Solomon Had It Easier : A Matter of Interest

SOLOMON HAD IT EASIER

Foreword

Well, it’s true that Solomon had it easier than today’s judges. After all, apart from that thing with the two women and the baby, what demanding cases did he try? Please don’t write in. Anyway, the Old Testament sage was a king, so had a good deal of latitude. His modern counterpart is more circumscribed and must try to extract justice from a morass of laws created by others. Perhaps no-one did this better than that demon of denouement, Judge Embert Wimple, as the cases presented here surely demonstrate. All were culled from those tried by the judge during his last year on the bench. It was no small task to persuade him to allow them to be placed in chronological order, nor was it easy to convince him that only a limited number could be included here. His final choice was made only weeks before he departed for the great courthouse in the sky. He gave no reason – for the selection, that is, not his departure.

Some readers may note that there is little reference to the apportionment of costs. This arises from the judge’s practice of making the relevant orders after giving his verdicts and declaring proceedings closed. It is felt that no great purpose would be served by the provision of case-by-case footnotes concerning this point.

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SOLOMON HAD IT EASIER : NUMBER ONE

A Matter Of Interest

Proceedings in the Grimshaw versus Pepper case began at ten-thirty a.m., Judge Embert Wimple presiding. The plaintiff alleged that the defendant was guilty of failure to repay a loan, the defendant responding hat he had not done so because the plaintiff had deceived him. Neil Grimshaw was represented by the redoubtable Desmond Oddley-Staggers, while Gordon Pepper was in the hands of the no less distinguished Rodney Melliflewes.

Judge Wimple, aged eighty-three and officially long-retired, still appeared frequently in court to assist hard-pressed colleagues. The hearing was to be held in camera, which pleased the judge, who foresaw some stimulating entertainment, which he was ill-disposed to share with a courtroom full of jurors and other undesirables. In fact, from this case onward until his retirement, the judge was to hold all his hearings with the public excluded, though he would continue to avail himself of a courtroom, as he considered his chambers inviolate.

After satisfying himself that he was clear as to the respective charges, Judge Wimple addressed prosecuting counsel. “Very well, Mr Taggart, you may begin.”

Oddley-Staggers was accustomed to the judge’s habit of addressing advocates by whatever names occurred to him, irrespective of true identities. His honour’s view was that he was dealing with a pool of lawyers and a like-sized array of names, and which of the latter he applied to any of the former was not important to him. On the occasions when his attention wavered more than average, he had been known to refer to barristers long dead. It had become a convention that, in the interest of reaching the end of a case within a tolerable period, nobody corrected Judge Wimple. The litigants were usually primed and almost always obliged.

Thumbs in waistcoat pockets, Oddley-Staggers inclined his head towards the bench. “May it please Your Honour,” he said, “the facts in this case are quite simple. Some fourteen months ago, my client loaned the sum of one pound to the defendant, the arrangement being that Mr Pepper would, at the end of one year from the date of the loan, repay the principal, plus interest. Mr Pepper did not honour this obligation and still has not done so. My client’s purpose here is to recover the amount owed. He appreciates that the sum concerned is a modest one, but contends that there is a principle involved, which must be upheld. Subject to a satisfactory outcome, he is willing to ignore any interest incurred after the one-year period.”

“Seemingly most generous,” said the judge inspecting his papers. “We must never ignore matters of principle, or indeed in this case also principal. Now, it says here that the amount owed is two pounds, seventy-two pence. I am puzzled as to how we get from the one figure to the other. Presumably this arises from either administrative charges or the interest rate. Were there any charges and what was that rate?”

Oddley-Staggers reddened slightly. “No charges, Your Honour. The interest rate was” – his voice fell to a mumble – “one hundred per cent, nominal.”

“Speak up, Mr Olliphant. I’m not sure I heard that correctly.”

“No charges. The interest rate was one hundred per cent, nominal.”

“Bless my soul,” said the judge. “I am not au fait with current trends, but if your client makes a habit of this, he must be in a lucrative business. Furthermore, my arithmetic, though possibly defective, suggests an amount of two pounds owing. I still don’t see how we get to two pounds, seventy-two pence. Please explain.”

“Your Honour, my client does not operate in the financial world, but was merely doing a favour. As to the sum involved, we are dealing here with a factor known as the exponential constant, which is the base of the natural logarithm. It is usually referred to by its initial letter, e.”

“Most interesting. Would you care to regale us further?”

“Yes. This kind of situation occurs frequently in certain areas of mathematics, physics and commerce, where two interacting elements are involved, one rising as the other falls. In this case, it concerns multiple compounding of interest. At the time the loan was made, there was no discussion between the parties as to the number of periods my client was to employ.”

The judge was enthralled. “And this makes such a large difference, does it?”

“Indeed it does. My client realised that, as the rate was nominal – or at least that there had been no agreement that it was not – there was no impediment to his compounding interest at periods of less than one year. He found that by doing so at increasingly frequent intervals, the sum owed became ever higher. He considered half-yearly periods, then quarterly ones, then monthly, then weekly and so on, until he reached the point at which no further meaningful increment could be achieved. It is a question of an arithmetical series, leading to the exponential constant I mentioned. This series consists of one, plus one, plus one divided by two, factorial, plus one divided three, factorial, and so – ”

“One moment” said the judge. “You say ‘factorial’. Perhaps you would expand?”

“Willingly. The expression is mathematical shorthand. Any number factorial means that number multiplied by the one immediately below it, then the result by the next lower one and so on until unity is reached. For example, five factorial means five, times four, times three, times two, times one, the last operation being of course academic, since it does not change the total. In this case, no matter how often the compounding occurs, there is an effective limit, which to two decimal places – the practical level in financial matters – is two, point seven two. We are concerned here with an irrational number.”

“We certainly are,” said the judge. “I never heard of anything less rational.”

“If I may explain, Your Honour, an irrational number is one which has no precise value, but which can be calculated to any desired degree of accuracy, the digits following the decimal point proceeding to infinity, with no repeated pattern and always with a remainder.”

The judge was well aware of the meaning of the term concerned, but was not inclined to miss an opportunity to allow any counsel, especially one of his regulars, to demonstrate a grasp of whatever was at issue. The more experienced ones enjoyed these diversions as much as he did. His honour’s view was that all of this added colour to the proceedings. “Fascinating!” he said. “Please continue.”

“I was about to say that mathematicians usually consider the result to five decimal places as satisfactory, this being two, point seven one eight two eight.”

“Well, well,” said the judge. “I imagine that financiers find the idea even more agreeable. Was there no obligation on Mr Grimshaw to reveal this multiple compounding to Mr Pepper as it proceeded?”

“Nothing to that effect was specified at the outset, Your Honour. The technique is widely used in commercial transactions.”

“Thank you, Mr Oddment,” said the judge, turning his attention to defending counsel, “Now, Mr Mildew,” he said. “What have you to say?”

Being as experienced as his opponent, Rodney Melliflewes had no difficulty in maintaining his poise. “May it please Your Honour,” he said, clasping his hands behind him, “there is no disagreement as to the simplicity of this case, nor is there any argument about the arithmetic. However, there are two points of significance. First, the plaintiff’s assertion that the amount due is two pounds, seventy-two pence. My client’s view is that this would represent overpayment, as the true figure, by the prosecution’s own calculation, is two pounds, seventy-one point eight two eight pence. This is less than the amount demanded. My client is willing to pay two pounds, seventy-one pence, but not the remaining nought point eight two eight of one penny, let alone the further nought point one seven two of a penny which would take the total to two pounds, seventy-two pence. He considers this excessive. Second, he contends that normal practice was contravened, in that the conditions of the loan were arbitrarily imposed upon him. Notwithstanding this, he agreed to settle in round terms, though he was thinking that the sum would be truncated to the penny below the true figure.”

Judge Wimple had been staring at the ceiling. Now, his gaze returned to defending counsel. “A combine harvester, was it?” he said.

“Beg pardon, Your Honour,” said Melliflewes. “A combine harvester?”

Having briefly lost interest in the matter before him, the judge had been silently reminiscing about a totally unrelated farming case he had tried many years earlier, when a casual labourer had lost an arm. “Askew versus Beaumont, some time ago,” he said. “That has an indirect bearing upon this matter. Do try to keep up, Mr Murgatroyd.” He was now in his element, especially as his impromptu comment clearly left Melliflewes floundering. “So, we have two parties who seem to be almost in agreement.” He turned his attention to Oddley-Staggers. “Have you anything to add, Mr Braithwaite?”

“Only one point, Your Honour. The arrangement in this case was verbal and informal and my client does not see how it could have been covered by consumer credit legislation.”

“Very well,” said the judge. “If all has been said, I think this would be an appropriate point at which to recess for lunch.”

Oddley-Staggers issued a political cough, causing the judge to eye him keenly. “Was there something else, Mr Oliver?”

“Your Honour, I would respectfully point out that both my learned friend and I are required to appear in other cases this afternoon. Since it is not yet eleven o’clock, I was mindful that –”

“No doubt,” snapped the judge, “and I was mindful that the visitors had lost eight wickets by close of play yesterday. Is it essential that you proceed immediately?”

“Er, no, Your Honour.” Prosecuting counsel knew of the judge’s addiction to cricket and, appreciating that the season had just begun, was unwilling to cast a cloud over the proceedings.

“Good. In deference to your other commitments, we shall reconvene at one o’clock, and a few minutes should suffice to complete this hearing. ”

The parties foregathered as ordered by the judge, whose eyes roved over the company. “Has either party anything more to say?” he asked. Neither had, so his honour continued: “Very well. I believe I have digested everything of consequence here and I must say that it is intriguing to be involved in a case so friv . . . ahem . . . grave. It remains for me to sum up and give my verdict.” He rustled his papers, all blank apart from a note that the home batsmen, pursuing a modest opposition first innings total, had lost early wickets in what promised to be a more absorbing encounter than the one in which he was involved.

With a final stare at the battling parties, he went on: “This case revolves largely around mathematics and I am no expert in such matters, but have considered the position as, I hope, a fairly intelligent layman. I am minded to dismiss Mr Pepper’s claim that he was deceived. He should have demanded a formal agreement. As to Mr Grimshaw’s charge, we seem to be dealing with a question of rounding up or down. My personal view is irrelevant, but insofar as it might have any moral force, it is that the plaintiff is a scoundrel. I have carried out some research during the lunch break and have found that credit may be obtained at vastly more favourable terms than were offered by Mr Grimshaw to Mr Pepper. Furthermore, I am fully conversant with the electronic calculator, as you will soon appreciate.” In fact the Judge, who never ate lunch, had been instructed in the use of the tool in question by a court officer, who as a consequence had missed a repast of steak and kidney pie.

Neil Grimshaw and Desmond Oddley-Staggers were by turns euphoric and glum. “Now,” said the judge, “we come to the question of the debt. My conclusion is that, having indicated his willingness to honour his obligation within reason, Mr Pepper should pay Mr Grimshaw the sum of two pounds, seventy-one pence, scandalous though that may be.”

Gordon Pepper and Rodney Melliflewes were pleased by their qualified triumph. but only momentarily. Judge Wimple went on: “However, I feel bound to comment on the lack of common sense exhibited by Mr Pepper, in that a grown man should have known better than to accept a loan without ensuring that the terms were clear and unchangeable. This demonstrates foolishness almost beyond belief. We are considering a transaction between a rogue and a simpleton. With respect to this, I can say only that a man may be excused for being the latter, but not the former.”

The judge had expected silence here, and wasn’t disappointed. He paused for ten seconds before continuing: “Now, the prosecution seems to be punctilious about decimal places and in respecting that, I see that we are left with nought point eight-two-eight of one penny in contention. The court will hold this amount in escrow, on a purely notional basis, and will allocate to it, also notionally, interest at one per cent per annum,” here the judge raised his voice as he glared at Oddley-Staggers, “compounded once a year”.

Satisfied that he had delivered a rebuke, his honour went on: “As the court cannot be expected to continue the action until the sum in question reaches one penny, we shall have to wait until we get to that level. I would caution the plaintiff against any expectation he may have of an automatic final finding in his favour with respect to the outstanding amount. Lastly, I indicated that I have not been idle during the break and you may wish to note that I have checked the length of time required for the initial capital to reach the total concerned, at the rate of return I mentioned. You may therefore regard my decision as an interim one. As to final disposition, we shall meet again in” – he examined his notes – “nineteen years. Proceedings adjourned.”

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