Deeper than primes

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A try to write by hand the all forms of n=1 to 3 n-Uncertainty x n-Redundancy matrix (order has no significance):
Code: 
1x1                                                
                                                   
A .                                                
                                                   
(1) = (A)                                          
                                                   
                                                   
                                                   
2X2                                                
                                                   
A . .                                              
                                                   
B . .                                              
                                                   
(2,2) = (AB,AB)                                    
(2,1) = (AB,A),(AB,B)                              
(1,1) = (A,A),(B,B),(A,B)                          
                                                   
                                                   
                                                   
3X3                                                
                                                   
A . . .                                            
                                                   
B . . .                                            
                                                   
C . . .                                            
                                                   
(3,3,3) = (ABC,ABC,ABC)                            
(3,3,2) = (ABC,ABC,AB),(ABC,ABC,AC),(ABC,ABC,BC)   
(3,3,1) = (ABC,ABC,A),(ABC,ABC,B),(ABC,ABC,C)      
(3,2,1) =                                          
(ABC,AB,A),(ABC,AB,B),(ABC,AB,C)                   
(ABC,AC,A),(ABC,AC,B),(ABC,AC,C)                   
(ABC,BC,A),(ABC,BC,B),(ABC,BC,C)                   
(2,2,2) =                                          
(AB,AB,AB),(AB,AC,AB),(AB,BC,AB)                   
(AC,AC,AC),(AC,AB,AC),(AC,BC,AC)                   
(BC,BC,BC),(BC,AB,BC),(BC,AC,BC)                   
(2,2,1) =                                          
(AB,AB,A),(AB,AB,B),(AB,AB,C)                      
(AB,AC,A),(AB,AC,B),(AB,AC,C)                      
(AB,BC,A),(AB,BC,B),(AB,BC,C)                      
(1,1,3) =                                          
(A,A,ABC),(B,B,ABC),(A,B,ABC)                      
(A,C,ABC),(B,C,ABC)                                
(1,1,2) =                                          
(A,A,AB),(A,A,AC),(A,A,BC)                         
(B,B,AB),(B,B,AC),(B,B,BC)                         
(A,B,AB),(A,B,AC),(A,B,BC)                         
(A,C,AB),(A,C,AC),(A,C,BC)                         
(B,C,AB),(B,C,AC),(B,C,BC)                         
(1,1,1) = (A,A,A),(B,B,B),(C,C,C),(A,B,C)

It must be noticed that this list has to be taken at-once (in parallel), in step-by-step (in serial) or in any parallel\serial combination.
 
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A detailed representation of 2-Uncertainty x 2-Redundancy matrix:
Code: 
2X2                                             
                                                
(AB,AB) (AB,A)  (AB,B)  (A,A)   (B,B)   (A,B)   
                                                
A * *   A * *   A * .   A * *   A . .   A * .   
  | |     | |     | |     | |     | |     | |   
B *_*   B *_.   B *_*   B ._.   B *_*   B ._*   
                                                
(2,2) = (AB,AB)                                 
(2,1) = (AB,A),(AB,B)                           
(1,1) = (A,A),(B,B),(A,B)

Correction of 3x3 case (1,1,1):
Code: 
(1,1,1) = 
(A,A,A),(B,B,B),(C,C,C)
(A,A,B),(A,A,C),(B,B,A)
(B,B,C),(C,C,A),(C,C,B)
(A,B,C)
 
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The Man said:
Well I tried that before, but I'll try it again.

Why are ordering distinctions excluded? You referred to them as being significant in serial observations, but did not answer as to why they are excluded. So the question simply became why are ordering distinctions or significant serial observations excluded?
Click to expand...

have you seen my presentation in Sweden ?
I think that I explain it there.

Moshe
 
jsfisher said:
If there are no distinctions for 1, then Or(1) should be 0. But it isn't, is it? In actual fact, you get Or(1) = 1 by using the only partition of 1, and that action is an inconsistency in your process, just as your forced definition for Or(1) is an inconsistency in your formulae.



Euclidean Mathematics?



Not likely. Your OM is founded on an inconsistent set of special cases and arbitrary results. That makes it totally incompatible with Mathematics.

By the way, neither you nor Doronshadmi have shown any utility for OM. Got any?

Also, even though you and Doronshadmi agreed to the description I presented for distinction, Doronshadmi has been back-pedaling ever since, but he has been unable to define his meaning for distinction. Can you provide a definition?
Click to expand...

n=1 have one clear distinction (not as I wrote before) so On(1)=1


Non Euclidian Mathematic is a bridge between the deduction system and the inductive system - this is what OM all about.
 
doronshadmi said:
A detailed representation of 2-Uncertainty x 2-Redundancy matrix:
Code: 
2X2                                             
                                                
(AB,AB) (AB,A)  (AB,B)  (A,A)   (B,B)   (A,B)   
                                                
A * *   A * *   A * .   A * *   A . .   A * .   
  | |     | |     | |     | |     | |     | |   
B *_*   B *_.   B *_*   B ._.   B *_*   B ._*   
                                                
(2,2) = (AB,AB)                                 
(2,1) = (AB,A),(AB,B)                           
(1,1) = (A,A),(B,B),(A,B)
Click to expand...

see you tommorow in Tel Aviv
:c2:
 
Still waiting for a practical example of ONs in use...

And where ethics and morals are incorporated (a worked example please).
 
MosheKlein said:
n=1 have one clear distinction (not as I wrote before) so On(1)=1
Click to expand...

No, you would have to use the partition 1 = 1 to get the one clear distinction. You are supposed to exclude the n=n partition, remember?

This would be some much easier if you could define what you mean by distinction. Unfortunately, what seemed to me to be the description for distinction you presented in Sweden isn't at all what you mean. Your "one clear distinction" isn't at all clear.

We are also all waiting for some demonstration of the utility of ON and OM.
 
doronshadmi said:
A try to write by hand the all forms of n=1 to 3 n-Uncertainty x n-Redundancy matrix (order has no significance):
Code: 
1x1                                                
                                                   
A .                                                
                                                   
(1) = (A)                                          
                                                   
                                                   
                                                   
2X2                                                
                                                   
A . .                                              
                                                   
B . .                                              
                                                   
(2,2) = (AB,AB)                                    
(2,1) = (AB,A),(AB,B)                              
(1,1) = (A,A),(B,B),(A,B)                          
                                                   
                                                   
                                                   
3X3                                                
                                                   
A . . .                                            
                                                   
B . . .                                            
                                                   
C . . .                                            
                                                   
(3,3,3) = (ABC,ABC,ABC)                            
(3,3,2) = (ABC,ABC,AB),(ABC,ABC,AC),(ABC,ABC,BC)   
(3,3,1) = (ABC,ABC,A),(ABC,ABC,B),(ABC,ABC,C)      
(3,2,1) =                                          
(ABC,AB,A),(ABC,AB,B),(ABC,AB,C)                   
(ABC,AC,A),(ABC,AC,B),(ABC,AC,C)                   
(ABC,BC,A),(ABC,BC,B),(ABC,BC,C)                   
(2,2,2) =                                          
(AB,AB,AB),(AB,AC,AB),(AB,BC,AB)                   
(AC,AC,AC),(AC,AB,AC),(AC,BC,AC)                   
(BC,BC,BC),(BC,AB,BC),(BC,AC,BC)                   
(2,2,1) =                                          
(AB,AB,A),(AB,AB,B),(AB,AB,C)                      
(AB,AC,A),(AB,AC,B),(AB,AC,C)                      
(AB,BC,A),(AB,BC,B),(AB,BC,C)                      
(1,1,3) =                                          
(A,A,ABC),(B,B,ABC),(A,B,ABC)                      
(A,C,ABC),(B,C,ABC)                                
(1,1,2) =                                          
(A,A,AB),(A,A,AC),(A,A,BC)                         
(B,B,AB),(B,B,AC),(B,B,BC)                         
(A,B,AB),(A,B,AC),(A,B,BC)                         
(A,C,AB),(A,C,AC),(A,C,BC)                         
(B,C,AB),(B,C,AC),(B,C,BC)                         
(1,1,1) = (A,A,A),(B,B,B),(C,C,C),(A,B,C)

It must be noticed that this list has to be taken at-once (in parallel), in step-by-step (in serial) or in any parallel\serial combination.
Click to expand...

Most popular question of the week:
What does this represent?

Warning! The following is not an authorized presentation of the use of Organic Numbers!

Here's Anthony with his three shiny, newly minted quarters.
As specified before, each is minted in the same state (Let's say Alaska with the grizzly bear) and the same year, so that they look alike.

We're going to ask Anthony to count the quarters and tell us how many cents he has. (A quarter equals 25 cents.)

Now Anthony is a bright kid. He’s brilliant! He's also a deviant little brat.
(As I was!)
He's not going to regard these coins the way we'd habitually expect.
He doesn't immediately announce 75 cents, but plays with our minds.

First he points out to us that the quarters are all the same; that is they are all copies of the same thing. There's one and the one again, and the one again. Two are just copies. There’s only the single value of 25 cents.
(1, 1, 1)
The same value is presented three times.

Doron calls this "Redundancy." It comes from an interaction of two principles:
Sameness and Difference. In pure sameness, everything is the self same.
In pure difference everything is wholly different and shares nothing in common with anything else. The Non-Local Principle has seamless sameness, where there are no individual elements. The Local principle has absolute difference where each element is totally, unique and separate.
The "Redundancy above partakes of both principles in that there are separate instances of the same entity.

Next Anthony asks for a hammer. He whacks each of the quarters so they have their own individualizing dents. (Like when can tell twins apart by a dimple)
Then he counts each of them as an entity of itself.
There's quarter number one, quarter number two, and quarter number three.
(1, 2, 3)
Each has a value of 25 cents, So 1 quarter + 1 quarter + 1 quarter and the total is 75 cents.
Three unique values are presented.

Doron calls this "Uncertainty" It's uncertain if these are unique values or just flawed copies of one unique value.
The idea is that the situation is regarded as having more than one unique value.
Again this is an interaction of the Non-Local-Same and Local-Different Principles. This time difference is primary, but they are of the same sort thing to be counted together.

Redundancy has the times (*) operator.
Uncertainty has the plus (+) operator.

Doron says it takes both of these aspects to have math, especially Organic Math.
Here visualize again his colorful charts and partitions that illustrate Organic Numbers.

Organic numbers allow our Anthony to take Redundancy and Uncertainty (and with them the Non-Local) into consideration.

Redundancy! He has one value worth 25 cents.
Uncertainty! He has three values when added together are worth 75 cents.
And with the interaction of Redundancy and Uncertainty in the Organic Numerals, one of those quarters can be regarded as an indistinct, non-local (Redundant), while one of the others is a distinct local (Uncertain), so that the total can be 50 cents!

By using Organic Numbers, Anthony can exhibit the observer's contribution to the outcome. He shows how the mathematical result depends upon his own state of mind. With Organic Numbers, his humanity has a telling role in the outcome.

If he only had traditional math, all he'd have to show for his effort is just 75 cents. Instead, he can be creative with the sum! :D

You feel uneasy?

Remember what Doron said:
The word "amount" is not important.

What important here is what number really is as a result of the real-time interaction between the knower and the known.
Click to expand...
Post 4220
 
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jsfisher said:
No, you would have to use the partition 1 = 1 to get the one clear distinction. You are supposed to exclude the n=n partition, remember?

This would be some much easier if you could define what you mean by distinction. Unfortunately, what seemed to me to be the description for distinction you presented in Sweden isn't at all what you mean. Your "one clear distinction" isn't at all clear.

We are also all waiting for some demonstration of the utility of ON and OM.
Click to expand...
jsfisher,

Distinction (since you can't grasp the abstract meaning to this concept) is the all possible results of n-Uncertainty x n-Redundancy matrix.

What was represented at Sweden is a partial case of n-Uncertainty x n-Redundancy matrix, that is based on recursion of partial cases of this matrix.

It was done for purpose, in order to save time and energy for the important thing, which is the inseparable relations of the researcher's cognition with the measurement tool that is the result of the bridging between Non-locality and Locality (which is something that you can't grasp, as clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=4862966&postcount=4240 ).

You still waste your time on nonsense instead of get (at least) n-Uncertainty x n-Redundancy matrix.

Look again at n=1 to 2 full n-Uncertainty x n-Redundancy matrix, and follow its notion from there:

Code: 
1x1                                        
                                           
A .                                        
                                           
(1) = (A

                                          
                                 
2X2                                             
                                                
(AB,AB) (AB,A)  (AB,B)  (A,A)   (B,B)   (A,B)   
                                                
A * *   A * *   A * .   A * *   A . .   A * .   
  | |     | |     | |     | |     | |     | |   
B *_*   B *_.   B *_*   B ._.   B *_*   B ._*   
                                                
(2,2) = (AB,AB)                                 
(2,1) = (AB,A),(AB,B)                           
(1,1) = (A,A),(B,B),(A,B)

Again, it must be noticed that this list has to be taken at-once (in parallel), in step-by-step (in serial) or in any parallel\serial combination, where each given form is both global and local state of the entire system, where your cognition is a significant factor of any result.
 
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doronshadmi said:
jsfisher,

Distinction (since you can't grasp the abstract meaning to this concept) is the all possible results of n-Uncertainty x n-Redundancy matrix.
Click to expand...
He's not the only one not to grasp it, but I don't think the fault lies with him. What does it mean, and what can you do with it?


You still waste your time on nonsense
Click to expand...
Yes, yes we do. Call it light relief.
 
zooterkin said:
Why should that stop you sharing an example?
Click to expand...
Because my example to you can't help you to understand ONs.

An inseparable requirement of understanding ONs it to provides the examples by their user\researcher.

The days of non-direct perception of the learnd subject are gone.
 
http://www.geocities.com/complementarytheory/OMDP.pdf is a further development of http://books.google.com/books?id=ja...5KGvBQ&sa=X&oi=book_result&ct=result&resnum=2 Charles Sanders Peirce's ( http://en.wikipedia.org/wiki/Charles_Sanders_Peirce ) potential "welded" points along the real-line.

In 1908 Charles Sanders Peirce gave up on that particular conception of continua (based on potential "welded" points along the real-line) without knowing that it will return as a superposition of elements' identities.
 
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doronshadmi said:
Because my example to you can't help you to understand ONs.

An inseparable requirement of understanding ONs it to provides the examples by their user\researcher.

The days of non-direct perception of the learnd subject are gone.
Click to expand...

Translation: Doron is incapable of explaining things.
 
doronshadmi said:
:boxedin: like you can't get anything. Go play with zooterkin because http://www.internationalskeptics.com/forums/showpost.php?p=4866938&postcount=4257 is beyond your mind.
Click to expand...

All the evidence, doronshadmi, is to the contrary. The failures are entirely with you.

You have told us distinction is the first order property at the very essence of organic numbers. As it turns out, even though you can't provide any sort of operational definition of distinction, it is clear that it is not first order, it is not a property, and it is not at the very essence of organic numbers. In fact, your organic number sequence is arbitrary and inconsistent.

So, you failed.

You also told us how organic numbers answers the question, "What is a number?" From what you assert, organic numbers necessarily would need to be fundamental, along side set theory and logic. As it turns out, organic numbers are numbers only in the sense elements of the Fibonacci sequence are numbers. Moreover, the generation of the organic sequence requires a rather mature arithmatic, so they are in no way basic to anything. Also, the rules for generating the sequence are, by your own admission, arbitrary.

So, you failed.

You told us organic mathematics (whatever that really is) provides unity across all of the branchers of Mathematics. This, like so many other things you have asserted, is nothing more than a bare allegation with no substance. When pressed for even one example, you shrink from the task.

So, you failed.

You haven't a single success to your credit, Doronshadmi. You assert, you misinterpret, you argue in circles, you wallow in inconsistencies, you fathom the trivial, but you never reach a conclusion of any substance.

...and for this, you blame everyone else in the world (except possibly Mosheklein).
 
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