Originally posted by Organic
master_coda,
First, BL and ZL are private cases in CL.
But CL has the built-in ability to deal with non-linearity, by connecting in a coherent way concepts like symmetry-degree that related to information’s clarity-degree.
Please look at: http://www.geocities.com/complementarytheory/ET.pdf
where I construct the natural number by complementary associations between its integral side (its sum) and its differential side (some finite collection of 1’s).
Through this attitude addition and multiplication are complementary operations.
Show me how can you do that by using Boolean Logic.
Originally posted by Organic
But if you want to understand someone's point of view then please ask specific questions about something that you don’t understand in ET.pdf and please stop giving me general lecturers about what is Math how Math should be and so on.
<-Redundancy->
c c c ^<----Uncertainty
b b b | b b
a a a | a a c a b c
. . . v . . . . . .
| | | | | | | | |
| | | |___|_ | |___| |
| | | | | | |
|___|___|_ |_______| |_______|
| | |
Where:
c c c
b b b
a a a
. . .
| | |
| | | = {a XOR b XOR c, a XOR b XOR c, a XOR b XOR c}
| | |
|___|___|_
|
b b
a a c
. . .
| | |
|___|_ | = {a XOR b, a XOR b, c}
| |
|_______|
|
a b c
. . .
| | |
|___| | = {a, b, c}
| |
|_______|
|(1*4) ={1,1,1,1} <------------- Maximum symmetry-degree,
((1*2)+1*2) ={{1,1},1,1} Minimum information's clarity-degree
(((+1)+1)+1*2) ={{{1},1},1,1} (no uniqueness)
((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)
============>>>
Uncertainty
<-Redundancy->^
3 3 3 3 | 3 3 3 3
2 2 2 2 | 2 2 2 2
1 1 1 1 | 1 1 1 1 1 1 1 1 1 1
{0, 0, 0, 0} V {0, 0, 0, 0} {0, 1, 0, 0} {0, 0, 0, 0}
. . . . . . . . . . . . . . . .
| | | | | | | | | | | | | | | |
| | | | |__|_ | | |__| | | |__|_ |__|_
| | | | | | | | | | | |
| | | | | | | | | | | |
| | | | | | | | | | | |
|__|__|__|_ |_____|__|_ |_____|__|_ |_____|____
| | | |
(1*4) ((1*2)+1*2) (((+1)+1)+1*2) ((1*2)+(1*2))
4 = 2 2 2
1 1 1 1 1 1 1
{0, 1, 0, 0} {0, 1, 0, 1} {0, 0, 0, 3} {0, 0, 2, 3}
. . . . . . . . . . . . . . . .
| | | | | | | | | | | | | | | |
|__| |__|_ |__| |__| | | | | |__|_ | |
| | | | | | | | | | |
| | | | |__|__|_ | |_____| |
| | | | | | | |
|_____|____ |_____|____ |________| |________|
| | | |
(((+1)+1)+(1*2)) (((+1)+1)+((+1)+1)) ((1*3)+1) (((1*2)+1)+1)
{0, 1, 2, 3}
. . . .
| | | |
|__| | |
| | |
|_____| |
| |
|________|
|
((((+1)+1)+1)+1)Your multiplication is not well defined then, because your 'numbers' are not well defined, that is there is no single element that represents it uniquely. For instance you give me several different answers for 2*3. To deduce anything from this you must acknowledge that '3' is not a number in your system and to call them numbers is misleading.
Your numbers aren't the numbers of mathematics,
Originally posted by Organic
Matt,
You still don't understand what i am talking about.
1) There is no such objective thing called "Mathematics", it is only a rigorous agreement between some group of people in some period of time, no more no less.
2) Its most basic paradigms can be changed from today to tomorrow , when new fundamental ideas air their view.
3) Let us not forget Godel.
4) The new Natural numbers have the structure of a wavicle, therefore concepts like symmetry, redundancy, uncertainty , entropy and so on, are their inherent properties.
5) Boolean logic is an obsolete logical system for more then 70 years, and logical systems like Complementary Logic are going to take their place in the near future.
6) Theoretical mathematicians like Alain Connes (http://www.alainconnes.org/) say it, and a lot of great physics theoretical mathematicians developing an unordered tailor made pieces of non-Euclidean methods that helping them to solve their problems.
7) Only pure mathematicians are still dreaming in their “Cantor’s paradise” (which is by the way a very ironic name, gave by a community of people that sent Cantor to Mad House for the rest of his life because of their “rigorous” attitudes).
8) Realty and Philosophy were, are and will be the source of any meaningful Mathematical system.
Originally posted by Organic
Matt,
The main idea of the pervious post is:
Probability is fundamental property of the Number concept.
Originally posted by Organic
Matt,
1) From your reply it is easy to show that you did not read my last 2 posts to you.
2) If you read my last post then you can see that Entropy is any partition to equal parts.
This line shows that you simply don't understand what I am talking about.You presume to use 'the axiom of infinity induction' to complete some list of 'combinations'