the trial…

12-ness and 10-ness (and all number-nesses) are not in space-time. The humans however, are. At least they are normally considered to be so…

If one decides to ‘reduce’ 12-ness and 10-ness to objects in the world perceived as ‘normal’ by these humans, and further, if one desires them to be yet even more reduced into identical objects in what is known as ‘reality’, then let us then ascribe to them the property generally known amongst them as ‘cubic’ and let us then use these ‘cubes’, sometimes known as dice, in the following court case:

These are the statements to be put to the people:

Prosecution:  “These 10 cubes are henceforce to be considered superior to these 12 cubes.”

Defence: “These 12 cubes are henceforth to be considered superior to these 10 cubes.”

Challenge: Set up a situation in which the pros and cons of this matter are considered and then judged by a jury of impartial citizens…

huatou: is 12 in the ‘real’ world ‘better’ than 10 ?

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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.

WARNING: DEFINITELY DO NOT USE IT RIGIDLY AS A ‘COURSE’

awareness 2 some examples in rod pre-number…

some algebra before arithmetic pre-number awarenesses

examples of free play awarenesses:

rods are good things to play with

we can make pictures

we can build models and buildings

we can play games

we can invent games

we can share our ideas

we can learn from each other

rod colours are in families

rods can be packed away in family colour order if we like

rods can be packed away in other ways

rods have a definite regular order of size

I can recognise rods by how they feel

rods can be named by colour and in other ways

directed informal awarenesses:

rods of same colour are same length

rods of same length are same colour

groups can be made of the same colour

groups can be made of the same lengths

language (word concept) awarenesses:

trains can be made in a variety of ways

rods can be swapped for others

 staircases can be made in a variety of ways

 mats can be made

mats can be made with rows of rods of the same colour

we can answer questions by making patterns of rods

awarenesses relating to adding and its inverse:

I can find one rod to fit two others

I can find two or more rods to fit one

I can find rods to fit long trains

I can find the difference between two rods in different ways

I can find the difference between two trains of any length

awarenesses relating to equivalence, multiplication and factors:

I can find one rod which fits two or more rods of the same colour

I can find rods of the same colour to fit some other longer rods

I can find rods of the same colour to fit some, but not all trains

the ferrer diagram of 12 as monochrome trains…

‘Ferrer’ means ‘complete breakdown’ that is all.

This below is a breakdown of 12 showing its prime factors:

12

Each row contains ‘trains’ of the same colour. You would ask children to ‘make as many trains of the same colour as you can find that will fit underneath twelve’

(or something else of the same meaning…)

you can call 12 a composite number if you wish…

if a number only has trains of white and itself it is called a prime number…here’s a few:

ferrer 2 comp primes

however the main thing here is to notice that

the number twelve has a very rich internal structure

If you are completely and utterly aware of this, many things become easier to see, conversely, or should I say, inversely,

if you are not totally and instantly aware of the inner structure of 12

THERE WILL BE PAIN…

(particularly with operations involving fractional parts)

let’s hear it for the rods…

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.

Welcome to OBJECT ORIENTED REALITY…

huatou: I am the world