The method has been earlier elaborated in THIS VIDEO.
But there is one thing I failed to clarify: what are the other potential four categories? After I made the video, I realized that those categories might be equally important from most points of view. Although the four original categories are important, they are not the whole picture.
So, here are the official eight categories for the 64-square diagram, with the final four categories restored:
CATEGORICAL DEDUCTION FOR 64 CATEGORIES
(1) 1A2A 3B4B
(2) 1A2B 3B4A
(3) 1B2A 3A4B
(4) 1B2B 3A4A
(5) 3A4A 1B2B
(6) 3A4B 1B2A
(7) 3B4A 1A2B
(8) 3B4B 1A2A
The four parts of each subset of the deduction refer to specific combinations of coordinates. Notice that every number has different coordinates, and each number is used just once for a given subset of the deduction. The letters are used once as well, but must remain opposite in opposite positions, as recorded above. Note that the major numbers (1,2,3,4 going with As and Bs) cycle counterclockwise, thus appearing in the modular order 1,2,4,3. This could easily be re-written for modular format by putting 4A and 4B over the 3A and 3B positions, and 3A and 3B over the 4A and 4B positions. The category numbers (1-64) however, have been recorded in modular order for the sake of objectivity. The entire set must be re-written, for which there are simpler notations, if subset numbers take cyclical order instead of modular. Modular order in my diagrams is written from upper right linearly to lower left. However, as long as it is noticed that the spatial location changes, the same system can be used for different linear-scripted writings, although it may modify the order of the major quadrants.However, the quadrants will remain counterclockwise from the starting position. For most purposes, it may be most convenient simply to imitate my methods as best you can, or to work with simpler diagrams, including the standard quadra, in which the formula is much simpler: AB:CD and AD:CB, in which neighboring letters are joined by choosing the quality of one and the noun ('property') of the other.
ACTUAL SETS FOR 64-CATEGORY CATEGORICAL DEDUCTION
These follow the sentence order of the individual categories, which involves maintaining opposites in opposite positions, and standardizing the order of the contingent categories so as to correspond with their coherent positions within the data:
1,2,10,9 | 3,4,12,11 | 28,27,19,20 | 26,25,17,18
1,2,10,9 | 3,11,12,4 | 28,27,19,20 | 26,18,17,25
5,6,14,13 | 7,8,16,15 | 32,31,23,24 | 30,29,21,22
5,6,14,13 | 7,15,16,8 | 32,31,23,24 | 30,22,21,29
64,63,55,56 | 62,61,53,54 | 37,38,46,45 | 39,40,48,47
64,63,55,56 | 62,54,53,61 | 37,38,46,45 | 39,47,48,40
60,59,51,52 | 58,57,49,50 | 33,34,42,41 | 35,36,44,43
60,59,51,52 | 58,50,49,57 | 33,34,42,41 | 35,43,44,36
ABOVE: A 64-Category Diagram Following Modular Order. Notice that in modular order every position in quadrant A (upper right) is opposite to every category in quadrant C (lower left). Also, every category in quadrant B (upper left) is opposite of every category in quadrant D (lower right). This is not true with every set ordering, but only with cases where the order proceeds across the entire (square) diagram from the first position, and ending in the last. Two other potential orderings include numbering individual sub-cycles in cyclical order, or proceeding linearly, but adapted to the cycle of the diagram. Thus, 1,2,10,9 would instead appear 1,2,3,4, or in the next case 27,28,36,35 would instead appear 6,2,1,5, since the enumeration would begin in the center near the mote, and proceed contingently to the motion of the cycle. But those are alternate methods. Modular order is in some ways preferable, although in some cases it is simpler to explain in terms of sub-cycles.
International Society for the Philosophy of Architecture » Ethics and Aesthetics of Architecture and the Environment