In church on Easter Sunday, it suddenly occurred to me that 17.5 per cent of 25 was exactly the same as 25 per cent of 17.5, so the simplest way to do the sum was to divide 17.5 by four.
From this, it was a small step to appreciate that any first number produced as a percentage of a second number will show the same result as the second number produced as a percentage of the first.
Just as 17.5 per cent of 25 is the same as 25 per cent of 17.5, so 29 per cent of 97 is the same as 97 per cent of 29, and so on. Others must have made this discovery before me. In fact it is so elementary as to reveal an instant tautology as soon as it is set down in arithmetic: 29/100 x 97 = 97/100 x 29, or even more recognisably in algebraic form: xy/100 = yx/100.
On the other hand, it occurred to me that nobody had ever spelled it out in the form of a mathematical law, and many people are not aware of it.
'The strife is o’er, the battle done;
Now is the Victor’s triumph won;
O let the song of praise be sung.
sang the congregation.
The only immediate application for Waugh’s Law which I can spot lies in the field of mental arithmetic, where, by reversing the order of numbers, it is sometimes possible to produce a recognisable vulgar fraction which will reduce to simple division, as in the first example.
But it is most unlikely that Pythagoras, if indeed he did formulate the theorem ascribed to him, ever imagined that it would form the basis of trigonometry and thus shape the sciences of surveying, navigation, etc. Archimedes was in his bath when he discovered the law governing displacement of water and flotation, and here was I in church on Easter Day:
'Death’s mightiest powers have done their worst,
And Jesus hath his foes dispersed;
Let shouts of joy and praise outburst. Alleluia!'
Like Archimedes, I find I often engage in mental arithmetic when I have nothing else to occupy my mind.
Over the years, I have meditated quite a bit about the Passion and Resurrection, and doubt whether there are new discoveries to be made. According to a Gallup poll published by the Sunday Telegraph, 31 per cent of the population (that is very nearly one in three) have no idea what Easter is about.
One addresses oneself, of course, to the remaining 69 per cent, leaving the first lot to watch Sky TV and read the Sun, but let it be said that I have never been happy with history’s treatment of Judas.
He was given a rotten part to play in the drama, but it was an essential one. No betrayal, no crucifixion, no redemption. How can one talk of Judas’s free will in the face of such overwhelming historical imperatives? It would make as much sense to talk of Judas as a saviour, since he undoubtedly played a vital part in our salvation.
Similarly, but not identically, with Pontius Pilate. If Pilate had had his way - he was a thoroughly civilised man, just like you, me or Roy Jenkins - there would have been no crucifixion, no resurrection, no redemption.
Under these circumstances, we would have no excuse to let the song of praise be sung, or let shouts of joy and praise outburst. Yet Pilate is blamed for his pusillanimity. He is cast as one of history’s greatest villains, a sort of chinless ditherer. If Pilate had stuck to his guns and been a hero, there would be no Christian religion and Jesus’s trip to earth, would, by any reckoning, have been a bit of a waste of time.
Four out of five people in Britain, according to the Sunday Telegraph, actually and consciously disbelieve the Gospel story. Is there any useful purpose in persuading them to the contrary?
The Sunday Telegraph, as might be expected, ascribes many of the evils of modern society to this lack of religious faith - the glorification of selfishness as self-fulfilment, the exaggerated sentimentality about animals - ‘more greed, more crime, more family breakdown, more violence, and an extreme restlessness...’
All these things get worse and worse the more one worries about them. My chief doubt is whether the Bible story is capable, any more, of inspiring whatever degree of unselfishness is necessary to rescue the situation, especially among people who have more or less made up their minds that they disbelieve it.
If one examines the narrative of the New Testament, one sees that it was not really Judas or Pontius Pilate who forced the crucifixion to happen. It was the multitude, the voice of the people.
In former times, Christians were taught that it was most specifically the Jews who shouted ‘Crucify Him’ to the dithering Pilate, and there was particular mention in the Good Friday liturgy that the guilt of Christ’s blood was on the Jews of that and every succeeding generation. Hence the long years of Jewish persecution, culminating in the worst atrocity of human history. Since the Holocaust, it has become more apparent to Christians that the bloodthirsty crowd did not represent the Jews so much as the voice of democracy. Pilate was a weedy, public-school liberal judge, the crowd were Sun readers telephoning in (as they so often do) to demand the death penalty and express their opinion that hanging would be too good for Him.
Although, in history, blame has attached to Judas, to Pontius Pilate, to the Jews of that time and to Jews generally, nobody has ever thought to blame the multitude, the people. In a sense, of course, they should be praised, along with Judas and Pilate, since their role was a vital one in the scheme of things... but is this how we really want to be governed? Is this really going to produce the philosophical optimism necessary to inspire a selfless love of mankind?
Next year, in church, I think I will try to work out a method of finding square roots which I was taught about 40 years ago but have long forgotten.