looking through my earlier long response I have thought of things:
I suggested that three categories seen again (which I described as conservation of the definition of three categories; so "again" is implied) gives:
"mark" as the "again"? (interaction or observation is implied by "again"?)
The six possible views as "six quarks".
"But where are the three quarks? Of three categories that meet, where a question is asked "which are the "first" two say?" for which there are three possibilities for the say "last" one in the quark "line-up" (Superstring theory!?); and where the categories meet again and the question is asked again:"
Now it occurs to me:
if you generalise "first two" and "three possible as the last one": you get:
(choose first 2 out of 3; 3 options for last one)
times 2 times 3.
This allows the definition of "2" and of "3" to be undecided? But an outside look (count this uncertainty cell by observing it) gives:
five string theories in 3 x 3 that is nine dimensions? (just as they say in physics...)
You get a 2 x 2 aspect that is a "branes" aspect.
You get a (2 x 2 view of 3 x 3) that is a loop with "randomness" (that is with "double-booked or interfering definition overlaps since have 2 + (3 x 3) as "five" so need quantum electro-dynamics (the distributive law mixed through itself by changing roles of addend in brackets with multiplier on outside of brackets).
Idea is choose either, 2 x2 view OR 3 x 3 view; if superpose both must have 3 x 3 IN 2 x 2; AND 2 x 2 IN 3 x 3:
so 9 in 4 and 4 in 9:
so 4 x 9 = 36 dimensions for string?
Quantum: divide the loop gives gravity: condensing the "randomness" into a cell as get breaking of (2 x 2)/ (3 x 3) into (2/(3 x 3) ) + ( 2/ (3 x 3) ) seems like quadratic formula a squared + 4ac + b squared.
Generalise 3,3 as "time/space but if map this "as a new view of 3" as "4 where one of the four is the other view of three" you get five-fold symmetry when interact with a cell of this "3 new 3" seen as "4-ness"?
Dr. Stafford's paper then maps this generalised 4-ness as a 4-geometry so he gets a polygon rotated in n-dimensions (he is counting 4 x4 space that is ways of finding 4 in 4?)
He gets space 4s (polygon) and time 4s mixing cause and effect in his paper's perspective?
A 2,2 view of (3,3) 3 gives fixed grid a 2 with "1" (second 2 seen as a unit i.e. 1) view of 3 x 3 x3 or 27 so get 27 and sub-atomic particle symmetries?
I will call a category a "cat." for short.
"cat.cat.cat" means here that these three categories may share common ground so may overlap.
Consider three such cat.cat.cat 's:
cat.cat.cat; cat.cat.cat; cat.cat.cat:
the whole thing might be CAT.
Internally there might be c a t (sort of ghost-cat) that is the non-common ground that separates them inside CAT.
This looks like Dr. Stafford and his "adding unknown data".
Maybe "add unknown data, add unknown data minus any one item to make set items unique" becomes:
add ghost-cat, add CAT so minus any one item to make the cat.cat.cat.; cat.cat.cat.; cat.cat.cat unique SO he quantizes the cats?
#1: CAT; #2: cat.cat.cat; #3: cat.cat.cat.; #4 cat.cat.cat; #5 ghost cat.
But Dr. Stafford uses a 4-geometry which gives 4 x4 so polygon in n-dimensions.
A 4 x 5 view gives a way to have negative-mathematics (cancelling mathematics say)?
So have 4 x 5 = 20; but take one (4 x 5) perspective (one definition of 4 x 5?) or of space-time complexity say? get 20 minus 1 = 19 constants in physics standard model?
Generalise "minus 1" to the 4-ness get square root of minus one seen in 5-ness?
Or get 5 theories of "4-1" that is five string theories with dualities (as the 5 is from a 4 and a 1 in "4 minus 1"?
These seen in a 4 + 5 that is in 9 dimensions?
CAT (that is overall category or "supposed universe say") may be seen as "definition"?
ghost-cat (the uncommon ground that keeps cat.cat.cat 's from being muddled inside CAT) may be space between cat.cat.cat; cat.cat.cat.; cat.cat.cat may be seen as "rule"?
Defining CAT (external overview) and ghost-cat (internal space betwen cat.cat.cat 's)
the question is like what Chris Langan says in conspansive duality?
Not knowing how you get CAT or ghost-cat in terms of each other; this might be called "stochaistic process" ("random") as 1/4 turn in cat.cat.cat is what separates it from another cat. in that other cat.'s cat.cat. company?
Two views of cat.cat.cat gives coming together as gravity when take 1/4 turn view (take one cat. view from cat.cat.cat. of other cat.cat.cat.?)
But the other two cat.s in the other cat.cat.cat give a ready available two views of cat. to give a 1/4 angle on cat. and cat.cat.cat.?
Thus gravity (1/4 turn -ness) is quantized here as a potential shell.
To see it (fill the shell) you have to count it: requires another cat.; so you get a loop, a quantizing, a 1/4 turn that is uncertain (possible gravity) but which is which? You are stuck with a "graviton" and that whole double slit business (where is the graviton?). (Double slit business: two cat.'s in a cat. surface in possibly linked to otherwise with another cat.cat.cat.)
The other two cat.cat.'s in the cat.cat.cat. from which you took one cat.'s view: gives a loop?
Or is it a quantum (as it involves two so division)?
But if count this from outside you get opportunity to make up who is to play the role of "loop"; who is to play the role of "quantum", and who is to make the play "gravity"?
Spinors and twistors:
may regard cat.cat.cat. as "spinor"?
may regard cat.cat.cat. and cat. as "twistor"?
may regard cat.cat.cat. and cat.cat.cat. as spinors and twistors in complex number space IF freeze two of the cat.s?
cat.cat.cat.; cat.cat.cat.; cat.cat.cat.
ghost-cat (as creates space between the cat.cat.cat.'s so puts a twist on the scene.
-just a rough sketch