A teacher’s confession

10 07 2010

It was my daughter’s last day at Junior school yesterday. She said a warm goodbye to the teacher she’d had in Year 3, who was leaving the school. She, like my wife, was brought up on the continental system of maths teaching. The teacher confided to my wife, whom she felt an affinity with because of their shared educational heritage, ‘I’m so glad I don’t have to teach maths the way we’re told to here any more. I don’t understand it at all – the only thing I understand about the way they want us to put maths across is number bonds’.


Defining the perception of zero

9 07 2010

David – I’ve just finished reading the section in your book ‘XQ Solution‘ (pp 34-36).

As I am getting to grips with your ideas, I am also comparing and contrasting them to other ideas of number and its relation to thought – in particular R A Schwaller de Lubicz’s Symbolist ideas of Ancient Egyptian thought.

I was surprised to find (and on the conscious realisation of that surprise, it immediately struck me as not really being surprising) that you have found a way to reconcile 2 very different number systems … in your approach.

You contrast 2 to negative-2.

Schwaller contrasts 2 (actually 2/1) to 1/2.

You place zero at the centre of your number line.

Schwaller places 1/1 – an expression of unity made manifest in a dualistic world – at the fulcrum of the Ancient Egyptian number line.

In contemplating that central point, that fulcrum between two points of a dualistic scale, you avoid the trap of dualist thinking – of either going into nihilism or intellectualisation of unity.

Where you meet is in a wonderful phrase you penned as if in passing ‘whatever is in our heads, is to be ignored.’ And you end up in exactly the same place through contemplating an irreducible unity made manifest within you as Schwaller talks of in his contemplation of that point.

You seem to have found a modern way, an original way, of expressing what Schwaller calls ‘the intelligence of the heart’ – to explore the irrational, beyond reason – internalise it, recognise it, celebrate it, live it.

I’m surprised I’ve ceased to be surprised at how rare a quality this is to find and I’m not surprised I’m not surprised at just how wonderful it is when you do find it.

The amazing thing is … it’s out there, within us all … if we care to access it.

The nearest equivalents in the world of rhetoric I can think of are paradox, oxymoron, and improvised connective storytelling – perhaps along the lines of the kind of thing I’ve done with Touchwaves.

Brain gym

7 07 2010

“What are ideas?”

“Hmmm – not sure how I’d define an idea. I’d have to think about it … One thing I do know is that you have them – like having a baby … or sometimes they are so much a part of you it’s more like having a nose, or a navel.”

“What, like conceiving of concepts?”

“If you want to play on words – yes. I think great ideas are self-conceptual.”

“So what makes a great idea?”

“You know (at first the words are spoken eagerly … fast, to gain time to think, and to attempt to seek affinity within the void of uncertainty) … you know (this time, the words are spoken affirmatively, definitively, confidently). It’s not about what the idea is about … it’s the energy, the phenomenon of idea itself. The quality of that idea, irrespective of its content.

It also has something to do with individual expression. Is it your idea? Or is it someone else’s? How original is it? If it’s someone else’s, what do you think of it? What’s your take on it? Where do you stand in relation to it? Which part of you senses the idea the best?

How much energy is contained within your idea? Does it make you feel relaxed or active?

‘What makes a great idea?’ you ask … I don’t know, but I do know that we can recognise it and build that capacity of recognition. Just like training muscles in the gym. We build biceps. We can see them. We also build strength. We feel it. Same with brain muscles. We can train them. It’s not something I’d recommend doing all the time. Chilling out is important, but so is exercising the brain. Sit down (or stand, dance, lie, jump, whatever) to think. Flex those mental muscles. Do some mental sit ups and then see how your mind responds. Questions like that are just signs you know something, you just don’t know how to re-cognise it.”

How do we know?

7 07 2010

“That’s a fantastic idea!”

I looked at David, my mind doing a double flip.

“Yes! But … here’s something … we both felt it … but how? How can you tell?”


“Forget the idea for a moment – how can you tell it’s a fantastic idea? What if we turned our way of thinking right round and decried any kind of ‘good / bad’ ‘fair / foul’ dualistic paired set of labels or thinking? Would we still think it was a fantastic idea? Would it still be a fantastic idea? How do we know? How can we tell?”

“We could … but we both agree that it is a fantastic idea … and I trust that feeling. Plus it makes sense. I’m mature enough not to worry about putting it through the cross-checking mangle to ensure the value is in the fabric, not the transient water which was clinging to it, or send the water to a mental lab to see if it was really Fanta clouding the results – heck, there may be a bit of both. We can think it. We can feel it. Feeling isn’t dualistic. It checks out rationally. It checks out emotionally Both are valid. It checks out on both levels.”

“Fair enough. Let’s agree that we’re being open and honest with ourselves, our thinking and our evaluation is correct … how did we get to it? I’m talking about that first moment of realisation. It’s certainly not conscious. Is it something like finding a perfect mathematical construction, but in the world of ideas, not numerical processes? Is there some kind of internal process going on like a gyroscope finding its own balance, spinning in harmony with its environment, like a mental gravitational pull, drawing our minds towards a spinning ‘sweet spot’?”

“Perhaps, but then who or what sets it in motion? What’s it responding to and why?”

Thinking in public

7 07 2010

My preference is to do in public what I advise students to do … give people mythoughts, not my thought process. This is to avoid the awful ums, ers, embolalia that can mar public speaking. However, since this project is about the thought process itself, perhaps different rules apply.  

I am simultaneously both acutely conscious of my ignorance of anything but the most basic mathematical language and also celebrate that, as I come to your specialist subject as a neophyte and the knowledge that I’m no fool – just ignorant of that particular way of looking at things. It’s a unique viewpoint that has its advantages and disadvantages – simultaneously positive and negative.

As a result of my interest in rhetoric, I have delved into classical studies and see a possible connection in philosophical and/or mathematical logic … see




Perhaps there is a link within these disciplines to Applied XQ?

All the above serves is to outline a strand of my current thought processes around Applied XQ for what it’s worth. Do you see any connections yourself at first glance?

contributions welcome

7 07 2010

The new applied XQ direction enables peeps to contribute thinking that springs out of our understanding of our own existence, directly or indirectly related to maths.

I hate stats

5 07 2010

Ok, I don’t really hate them. I am deeply suspicious of their use, especially when applied to eliciting aspects of the human condition. So, it was with great relief that I came across an article by Karl who quotes Jung:

“If, for instance, I determine the weight of each stone in a bed of pebbles and get an average weight of 145 grams, this tells me very little about the real nature of the pebbles. Anyone who thought, on the basis of these findings, that he could pick up a pebble of 145 grams at the first try would be in for a serious disappointment. Indeed, it might well happen that however long he searched he would not find a single pebble weighing exactly 145 grams.”

Quite simple, quite brilliant.

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