Dear peolpe,
I am a poor formalist, but have some ideas, which are based on structuralquantitative point of view on Math language.
They can be found here: http://www.geocities.com/complementarytheory/CATpage.html
Maybe you can help me to address these ideas in a rigorous formal way.
By doing it, we can check what idea can survive rigorous definitions.
I think that only then we can move to the next step, which is: to examine its originality.
Thank you,
Yours,
Organic

Short overview:
Boolean logic is based on 0 Xor 1.
Fuzzy logic is fading transition between 0 Xor 1.
A nonBoolean logic is based on 0 And 1.
My point of view leading me to what I call Complementary logic, which is a fading transition between Boolean logic (0 Xor 1) and nonboolean logic (0 And 1), for example:
Number 4 is fading transition between multiplication 1*4 and addition ((((+1)+1)+1)+1) ,and vice versa.
This fading transition can be represented as:
Multiplication can be operated only among objects with structural identity .
Also multiplication is noncommutative, for example:
2*3 = ( (1,1),(1,1),(1,1) ) or ( ((1),1),((1),1),((1),1) )
3*2 = ( (1,1,1),(1,1,1) ) or ( ((1,1),1),((1,1),1) ) or ( (((1),1),1),(((1),1),1) )
Through my point of view, there are connections between structure's symmetrydegree and information's claritydegree.
High Entropy means maximum level of redundancy and uncertainty, which are based on the highest symmetrydegree of some system.
For example let us say that there is a piano with 3 notes and we call it 3system :
DO=D , RE=R , MI=M
The highest Entropy level of 3system is the most left information'stree,
where each key has no unique value of its own, and vice versa.
An example of 4notes piano:
DO=D , RE=R , MI=M , FA=F
I am a poor formalist, but have some ideas, which are based on structuralquantitative point of view on Math language.
They can be found here: http://www.geocities.com/complementarytheory/CATpage.html
Maybe you can help me to address these ideas in a rigorous formal way.
By doing it, we can check what idea can survive rigorous definitions.
I think that only then we can move to the next step, which is: to examine its originality.
Thank you,
Yours,
Organic

Short overview:
Boolean logic is based on 0 Xor 1.
Fuzzy logic is fading transition between 0 Xor 1.
A nonBoolean logic is based on 0 And 1.
My point of view leading me to what I call Complementary logic, which is a fading transition between Boolean logic (0 Xor 1) and nonboolean logic (0 And 1), for example:
Number 4 is fading transition between multiplication 1*4 and addition ((((+1)+1)+1)+1) ,and vice versa.
This fading transition can be represented as:
Code:
(1*4)= (1,1,1,1) < Maximum symmetrydegree,
((1*2)+1*2)= ((1,1),1,1) Minimum information's claritydegree (no uniqueness)
(((+1)+1)+1*2)= (((1),1),1,1)
((1*2)+(1*2))= ((1,1),(1,1))
(((+1)+1)+(1*2))= (((1),1),(1,1))
(((+1)+1)+((+1)+1))=(((1),1),((1),1))
((1*3)+1)= ((1,1,1),1)
(((1*2)+1)+1)= (((1,1),1),1)
((((+1)+1)+1)+1)= ((((1),1),1),1) < Minimum symmetrydegree,
Maximum information's claritydegree (uniqueness)
Also multiplication is noncommutative, for example:
2*3 = ( (1,1),(1,1),(1,1) ) or ( ((1),1),((1),1),((1),1) )
3*2 = ( (1,1,1),(1,1,1) ) or ( ((1,1),1),((1,1),1) ) or ( (((1),1),1),(((1),1),1) )
Through my point of view, there are connections between structure's symmetrydegree and information's claritydegree.
High Entropy means maximum level of redundancy and uncertainty, which are based on the highest symmetrydegree of some system.
For example let us say that there is a piano with 3 notes and we call it 3system :
DO=D , RE=R , MI=M
The highest Entropy level of 3system is the most left information'stree,
where each key has no unique value of its own, and vice versa.
Code:
<Redundancy>
M M M ^<Uncertainty
R R R  R R
D D D  D D M D R M
. . . v . . . . . .
        
3 =    ____  ___ 
      
_______ _______ _______
  
DO=D , RE=R , MI=M , FA=F
Code:
>>>
F F F F F F F F
M M M M M M M M
R R R R R R R R R R R R R R
D D D D D D D D D R D D D D D D
. . . . . . . . . . . . . . . .
               
    ___   __   ___ ___
           
           
           
_______ ________ ________ _________
   
4 =
M M M
R R R R R R R
D R D D D R D R D D D F D D M F
. . . . . . . . . . . . . . . .
               
__ ___ __ __     ___  
          
    _____  _____ 
       
_________ _________ ________ ________
   
D R M F
. . . .
   
__  
  
_____ 
 
________

Last edited: