Sky's Dark Labyrinth

by Stuart Clark

  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 i
n 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.

  ‘… The idea dates from the Greeks but no one has pursued it for a thousand years. As a planet moves through its orbit, so its sphere resonates and makes a note. Each planet makes a different note and together they form a divine harmony, musically rich and beautiful – for God could scarcely have designed things otherwise. Do you not agree?’

  ‘You’re speaking to a man who hasn’t taken communion in eighteen years.’

  ‘But you are working to reveal the glory of God.’

  ‘I prefer his indifference. And perhaps that is the best I can hope for after what I have seen. I know that the heavens vary their appearance, the very realm that Aristotle claimed to be immutable – I’ve seen it change. The new star of 1572; I watched it for two years, blazing brightly at me yet as fixed in its position as any of the stars. It had to be located on that final sphere – the very furthest from Earth – yet who will back me? No one. The philosophers still talk of it as being an atmospheric phenomenon of the Earth.’

  ‘I will back you. Together we can remake astronomy.’

  ‘But we differ on whether the Earth or Sun lies at the centre of creation,’ said Tycho, as if discussing a triviality, but Kepler could hear the suspicion.

  ‘We can find common ground.’

  The two men regarded each other; the only sound between them was Tycho’s laboured breathing. Eventually he broke the silence. ‘Tell me of your background, Johannes. Is your father a learned man?’

  ‘My origins are not as noble as yours, Lord Brahe.’

  Tycho’s eyes flickered in a curious manner and he spoke brusquely. ‘Nevertheless, I am interested.’

  Kepler scrutinised the globe, shuffling so that its great bulk was between him and Tycho. ‘I was born in Weil de Staadt. My mother is a herbalist. My father, well, my father was a soldier.’

  Kepler’s insides squirmed at that word – soldier. It meant only one thing: mercenary.

  ‘Do they live?’

  ‘My mother, yes. My father, no.’ The sentence was only half correct. Aged seventeen, Kepler had watched from the shadow of a magnolia bush as the man swaggered down the street, swigging from a flagon, letting the townsfolk know that he was off to war. It was soon afterwards that Kepler discovered his father had once fought a Protestant uprising in Holland, despite his own Lutheran roots. The realisation was sufficiently painful even now to flush Kepler with shame.

  That departure was Kepler’s last memory of his father. When the months turned into years, the family gave up waiting. Yet it was only recently that Kepler had stopped snatching a second look at any grizzled face that passed, just in case there was a resemblance.

  His thoughts were drawn back by the sound of Tycho taking a deep breath. ‘I have to decide what to do with you.’

  ‘Sir?’

  ‘What task of calculation do I set you?’

  Kepler turned at once. The Master was watching him carefully. ‘Mars perhaps? Longomontanus has done more than any man alive, yet he is mired. What if I were to ask you to work with him on it? I think that might suit you, would I be right?’

  A shiver passed through Kepler. Did Tycho know of his conversation with Longomontanus? He spoke carefully. ‘I will not disappoint you. I will have its orbit in eight days.’

  Tycho cocked his head. ‘Will you now?’

  ‘Eight days, sir, or I am not the greatest mathematical astronomer alive.’

  ‘I once thought that I was the greatest mathematician, too. You know what I got for it?’

  Kepler shook his head.

  ‘This.’ Tycho raised a finger and pointed at the metal nugget in his nose. ‘I fought a duel because a classmate dared to claim superiority with numbers over me. I knew he was more gifted but I couldn’t admit it. And that sliver of truth allowed his blade to slip through. The constant ache of this wretched thing is my reminder of the cost of misplaced pride.’

  ‘Yes, sir.’

  ‘We are a family here, Johannes. We work together.’

  ‘I understand.’ But as he hurried away, Kepler’s thoughts were full only of the discoveries he was soon to make.

  6

  Rome, Papal States

  By the time Bellarmine reached the steps leading to one of the giant doors of the Roman College, the building filled his entire field of view. He smiled inwardly; the Jesuits knew how to impress, and how to intimidate at the same time, if he were being honest. It was a formula that served them well. Even Pippe beside him had gone quiet.

  The Jesuits had been in existence for only twenty years when Bellarmine had joined the
m, himself only just eighteen. In those days, Rome had been floundering, having still not recovered from its sacking by Emperor Charles V’s mutinous hordes. It was an aimless city, its people undirected and the Pope’s authority withered to a dry thread. In the face of this emasculation, the Jesuits had offered a new way forwards, a fearless way built on the intellectual mastery of spirituality, theology and philosophy.

  Bellarmine thanked God every day for guiding him into their ranks. His father had hoped he would become a politician and restore the family’s ebbing prestige, but his mother had seen the real path. She had believed in Church over State and had quietly urged him into the Jesuits. ‘They need thinkers like you,’ she would whisper to him, stoking his young ambition. ‘Lutheranism is a plague; their beliefs are the buboes of evil. Only Catholicism can lead people to salvation.’

  As Bellarmine had matured and studied, so he had watched Rome become strong again. As the buildings rose once more, so the people remembered their purpose, and a new determination took hold to lead the rest of Europe back to the one true Church. He also understood how the Jesuit determination had led this charge. The Vatican owed them a mighty debt. Without them … Bellarmine shuddered to think how far the Protestant heresies would have spread and how many souls would have been lost to the fires of damnation.

  Reaching the top of the familiar steps, he glanced over at his hesitant companion. ‘Don’t worry, Cardinal Pippe, Father Clavius can’t take your birthday away from you again.’

  Pippe pulled a sour face.

  They disappeared into the shadows of the entrance hall, and the heat of the day dropped immediately. Bellarmine led the way through the stone pillars supporting the domed ceiling, down the lofty corridors that skirted the courtyard, and finally up a sweeping staircase to an office on the first floor.