Doron Shadmi
Member
Member # 965
|
posted 01. November 2003 11:08
Dear peolpe,
I am a poor formalist, but have some ideas, which are based on structural|quantitative 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,
Doron Shadmi
----------------------------------------------------------------------------
Short overview:
Boolean logic is based on 0 Xor 1.
Fuzzy logic is fading between 0 Xor 1.
A non-Boolean 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 non-boolean 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 can be represented as:
code:
(1*4)= (1,1,1,1) <------------- Maximum symmetry-degree,
((1*2)+1*2)= ((1,1),1,1) Minimum information's clarity-degree (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 symmetry-degree,
Maximum information's clarity-degree (uniqueness)
Multiplication can be operated only between 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 symmetry-degree and information's clarity-degree.
High Entropy means maximum level of redundancy and uncertainty, which are based on the highest symmetry-degree of some system.
For example let us say that there is a piano with 3 notes and we call it 3-system :
DO=D , RE=R , MI=M
The highest Entropy level of 3-system is the most left information's-tree, 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 = | | | |___|_ | |___| |
| | | | | | |
|___|___|_ |_______| |_______|
| | |
An example of 4-notes piano:
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
. . . .
| | | |
|__| | |
| | |
|_____| |
| |
|________|
|
[ 01. November 2003, 11:09: Message edited by: Doron Shadmi ]
IP: Logged
|
Printer-friendly view of this topic