Categorical Deduction for 64-Sq. Diagrams

Note: this paper shows the

**WRONG METHOD**, although with a lot of promise. For the real method, see:

https://www.academia.edu/10161352/Categorical_Deduction_for_64_Categories
[THIS METHOD REMAINS INCOMPLETE! (HERE BUT NOT THERE)]

Recall that the method for 16-SQUARE DIAGRAMS

Involved FOUR DEDUCTIONS

Those deductions were:

[A] ABFE-CDHG-KOPL-IMNJ

[B] ABFE-CGHD-KOPL-IJNM

[C] AEFB-CDHG-KLPO-IMNJ

[D] AEFB-CGHD-KLPO-IJNM

Each of the letters shown in the

previous diagram

DCBA

GHFE…

LKJI

PONM

Now refers to four squares in the new diagram.

The new diagram has:

A first row:

8,7,6,5,4,3,2,1

A second row: 16,15,

14,13,12,11,10,9

A third row: 24,23,

22,21,20,19,18,17

A fourth row: 32, 31,

30,29,28,27,26,25

A fifth row: 40,39,

38,37,36,35,34,33

A sixth row: 48,47,

46,45,44,43,42,41

A seventh row: 56,55,

54,53,52,51,50,49

And,

An eighth row: 64, 63

62,61,60,59,58,57

Remember, there are other

methods

For showing the categories

The categories could be shown

cyclically

Within each quadrant for example.

I will keep the method I showed here

Because I feel it is the most objective.

Now remember, each of the

categories from 16 square

Corresponds to four of the categoiries

In 64 squares.

64 = 16 X 4

Otherwise the method would not

Reveal itself

So easily.

Now we know that:

‘A’ refers to

1.2,10,9

[Listed in cyclical order]

‘B’ refers to

3,4, 12,11

‘C’ refers to

5,6,14,13

‘D’ refers to

7,8, 16,15

‘E’ refers to

17,18,26,25

‘F’ refers to

19,20,28,27

‘G’ refers to

21,22,30,29

‘H’ refers to

23,24,32,31

‘I’ refers to

33,34,42,41

‘J’ refers to

35,36,44,43

‘K’ refers to

37,38,46,45

‘L’ refers to

39,40,48,47

‘M’ refers to

49,50,58,57

‘N’ refers to

51,52,60,59

‘O’ refers to

53,54,62,61

‘P’ refers to

55,56,64,63

Now, we know that opposite

numbers do not combine!

In terms of coherent quadra,

That means position A

Does not go with position C

Position B

Does not go with position D

That process was used once in

The 16-SQ diagram

Now we apply it again in the

64-SQ diagram

AGAIN,

The deductions for 16-SQ.

WERE:

[A] ABFE-CDHG-KOPL-IMNJ

[B] ABFE-CGHD-KOPL-IJNM

[C] AEFB-CDHG-KLPO-IMNJ

[D] AEFB-CGHD-KLPO-IJNM

So, the deductions for 64-SQ.

Merely involve:

Applying the cyclic order

For each quadrant

(within the numbers…)

SUCH THAT:

The two combinations for

Each cycle

Are maintained AT

EVERY SET LEVEL

Before we ascertain that,

We must find the quadra for every level.

The first two quadrant levels refer to the

16-SQ. diagram.

The third quadrant level refers to the

numbers.

We have already determined

the corresponding numbers

Quadrant A refers to:

ABFE

Quadrant B refers to:

CDHG

Quadrant C refers to:

KLPO

Quadrant D refers to:

IJNM

Now we substitute the

numbers:

QUADRANT A =

A: [1.2,10,9]

B: [3,4, 12,11]

F: [19,20,28,27]

E: [17,18,26,25]

QUADRANT B =

C: [5,6,14,13]

D: [7,8, 16,15]

H: [23,24,32,31]

G: [21,22,30,29]

QUADRANT C =

K: [37,38,46,45]

L: [39,40,48,47]

P: [55,56,64,63]

O: [53,54,62,61]

QUADRANT D =

I: [33,34,42,41]

J: [35,36,44,43]

N: [51,52,60,59]

M: [49,50,58,57]

NOW,

Part A of every level

Only relates with part B,D

Of every level

Part B of every level

Only relates with part C,A

Of every level

Part C of every level

Only relates with part D,A

Of every level

Part D of every level

Only relates with part A,C

Of every level

THEREFORE,

Nothing from quadrant A

Relates with quadrant C

Nothing from quadrant B

Relates with quadrant D

And vice versa

This includes the sections of

The numbers which

Correspond to those quadra

At the third set level.

Therefore, we take the 16-Sq.

Deductions:

[A] ABFE-CDHG-KOPL-IMNJ

[B] ABFE-CGHD-KOPL-IJNM

[C] AEFB-CDHG-KLPO-IMNJ

[D] AEFB-CGHD-KLPO-IJNM

The simplest answer is to apply it

To each of the quadra.

This would leave us with eight

deductions, as predicted

Once the deduction is applied

to the overall quadra.

In QUADRANT A:

ABCDEFGH

IJKLMNOP

Refers to:

1,2,3,4

9,10,11,12

17,18,19,20

25,26,27,28

In QUADRANT B:

ABCDEFGH

IJKLMNOP

Refers to:

5,6,7,8

13,14,15,16

21,22,23,24

29,30,31,32

In QUADRANT C:

ABCDEFGH

IJKLMNOP

Refers to:

37,38,39,40

45,46,47,48

53,54,55,56

61,62,63,64

In QUADRANT D:

ABCDEFGH

IJKLMNOP

Refers to:

33,34,35,36

41,42,43,44

49,50,51,52

57,58,59,60

Now a 16-SQ deduction

for Quadrant A

[A] 1,2,10,9-3,4,12,11-

19,27,28,20-17,25,26,18

[B]1,2,10,9-3,11,12,4-

19,27,28,20-17,18,26,25

[C]1,9,10,2-3,4,12,11-

19,20,28,27-17,25,26,18

[D]1,9,10,2- 3,11,12,4-

19,20,28,27-17,18,26,25

Now a 16-SQ Deduction

for Quadrant B

[A] 5,6,14,13-7,8,16,15-

23,31,32,24-21,29,30,22

[B] 5,6,14,13-7,15,16,8-

23,31,32,24-21,22,30,29

[C] 5,13,14,6-7,8,16,15-

23,24,32,31-21,29,30,22

[D] 5,13,14,6-7,15,16,8-

23,24,32,31-21,22,30,29

Now a 16-SQ Deduction

for Quadrant C

[A] 37,38,46,45-39,40,48,47-

55,63,64,56-53,61,62,54

[B] 37,38,46,45-39,47,48,40-

-55,63,64,56-53,54,62,61

[C] 37,45,46,38-39,40,48,47-

-55,56,64,63-53,61,62,54

[D] 37,45,46,38-39,47,48,40-

55,56,64,63-53,54,62,61

Now a 16-SQ Deduction

for Quadrant D

[A] 33,34,42,41-35,36,44,43-

51,59,60,52-49,57,58,50

[B] 33,34,42,41-35,43,44,36-

-51,59,60,52-49,50,58,57

[C] 33,41,42,34-35,36,44,43-

51,52,60,59-49,57,58,50

[D] 33,41,42,34-35,43,44,36-

51,52,60,59-49,50,58,57

We are nearing our final solution!

Now we simply apply the

Formula:

ABCD and ADCB

On two levels!

In every quadrant

It also takes the order:

ADCB.

Thus, Quadrant A

Is not only:

[A] 1,2,10,9-3,4,12,11-

19,27,28,20-17,25,26,18

[B]1,2,10,9-3,11,12,4-

19,27,28,20-17,18,26,25

[C]1,9,10,2-3,4,12,11-

19,20,28,27-17,25,26,18

[D]1,9,10,2- 3,11,12,4-

19,20,28,27-17,18,26,25

But,

[A] 1,2,10,9-3,4,12,11-

19,27,28,20-17,25,26,18

[D]1,9,10,2- 3,11,12,4-

19,20,28,27-17,18,26,25

[C]1,9,10,2-3,4,12,11-

19,20,28,27-17,25,26,18

[B]1,2,10,9-3,11,12,4-

19,27,28,20-17,18,26,25

Quadrant B is not only:

[A] 5,6,14,13-7,8,16,15-

23,31,32,24-21,29,30,22

[B] 5,6,14,13-7,15,16,8-

23,31,32,24-21,22,30,29

[C] 5,13,14,6-7,8,16,15-

23,24,32,31-21,29,30,22

[D] 5,13,14,6-7,15,16,8-

23,24,32,31-21,22,30,29

But,

[A] 5,6,14,13-7,8,16,15-

23,31,32,24-21,29,30,22

[D] 5,13,14,6-7,15,16,8-

23,24,32,31-21,22,30,29

[C] 5,13,14,6-7,8,16,15-

23,24,32,31-21,29,30,22

[B] 5,6,14,13-7,15,16,8-

23,31,32,24-21,22,30,29

Quadrant C is not only:

[A] 37,38,46,45-39,40,48,47-

55,63,64,56-53,61,62,54

[B] 37,38,46,45-39,47,48,40-

-55,63,64,56-53,54,62,61

[C] 37,45,46,38-39,40,48,47-

-55,56,64,63-53,61,62,54

[D] 37,45,46,38-39,47,48,40-

55,56,64,63-53,54,62,61

But,

[A] 37,38,46,45-39,40,48,47-

55,63,64,56-53,61,62,54

[D] 37,45,46,38-39,47,48,40-

55,56,64,63-53,54,62,61

[C] 37,45,46,38-39,40,48,47-

-55,56,64,63-53,61,62,54

[B] 37,38,46,45-39,47,48,40-

-55,63,64,56-53,54,62,61

Quadrant D is not only:

[A] 33,34,42,41-35,36,44,43-

51,59,60,52-49,57,58,50

[B] 33,34,42,41-35,43,44,36-

-51,59,60,52-49,50,58,57

[C] 33,41,42,34-35,36,44,43-

51,52,60,59-49,57,58,50

[D] 33,41,42,34-35,43,44,36-

51,52,60,59-49,50,58,57

But,

[A] 33,34,42,41-35,36,44,43-

51,59,60,52-49,57,58,50

[D] 33,41,42,34-35,43,44,36-

51,52,60,59-49,50,58,57

[C] 33,41,42,34-35,36,44,43-

51,52,60,59-49,57,58,50

[B] 33,34,42,41-35,43,44,36-

-51,59,60,52-49,50,58,57

Thus, the overall set

takes the order

ABCD and ADCB

With alternation within

each category.

According to the above

dualities…

However, B must

remain opposite of D

And A must remain

Opposite of C…

Thus,

With A.A is

C.B…

With A.B is C.A…

With B.A is D.B…

With B.B is D.A…

With C.A is A.B…

With C.B is A.B…

With D.A is B.B…

With D.B is B.A…

3/4ths of these are

superfluous…

Thus, we have the

combinations:

A.A w/ C.B and

A.B w/ C.A and

B.A w/ D.B and

B.B w/ D.A.

The remaining half of

The categories

Are resolved by

the duality

In which A refers

to B or D…

So we have:

A.A (w/ C.B)

=

A.B (w/ C.A)

=

B.A (w/ D.B)

=

AND

B.B (w/ D.A)

=

Thus, the result is actually

equal to

2^2^2 as predicted…

However, notice, that in spite of the two levels of deductions, the 16-deduction level resulted in four SEPARATE DEDUCTIONS for each quadra, which is inadequate.

Note: this paper shows the

**WRONG METHOD**, although with a lot of promise. For the real method, see:

https://www.academia.edu/10161352/Categorical_Deduction_for_64_Categories
[THIS METHOD REMAINS INCOMPLETE (HERE, BUT NOT THERE)]