by Graham Brack
However, Heereboord’s point was that whereas lawyers and physicians could augment their salaries with private work, that option was not open to the masters of the school of philosophy because, by and large, people do not go out and hire a personal philosopher. It was therefore unjust, he claimed, that the university preferentially rewarded those who already had more earning potential. Much to my surprise, the authorities had finally conceded the point. No doubt they found it easier to do so now that Heereboord was dead. Anyway, the outcome was that some of us had received a very nice pay increase. Now, I supposed, the Rector was going to ask us to give it back.
‘How can I help you, Rector?’
‘The fact is, Mercurius, that at least a part of the recent controversy came about because the pay scale is so transparent. Everyone can work out what everybody else gets and that simply engenders envy, covetousness, and wrath. As you will appreciate, I cannot be a party to the encouragement of sin in my academic staff, any more than I can turn a blind eye to it amongst my students. So what I want you to do, Mercurius, is to come up with a system that is much more complicated. Of course, nobody who is here now will be disadvantaged, but we want to ensure that the Regents have much more … flexibility … in future appointments. We don’t want to be seen to be making special cases all the time.’
‘Don’t you need a Jesuit for this?’ I asked. ‘They’re good at this kind of thing.’
‘Perhaps so, but we don’t have any, and if I commissioned one to do the work for us I think he would smell the largest of rats.’
‘I’ll do my best, Rector,’ I said, and began to lever myself out of my seat.
‘There is one complication,’ came the reply.
Of course. There always is. Nothing in my life is simple, except the lad who waxes my boots, preferably on the outside.
‘The Stadhouder himself wants to approve the reform before it is promulgated. He has taken a keen interest in the affairs of the university and is distressed by the past instances of disorder.’
I told you that the Rector was very clever. Note the cunning way he had managed to shift the Stadhouder’s potential displeasure onto someone else even before the work was done. And yet I still liked the man.
‘How long do I have?’ I asked.
‘Oh, there’s no rush. It’s much more important to spend time getting this right than doing it quickly just to get it finished. Shall we say the end of the month?’
If I had protested it would have been to his back, since he immediately broke eye contact and turned away from me. So many little tricks I had to learn!
‘And Mercurius…’
‘Rector?’
‘When you give the philosophy department the pay rise that will undoubtedly seem reasonable to you, may I suggest moderation?’
‘Of course, Rector.’
‘And discretion. It’s probably best if nobody knows you’re doing this.’
There’s no “probably” about it, I thought. ‘No-one shall hear it from my lips, Rector.’
‘Excellent. The only people who know are you, me and, of course, Van Looy.’
I must have shuddered at the mention of his name or made the sign of the Cross or some such solecism, because the Rector continued: ‘He is not a member of the teaching magisterium and therefore not included in your plan, but I have seen no reason to tell him so.’
Oh, what fun I shall have, I thought. Three whole weeks of Van Looy thinking that I’m setting his salary. That must be worth some favours. Or at least a bit of respect.
CHAPTER TWO
Coming from chapel a couple of days later, I chanced upon mijnheer Van der Horst again, in company with a couple of others of his age. One was a dark-haired man, possessor of a sparse beard and sallow skin, introduced to me as Molenaar. The other was a spotty youth with sandy hair and hardly any beard at all. While Molenaar seemed reserved and cautious in his speech, the other seemed angry about everyone and everything.
‘You must forgive mijnheer Terhoeven, Master,’ Van der Horst said with a faint smile. ‘He finds much in the world in need of reform.’
‘As do we all,’ I answered. ‘What is the point of the gospel, if not to change the way the world works?’
‘My point exactly,’ agreed Van der Horst. ‘There is change ordained by the Almighty, and there is chaos. We must distinguish the two.’
I almost added there is change brought about by the authorities, which was usually a mixture of the two, but I let it pass. In those days you still had to guard your tongue to some extent.
‘We all appreciated your little speech the other day,’ said Molenaar.
‘I cannot imagine why young men waste their time and money on wenching when there is so much to be done in the world,’ added Terhoeven.
‘Quite, quite,’ I agreed. ‘Though, of course, I am not well placed to judge what pleasure there might be in the company of a young woman.’
‘A young lady is a very different thing to a whore,’ offered Terhoeven, and was rewarded with a shudder from Molenaar at the very mention of the word whore.
Whatever this little group was, I was inclined to think that Molenaar was its brains, Van der Horst its mouth, and Terhoeven its heart. He was all energy and action, Van der Horst was suave and elegant, while Molenaar was made of caution. I suspect the first word he uttered as a child was “perhaps”.
‘I fear that we are giving you a misleading impression, Master Mercurius,’ Molenaar said. ‘We were on our way to the chapel to practise our music. Do you play?’
‘Barely,’ I answered, and even that was an exaggeration. My father bought me a viol when I was young, but I gave up when it could not be mastered in an afternoon. ‘I sing a bit.’
Van der Horst’s face lit up. ‘You’re not a bass, by any chance?’
‘No, sadly not,’ I replied, ‘just a reedy tenor.’
‘Ah, we already have one of those,’ Van der Horst announced gravely, accepting a peeved buffet from young Terhoeven who had belatedly recognised the slight he had been offered.
‘I hope, Master,’ Molenaar interrupted, ‘that you are not offended by the playing of music. It seems to us that so goodly an art cannot have been forbidden us by a God who is the source of all human gifts and knowledge.’
I understood his concern. There were those of a puritanical cast of mind who regarded music and musicians with suspicion. In the case of musicians this was understandable, since a more lascivious bunch of reprobates has not walked the earth, but anyone who has heard the great choral music of our age cannot object to its use by pious men and women. It was not many years since the Puritans of England had banned Christmas, the maypole, theatres and dancing, not to mention bear-baiting, of which they disapproved not because the bear did not enjoy it but because the spectators did. There were plenty of churches in the Low Countries without music, but others that cherished it. Within Leiden, the Marekerk had a fine organ, though in need of a bit of refurbishment.
‘I certainly have no objection to music, mijnheer, any more than I reject art. The gifts bestowed by God can be used for good or ill as man chooses.’
Molenaar appeared almost enthused by my response. ‘May we ask, Master, when you next preach? We must make sure that we are there.’
The ordained staff were wheeled out now and again for the edification of students. There were a lot of us, and since we employed a chaplain it was my view that he should do the bulk of the work, but the occasional sermon was unavoidable.
‘31st October,’ I replied.
‘All Hallows’ Eve! How splendid!’ chuckled Van der Horst. ‘It will be one for Satan to remember, I’m sure.’
He bowed politely, and his companions followed suit, though I think I detected that Molenaar was displeased at any teasing of Satan, and quite right too. It does no good to tweak the Devil’s tail unnecessarily.
I took a long draught from the tankard and signalled for another. A sailor by the fireplace was in the middle of a highly entertaining and invent
ive story about a woman of the East Indies which was distracting me from the task in hand, namely, the devising of a system of remuneration for the magisterium that would defy any attempt at understanding.
The potboy put down my tankard and asked if I would be supping with them. As part of my employment, I have the right to eat in the university hall free of charge. Unfortunately, this arrangement does not include covering the physician’s bill that would undoubtedly arise if a man were reckless enough to eat Albrecht’s food every day. For that reason, a few coppers spent in the inn was often well invested.
‘What’s for dinner?’ I asked.
‘Rabbit stew,’ came the answer.
There had been a certain monotony to the menu for a little while, so I should not have been surprised to hear this. The fields were filled with rabbits, and since a country that depends heavily on food it grows locally must be threatened by their incessant nibbling, rabbits were regularly hunted and the markets were full of the proceeds. Rabbit stew was cheap and nourishing, but you can have too much of a good thing.
The curious question was why there were so many of the large-toothed larcenists that year. A late summer was usually blamed, but I was inclined to the opinion that the flooding had killed many of their natural predators, allowing them to increase in numbers.
I declined the offer of supper, deciding instead to brave the incinerated delights of Albrecht’s kitchen whilst hoping — I confess my sin — that he might burn his hand again and have to let Mechtild cook instead.
It was then that inspiration seized me and my prayers were answered. Whether this was the work of the Holy Spirit or three jugs of ale I leave to my readers to judge, but I found myself musing on the spectacular multiplication around us and the explanation offered by Master Hubertus, who taught mathematics to a small band of students who found such things interesting, often because they wished to become bankers in the hope that one day they would outstrip the Fuggers of Augsburg in their acquisitiveness. Holy Scripture tells us that the love of money is the root of all evil (First letter to Timothy, chapter six, I believe), which I have always thought a bit harsh on bankers and rather lenient on lawyers. Be that as it may, Master Hubertus introduced us to the rules of compounding, which is to say that rabbits do not simply multiply, but as more rabbits are around, the rate of rabbit production accelerates. If each pair of rabbits produces five baby rabbits who in turn produce five baby rabbits per couple, the increase can be precisely calculated. Not by me, of course, but Master Hubertus knew how it was done, so I gathered up my papers and headed for his room.
Mijnheer van Looy crossed my path as I proceeded thither. The man turned up everywhere. One would almost think he spent his days lurking in corridors.
‘Your pardon, Master!’ he said as I raced past him. ‘You seem to be in a hurry?’
‘I’m going to learn about compound interest,’ I announced.
‘Indeed? I’m sure any moneylender could explain it to you.’
‘I’m sure they could, but I don’t know any. Do you?’
We bowed politely and went about our business.
Master Hubertus conformed to all the stereotypes one can imagine about a university lecturer. His hair was unkempt and he made extravagant gestures with his arms as he explained things. If he had not worn a cleric’s gown, he might well have been taken for a lunatic. Even so, he looked like a clerical lunatic.
His chamber was more untidy than mine, a circumstance which would have astonished many of my friends. The sense of disorder was heightened by the large slate hanging on the wall upon which he chalked his calculations, continuing along the wall when he ran out of space. I had seen such boards used by choirmasters but never by a mathematician, which led me to feel new respect for one who was such an early adopter of teaching technology.
‘I hope I’m not disturbing you,’ I said, indicating the abrupt end of the scribbling on the wall.
‘Ah, no,’ replied Hubertus. ‘It continues over there.’
He pointed to a further area of scrawl behind the door. If a child had done this, we would punish him severely. The university, by contrast, had just promoted Hubertus.
‘Are you interested in mathematics?’ he enquired.
‘Who isn’t?’ I responded, with my most encouraging smile.
‘Most of my students, sadly,’ he answered. ‘They’re only interested in double entry bookkeeping and calculating gambling odds correctly.’
‘Shocking!’ I tutted. I can tut with the best of them. It goes with the moral philosophy turf.
‘What can I do for you, Master?’
‘Rabbits!’ I announced.
‘I don’t have any, I’m afraid.’ He gestured about him to prove his point. He was quite right; his room was marked by a complete absence of lagomorphs.
‘I’m not being clear, Master Hubertus. You told me once about a method for calculating the number of rabbits in a country after a period of time.’
‘Compounding, yes, I recall. It has more practical uses too,’ he added.
I sensed this would be a long visit and looked about me for a stool. Hubertus lifted some papers to reveal one and invited me to sit. Before doing so himself he poured two beakers of wine, managing to soak his cuff in the process.
‘Let me lay out my problem for you, Master Hubertus. A certain man has some servants. He wishes to reward them for their service. He could simply divide the sum he has in mind between them, but that would reward the newest equally with the longest-serving. Then he recalls that a friend —’ and here I raised my beaker to salute Hubertus — ‘has recently explained to him how compounding can reward them more equitably.’
‘Why doesn’t he just give them one or two guilders for every year’s service?’ Hubertus asked.
‘He could! Indeed he could!’ I answered, having failed to think of this myself. ‘But he wishes to honour his friend’s ingenuity and adopt a more subtle approach.’
Hubertus took a draught from his beaker and stared into the distance. ‘You — your friend — might apply an incremental rate and compound it according to the years of service, I suppose,’ he murmured.
It was obvious that he considered this a complete explanation and proposed to say no more, so I was compelled to coax it from him.
‘Which means?’
‘Ah, you — your friend — will proceed thus. Let the man’s portion be one.’
‘One what? One guilder? One ducat?’
‘One whatever. The unit is unimportant.’
‘I think it’s important to the recipient.’
‘I am viewing it as a mathematical matter, Master. To me, the unit is unimportant. The calculation does not require to know it.’
‘I beg your pardon,’ I said, inwardly thinking that mathematics is a nonsense if it thinks that.
‘Then let his portion at the outset be one. For each year of service, let his portion be increased by a fraction of one that we shall call x.’
‘What is x again?’
‘The incremental fraction.’
‘Yes, but what number is it?’
‘Any number you like. It might be a tenth or a twentieth part, for example.’
‘Ah. I beg your pardon,’ I said again, and indicated that he might continue.
‘Then, after one year, his portion will have increased to one plus that twentieth part.’
‘I see.’ Surprisingly, I actually did. If you set a sum to increase by an increment of one twentieth part each year, after one year it will be one twentieth part larger.
‘Now, after two years, how large will it be?’ Hubertus asked.
‘Two-twentieths?’ I stuttered.
‘No!’ he cried, as if I were the greatest dunce in Christendom. ‘That is the beauty of compounding! That would be to ignore the increment of the first year. After one year our man has not one guilder, but one guilder and one stijver, and you must increment both parts by that twentieth part. For the guilder he receives another stijver, but he also receives a
twentieth part of his new stijver.’
A twentieth part of a stijver would be such a tiny sum that it would not be worth having, but I judged that to say so would expose me as a mathematical fool, so I just nodded sagely.
‘And, in general, we may say that the man’s portion after n years can be expressed as (1+x) to the power of n, where x is the incremental rate.’ Hubertus bounded up and wrote this formula on a corner of his slate. I hoped he would remember to rub it out before he included it in whatever calculation he was undertaking on the rest of the slate.
‘So if we set x to be a twentieth part, how much would a man get after, say, thirty years?’
Hubertus set to with a will. ‘About four and one-third guilders for every one he had at the outset,’ he announced.
I could not imagine that the Rector would stand for a man’s stipend being four times as large at the end of his career as at the start.
‘What if it were a fiftieth part?’
Hubertus gulped, but reworked his calculations. ‘One and four-fifths,’ he finally announced, and finished off his beaker to recover the animation of his spirits, which must have been depressed by his efforts.
‘I think my friend would be well satisfied with that result,’ I exclaimed, patting Hubertus on the arm before I remembered his cuff was wet.
The intelligent reader, if such a man would deign to peruse this volume, might be asking himself why I have lavished so much attention on this mathematics. And, being intelligent, he will then recall that the Stadhouder himself had expressed an interest in my plan.
I took it to the Rector, suggesting a base salary for each grade of teacher, an augmentation depending on the subject taught, and then compounding to reflect the lecturer’s length of service. This resulted in a number that could not easily be recalculated by anyone who had not had the method disclosed to him.
