Pythagoras’ Theorem Examination

exam2

sorry…

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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

the flip law 2

it works for multiplication and addition but not subtraction and division.

in multiplication it works for fractions as operators too

play yourself…you must own flip it as second nature

ps the normal name for flip it is the commutative rule

pps dressing is not commutative – you don’t put your socks on over your shoes

the flip law 1

This rule is profound and will change many things, illustrated here with a few rods:

SONY DSC

language and rod domain (with a bit of number):

two threes is just as long as three twos, and also they have the same volume

number domain with some signs:

2 x 3 = 3 x 2 = 6

al-jebr domain with signs:

a x b = b x a = c

more and more abstract, more and more general

disambiguation blurb: in the ‘real’ world, two green rods is not the same as three reds. This is why some people object to agreeing that 2 x 3 is the same as 3 x 2. They are correct. However, in the number domain, the answer, which is a pure number, is not affected by the order. The product as a number is invariant to the transformation. If you want another example, it is as invariant as taking a homotopy group functor on the category of topological spaces. You probably don’t need this information. As most people working on calculations are looking for ‘the answer’, one can say that for all intents and purposes, calculationally speaking,

the order of operations in multiplication is irrelevant

further more, if you wish to mention it, and which also makes no difference to the product, the number sentences, transformations or equations, whatever you want to call them, contain the sign ‘x’. This sign is called an operator and it has to be attached to something. It has to be attached either to the first numeral or the second in this case. If it is attached to the first numeral, like this ‘2x’, this ‘whole’ is again called an operator, in this case a ‘doubling’ operator. In language it says ‘two lots’ or ‘two groups’, so this, 2x  3 says

two lots of three or two threes

2x  3

with little children, the easiest and most meaningful form is by using this choice in the attaching of the operator

because:

a) just like in reading, one reads the first numeral first and

b) one doesn’t have to hold the first number in the mind to the same degree as the form below whilst reading the second number. (Saying ‘two threes’ seems somehow less complicated for little learning minds than saying ‘two multiplied by three’)

c) one doesn’t even have to mention the ‘x’ in language, merely recognise it ….two threes

nevertheless the product is still invariant to order

if the operator is attached to the 3, we get 2  x3 which says:

two multiplied by three

2  x3

most teachers call this the ‘correct’ way, but it is just one way

the x3 becomes a ‘trebling’ operator

so, in summary, and for the benefit of little children:

THE ORDER IS IRRELEVANT

and this 2 x 3 with the operator ‘x’ in the middle, at first means ‘two threes’ to little people

later, with much practice, it looks like ‘two threes and three twos’ at the same time

(ps you can introduce all the other ways of saying it whenever you feel it’s appropriate)

JUST UNDERSTAND WHAT’S GOING ON…