48

 

 

48 6x8 2x3x2x2x2

 

The LHS shows 6×8

The RHS shows 2x3X2X2X2  dust ( the 8 is 2x2x2 and the 6 is 2×3 )

As far as the number 48  is concerned the order of rods in the tower is irrelevant, but this needs ‘proving’. Take my word for it at the moment.

48 6x8 2x2x2x2x3

 

So long as the tower is constructed using the rods on the right, the order is irrelevant.

So, as 2x2x2x2x3 is the dust, this means we combine these a pair at a time in any order:

try it yourself..that’s best…but

here’s my mind at work for example:

start with 2, double it double it double it, that’s 16, times 3 is 48 (2 4 8 16 48)

2 threes are six, double it, double it, double it, that’s 48  (6 12 24 48)

2 twos are 4, two fours are 8, three of them is 24, double it, 48

and so on…..

IF YOU HAVE THE TIME AND THE SPACE IN SCHOOL TO DO THIS TILL THE COWS COME HOME AND YOU ARE LITTLE, AND YOU START SLOWLY WITH THE NUMBERS UP TO 10 AT FIRST, STUDYING THE NUMBERS ONE BY ONE FOR A DAY OR TWO EACH FOR EXAMPLE WITHOUT STRESS, YOU WILL ‘GET A FEEL’ FOR THE NUMBER YOU ARE STUDYING WHICH WILL BE VERY POWERFUL IN YOUR FUTURE STUDIES OF THE NUMBER SYSTEM AND OPERATIONS YOU WILL NO DOUBT BE REQUESTED TO CARRY OUT…

(In general, the present school arrangements almost totally inhibit this…)

ps 6×8 is one piece of your ‘tables’, using the dust you see and get the ‘feel’ for 6×8, 8×6, 3×16, 16×3, 2×24, 24×2, 4×12, 12×4, never mind ‘half of 48 is 24’, ‘half of 12 is 6’, ‘half of 48 multiplied by 2 is 48’, ‘a quarter or fourth of 48 is 12’, ‘an eighth of 48 is a half of 12’…and so on till the cows come home…

yap yap yap…

TRY IT

 

 

 

 

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the huatou, ‘dust beats tables’

dust beats tables

A huatou is a short phrase which embodies an insight into the Dharma. The Dharma is ‘The way of the Buddha’, but here we are obviously not using it in that sense. It is used in the whimsical sense of ‘The way of the Rod’. However it is not entirely whimsical.

Longer versions are called koan (from the japanese) or gongan (from the chinese).

In the correct use of gongan or huatou one should not seek an intellectual understanding, philosophical ideas or verbal insight but rather an intuitive apprehension of heart-felt meaning. It is similar to the appreciation of a poem. The result is felt more than thought.

‘zen’ is the japanese transliteration of the chinese ‘chan’, which is in turn derived from the sanskrit ‘dyana’…

Here is a traditional chan huatou:

‘In this red hunk of meat, there is a person of no rank who goes in and out the gates of the face. Who is that person?’

dust lies on top of tables…

SONY DSC

Here’s 8 with its factors: ‘two fours’ and ‘four twos’ which you see to the right.

Remember if you can find rods of the same colour which are the same length as another rod, as in the picture to the left, they are called factors of that number.

At the extreme right is the DUST of 8, ‘two times two times two’, 2x2x2

This is the ATOMIC STRUCTURE OF 8 in terms of multiplication.

Why is it useful and very very good indeed?

Because from the dust, 2x2x2, you can, if you feel like it:

Build ALL combinations of factors of a product

THIS BEATS ‘tables’

DUST EATS ‘tables’

DUST IS ABOVE ‘tables’

DUST BEATS ‘tables’

DUST LIES ON TOP OF ‘tables’ AS WE KNOW ONLY TOO WELL!

ps if you keep saying ‘tables’ it sounds weird too…

dust – your first view of the number 6

Here is  a six rod, with a mat pattern beneath.

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Each line of the pattern can only have rods of the same colour. Only ‘same-coloured’ rods that fit the 6 are allowed this time and for this reason:

These same- coloured rods are FACTORS of 6… (2 and 3 are factors of 6)

6 is called the PRODUCT

The towers to the right say ‘three twos’ and ‘two threes’. They are ‘crossed rods’ and we read them as multiplications. They are equivalent to the line of red rods and the line of green rods to the left.

They are DUST

They are FACTOR TOWERS in their simplest form

They show the ATOMS of 6, if you like…

The INNER STRUCTURE of 6

6 can be re-constructed from this DUST in EVERY (multiplicative) WAY 

The TOWER OF DUST shows the INNER STRUCTURE of the NUMBER 6

(in the multiplicative domain)