An Interview with Colin Hannaford: About Being 473959

Sep 11, 2007 by

Michael F. Shaughnessy
Eastern New Mexico University

1) Colin, you have recently published a book enigmatically titled 473959. Basically what was the book about and why the title?

Basically the book is concerned with the aim of education. It seems to me an obvious fact that a country’s education system should be about laying the foundation of a unified society; a society with a roughly common understanding about the nature of the world, about the importance of diversity of opinion, about respect for a diversity of people; about respect for the past, present, and future.

Instead, I argue, education in the West especially is fracturing and weakening society, building on and then exaggerating the social and moral divisions that already exist and creating a literal stratification of mutual distrust and exclusion. Our schools do too little to assist successive generations to dissolve these divisions. But this is not – and having been a teacher for nearly thirty years I cannot emphasize this too strongly – because teachers do not care.

They care. But the system of education they are obliged to serve, with its main emphasis on instruction, actively prevents any seriously systemic change. In all societies – in any, that is, smaller than a two-seat canoe – there is naturally a rivalry between tribalism and socialism.

Tribalism, with its chiefs, its warriors and police and workers, is the simpler dynamic. Traditionally the upper tiers are men; the workers, women.

Ideally, socialism offers equal and above all peaceful means for the talented to benefit their society. But socialism is also not new. The Greeks had begun to experiment with it by 500 BC.

Working against this ideal is not just tribalism as a wholly complete, coherent, well-tested culture in itself, but also the very human inclination of the advantaged to maximize their advantages and pass them down to their descendents.

The ideal of most Western schools is precisely to offer ‘equal opportunities’ in order to raise up the talented to equal status with the privileged. But as soon as a teacher begins to teach by instruction, any potential for such opportunities simply disappear. They cannot exist for any average group of youngsters if they are all are required to learn from their teacher’s instruction as individuals.

The inequalities they enjoy – or suffer – then remain essentially intact. There will be those who can fully understand the teacher’s instruction; those who cannot fully understand, but can copy and obey; and finally are those who can do neither.

This is the true situation in most schools. It might not be true if all schools were fully staffed with expert, sensitive, and experienced teachers and if all pupils were attentive, respectful, and ambitious. I have reported on such a school in 473959: an educators’ – and pupils’ – paradise. But since these conditions are only very rarely true, I believe the previous remarks are true nearly universally.

Generally speaking, our systems of education first create a fraction of high achievers. These fortunate young people, most from already privileged backgrounds, are generally held up as the proof that their education ‘works’, that it is effective. The success of obviously less privileged students is also held up, with even greater excitement, as yet more definite proof that the system selects for ability alone.

But even before they leave their teens, many of these successful students are also being conditioned to be both selfish and amoral. They become selfish because they are envied and disliked by everyone less able themselves: who call them nerds. They return this unpleasantness by thinking of everyone less able as stupid. As adults, they are likely to decide that they have a right to reward themselves – as they were rewarded academically – materially without limit or in any way they please. Except if it may profit them directly, they will have little interest in politics; for politics, they will understand, is undertaken to distract, confuse, and entertain the Stupids.

A much larger fraction of young people below this first division are both capable and ambitious. But they are pressed so hard to produce the results that their schools need to prove that they also ‘understand’ the instruction of their teachers that they are obliged both to be selfish and to be dishonest.

Although fundamentally respectful of laws, inclined to think that laws alone restrain both those more able and less able than themselves from destroying order altogether, these students will retain a sneaking belief that success must be accompanied always by a certain degree of concealed dishonesty. As a consequence of this, despite their insistence on the letter of formal regulations, they will not hesitate to cheat or to lie if it seems to them that the alternative, the unacceptable alternative, is to fail. In most Western societies they will form the demographic adult majority. They will be the majority who vote. Generally they can be expected to vote for the kinds of people they expect to represent their values. They will also continue to vote for revealed cheats and liars provided they appear to succeed.

Finally, there is a third division. These are usually already unfortunate before they even get to school. They expected that school will also help them to succeed. Instead they find themselves overwhelmed by demands that they cannot possibly satisfy. Although some teachers will certainly do their best to help them, the endless tests and the remorseless individual competition progressively bewilders, humiliates, and demeans them. The other fractions will soon add to their increasing sense of unworthiness by beginning to reject them as a burden and a nuisance.

In order to give themselves a sense of importance, they are most likely to be the first to be disruptive in the classroom. This is a form of self-defense. It stops anyone from learning. Initially it may be encouraged by the others as a form of entertainment. Later they may turn more violent, more criminal, involve more self-abuse. These youngsters will soon hate all form of authority. They will hate the system. Above all they will hate all who have abandoned them. A glance of disrespect can invite a murder.

So, first of all the book is about the creation of what I have called these ‘social identities’, the labels that schools are actively required to fix on people to make later social engineering easier. Social engineering is the fundamental aim, and I would be against it, even if it promised the most perfect societies, for I do not believe that any group of people, however select, however large, however powerful, has the right to decide other people’s futures: even when it is through neglect; through walking past on the other side.

Whatever their ambitions and claims, this is actually what most of our schools are doing most of the time. I repeat: it is not the fault of the teachers. They, like most of us, obey their orders. It must also be stressed that these divisions are natural. They are inherited from previous generations. What we must do is to find a way to teach youngsters to learn which does not depend on continuing the divisions and exaggerating them. This is possible. We can show them how to work as a team. We can show them how to think and succeed as a team.

2) Now, who is the fellow on the cover of the book ? ( or can I say bloke and practice being British? “)

That young feller on the cover is just me over forty years ago. I was already a high achiever. As a young army officer I had achieved a social identity that gave me an entrée into virtually any level of society. I believed myself, and was believed by others, to be pretty bright. I was also superbly fit with a body like young Arnold. I had my degree, a commission, a uniform, a badge, a rank, and a number.

Although I did not think it at the time, a number is actually as minimalist an identity as any. Part of my thinking in designing the cover – yes, it was ‘designed’! – was a recollection of all those thousands of photographs of young people as young I was then facing a camera which recorded what remained of their identity, just a face and a number, before they were killed. Actually of course there were millions of these, far too many to store. I imagine most were pulped.

But the frighteningly influential German philosopher Georg Hegel, the great high priest of socialism who influenced both Adolf Hitler and Karl Marx, once wrote somewhere (and of course in German: this is my translation) something very appropriate here: ‘Everyone’ he wrote, ‘owes their entire existence to the state, and they have their being in it alone. Whatever worth and spiritual reality anyone possesses are provided to them solely by the state.’

The whole point is that socialism does not need people who know and value their individuality. It finds these people dangerous, disturbing. Most easily it can simply call them mad; a bullet can solve the problem permanently; work and starvation is cheaper.

Socialism only needs social identities. It follows that if you strip anyone of all their social identity – as had just happened to those of millions of solemn faces: suddenly non-persons to their state – you kill them almost as efficiently as in any other way. What may then survive, if anything at all survives, can be very interesting indeed.

3) [Okay], but let’s talk about math instruction – many students here in the States hate it and probably some do also in Britain. What is wrong with the way we teach math?

What is wrong is that the primary purpose of learning mathematics is not well understood. One can even say that it has been completely forgotten: and not just in this past century. I mean it seems to have been forgotten by the early years AD.

People generally imagine today that the purpose of teaching mathematics is first and foremost to detect the higher level intelligence of the high achievers. This is not always achieved; but it is certainly true in a very limited sense. Most high achievers are very like their teachers who are also high achievers: so there is a natural affinity.

Secondly people believe that mathematics is capable of telling these same high achievers a lot of important information about the world, so that they can make the best decisions.

Both of these ideas are very wide-spread. Because both are approximately true, but only within strict limitations, when the limitations are ignored, both are highly dangerous.

The ability to do mathematics – even more, the ability to enjoy doing mathematics – certainly is rare. Both are highly valued – even celebrated – because over thousands of years humankind has made a perfectly marvelous discovery.

It is that just one kind of language can be used to describe and predict perceptions accurately on a perfectly astonishing range of scale: a scale ranging from the unimaginably small to the inconceivably large. It can do this repeatedly. It can do this consistently. It can produce, all by itself, a seemingly infinite variety of sentences. Some of these are found to describe features of the physical world never known before. Others appear to be describing features of an entirely different level of reality which is, it would seem, just as real, even more real, than our sensory world.

So this is magic, pure magic. Mathematics is the most perfect common language ever created, ever imagined, by humankind.

But there are very real dangers when people begin to believe their instruments – or they – are infallible. From natural catastrophes to scientific failures to political mayhem and financial disasters, mathematics has repeatedly failed to describe or predict accurately enough for wise actions to be taken. History and experience has not proved that the rarest performers of this rare art are themselves more perfect individuals, morally, socially, even in some respects rationally more perfect, than the rest of us. They just have their art. Otherwise they are just as imperfect as we are.

But the most serious mistake – primarily the reason why so many students in the States, and in Britain, and, indeed, in most cultures in which individual creativity and freedom, is prized – has nothing to do with the rational perfectibility of any minds.

(I respectfully suggest that you may more safely read the next sentence whilst sitting down, possibly holding onto something fixed to the wall or the floor of your room.)

The primary function of mathematics is spiritual. Its primary aim should be to help young people to explore, relatively safely and together, the whole range of human emotions, both public and private. It should allow them to know something at least of the depths and heights of the emotions, the frustration, the courage, the despair, the sacrifice and joys that have created over millennia the history of mathematics itself.

It should tell them of the quite remarkable range of personalities – the sane, the mad, the sad, the bad, and the becoming mad – of those who have helped create it.

And then it should allow them to share something of the wonderful excitement of exploring the abilities of their minds together: not individually and competitively – for that only destroys their trust and affection for each other; destroys compassion; destroys sympathy. By thinking and arguing and inventing collectively and co-operatively, as a team – and Americans, above all, know the power of the team – in which the strong take pleasure in helping the weak, in which the weak feel no embarrassment at all in being helped; a team in which the great goal is to achieve an understanding that is a genuine surprise and satisfaction to all. In this way they will learn the truth of the spiritual and the intellectual fellowship that is their heritage: E Pluribus Unum

4) When I studied both parametric and nonparametric statistics, I always enjoyed how Dr. Barbara Plake often explained statistical concepts in natural language. Should math teachers be using more verbal language and discussion to teach statistics and higher order math?

Yes! And just look at the deep impression Dr Plake made on you! But it should not be just ‘statistics and higher order math’. I remember my horror – after I had been teaching, as I supposed, and as had also been repeatedly confirmed by the solemn ritual of regular inspections, satisfactorily for nearly ten years – when I discovered that my young pupils had not the least verbal understanding of whatever they were doing in ‘solving’ mathematics problems. I was simply creating teams of little robots. They were programmed to do ‘this’ and then ‘that’ and then ‘that’ and then ‘cross over and do this’. That was fine. But if anything went wrong, they had not the least idea why.

Even more alarming was that when I tried to explain why they had gone wrong, they often not only could understand my explanations, and they did not want to hear them; they only wanted me to show them ‘what to do’. Here is an excerpt from a letter I got just the other from a lady describing her own experience of thirty years ago.

‘When I was 11 I was one of two children sent from my small primary school to a convent grammar school in the days when nuns still taught. Maths is tricky for an unconfident child and it wasn’t long before I was struggling just a bit. I remember a lesson where something had been explained and we were all then left to work from the exercises on the board. Everyone else seemed to be working away but I had no idea what to do, so I thought to myself that I would ask and up I went to the teacher’s desk and I said ‘I don’t understand’.

The reply was a quick and terse explanation of the maths. I still didn’t understand so I said so again. [There was] one more speedy explanation. I still didn’t understand, so the teacher said ‘you are a stupid child, go and sit down.’ I remember feeling horrified and confused and ashamed and over the next few years I slid steadily down the streams to the D stream despite the fact that in every other subject I was an A student. At last in GCSE year, when I was in the CSE class for those dunce-ly students we had an Irish teacher (not a nun) who was gifted in her ability to explain maths and who was also approachable and ready to go over and over things and she encouraged discussion. For the first time I felt joy as I understood maths and I flourished and by the end of the year I passed with an A grade! But I remember well the rage and fear I had felt until that point and I have always thought that I never wanted to do that to a child..[1]


But this is clearly the experience of millions of kids every year. They are humiliated, shamed, and dismissed: not once, or twice; weekly, repeatedly. No wonder, as you say, that many students hate being ‘taught’ mathematics.

And somewhere in this fabulous and indispensable Education News is an article of mine entitled: ‘So, what exactly is a number?’ This is a record of my discovery, repeated every year after the first time I made it, that my new bright class of eager young kids coming to my first school math lesson (this would be fifth or sixth grade to you) had not the slightest notion of what a number is.

I have colleagues who think this unimportant. I have a friend, a professor of number theory, who told me, quite furious at my temerity in exploring this interesting fact with eleven year olds: “I and my colleagues have been trying to decide for the past forty years what a number is: and we still can’t decide!”

But I found that what matters to most of my school colleagues is that these youngsters understand a number as a way to be sure of one-to-one matching: so many in the class means so many bottle of milk; so many at table means so many plates’ so many inches on the rule means so many inches between these two points – and so on.

Which I also agree is fine, up to a point. And yet if this is all that children learn to do: to match one set of objects with another; to match the pattern they create with the pattern their teacher creates, and so on -it must surely be clear that they are really only activating that part of their brain which matches patterns!

“How much of your brain – of your ‘EYE-KWEW’ – do you think you need to do that?” I would ask the class; and the answers would come back: “Not all that much.”

“So how do you think you are going to manage in maths (I’m English) in another few years time if you are STILL only using a half, or a third, or a quarter of your EYE-KWEW.”

If eleven year olds can get the point, everyone should. To gain any deeper understanding of why this or that pattern or action is necessary requires a much deeper understanding altogether than that a pattern seems to look the way it ought to. This deeper understanding begins to be activated only when the mind is required to explain – in words that it articulates itself: and this is also absolutely vital – why.

This is a habit that parents or teachers should begin at the earliest possible age, even as soon as children can read. “What did the Tar-baby do to anger Brer Rabbit so much?” “Why did Brer Fox throw him in the Briar Patch?”[2]

That ought to be easy enough. But by the time students are ready for college, the habit of working out their own explanations of what they are doing and why they are doing it – or even not doing it – must have become second nature. Without this ability, as I once told a very angry young lady, who just wanted me to tell her and her class what to do to pass their exam: “In another two years you will be sitting in a college study bedroom with a pile of books beside you. The door will be closed. You will be alone. Unless you can read what you need to know out of those books and understand it, you might as well stay home.”

She and her class got the point. I did very little board-work from then on.

5) I understand that you are currently attempting to organize a conference in England. What would be the topic and why is the topic important?

There is a clear global crisis in education that various interested bodies – in Britain politicians especially and most disastrously – have been tinkering and meddling with ever since universal schooling was introduced. The crisis keeps getting worse.

An educational consultant, unusually prepared to speak his mind more freely than most, wrote to me recently:

The whole pedagogic model to which we seem so attached – students being told things by teachers – is absolutely flawed. There is little point in the answer to anything unless an authentic question was asked. … I don’t think most teachers have any serious strategy for exploring the depth or integration of student understanding. They are more likely to see a topic as delivered and tested with satisfactory results. Most students (and not a few teachers) anyway lack the foundation concepts on which to build or the crucial wiring together of knowledge in different ‘subjects’ or leaning zones. Alienation from the whole language of learning is widespread. … Knowledge that is held on an instrumental and contingent basis is a transactional currency with little underlying value.’

He also warned: ‘the style of learning [that you propose] would require a huge change in the culture of schools (and teachers) with many basic assumptions challenged. At present negative peer group norms are very powerful and ironically reinforce the sterile delivery and checking culture prevalent in many schools.’ [3]

The ‘negative peer group norms’ used to involve anyone trying to rise out of the second division to the first or from the third to the second to risk being invited to inspect the bottom of the toilet-bowl by their peers. Today the greater likelihood is being beaten or killed. And just when we thought that anyway it couldn’t get any worse, the Remington and the Browning came to school.

But if changing the education culture in just one class is difficulty, how much more difficult is it to change a national culture?

The answer is: it depends on political will. It is now just over fifteen years since I first told a conference of German math teachers that teaching by instruction was destroying the social and the moral basis of their society and their democracy.

They had also just been told by their government that Germany was ashamed of its poor showing compared with other nations – like Korea and Japan – and they had better find a better way to teach mathematics overall.

I was rescued from a lynching by my now colleague, Dr Hartmut Köhler, who with two years initiated a European Union study entitled ‘Mathematics teaching and democratic education’. He and his colleagues are now credited with starting a renaissance of mathematics education in Germany.

Working with teams of teachers in over 50 schools, they have produced volumes of math exercises with the emphasis on finding solutions through discussion by the whole class.

The truth is that none of this is new! It is so very ancient that my American colleague, Professor Hani Khoury, has called it, without too much originality: the ‘Socratic Methodology’.

The basic principle is simple: in order to learn, children must talk, argue, observe, describe, discuss. They will all have a textbook. In the simplest, basic, stripped-down, most Spartan approach, which I favor, they must try to explain to each other the meaning of the explanations in their text-book to each other. Most of the time their teacher, listens, directs, adjudicates, but does not teach. The pupils learn to teach each other.

Since my German friends began their initiative, I and my American and Hungarian professor colleagues have been twice been invited to address the Qatar Foundation on ‘Innovations in Education’.

For over forty years Professor Martin Haberman has become America’s most powerful critic of its own education culture. Recently he wrote the following extraordinarily powerful and simple analysis of what is going wrong: ‘Rather than harnessing “growth” and “socialization” to foster student learning, school people seek to merely cope or compensate for these powerful forces while they never stop trying (and failing) to apply the learning theory of psychology to school learning.[4]

This fits rather well with my own experience. The learning theory that he refers to is the one which concentrates on attempting to isolate the learning of the individual from the distractions of the class. But his point, and also mine, is not only that this is ineffably stupid (one wonders has any one of these ‘learning psychologists’ ever attempted to isolate the attention of even one individual from the rest of the class on a hot, humid winter afternoon?), but that the powerful force that a teacher can enlist is the learning ability of the class as a whole!!!

The Qatar Foundation is headed by Her Highness Sheikha Mozah, consort of the Emir of Qatar and UNESCO Special Envoy for Basic and Higher Education. It is unquestionably one of the most energetic forces for innovative education in the Middle East. Last year I was invited by it to write a program to explain how the Socratic Methodology can be introduced with as little disruption as possible into working schools.

Called ‘Evaluating Change’ – and already published by EdNews – it explains how the culture of individuals learning competitively from instruction, which clearly does not work, can be progressively transformed into the process of whole classes learning to learn competitively and co-operatively, which does!

So, finally to answer this question: the Qatar Foundation has agreed to support a major international conference – either in England or Qatar – to offer this program to national governments globally. Watch this space!

6) On page 47 of your book, you comment “the two most dangerous issues of our times are the fracturing of our societies and the competition of religions”. I concur. Why do you think that religions, that are supposed to profess peace and love and “good will toward men “are so competitive and in some instances, so violent?

If you found my book title enigmatic, the following two statements once seemed to me amongst the most enigmatic ever. There are recorded as being made by the teacher Christians like to call the Prince of Peace. Do you see how they relate to each other?

You probably know the first: “I assure you that, unless you change and become as little children, you will never enter into the heavenly kingdom.” Matt 18.3.

But do you also know the second as well? “Do not think that I have come to bring peace to the world. No, I do not come to bring peace, but a sword. I came to set sons against their fathers, daughters against their mothers, daughters-in-laws against their mothers-in-law; a man’s worst enemies will be the members of his own family.” Matt 10.36 (and see also Luke 12.48).

What did he mean, ‘to become as little children’? Clearly he expected people to understand him easily. He asked for no fee. He was no tease. It is almost as if he is asking people to do something as easy – and he says something like this elsewhere – as just throwing off their coats.

But if it is so easy, if it was so easy – if anyone could become as little children just like that, almost in an instant – then surely there wouldn’t be any need for several thousand kinds of religion, all offering to show people the way to heaven. Surely it would never be necessary for many to have been prepared, or even now to be prepared, to imprison, torture, murder and destroy people: individuals, families, tribes, even entire populations, in order to prove that they alone know how to enter the heavenly kingdom.

Yet since there really is all this competition; since there really is all this violence, in the name of faith in faith, as also of faith in reason, it can’t be very easy. Can it?

The first time I got to put this question to an audience was also the first time that I realized how easy it is.

Mercer University in Georgia invited me to talk about this particular method of learning mathematics. The method is not terribly difficult to understand. It certainly isn’t very difficult for the pupils. As they begin to appreciate what is happening, that they are no longer being pitched into usual daily game of dog-eat-dog or die, they soon begin to show that they enjoy it. Once they to start to learn to think critically and constructively for themselves, they start to feel they are taking charge of their lives. Boredom disappears. Disruption becomes a nuisance. They may even start liking their teachers.

But in addition to my formal lecture, I was asked if I would like to take an evening class in philosophy. This was a very serious honor. I knew the professor and trusted him. I knew that he trusted me. What I did not expect is that the class would be four hours long.

What I supposed to talk about was the theory of Moral Values of the famous philosopher Immanuel Kant. Since I did not know much about Kant, I actually told the story of the chickens and their chicken-house. But then, after an hour or so, I simply ran out of steam. The students in this class were from all kinds of background, but most were women and most were mothers. Most were also black. Their average age was 33.

I soon learned a deep respect for these ladies. Georgia is not deepest South of America, but deep enough. Fifty years ago, most of the parents and grandparents of these students would not have had any thought for their identity. They would have had a place. And that was all they were supposed to know.

Even now most had not been born with any particular privilege. They had been labeled already by their society as belonging to that class that others need have no worries about at all. They used to hang uppity niggers in these parts. Now their place was still roughly where it always was. They could earn enough to live on. They could bring up their families, usually in the same part of town that had always been their place. They could get by. And why should any one of them want any more?

But they did. They all wanted the qualifications that Mercer could give them. Twice a week, from 6 to 10 pm, that was what they were working hard for. They worked by day as well. Most of them got their children up, gave them breakfast, got them on the bus; then they went to work. At least the buses now are color-blind.

Their professor is a kind and gentle man, and when he saw that I really couldn’t think of anything more to say, he prompted me gently from his place against the wall

“Why don’t you talk a little bit about your ideas about identity?”

I threw him a rather worried glance. He nodded: go ahead. But the previous evening we had talked; and we had agreed that this particular idea is perhaps most dangerous and most explosive in history. But it is not new, which means that even now a lot of effort has to go into keeping it quiet, under the wraps, buried.

Everyone today understands the notion of identity. Sex, race, age, color, class, education, appearance, manners, speech, experience, place, religion, history – all of these, we had agreed, still very largely decide the present and future lives of all but the most determined rebels in every culture, in every society, in every age.

All of these are our social identities. Most social identities are complex. Some are unique. But what makes them very special is that once they are formed, once they are given by a mixture of implicit and explicit social agreement and various cultural rituals: this is who you think you must be.

In very many conservative cultures – and that is a very wide spectrum – they are then virtually impossible to challenge or to change. Even in comparatively more socially mobile cultures this included me with my rank, and my uniform and my number. It included their professor. It includes the next President of the United States. For the great majority of people in any culture their social identity is actually who they are.

“But, then,” I asked the class, and I was not just then intending to be especially provocative, “Can you imagine an identity of yours that does not depend on society? If, just for a moment, you can imagine that possibility, this is what I mean by intrinsic identity. This identity is yours alone.”

Even a four-hour long evening class has to end. There wasn’t much more time to talk. But I found myself thinking in that moment that just to ask this very simple, very elemental question: “Am I anything other than who my society says I must be?” has been the beginning everywhere of every advance of the human spirit.

It has also very often been just this thought that has caused sons to be set against their fathers, daughters against their mothers, daughters-in-laws against their mothers-in-law, even making a man’s worst enemies the members of his own family.’

Jesus knew what happens when an adult is reborn. Such people are dangerous to any established social order, even within their own families.

7) Discuss democratic ideas and ideals in terms of teaching math.

At last, I have a simple answer! People very often ask: ‘Why math especially? You claim that math lessons can be used to teach better social manners; to reformulate democracy;that learning to judge and form logical argument in mathematics lessons enables young people to learn to respect, and even value, differing opinions; to learn to give and receive correction without resentment; to learn to listen to one another respectfully; to learn to form and articulate persuasive argument based on evidence and logic.

Sure: this is clearly the basis of democracy. But then why not teach it via other subjects?’

Answer: Of course, one can. But let your pupils know that the first forms of argument that we now call ‘mathematical’ were originally developed in Athenian Greece over two and half millennia ago. But they were not developed to do mathematics. Their purpose was to give ordinary people confidence in reasoned debate, in techne logos as it was called in Greek. Learning techne logos is still a part of learning mathematics. It is not first of all about technology, about respect for machines: it is first of all about respecting people.

8) Is there a better way to teach basic math, I am here talking about addition, subtraction, multiplication and division, than we are currently doing and ensure that children learn it?

The Kumon method of Japan (I own no shares in this company) has much to commend it. It was developed in 1954 by Toru Kumon, a Japanese teacher alarmed that his son was only slowly learning basic operations in arithmetic. It proved so successful that it became a business. (I think the business started by his wife!) It is now world-wide. It requires pupils to complete many hundreds of simple arithmetic sums every week until this practice becomes virtually automatic. This ability gives children much greater confidence throughout their entire future work with numbers. There is also much to commend in the old habit of simply learning tables. That’s how I got started: and just look at me now!

But notice my italics. It is important for children to realize that even such a statement as two plus two is four is not a fact. It is an argument. They should also learn how to prove such arguments are true. They should also know that any argument can be false. They should know that our experience with numbers does not mean that everything can be numbered that is important in life.

9) Should people read your book, learn from it, experience it, reflect on it or be annoyed by it?

Naturally I hope they will do all of those! And sometimes you learn the most from people you most annoy. Once I annoyed, very excessively, an important British professor of pure mathematics. After he had heard me talk about this connection between social value and teaching, he approached, stuck his face into mine and hissed: “You just keep your politics out of our mathematics!”

Alas, I think he had a poor grasp of history. Remember the notion of the Final Solution: the final, complete, definitive solutions to the most maddeningly difficult problems? That phrase came from mathematics into politics. Remember those ‘calculations’ of how many millions Russia and the US could afford to lose to win a nuclear war?Logic is not wisdom. Mathematics can be spelt MAD.

10) What question[s] have I neglected to ask?

The chapters which may be the most challenging for your readers are those which include and follow what you seem to think was an authentic revelation in an Army mental hospital. This is now over thirty years ago. Do you still regard it as important as you may have at the time? Does it have any importance to anyone now: even to you? What do you now think it was? Have you any explanation for it as a real event? Psychiatric doctors at that time are now known to have been playing around with all kinds of psychedelic drugs, with or without their patients’ knowledge. So, here are the harshest questions of all. Could it have been drug induced? Finally, couldn’t you just have imagined it? Couldn’t you just have invented it?

The event described in the 8th letter to Henry County remains the most impressive experience of my life. I believe this would be true of anyone’s life. In my own case the only close second is falling in love. There are very important affinities here, I believe, which should interest you as a professional psychologist; but just for the moment we should – must, I suppose – leave them aside.

In the case of this experience perhaps one remarkable fact is that thirty years on it is just as if there is a high-fidelity recording of it somewhere in my mind. I have only to begin to think about it for it to begin to replay itself: never as powerful as on the first occasion – then I really would think myself mad – but with all the sensations repeated.

First that unbelievably powerful launch clear across the universe, into the void; then the brief wait in blackness; and then this explosive, astonishing, all-enveloping force, like being hit in the night by a train.

But not then splattered and eviscerated like a bug on a windscreen.

Held, instead! Embraced suddenly; held hard; held by an eager, joyful, intensely physical, intensely happy, totally securing, totally identifying, totally possessing, breast-to-breast presence – and then to be told, as if with a great booming, cheerful laugh : ‘What can you fear? You are of me!”

Of course, this is all physically impossible. What is important that it is a real human experience.

The first immediate condition was that all social identity had suddenly been stripped away. There was no pain, no fear of pain – that must be important: fear of the expected but as yet unknown would have been very distracting. There was a certain amount of anger. But certainly, with the knowledge that one is in a madhouse and that one is about to be treated as a madman, every protective layer, every skin, every plate of social identity disappears. This is an unusual state of being.

And we may be absolutely sure of such an experience, that if it is humanly possible, the chance are high – even very high – that it has happened before.

How fortunate for me then that for many years the British press had been scoffing at the nasty habit of the Soviets of dumping political dissidents into psychiatric hospitals and blowing their minds with drugs and electro-shock.

I do not think that I was ever really in danger of this. I was fortunate in meeting the hospital’s military director within hours of arrival. Three weeks later, in our final interview, he told me: “I knew there was nothing wrong with you as soon as we met.” That first evening, however, suddenly I trusted no-one.

I was certainly supposed to be shut up. That was the main idea. The director told me later that his hospital had been ordered to begin my ‘treatment’ as soon as I arrived: ‘without the least clinical examination!’ he snorted.

I have been asked if I think I am a saint. I have also been asked to act as a saint. Neither option had ever seemed to me remotely interesting, far less appropriate. I think of myself as a perfectly ordinary person. I know I am not at all as clever as I would like to be. I have somewhat untidy morals. Most of the time, I drink too much. And by the measure of our societies, I am very far from being rich.

I am perfectly sure that it would have been comparatively easy to get rich on the back of this experience. When Phineas Barnum made his famous estimate of the number of suckers born daily, he was thinking only how many he could get into in his circus tents. When he died in 1891 he was worth 5 million dollars. But in the business of religion – as well as in the military-industrial complex, with which many religions have surprisingly close links – suckers are being born so fast that buildings just can’t keep up.

And the suckers for religions all want to be told: it costs! No-one wants to be told how easy and inexpensive it is to live a life close to God – not to die, I say, but to live – for that would let every scruffy, undeserving deadbeat into the club!

This cannot be allowed. Let us have special rules for entry – and lots of regulations – whisper those who are, or think they are, already safe inside. And let us have lots of special signs and rituals – expensive, by all means – that the riff-raff will never afford. And let us pass down our advantages, each his own – generation after generation, so that we can become a tribe again!

And for every reformer who has ever tried to tell them how inexpensive and easy this is – one of my favorites: one that always makes my skin tingle is that whisper which itself reveals the whisperer’s knowledge of the truth: “He is closer to you that your neck-vein” – for every one of those reformers, I say, who have tried to explain how to take the first step, then the next, then the next – all of them the same: staying close to one’s real identity – there have been entire armies of shysters and con-men who take your money to pay for false identities; always more money, more blood, more lives, more sacrifice, promising always that the final victory is now very, very near now, needing just a few more millions for prayers and a few more billions on arms.

I am not powerfully against religions. I am not powerfully against atheism either. Both, in their different ways, comfort and support; regulate; and explain. Both have used terror and atrocities to further their aims. Both have been infected by the deadliest virus of all: the one that makes people certain; the one that makes them believe that everything that can be known is already written; the one that makes them think they know it.

In the final analysis, however, I submit, it actually does not matter in the slightest whether I imagined that experience of mine, or invented it, or whether it was drug-induced, or whether I learnt it from the lips of some babbling, brain-damaged psychotic, systematically coshed by drugs and electrically lobotomized.

All that really matters is that I spent the next thirty years believing that there ought to be connected answers to the following questions – and quietly sought to find them:

·Is it possible that human minds are inspired to help others?

·Is it possible that the results of this inspiration can be traced throughout all cultures and their histories?

·Is it possible that the result would have a universal, culturally-neutral, common form and direction?

·What would this look like?

·Does it matter what its inspiration is called?

I think I have found these answers. And that, finally, is what 473959 is about.

Oxford, 9th September 2007.

[1]Furtado 2007
[2] Joel Chandler Harris, 1880
[3] Barnes, 2007.
[4] Haberman, 2007.

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