“He found his release and fulfilment in the classes in which he himself was a student. There he was able to recapture the sense of discovery he had felt that first day, when Archer Sloane had spoken to him in class and he had, in an instant, become someone other than who he had been. As his mind engaged itself with its subject, as it grappled with the power of the literature he studied and tried to understand its nature, he was aware of a constant change within himself; and as he was aware of that, he moved outward from himself into the world which contained him, so that he knew that the poem of Milton’s that he read or the essay of Bacon’s or the drama of Ben Jonson’s changed the world which was its subject, and changed it because of its dependence upon it.”

‘Stoner’ by John Williams

what drives exploration and investigation?



Surprisingly, it is not the intellect.

The intellect may well be utilised as a tool but it is not the driver.

How do you lay yourself open to inspiration?

There is a big difference between simile and metaphor: If you are asked to dance, quietly feel the difference between ‘dance like a bird’ and ‘you are a bird’. If your presence can be filled with images , thoughts and feelings of you as a bird, and you forget the other story of yourself, you will dance well. As soon as you become aware of dualities, for example between what you are being and what others think you are doing it will fail.

When you are the bird you feel your feet clutching the branches, the wind in your face, the hardness of your beak. When you slip out of this into dancing like a bird, the duality reappears and you become fragmented as usual.

This non dual deep belonging is not a mental visualisation. All activity is transformed. Spontaneity appears. The person you were, or you normally think you are is not present. That story has vanished.

There is no one left who dances, there is only the dance.

The actor does not act the part. Only when the actor as person is absent does the other temporarily emerge. The other is the creative mathematician, the scientist, the artist, the writer.

That’s all I can say about becoming an explorer.

The main problem is that people do not believe they can explore, they do not believe they are capable, they believe the story of themselves that is their normal story which has unfortunately been constructed over the years by inadequate experiences.So treat yourself how you would wish to become.

Do not fear the judgement of others.

Forget ‘can’t’, ‘don’t want to’, ‘don’t like’………….

Be imaginative, be explorers.

Find things that have never been seen by you before.


Find out something you didn’t know before about a square

like learning a language…

Some methods, especially those that rely on memory and de-contextualised vocabulary and intense grammar are awful. They start with lists of words and complexities of grammar that generally mean something to those who have studied grammar in their own language but feel so fragmented and distant from speaking that one senses its going to be very hard going. The best (in my opinion) way of learning a language is through a live course using ‘The Silent Way’, which was created by Caleb Gattegno as he learnt how people learn. Some other methods however such as the Michel Thomas courses are very good for learning at home. I personally am learning arabic using this method and find in some ways it is like learning maths in the style of the subordination of teaching to learning. I could not find a course on arabic using ‘The Silent Way’.

One immediately feels useful learning is taking place and a certain hopefulness and confidence to continue takes over. It feels optimistic and fruitful. Arabic is a bit tricky because of the written language, the unfamiliar sounds and the unfamiliar words having in general no Latin roots. Most words are completely different to what an english speaker knows and the word order and other things are also unfamiliar.

OK so this sounds a bit like coming across mathematical ideas when you are little.

The knowing use of algebraic ideas in simple conversations and question and answer ‘sessions’ using the rods is similarly freeing and powerful. You can just see it so easily in the children’s eyes and actions. There must be no pressure at all. Certainly no pressure to write anything down, unless it comes from the children, and even then do not force them to ‘write it down correctly’. Do not ‘be a teacher’ in that sense. Bide your time.

Look at Caleb Gattegno’s  ‘Mathematics with Numbers in Colour’ Book 1, part II, ‘Qualitative Work with the Rods.’  ONLINE…

Don’t take it as a ‘course’, just read it through three times:

1. As if you were reading a newspaper

2. As if you were reading it out aloud to another person and

3. Try and fathom the general flow and gist of the chapter.


the symbol of infinity…

Norman Cantor notes the three roles Boniface played that made him “one of the truly outstanding creators of the first Europe, as the apostle of Germany, the reformer of the Frankish church, and the chief fomentor of the alliance between the papacy and the Caroligingan Family”. Well that’s as maybe , but people say that the first instance of the appearance of the sign for infinity was in St. Boniface’s cross…

I am doubtful.

here it is:


and again, somewhat purified:


I would say these are re-arrangements of arcs drawn by compass and not this:

Dekes-Techniques-103-infinity-symbolThis sign was first given its current mathematical meaning in “Arithmetica Infinitorum” (1655) by the British mathematician John Wallis (1616-1703).

Thanks John…

gattegno buddhism and critical theory..ah well…

Gattegno maintained there were 4 stages in learning:

1. there is something to be explored

2. the exploration of this ‘field’

3. practice in this field leading to mastery

4. transfer of this knowledge to wider fields

The Four Noble Truths of Gotama Buddha, the cattari ariyasaccani are:

1. an unsatisfactory state exists

2. how this ‘suffering’ arises

3. how to end this ‘suffering’

4. the means by which this ‘suffering’ can be eliminated

In his book ‘The Idea of a Critical Theory’, Raymond Geuss describes a typical critical theory as being ‘ a transition from an initial state of bondage, delusion and frustration to a final state of freedom, knowledge and satisfaction.’ Further, he defines a typical critical theory as consisting of three parts:

1. the belief that a transition from the initial state to the final state is in fact possible

2. the demonstration that this is in fact necessary

3. this transition can come about if one follows the particular tenets of that critical theory.

Well, at least, Gattegno, the Buddha and Raymond Geuss have in common the idea that…


but it is clearly not going to be a push-over

huatou: is it possible to change?

refutation of previous post…bugger

An instance of a class is maybe too like the class itself and each instance has the same behaviour other than by variation in its member variables. A sub-class in an OO hierarchy takes the behaviour of its parent and adds characteristics. These additional layers are maybe what our own selves add to what it really is. So this analogy is better:

Traversing the class hierarchy back to the root class

with many thanks to Myrthis Lathrop Jnr.

huatou: what is my root class?

the ultimate zen assessment – pseudo object oriented reality…

Warning – the analogy to object oriented programming is FALSE

(if you want to see the point of this post go here)

Everything you and I perceive takes place in the mind. Your senses provide information to your mind. Your mind becomes aware of what you call reality due to information supplied by your senses which is then subsequently processed according to your established interpretative neural networks. These networks are evolved through awareness and analysis of these perceived conditions during your evolution as a perceiving, conceiving being… i.e. whatever you have experienced and then ‘made of’ these experiences.

Clearly, this involves your total historical and psychic environment. It is then clear that ‘this certain something’ that ‘you’ perceived was an interpretation of an interpretation, and was only an image of ‘the real thing’ whatever that was. This certain ‘real thing’ cannot be known absolutely. That is why great masters such as HUANG PO pointed out the ‘error’ of conceptual thought processes:

“There is no  “self”, no “other”. There is no “wrong desire,” no “anger,” no “love,” no “victory,” no “failure.” Only renounce the error of conceptual thought processes and your nature will exhibit its pristine purity-for this alone is the way to enlightenment.” HUANG PO, Wan Ling Record 24, p.86.

This ‘error’, is merely the knowing that what is perceived as ‘the truth, the Absolute Real Reality,’ even in its brute external form, as Searle would describe it, is NOT IT ITSELF. It is only ‘one interpretation of it’, and this is all we CAN KNOW. We cannot know ‘IT ITSELF’, because for us there is no ‘it itself.’ All we can know is what we perceive and then conceive through interpretation. This is relative reality and is different for all beings. This is ‘our world’… This is ‘my world’, this is ‘your world.’ This is why it is said that we ‘create the world.’ This is why there are as many cities you live in as there are perceivers of the city. There is not ‘a city’. There are no unique events.

Clearly there are ‘events’ at some level. There are earthquakes, there are floods. There are divorces. There is love. You will be hurt by the master’s stick. Yet you are the perceiver. You ‘create’ your specific take.  You create ‘your’ world. The external, the unknowable, is the CLASS which is knowable to us only as a fragment or ‘taste’. The specific, our individual  realities, are the INSTANCES.


huatou: I am the world

borges and the infinite book…

I made the image below because I was inspired by Jorge Luis Borges ‘The Book of Sand and Shakespeare’s Memory’ from the story of the same name. A Bible peddler from the Orkneys knocks on the door of a fifth-floor apartment on Calle Belgrano and persuades the occupier to buy it or rather trade it for a black-letter Wyclif bible and a week’s pension. “Summer was drawing to a close, and I realised that the book was monstrous…….I considered fire, but I feared that the burning of an infinite book might be similarly infinite, and suffocate the planet in smoke.”


It is a very high resolution image which can up to 2 metres long at photographic quality. Here’s a tiny sample:


I made the old book by scanning and knitting together an antique book I have, given to me by my father. The book could be called ‘The Book of all Books containing the first four letters of every book that has ever been written, ever will be written or ever can be written.’ I wrote a computer program to generate every combination of the first four letters of our alphabet then selected some of it to include in these two pages using an old english font. The program generated over 600 pages of Word as it found combinations of even the first four letters. Every beginning is there, including the Bible and Trainspotting etc, for any writing. It is at one level a little representation of that awkward idea infinity.

huatou: all is love