## Thursday, January 15, 2015

### Demonstrating all the Headache that Can Happen When You Use the Wrong Method

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

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!

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

(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.

the corresponding numbers

ABFE

CDHG

KLPO

IJNM

Now we substitute the
numbers:

A: [1.2,10,9]
B: [3,4, 12,11]

F: [19,20,28,27]
E: [17,18,26,25]

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

H: [23,24,32,31]
G: [21,22,30,29]

K: [37,38,46,45]
L: [39,40,48,47]

P: [55,56,64,63]
O: [53,54,62,61]

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,

And vice versa

This includes the sections of
The numbers which

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

This would leave us with eight
deductions, as predicted

Once the deduction is applied

ABCDEFGH
IJKLMNOP

Refers to:

1,2,3,4
9,10,11,12

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

ABCDEFGH
IJKLMNOP

Refers to:
5,6,7,8
13,14,15,16

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

ABCDEFGH
IJKLMNOP

Refers to:

37,38,39,40
45,46,47,48

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

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

[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

[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

[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

[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:

On two levels!

It also takes the order:

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

[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

[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

[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

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)]