful as a dance. The operators merged with their mechanisms, each contributing to the
choreography
. An armature glided up a curving frame; a semicircular
framework
rotated into place; a triangular chassis tilted like an eagle catching an updraft. He followed the line of the instrument upwards, marvelling at the glittering stars.

Kepler thought briefly of his own hopeless attempts at coaxing the sky out of its secrets back in Graz. He had built a mound of earth on which to rest a lashed-up cross-staff of wood – and he had dreamed of measuring the parallax like that. What a fool he had been.

Below the insulation of the night sky, all dreams seemed real but all fears were magnified too. ‘I have something else to tell you,' he said to Longomontanus's shadowy face. ‘I'm not a good observer. I have tried, but my eyes are weak; the result of smallpox when I was a child.'

Longomontanus handed him the observing logbook. ‘Then you will be my amanuensis, and no one need know.'

The Dane unlocked the giant sextant and swung it towards Deneb, their reference star for the first half of the night. They were to measure the angles between it and its neighbours to map that section of the sky.

Each star would be observed over and over again to check the
accuracy
, not just tonight but on different nights by different observers and using different instruments. Then all the results would be used to calculate a definitive position for it on the celestial dome.

On a night like this, with no moon, it was so dark that the assistants used specially made candleholders mounted on poles and lines to see what they were doing. Longomontanus held his own cylinder of smoked glass close to the etched scale on the sextant and read out the coordinates for Kepler to scribble down.

Around them, soft voices uttered other numbers, and there was the occasional squeak of a metal joint as the contraptions were turned from one target to the next.

Tycho would intermittently appear from below to check on progress, dressed only in his everyday attire despite the cold. He squeezed his bulk around the overcrowded rooftop, breathing out wine fumes and occasionally supplanting an assistant to bellow out a reading himself. After the third such round, Kepler realised this was Tycho's way of helping.

When one of the quadrants over near the castellations jammed, Tycho yanked on it, creating a squeal of metal that set everyone's teeth on edge. ‘We will grease it in the morning. Proceed as best you can for now,' he said, disappearing back into the castle below.

‘You were with Tycho on Hveen Island, were you not?' asked Kepler.

‘Yes.' Longomontanus repositioned the sextant and drew his bead along the instrument at the next target star.

‘Tell me, was it always like this?'

‘Like what?'

‘Chaos.'

Longomontanus smiled in the dark. ‘The Master has mellowed with age. On Hveen we lived with an elk for company. It was allowed to roam the corridors and feed from our tables. On cloudy nights, the drinking would go on until dawn, and the elk would drink with us.'

‘Yet still you managed to work?'

‘And how we worked. Wait until you see the ledger room: pages and pages of raw measurements – a vast archive – most of it just waiting to be converted into useable coordinates. I guess that is what the Master wants you for.'

‘The planets too?'

‘The Master has data for ten oppositions of Mars, stretching back over twenty years.'

Kepler's breath quickened. ‘With those riches it would surely be possible to compute the orbit of Mars within … within eight days!'

Longomontanus chuckled. ‘You make me feel like the wise old man, though I can scarcely be more than five years ahead of you. I have worked with the data for a long time. It is not as easy as you assume. I can reproduce the latitudes at opposition but not the longitudes.'

‘Let me help you. Together, let us dethrone Mars from its position as confounder of astronomers. Let us bring it to heel and claim the gold of Egypt! Once we have Mars in yoke, so our method will harness the other planets too.'

Longomontanus eyed Kepler, his face sceptical.

‘It's true,' continued Kepler. ‘Mars shows the greatest differences in her speed. Determine why these differences occur and the other planets will tumble at our feet. Do you use an equant in your calculations?'

‘Of course, and a deferent too.'

‘I have my doubts about them. They're only needed if we assume each planet moves with constant speed. But what if they move with different speeds in different parts of their orbits?'

‘Now you're being fanciful. How can the planets speed up and slow down? Do the angels that move them become fatigued?'

‘I don't believe that the planets are moved by celestial intelligences within the heavenly spheres; I believe they're moved by a motive power coming from the Sun. The further this force reaches into the void, the weaker it gets. So, the further a planet's distance, the slower the planet is driven to move.'

Longomontanus's mouth dropped. He checked that the others on the roof were not listening. ‘No celestial intelligences? It's as well you're not in Rome. They would burn you for that – you've heard about Giordano Bruno, I take it? Where is God in your blasphemous design?'

‘God's seat is the Sun, at the centre of creation. No blasphemy there.'

‘You remove him from the fixed stars of Heaven and place him at the centre of things, where damnation lies. You turn the universe on its head and say there is no blasphemy. Are you mad? There is no evidence that the Earth is moving. Tycho's arrangement is the only one that makes sense.'

‘You mean that Mercury and Venus orbit the Sun, while the Sun and the other planets orbit Earth.'

‘Yes, it's the only system that takes into account all the
observations
.'

‘It's not elegant enough. All I need is sight of the measurements and I can correct the Copernican system. First, I will solve Mars and prove that it orbits the Sun. Show them to me.'

Longomontanus turned back to the sextant. ‘I cannot – even if I wanted to. The measurements are the jewels of this castle and kept under lock and key.'

‘Astronomy is not like ironmongery where one man makes
horseshoes
and another gateposts. We are a brotherhood, spread across Europe, all searching out the secret of the cosmos. We should share.'

‘It's beyond my authority. I value the Master's trust above all else. Now, we must get on, there's a lot to do.'

There was a pause between them.

‘Very well, but if you cannot help me, at least tell me what I must do to gain Tycho's trust?'

Longomontanus sighed. ‘First, you must believe in the Tychonic arrangement of planets – not the Copernican one – and, second, you must work with him unswervingly for half a lifetime.'

Morning light fell through the domed skylight, striking a great brass globe that shone as though the smith and his polishing cloth had not one moment ago left the room. From the globe, the light bounced off to create golden murals around the circular chamber.

At sight of the monument, Kepler's stifled yawns vanished. He circled the globe with his mouth parted in awe. Drilled into the metal were a multitude of small holes around which were etched the figures of the zodiac and other constellations: the twins of Gemini with their
backs turned in disdain to Cancer's nipping pincers; Orion standing proud in the opposite hemisphere to his nemesis, Scorpio. But it was the dots that truly caught Kepler's attention. He reached out to touch them, as if feeling the indentations would make them more real.

‘One thousand stars.'

Kepler jumped. Tycho was inching into the lobby.

‘Each one drilled into its precise position. The positions
accumulated
over decades, measured by my own instruments. Let no one tell you that I don't know what to do with my observations.'

Kepler felt his cheeks colour and he turned back to the globe. ‘I had once thought to fashion my own contribution to astronomy in metal.'

‘How so?'

‘I convinced the Duke of Württemberg to commission a model of the universe for his court, based upon my nested arrangement of the perfect solids.'

‘Ah, the central premise of your
Mysterium
.'

Kepler nodded. His epiphany had occurred in Graz, back in the lofty rooms of the Stiftschule where he taught geometry. Chalk squeaking on the board one day, Kepler drew a circle, then enclosed it with a triangle so that the midpoints of each straight line just touched the circle. Finally he drew a larger circle, its circumference touching each of the triangle's three points.

‘In this arrangement,' he explained to the usual handful of students, ‘the radius of the outer circle is twice that of the inner circle …'

That was when it hit him so clearly. It was as if this piece of
knowledge
had been woven into his soul since the moment of his birth, waiting to be remembered.

According to Copernicus, Saturn lay twice as far from the Sun as Jupiter – exactly the same ratio as the two circles separated by a triangle. Had God used such geometrical shapes as the invisible scaffolding to hold the planetary spheres in place? If so, the orbital distances of the other planets could be similarly derived by placing other shapes between them.

It had always struck him as curious that the planets were not uniformly spread throughout space. This could be the answer.

All summer he set about furious calculation. At the conclusion of his toil, he discovered that the best arrangement was to use
three-dimensional 
shapes: a cube between Saturn and Jupiter, a pyramid between Jupiter and Mars, a dodecahedron between Mars and Earth, an icosahedron between Earth and Venus, and finally an octahedron between Venus and Mercury – and all of them centred on the Sun.

Plato had declared these shapes perfect because of the way they were constructed using precise geometrical rules. And Kepler thought he had found them mirrored in the stars, holding the planets apart. With his tutor's begrudging help at Tübingen, Kepler had published a book,
Mysterium Cosmographicum
, to announce his idea to the world. Then he set about constructing it in silver and that was when the problems began.

He explained to Tycho: ‘Different silversmiths would make the various components so that no one would be able to steal the secret of the universe before it was assembled at Court. Each planetary frame would be hollow and contain a drink to be dispensed through taps at the edges of the model: brandy from Mercury, mead from Venus, strong vermouth from Mars, and a delicious new white wine from Jupiter. I even suggested that Saturn's cup should be filled with a bad red wine, so that we could ridicule those ignorant of the planet's bitter qualities.'

The old man slapped his meaty thigh in appreciation. ‘What happened?'

This was the moment when Kepler regretted starting the story. ‘It wouldn't fit together. What I thought were trivialities in the
computations
proved impossible for the craftsmen to interpret. That's how I knew I needed more precise measurements to refine my calculations.'

‘And so you wrote to me.'

‘Yes, sir.' Kepler felt transparent.

‘Did it occur to you that your model did not fit because it was wrong?' Tycho's voice was almost as patrician as Kepler remembered his tutor's could become.

‘Never. It is the only arrangement that makes sense of the Holy Trinity. God in the Sun, Christ in the sphere of the fixed stars and the Holy Spirit spread between the two.'

‘So you still believe in the nested shapes?'

Kepler turned away. ‘I confess my thinking has moved on. I now believe that the planetary distances may be understood using the laws of musical harmony …'

Out of the corner of his eye, Kepler saw Tycho raise a scraggy eyebrow.