Desire, Science and Religion
Delivered on Friday 12 February 2010 in St George's Chapel
Exodus 34:29-end and Luke 9:28-36
This morning let's begin with a game. I want you to think of a number between 1 and 10, any number you like. Now take that number and multiply it by four. Take that number and double it. Add the original number. The next step is to take the digits and add them together. So, for example, is you have 16 at the moment you should add 1 and 6 together. Subtract 5. Now I want you to turn your number into a letter as follows: if your number is 1, the letter is A, if 2, then B, if 3, then C, and if 4, then D, and so on. Think of a country that begins with your letter. Have you got one? Take the second letter of your country and think of an animal that begins with that letter. ... I wonder how many people are thinking of an elephant from Denmark.
Well, that little piece of trickery depends only on the characteristics of the number 9 and a linguistic force. In celebration of the 350th anniversary of the Royal Society, my final inquiry starts down the road of mathematics. That elephant trickery - at least the first part of it - will always work because we know for certain how the number 9 behaves. Galileo, whom we looked at last week, once wrote that
There is not a single effect in nature ... such that the most ingenious theorists can ever arrive at a complete understanding of it. ... [But ] the human intellect does understand some propositions perfectly. ... Those of the mathematical sciences alone; that is geometry and arithmetic.
Physics and astronomy, says Galileo, can never lead to certainty but mathematics can. This picture of mathematics is understandable and seems to hit home in terms of our everyday experience. Indeed it feeds our apparent desire for certainty. However, the world of mathematics is broader, deeper, stranger, more mysterious than we sometimes allow.
In 1786 a nine year old boy was at school in Braunschweig. His teacher was a certain Herr Büttner, a barrel-chested man with a small beard. He patrolled his classroom with a whip in his left hand, striking out at even the smallest misdemeanour. Carl Friedrich Gauss, the pupil in question, was beginning to learn arithmetic. Herr Buettner wanting to have a bit of a rest so he set the class a task. He bellowed: 'Add the first one hundred numbers', and he sat down with every hope of a well earned rest. The boys began, 1+2 =3; 3+3=6; 6+4=10. Not Gauss. He thought for a moment and then wrote on his slate 5,050. Herr Büttner demanded an explanation. "Well, sir, I thought about it. I realised that those numbers were all in a row, that they were consecutive, so I figured there must be some pattern. So I added the first number and the last number: 1+100 =101. Then I added the second and the next to last numbers: 2+99=101. It started to make sense. 3+98 = 101; 4 + 97 = 101; 5+96 = 101. If I continued adding pairs of numbers like that, I would eventually reach 50+51. That meant I would find 50 pairs of numbers that always add up to 101, so the whole sum must be 50x101, which is 5,050. There was no need to add up all the numbers, sir."
Gauss was a genius soon to be known worldwide as The Prince of Mathematics. What he had seen as a nine year old was that certain arithmetic progressions had characters all of their own. The one he was working with was the simplest of all series, just the numbers all in a row, 1, 2, 3, 4, and so on. But there are infinitely many kinds of progression. A very famous one is known as the Fibonacci numbers. Fibonacci was a thirteenth century traveller and mathematician. (It was he who first introduced the Hindu-Arabic system of numbers to the Western world.) Anyway, in his book Liber Abaci, he posed a scenario around rabbits. He laid down some rules. First, the rabbits never die. Second, it takes one month for a rabbit to mature. Third, mature rabbits produce one male and one female rabbit every month. And so he asks us to start off with a pair of newly born rabbits, one male and one female, and see what happens. In month one we have one pair of baby rabbits. After two months we still only have one pair of rabbits but now they are mature. After three months we have our original pair and a baby pair, two pairs. After four months our original pair have had another baby pair and our baby pair is now mature. We now have three pairs. And after five months our original pair have yet another baby pair, their first children have had a baby pair, and the baby pair from last month are now mature, leaving us with five pairs. And now it starts to look complicated but in fact its not. The numbers series works like this: 1, 1, 2, 3, 5, 8 and without worrying about rabbits at all you can get the next number in the series by simply adding the previous two. The next number, therefore, will be 8+5=13. It turns out that this innocent looking series of numbers has the most extraordinary set of characteristics. Not least is the relationship between this series and what we call the golden ratio. Of course, the Fibonacci series never ends, it goes on infinitely but the larger the numbers get, the more closely the ratio of one number to the next approximates to the golden ratio. In other words if you any Fibonacci number and divide it by its immediate predecessor in the series you will get the golden ratio (or close to it). So what, you might well say. But the golden ratio, one of those never repeating numbers like Pi, and working out at 1.6180339887...., seems to crop up everywhere. It crops up in nature. Sunflower seeds are packed in spirals, typically with thirty-four going one way and fifty-five going the other (two numbers from the Fibonacci series); a snail's shell is constructed according to the principles of the golden ratio; and Falcons attack their prey using a golden ratio spiral flight path. But the strange thing is that while you find the golden ratio in nature, we also find it in the things we make. It seems as though human beings are particularly attracted to rectangles constructed according to the golden ration. You need only think of the Pantheon or many of the art frames in the Louvre, or more recently of postcards, credit cards, and train tickets - all rectangles made in dimensions governed by the golden ratio. So Fibonacci has led us on a small journey. We began with a series of rabbits and with his guidance discovered a series of numbers. Adjacent numbers in these series produce the golden ratio. And the golden ratio seems to found all around us, in nature and in artefact. I want, here, to make one simple point. We started out with a brief excursion into what Galileo calls the most certain field, and yet we end up recognising that even this most certain field has deep connections to aesthetics. It seems that although we human beings desire certainty, we also desire beauty.
Moving on. Mathematics is of course based on agreed principles and we can understand why Galileo calls it the most certain field. But there are times when that certainty is threatened and even mathematicians have to work with sheer intuition. A good example of this is the Goldbach Conjecture. Goldbach suggested that every even number greater than 2 is the sum of two primes. For example, 54 is the sum of 13 and 41, and 14 is the sum of 11 and 3. The thing is that although we have been able to show this to be true of even very large numbers we have not been able to prove that it is true of every even number greater than two. Based on experience, based on our best guess, we have a hunch that it is true. But just maybe there is some huge number out there for which this conjecture is false. Even with this most certain of subjects, there is room for intuition, a hunch for what might be the case.
Maybe I would want to go even further. Once upon a time a rather hippy young Greek man, named Pythagoras, went to visit the very first mathematician, Thales. The purpose of the visit was to learn as much about mathematics as he could from the wise old man. Thales, however, apologised for his failing mental powers and told the young Pythagoras to go west, or at least to go to Egypt. And so he did. But Pythagoras didn't find any mathematical magic in Egypt - there, all maths related to practical problems. Things looked up, mind you, when the Babylonians invaded and took him prisoner, for back in Babylon, mathematics was more abstract. Lots of thinking outside the box. And it is abstraction, or at least abstract thinking, that gets mathematicians out of bed in the morning. A quick example: what is the square root of 9? 3. What is the square root of 225? 15. Well and good, but what is the square root of -1? Not so easy. 1 times 1 is 1; -1 times -1 is 1. The answer is imaginary. The square root of one is an imaginary number, we call it i. Imaginary it might be, but lots of engineering mathematics would be impossible without it. But that is not the point. I am more simply trying to show that even in the kingdom of certainty, the human mind desires creativity, it appeals to imagination.
We have now come to end of this journey. We began with certainty - the characteristics of the number 9 and some words from Galileo. We then explored a possible link between mathematics and aesthetics; we took a quick look at mathematics and intuition; and we have now seen how mathematics appeals to the human imagination. It would seem that even when human beings desire certainty but when we meet it, we desire yet something else, beauty, intuition, imagination. We are involved complicated creatures, much too complex to be restrained by certainty. We want to know that the area of a circle is definitely %u03C0r2, but we also want to deal in love (just think of the day that is in it).
These three inquiries have all been pointing in the one direction. Science, as we know it, is heralded as the ultimate measure of accuracy, of the standards of truth. Yet, while there is truth in this acclamation, it is wrong to think that that is all human beings require. We desire more. Religion, unlike Science, does not claim to be a standard of measurable truth because both God and his creatures are both beyond measure, but it does claim, nonetheless, to trade in the currency of truth. Religion goes further. This morning we have taken a quick look at the human desire for certainty, for beauty, intuition, imagination and love. Religion is in the specific business of educating our desire and thereby transforming us into what we just might be, of changing desire from lust into love. Like Moses, in the first reading today, we are open to transformation. To best define what I mean, I take my closing words from that giant of religious instruction, Augustine, when he wrote:
By love I mean the impulse of one's mind to enjoy God on his own account and to enjoy oneself and one's neighbour on account of God; and by lust I mean the impulse of one's mind to enjoy oneself and one's neighbour and any corporeal thing not on account of God.
Viewed 355 times since 00:00 14/02/10