Bach and The Tuning of the World. Jens Johler
no Luther, this whole witch-burning business is a nothing but insufferable nonsense. I have a very low opinion about it, truly. I’m not even sure that such a thing as witches ever existed. Nothing but figments of the imagination! For example:
They accused the mother of Johannes Kepler of being a witch only because people thought they recognized her in his novel about a trip to the moon. So this great man spent many years in his life defending his mother. Finally, they released her, but by then she was in miserable shape. And a year later, she died of exhaustion. Imagine that! Johannes Kepler’s mother!
The merchant said he didn’t know any Kepler.
Then he presumably didn’t know Christian Thomasius either?
‘I know a Christian Sartorius,’ said the merchant, ‘but you probably don’t mean him?’
‘No,’ said Erdmann, ‘I am talking about Master Thomasius at the University in Halle. Thomasius has given irrefutable proof that any kind of interrogation by torture is not only inhumane but useless. A person being tortured would confess to anything his torturers had put to him; truth never comes to light this way. Thus it happened not long ago that seven men were hanged for holding up a stagecoach; on the rack, all seven confessed, although it turned out later that only four robbers had been involved in that particular hold-up. But it was not merely three too many who were hanged, but seven. Because they caught red-handed the four who were actually responsible when they committed another robbery. And naturally, they too were hanged. So now, the total was eleven.’
‘Oh well,’ the cloth merchant said indifferently, ‘the others probably also had it coming.
In Wernigerode, the preparations for the spectacle were in full swing. Merchants from near and far had set up their stands. A wooden platform had been boarded together for the councillors and local notables who had come to town for the occasion. The stake had already been erected, although the burning was scheduled for the following day.
The cloth merchant could hardly hide his feverish anticipation. Even Bach was tempted to go along with the mood for a moment. Erdmann wanted to get out of Wernigerode as quickly as possible. He said he had an appointment in Wolfenbüttel.
‘An appointment? With whom?’
‘Well,’ said Erdmann evasively. ‘With an individual of some rank.’
‘Upon my soul,’ said Bach. ‘Not with the Prince, is it?’
‘With a Prince of the mind, yes,’ said Erdmann at last. ‘With Gottfried Wilhelm Leibniz, the philosopher.’
‘Oh, I can hardly wait,’ said Bach.
3. The Philosopher
Simply to walk through the dam-gate and cross the huge castle square, the aspect of the mighty castle itself towering over all other houses on the square, filled them with awe. And the no less impressive figure of the philosopher now received them in the library! He was wearing a flowing wig with a plethora of black curls, a magnificent coat cut in the French style, silk stockings and silver buckles on his shoes. Erdmann froze in awe. Bach felt uneasy. He was tempted to bow and scrape in front of the distinguished gentleman and was only just able to hold himself back.
As the philosopher showed them through the rooms of the famous library, Bach was flabbergasted. So many books, thousands of them! And each and every one of them identically bound in expensive light brown calf leather with gilt engravings. The shelves reached right up to the room’s awesomely high ceiling, crammed with works of natural philosophy, moral philosophy and theology.
He was in the process of converting the library to a new system, the philosopher said. Up to now, the books were catalogued according to their more or less arbitrary location on the shelves. Now he wanted to establish a new principle of arrangement, in alphabetical order by the name of the author, from A for Aristotle to Z for Zwingli. It’s more practical. You’ll find the books more quickly and save time. Indeed, the era in which they lived was an era of reorganization and cataclysmic inventions. Had they heard of the calculating machine?
Erdmann nodded.
Bach shook his head.
‘Here,’ said the philosopher, and turned to a table on which an oblong object was hidden under a cloth. With a swift movement, he pulled away the cloth and revealed a golden sparkling machine that sported confusing details: on the top side of the apparatus, Bach recognized the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. They were arranged in a circle around an adjustable pointer in the centre. Eight such circles of numbers adorned the top side. They were connected to eight perpendicular number discs that apparently could be set in motion by a large crank.
‘The turnspit,’ the philosopher joked, and turned the crank. Le Tournebroche.
Confused and fascinated, Bach and Erdmann looked at the enigmatic apparatus.
The philosopher could hardly hide his satisfaction. ‘This,’ he said proudly, ‘is an invention that will change the world. No more stupid calculating. Addition, subtraction, multiplication, division – no longer a problem. Ten times as fast as when you do it with your head alone.’
‘And how,’ Bach asked doubtfully, ‘does it work?’
‘Take a look here,’ said the philosopher, and motioned for the two to come closer. ‘The most important thing is the graduated roller. The teeth have different lengths and are slidable. All the digits of the summand can thus be translated to the results mechanism.’
Bach scratched his head.
Leibniz laughed, amused. ‘With this machine, gentlemen,’ he exclaimed, ‘we’ll be able in the near future to calculate everything and represent it in formulas.’
‘Everything?’ Bach asked in astonishment. ‘With this machine?’
‘Of course not with this still very imperfect specimen,’ the philosopher said, ‘but with the principles on which it is based. Incidentally,’ he added, ‘I’m in the process of inventing a completely different type of calculating machine. Maybe the honourable gentlemen can guess what type of a machine I mean?’
Erdmann expressed his bewilderment in a sigh that was difficult to interpret.
‘Well,’ said the philosopher in a confidential tone, ‘it will be a calculating machine for words.’ Yes, they had heard correctly, for words and sentences, for discourse! To do so, however, the words, sentences and the relationship between them must be brought into a calculable form. ‘I call it the universal characteristic. As all budding young scholars very well know, all words can be built with the twenty-four elements of the alphabet. Right?’
Erdmann nodded.
Bach refrained from commenting.
So, Leibniz continued, in just the same way as words can be traced back to twenty-four simple elements, he would be able to trace back all thoughts to their basic ideas. He would designate each of these basic ideas with a symbol or number – and before you know it, we’d be able to express all our thoughts this way. Our language would then be as accurate and infallible as mathematics.
‘Fascinating!’ Bach had not wanted to say it, but it had escaped him. He had an idea but didn’t dare to speak it aloud. It had to do with the fact that the number 24 played a role in music as well. There were twelve notes and thus twelve keys, and if you kept major and minor apart, you got to twenty-four.
‘Yes, fascinating, isn’t it?’ said the philosopher. ‘When we argue about something in the future, we will no longer get lost in endless discussions, probably settling them with our fists. Instead, we’ll simply say: Calculemus! Let’s calculate!’
But, Bach said, having found the courage after all, couldn’t such a machine be built for music as well? For example, a machine for counterpoint: You enter a theme, and the rest will simply be calculated. Counterpoint, dual counterpoint, triple counterpoint, quadruple counterpoint, whole notes