COLIN HANNAFORD

It is quite possible that you may also want to know a little about me and about my life, although in truth I have always been quite unimportant. As may be obvious by now, I was born quite a few years ago, in Plymouth, England, around the time when the German Luftwaffe was trying almost daily to bomb it, or burn it, to the ground.

One result of their endeavours is a very early memory of mine of being pushed in my pram on a hot afternoon past field after field of tumbled and broken stones. This, of course, was all that was left of Devonport, or the houses around the navy docks and yards which were the bomber’s primary targets. I grew up playing in bomb-sites. Our house survived, although an incendiary came through the roof and my sister and I used to pick up shrapnel from the streets. Even now I can still recall the peculiar stench of burnt wood and pulverised cement from those houses, and the mysterious depths of cellars opened to the sky. I can remember the great fat bulbous silvery balloons like spaceships floating above the Sound, Plymouth’s vast deep natural harbour from which Drake had sailed to sink and burn the Armada. They were there to keep the bombers away from the warships below, which also meant more bombs were dropped on Devonport. The Battle of the Atlantic was at its desperate height just after I was born, and from time to time the great four-engine Sunderland flying-boats would come thundering in across the Sound like great grey geese, gliding low above the long line of the distant Breakwater to touch down in a long straight street of foam.

I saw, of course, no-one killed, no-one burnt, no-one scattered in bits. But many years later my mother told me that one day, as the bombs began their heavy bumping tread across the city and as the earth began to shake, she crawled under her bed with me in her arms - presumably supposing that a 200 pounds shell of high explosive might bounce off the springs, and there she promised God that if, we survived this raid, she would dedicate my life to His.

“Well, thanks a lot, Mother”, when finally she told me this story, was my ungracious response. How ridiculous! How many millions of mothers the world over have done the same? Even so - although I still don’t believe in this kind of predestination, I admit that I have spent much of my life trying to understand God. And I suppose this is a kind of service. Perhaps is not what my mother imagined, but if a butterfly’s wings can begin a storm, who knows what a frightened woman’s prayer may do. Of course, there must be more to it than this, but clearly life is not all completely random. I mean by that that surely there may be some organisation in the world higher than life. To think otherwise would be vain, would it not?

I was a clever little boy and I wanted to be a chemist, I think because I liked the idea of making discoveries. I especially liked bangs, but by the time I was a young man my family could not afford to let me go to university to study chemistry as I had hoped. I joined the Army instead, and for the first half of my life I trained as a soldier and as an engineer. I enjoyed being both, and the Army did send me to college. But I was soon in secret, and later in much more open conflict, with the belief of my government – in fact a not unusual belief of most governments - that the freedoms that it valued, and that I value too, are best defended by military force.

In extremis, of course, this must be true. But because no other solution seems seriously to have been sought, many of the most ingenious minds in history were employed to build arsenals of horrifying weapons sufficient to murder all life on Earth.

I could not accept that this had to be accepted. And on even the smallest scale the same logic was being applied. For years I struggled with this absurdity: that so much genius was being directed to find ways of killing people more effectively, rather than to learn how to share their feelings and reconcile their differences.

Of course I simplify the problem. For much of the century the real problem was of movements emerging in consequence or as a reaction to one another, yet also sometimes apparently in complete isolation, but which all began with the premise that dialogue with others, let alone dialogue with their identified opponents, was simply impossible. It was as if they could not even translate their own thinking into any other language: as if only they knew and spoke the truth.

I did not understand why this was happening.

But then, without any actually conscious preparation for it, I was astonished by a most unusual experience. I could only recognise that it was unusual and that it was also dangerous to know. But it showed me that there is indeed an alternative.

At first I found it very hard to explain. Even now it is far easier to demonstrate that to describe directly. What I had realised was that as well being the best avenue to peace - other than the war that is so totally decisive that it destroys for ever all opposition - democracy is also an expression of the fundamental need of the spirit for freedom. By spirit I mean here that higher level of consciousness that does know that it is conscious, and the higher level of curiosity – which not all people have a lot of: it can be destroyed – which tells consciousness that there are always more questions to ask.

Perhaps I have not made it very clear just now why I find this insight so important. I think it is still the best that I can do. I also began to realise that without this fundamental understanding of its purpose, the forces and laws which would defend democracy lose the skills and subtlety which together are their strength. They become instead a blind and deaf and dumb and angry giant, lashing out at every injury and possibility of threat, trampling around the world until no differences are left.

But this is surely wrong. Freedom must encourage differences, not suppress them. Why is that we are we made to feel that differences are frightening?

I left the Army quite peaceably just a few years later, and needing an income for my family I became a teacher; and having some small ability in mathematics, naturally enough I became a mathematics teacher.

It is strange now to relate, but after I had first learn how to survive – a skill, incidentally, of a very special kind, for the terrors and dangers of a classroom are very real: the insolence of spoiled children; the disrespect of angry parents demanding that the teachers, and not to their children, succeed; the casual treachery and betrayal of one’s supposed managers and leaders; the exhaustion of spirit and humour and strength: all of these would seriously test the SAS.

But after I had learnt to survive, I began to realise as well that mathematics is inspired by the same spiritual imperative - has the same determination and the same courage to sustain it - that I had been privileged to glimpse as the source of democracy’s imperatives.

And I think this is secret of our age: that mathematics and democracy have the same source, and it is spiritual. We live in a world almost entirely dominated by mathematics, by its ideas, its strategies, and its creations. And therefore to learn to use mathematics as the tutor of democracy could create - I realised - the foundation of an enduring peace. If people believe it is God’s plan that only a fraction of mankind shall survive, and it is them, they should listen to another message. The Kingdom is not, actually, up there; it is within us. Instead of learning to kill those whom they are so sure are evil, or to let them die, which is much the same, people could learn to listen, to learn from others, to be unattached and attentive. The secret is: there is no secret.

But there is another connection. Mathematics has a close kinship with music. Professor Leonidas Xanthis, one of my newer friends, calls mathematics music’s younger sister. The fact is that creative mathematicians and musicians enjoy what is perhaps the greatest freedom of the human mind. Together they explore a universe of astonishing wonders and miraculous adventures far surpassing any fantasy of Tolkien or Harry Potter. All that we require of them, in return for supporting their adventures, is that they return to try to tell us of the wonders that they find.

And the fact is: they do. Musicians have an obvious audience: pairs, usually, of ears. But mathematicians instead ask us to learn with them with our minds.

Now at first this seems most surprising. But the more I thought about it, the less surprising and the more significant it became. Special knowledge, however it is gifted, was once understood only as a source of power. In many cultures it still is. But around three thousand years ago, out of the warring tribes of Greece, a miraculous nation was born. Instead of listening to and instead of only obeying their leaders and priests – instead of under standing them: the word is a relic of that time – they began to determine their policy and laws themselves, by consensus, even changing them from time to time as their needs changed.

I do not pretend that all this came to me as symphonies to Mozart: ‘just needing to be written down’. I am a slow and dogged thinker. Cautious, doubtful, and thorough, to be more sure of what I was discovering I needed to check with many authorities. One of the first of these to encourage me, most wonderfully and: generously, was Professor Noam Chomsky at MIT in Cambridge, Mass. “I think you may be onto something!” were his exact words. He also wrote that sometimes he is not ever sure of what he means to say himself until he hears himself speak! This is not modesty. Words are shaped by thoughts, but also form thoughts. Another was Horace Barlow, professor of physiology in Cambridge, England, who assured me that of course talking strengthens learning. Another was Professor Eugen Wendler of the Technische Hochschule in Reutlingen, the historian of Friedrich List, whose story deserves an entire other chapter. Although some ignored me, many others were generous as well. One day I promise I will make a list.

But altogether it was over a decade before I was ready to speak my thoughts out loud. The methods the Athenians had adopted they called techne logos, talking reason. We now call it mathematics. They called it democratic. Slowly I began to understand how these two ideas – today apparently so widely separate and even incompatible – actually should and can and do work together.

The Athenians’ democracy did not always work perfectly well. Their decisions were often vengeful and cruel. Socrates was a famous early victim of their spite. Women were publicly excluded from their decisions, but in their salons – and no doubt in the baths and their beds - they were as forceful and as influential as their men. Together their genius and courage of these early Greeks, a nation a few just million strong, changed forever the intellectual and spiritual evolution of mankind.

But even if I now felt ready to speak, it was not easy, as an ordinary and unremarkable classroom mathematics teacher, to find an audience to hear. Despite the personal approachability and friendliness of many professors, in England as in many other countries an academic apartheid is fiercely practised whose purpose is to keep supposedly lesser minds – lesser being unqualified - precisely where they belong: out of hearing and out of sight. I do not mean to sound angry. There are perfectly good reasons why cranks should not be heard. There is still a tendency to suppose that the qualifications gift automatic superiority. This in my experience is not the case.

To Ingolstadt, in Bavaria, therefore, on a frosty winter afternoon, to speak as an invited guest at a conference of distinguished German academics. They knew nothing about me but I was introduced – by their friendly president, only slightly bemused - as their honoured visitor from Oxford, I stood and addressed the room of politely smiling faces. I intended to stir them up a bit. “Gentlemen,” I told them, “I have come here today to tell you that if in the 19th century your predecessors had taught mathematics in Germany correctly connected with democracy, your country might not have lost its democracy twice: first to the Kaiser, then to Adolf Hitler.”

I paused to see the effect. And as what I had said – of course in English – was slowly understood, their smiles slowly froze. It was freezing outside. The temperature in the room seemed to fall so fast I expected to see my breath. I still believe I was saved from summary eviction by one of my listeners, today a friend, who in this chilly silence raised a bony finger to his colleagues and told them: “One of our philosophers, a German, Alexander Wittenberg, forty years ago said something like this. I did not understand him properly then. It seems this Englishman does. I think we should listen to him.”

And so they did, and later – bless them - they published my thesis. And this is how I began: with their help. Even now, many years later, I feel indebted to them for their kindness, patience and respect.

Mathematics is today the most common language of mankind. It succeeds because it depends on reason and persuasion - and never, ever, on secrecy, authority, or force. Mathematics has developed so widely because anyone can take part:, entirely regardless of their age, sex, class, religion, or race. To win the attention and respect of others in mathematics, all that is required is that your understanding and explanations make sense to them.

I am near retirement now, and although this will doubtless mean that soon I shall be poor again, I am looking forward to it. Although jumping inconvenient fences - real ones, I mean; as I tried recently - has become a painful scramble rather than airy leap, I am not really so old. But I am also tiring of battling dim officials and even dimmer politicians. The truth is unpleasant. They really do not care.

And so all of this is really my parting gift to all of you who wish to make a happier and more peaceful world by means of education, and not through cluster bombs or suicide attacks or corruption or buying the votes of starving peasants.

Teaching is not the key to peace. Teaching deadens minds. Learning is the key. Learning quickens and strengthens minds. It produces youngster who can think.

If you are a teacher, do not wait for officials to notice your efforts. Begin quietly to Teach like Socrates in school. This is rewarding in itself. Outside school you might try to begin teaching RA-AL! to small groups for small payment. One of my own students is a retired aeronautics engineer in Mauritius who wants to do just that. He will start with his grandsons.

If you are a parent, do not let your child’ or your children’s school misdirect and waste their energy, their natural interest and their enthusiasm. Begin to help them learn RA-AL! yourself. I guarantee that you and they will find it is easy, fascinating, and fun. In school they will also leave the competition standing.

Finally I hope that my own understanding and explanations have made sense. If so, this is why we can claim that whoever helps children to learn mathematics properly also creates democracy. Technology, by itself, will never save mankind from the damage it is doing to the world. But techne logos just might.   TOP