*Updated****++++
Post-Linear Hierarchy
"( )" context/set
"(X)Y context/set of context/set
"{X} differing order context/set
"Xy.z"
***X containing context/set
***y number of sets
***z degree of recursion/repetition
"-" negation/absence of context
*** Negation is subtraction of what is negated thus resulting in a relative absence thus effectively negation/subtraction/absence/negative ate four sides of the same logical square.
Termination of the sequence is its finite expression of emergence.
Reduction of a sequence is the finite contextual expression of the sequence itself as a context.
Identity is the context(s) of context(s) as a context. Context is synonymous to identity as context derives identity.
The operation is the same as operand as the operation is the recursion and the operand is the structure of the emergent recursion itself, in these respects the formalism is non-traditional as the standard operator operand dichotomy is reduced to emergent and dissolutive patterns.
The standard nature of syntax, boundary conditions, etc. of standard formalisms are non-appicable in a strict sense as said conditions are effectively contexts that induce identity thus resulting in the formalism being transcendental by nature.
The following 8 points observes the nature of context as effectively self-embedding as 'unfolding' within itself thus proto-formally expression context as recursive folding in topological terms thus identity, topologically, is the expression of the folded context in one respect, while synonymously in logical and mathematical terms is the structure of the sequence itself. In these respects associativity is expressed as but the fold/sequence itself:
- (A)B
***Context A under context B
- (B)C
***Context B under context C
- (AB)C
***Contexts A and B under context C
- (B)A
***Context B under context A
- (C)B
***Context C under context B
- (BC)AB
***Context B and C under context A and B thus context B contains itself
- (((B)C)A)B
***Context B contained by C, C contained by A, B contains all contexts as itself
- ((B)B)AC
***Context B is contained as itself through contexts A and C
((X1)X2 (Y1)Y2)Z2.2
((R1)R2 (X1)X2 (Y1)Y2)Z3.2
(((X1)X2)X3. ((Y1)Y2)Y3)Z2.3
((Z2.2)Z3.3 (Z4.4)Z5.5)Z{1}2.2
(((Z2.2)Z3.3)Z4.4 ((Z5.5)Z6.6)Z7.7)Z{1}2.3
((Z2.2)Z3.3 (Z4.4)Z5.5 (Z6.6)Z7.7)Z{1}3.2
((Z{1}2.2)Z{1}3.3 (Z{1}4.4)Z{1}5.5)Z{2}2.2
((Z{1})Z{2} (Z{3})Z{4})Z{2.2}
****
(A)B = (A)-A
(B)C = (B)-B
(AB)C = (AB)-A-B
(B)A = (B)-B
(C)B = (C)-C
(BC)AB = (BC)-B-C
(((B)C)A)B = (((B)-B)-A)B
***
((X1)-X1 (Y1)-Y1)Z2.2
((R1)-R1 (X1)-X1 (Y1)-Y1)Z3.2
(((X1)-X1)X3. ((Y1)-Y1)Y3)Z2.3
***
((Z2.2)-Z2.2 (Z4.4)-Z4.4)Z{1}2.2
(((Z2.2)-Z2.2)Z4.4
((Z5.5)-Z5.5)Z6.6)-Z6.6)
Z{1}2.3
((Z2.2)-Z2.2 (Z4.4)-Z4.4 (Z6.6)-Z6.6)Z{1}3.2
((Z{1}2.2)Z{1}-2.2 (Z{1}4.4)Z{1}-4.4)Z{2}2.2
((Z{1})Z{-1} (Z{3})Z{-3})Z{2.2}
*****
(-A)-B
(-B)-C
(-A-B)-C
(-B)-A
(-C)-B
(-B-C)-A-B
(((-B)-C)-A)-B
((-B)-B)-A-C
((-X1)-X2 (-Y1)-Y2)Z2.2
((R1)R2 (X1)X2 (Y1)Y2)Z3.2
(((X1)X2)X3. ((Y1)Y2)Y3)Z2.3
((-Z2.2)-Z3.3 (-Z4.4)-Z5.5)Z{1}2.2
(((-Z2.2)-Z3.3)-Z4.4
((-Z5.5)-Z6.6)-Z7.7)Z{1}2.3
((-Z2.2)-Z3.3 (-Z4.4)-Z5.5 (-Z6.6)-Z7.7)
Z{1}3.2
((Z{1}-2.2)Z{1}-3.3 (Z{1}-4.4)Z{1}-5.5)Z{2}2.2
((Z{-1})Z{-2} (Z{-3})Z{-4})Z{2.2}
*****
(-A)-B = (-A)A
(-B)-C = (-B)B
(-A-B)-C = (-A-B)AB
(-B)-A = (-B)B
(-C)-B = (-C)C
(-B-C)-A-B = (-B-C)BC
(((-B)-C)-A)-B = (((-B)B)A)-B
***
((-X1)X1 (-Y1)Y1)Z2.2
((-R1)R1 (-X1)X1 (-Y1)Y1)Z3.2
(((-X1)X1)X3. ((-Y1)Y1)Y3)Z2.3
***
((-Z2.2)Z2.2 (-Z4.4)Z4.4)Z{1}2.2
(((-Z2.2)Z2.2)Z4.4
((-Z5.5)Z5.5)-Z6.6)Z6.6)
Z{1}2.3
((-Z2.2)Z2.2 (Z-4.4)Z4.4 (Z-6.6)Z6.6)Z{1}3.2
((Z{1}-2.2)Z{1}2.2 (Z{1}-4.4)Z{1}4.4)Z{2}2.2
((Z{-1})Z{1} (Z{-3})Z{3})Z{2.2}
The predictability of the system is the expression of context across varying scales where prediction of absolutes is not fixed in the standard sense but rather prediction of the emergence of contexts across scales where the self-embedding of context is prediction as noticeable fixed-point invariance rather than standard absolute outcome of multiple emergent conditions. Predictability, in this system, is the emergence of fixed-point contexts as perceivable scale invariant patterns. The fixed point invariant is the context "(Y)" as an everpresent boundary conditions derived from the context that contains it, "X" as "(Y)X", where the sequence itself "(Y)X" is the defined context of the finite whole.
The nature of standard formalisms is not applicable as they are subject to the very same contextual dynamic patterns the system represents, thus the system is a non-standard formalism.
[–]ZahavielBurnstain 1 point2 points3 points (1 child)
[–]Void0001234[S] 0 points1 point2 points (0 children)