Colin Hannaford: Reflections on Math and Thinking and Progressions of the Human Mind?

Jul 25, 2015 by

Colin Hannaford

Colin Hannaford

An Interview with Colin Hannaford: Reflections on Math and Thinking and Progressions of the Human Mind?

Michael F. Shaughnessy –

1. Colin, you recently submitted an abstract of a report to the Carnegie Foundation on the Advancement of Teaching and to its Foundation for International Peace. You must believe you can offer them a proposal of immense importance! What exactly have you submitted, and what do you hope to accomplish by it?

What I have to offer is a path to international peace that children and young people everywhere will want to follow for themselves. The abstract suggests:

  1. that a new species has evolved from homo sapiens. I have named this emergent species homo aeternens;
  1. that homo sapiens lives in a constant present, learning knowledge as habits of belief, responding to challenge to these habits of belief, which it calls ‘facts’, with fear, anger, ultimately with violence;
  1. in contrast homo aeternens is alone in thinking into the future, of assessing alternative ideas and of possible outcomes;
  1. this ability is potentially active in all modern people, and is essential for the healthy democracy;
  1. inventors, explorer, historic innovators of all kinds, are examples of homo aeternens: homo sapiens cannot invent anything new;
  1. that the flowering of homo aeternens thinking in classical Greece necessitated the creation of ‘mathematical’ arguments and later scientific methodologies;
  1. that the essential social value of mathematics is in helping children to recognise thinking typical of homo sapiens or of homo aeternens;
  1. the classroom demonstration and method to achieve this
  1. the possible improvement to social stability and world peace consequent on popularising these concepts, helping young people everywhere to recognise the importance of both kinds of typical thinking and behaviour;
  1. its basis in scientifically established brain function.

2. Colin, I did ask you to be concise in your responses. But this is too concise! Where did you get these ideas!

I guess everyone knows that Isaac Newton saw an apple fall from a tree and discovered gravity. How many millions must have seen that, or something very similar, and did not think: ‘Hmm. That’s funny!’

We don’t find it mysterious now, of course. We say: ‘Ahh, gravity!’ It took an Isaac Newton to turn a simple observation into a major discovery.

3. And yours is?

It also started with an equally simple observation; but many years passed before I realised its nearly universal importance. I had been teaching mathematics for just a few years when I heard a young pupil telling a neighbour how to solve a particular problem: “You do this; and then you do that; and then you cross this out; and double everything … “

I realised, with dismay, that no matter how carefully I had explained the reasons for what they were doing, they were learning mathematics far more simply as habits: ‘You do this, and do that, dadah, dadah, dadah .. and that’s the answer.’

This is good enough to pass exams, at least the early exams. But I did not want my pupils only to pass exams. I wanted them to think!”

4. And how did you do this?

Let me ask your readers to pretend that they are eleven year-olds, and in my class for the first time.

“Clench your fists together,” I told would tell them. “And hold them in front of your face.”

They would all obey; and they would then be invariably astonished when I explained: “What you have in front of you is almost exactly the shape, and size, of your brain. Try it on yourself. Try it on your neighbour. You see, it fits!”

A famous neuroscientist that I had consulted told me that he and his colleagues no longer believed in exact left-right brain specialisation: “But you can tell your pupils. It will be true enough for them.”

So, I would tell them: “Your right fist is the right side of your brain. It has evolved mainly to learn habits: to ride a bike, swim, get dressed. It learns language as habit; manners as habit; identity as habit. But it will never understand why any particular habit is not useful anymore!”

“To understand why a habit works – or, even more important, if it doesn’t work – you need the left side of your brain. This is the side of your brain that can talk, and can ask questions. Learning useful habits is good. Your right brain can store an immense number of habits, many essential for survival. But habits of belief are not knowledge. If, in another few years, you are all still understanding mathematics only as a collection of habit, you will fail.

And the hardest part is that you will not understand why! From now on, with me in these lessons, you are all going to be using the right side of your brain AND the left side to understand mathematics: by hearing simple sentences in your textbooks being read by one of you aloud; by each of you deciding, just for yourself, what you have heard means; by listening to the other’s ideas of what it means; then deciding together which is best. You can disagree as much as you as you like: provided, only, that you wait until I ask your opinion; and provided no one – and I mean NO ONE – loses their temper.

Got that last bit? Good. Now, open your maths books, and we’ll start!”

5. And this works?

It’s magic. It makes learning math enjoyable for everyone; they all get engaged; they learn to think, to listen, to argue; above all, they learn to listen thoughtfully, and to change their minds.

6. But you haven’t explained these homo aeternens people. Nor why learning math like this connects with democracy!

But this IS democracy. This is their first experience of democracy. Once they have learned how powerful is getting agreement through discussion; not from being told what to think, but so that they can all work together, they will never forget it.

Here, too, I worried at first that I might be too far out on a limb. Everyone knows that the Ancient Greeks created mathematics. But could they all have argued about mathematics? This didn’t seem very likely. Most were like us.

An eminent historian rescued me from this anxiety by explaining that this was exactly how mathematics began. It began as a very special kind of argument, for ordinary people.

Democracy in ancient Greece had begun to fail because the rich, and their lawyers, and their speechwriters, were learning elaborate forms of argument called rhetoric. These always worked to their advantage. Ordinary people could not compete. They were being told nonsense. Too often the judges sided with the rich.

The spontaneous response – and this was part of Socrates’ crime – was to develop very simple but very powerful arguments, all with the same form.

Evidence: Connection: Conclusion.

Just three steps and finish. If you disagree, you tell me why!

This form of argument was so successful that rhetoric was cut down to size. Everyone could learn it. Everyone did. It restored everyone’s confidence in democracy. Only Socrates was condemned to die.

7. But then mathematics?

And then mathematics began to take the same form: with permanent success. Many people suppose that mathematics can be learnt as habits: as habits of belief; as facts. But mathematics is really nothing but argument. This is why real mathematicians delight in it so much. They delight in arguing.

And this is what math lessons should teach today.

Teaching mathematics as habits of belief is mentally paralysing, intellectually demeaning, socially divisive, and DULL.”

Forbidding children to question sucks the colour and the beauty, all the joy of invention and discovery, out of their world. Everything of interest becomes ‘facts’ that everyone must accept. They can only respond to disagreement as right brain people: with abuse, anger, ultimately with violence.

This, by the way, is how systems of enforced habit of belief engender contempt and hatred of those not sharing it. The more a system requires its followers to behave as a tribe of homo sapiens, the greater the cruelty justified for those who cannot be part of it. The tribe of the Nazis, of German National Socialism, was Das Deutsche Volk. That of Soviet socialism was called the New Russians.

A poem neatly expressed the contempt that Soviet socialists were supposed to feel for individuals: ‘Who needs a “1”?/Its voice thinner than a squeak./Who will hear it?/ A”1″ is nonsense/A “1” is zero.’

The Zeroes, of course, all ended up in the Gulags, or with a bullet in the brain.

Whenever possible, homo sapiens’ hatred of others leads to mass murder.

8) Colin, much of this is happening in many parts of our world today. And yet you still have faith in young people?

I have faith in the homo aeternens amongst young people.

9. Which you still haven’t explained. Can you please explain how you came to this idea?

It came much later. When I retired some of my ex-pupils asked me to keep in touch by opening a Facebook page. Most people tell others about their love-life or families. I decided to try to explain why wars happen.

10) Which everyone would certainly like to know! Why do you say they happen?

With the help of one of the United States’ most famous physicists, I’m going to tell you.

Professor Murray Gell-Mann is famous for discovering why anything exist at all, that everything is made up of quantum particles to which he gave the name ‘quarks’ to the most basic.

11) Colin, you mentioned a book by him that you found important. Can you tell us about it?

His book is called ‘The Jaguar and the Quark’, published in 1994. I read it only very recently, but it is the reason I sent my abstract to the Carnegie Foundations.

He likens discoveries in quantum physics with sighting the most elusive of all the big cats. I can’t follow all his quantum explanations, but in his final chapter he turns to human problems: ‘The world is experiencing simultaneous trends towards unity and ‘destructive particularism.’

12) Destructive I understand. But what is particularism? Can you explain this for our readers?

He means the habits most humans have of thinking that only their particular group matters: that every other group, and not only figuratively, will go to hell. This is a very serious topic in many parts of the world. It should be taken seriously. It fuels very vicious wars.

He goes on to write that unless these habits are reduced, we will have military competitions, breeding competitions, and competitions for resources at levels that will make sustainability of quality [of life] difficult or impossible to achieve. Seemingly, a dramatic ideological transition is needed, comprising a transformation of our ways of thinking, our schemata, our paradigms, if we humans are to approach sustainability in our relations with one another, to say nothing of interactions with the rest of the biosphere.’

And he insists that this transformation of our way of thinking must be ‘from the bottom up’.

13)  Meaning that it should be learnt by young children?

Meaning that it must be learnt by young people everywhere. Which means must be learnt from ordinary teachers in ordinary lessons in ordinary schools. What is needed is the kind of recognition that everyone can share: the kind that makes everyone respond: “Oh, yes. That’s obvious!”

14)  And you think everyone can learn this from your abstract?

No. I sent it to the Carnegie Foundations simply to establish priority; and in the very faint hope that someone will ask the kind of questions you are asking in this interview. We both know it is unlikely. It is just possible is that one or more of their specialists will start a cat-fight from which some fur may fly. Having some fur in the air could be useful. And then there is this: EdNews and the Internet

15)  But just who will say: “Oh yes. That’s obvious.”

Two of my ex-pupils came to lunch the other day. Notable as young girls, both are now impressive young women: elegant, smart as whips, and challenging.

The lunch I provided was steak pie and salad. They brought wine, with cherries for dessert. They also made a dressing for the salad.

“How,” asked one, “can you describe – very simply – the difference between what you call homo sapiens thinking and homo aeternens?”

“Homo sapiens want to make the past into the present; to have routines that never change; so that there is never any mental strain, or any need for social change. Generally they like to call themselves socialists. Their ideal is that everyone should be equal, in not being different from anyone else. They want to be told: ‘What we are taught to do is correct; what others do is wrong.’

“Because of this homo sapiens is naturally inclined to believing, without protest, whatever authority tells it is true; to doing whatever authority tells it to do; to feel virtue in dying, and killing, in its cause. It is content to depend entirely on the habits it is taught: its habits of behaviour; of feeling; of belief; of truth.

“What homo sapiens calls thinking does not need to produce anything new. Far better, indeed – for everyone – if it does not. Homo sapiens behaviour is entirely dominated by right-brain thinking.

“The modern term is not thinking but processing. The effect is the same. The only future that matters for homo sapiens is in the past, when everything was good. Mr Putin is working on this scenario. Russia must be great again.”

She nodded. “I see,” she murmured. “And I define myself by those from whom I am divided. Yes.”

“Well, alright,” commented the other. ”But just how is homo aet different? And why is it aeternens, anyway? What does the ‘aet’ mean?”

“The root is the same as that in eternal, and eternity,” I replied. “Because homo aeternens uses far more left-brain processing, it must ask questions. It is never happy with the present being the product of the past. It knows the world will change. We can’t stop change. To survive we must be honest about our mistakes; learn from them; do better. Only left-brain thinking can do this.

“Cogito: ergo sum’, declared Descartes, defiantly, and started the intellectual, left-brain, rebellion in the West against the intellectual paralysis created by the right-brain dominance of religions.

“In modern societies, the enormous presence of government, media and entrenched political ideas can easily twisted this into: ‘I think as I am supposed to think; how all sensible people think; how everyone must think. Only this can our country strong.’

“This is the kind of right-brain subservience that always welcomes authority. People too easily forget the wisdom of Benjamin Franklin, one of the brave men who declared America’s independence, who wrote that ‘the first responsibility of every citizen is to question authority’.

And what else could Jesus mean when insisting: “Suffer children to come to me, for God’s kingdom is made up of people like these.”

Young children constantly ask questions, and constantly offer their own opinion, because at this young age their left-brain is far more active than the right. In fact, most youngsters are more individual before they reach puberty, than they will ever be later in life. After that, it’s a struggle.

Which is why we should take Jesus’ advice far more seriously.

Perhaps we should ask: if there really is an eternity waiting for those selected for it, is more likely that those selected will have remained as individual as possible, or is it more likely that those selected will have made themselves as similar as possible to as many others as possible?

16)  What question have I neglected to ask?

That was it!

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