Are Non-Commutative Natural Numbers the Future of Mathematical Theory?

[pallidin]

Organic, are you proposing an advanced system of information science?
If so, OK, we're listening.
May I suggest that you take the admittedly difficult time to show validation and usefulness. That is, could you show a concrete example where your system is superior than the one(s) currently used. A side-by-side definitive comparison would be helpful, and indeed essential.

 

[Organic]

Hi pallidin,

First, thank you very much for your positive attitude.

I have learned during the last year that my simple idea about the ordered universe of information forms, which can help us to define the deep connections between, so called, different systems, cannot easily be understood by professional "pure" mathematicians.

Maybe at this point I have to think about applied mathematics, but I need help for my first steps.

Please first, read this paper of mine:

http://www.geocities.com/complementarytheory/Complex.pdf

Thank you,

Organic

 

[cookiemonster]

So are you saying that you have yet to find a concrete use for your numbers and need help finding one?

cookiemonster

 

[Hurkyl]

Plrease show me how can you define ((1*3)*(1+1)) when in my system

I have no clue how to define anything in your system.

It's easy enough to define it in ordinary mathematics, though.

Please give an example by using the lows of my system.

An example of what?

 

[Organic]

So are you saying that you have yet to find a concrete use for your numbers and need help finding one?

Yes, I need your help.

 

[matt grime]

I decided to check your score on the crackpot index. I'm doing this from memory of your posts. You can check this through jon baez's website. you score amazingly.

1 point for every statement that is widely agreed to be false (well, I reckon we'll go for 3 being generous) 3 points per statement that is logically inconsistent (you're scoring quite highly in the maths forum at the moment) then there's lots of intermediate ones but the peach has to be the end ones where you sail into the lead:

10 points for arguing that while a current well-established theory predicts phenomena correctly, it doesn't explain "why" they occur, or fails to provide a "mechanism".

10 points for each statement along the lines of "I'm not good at math, but my theory is conceptually right, so all I need is for someone to express it in terms of equations".

10 points for each new term you invent and use without properly defining it. (and let's face it this puts you off the scale)

10 points for claiming that your work is on the cutting edge of a "paradigm shift".

40 points for claiming that the "scientific establishment" is engaged in a "conspiracy" to prevent your work from gaining its well-deserved fame, or suchlike. (this one's arguable but I left out the one about saying how long you'd been working on the theory)

# 40 points for claiming that when your theory is finally appreciated, present-day science will be seen for the sham it truly is. (30 more points for fantasizing about show trials in which scientists who mocked your theories will be forced to recant.)

# 50 points for claiming you have a revolutionary theory but giving no concrete testable predictions.

those last two.. well I've not seen anyone take both of those awards before.

 

[Organic]

Matt,

And what you haveto say about that?:

If we use again the example of transformations between multisetes and "normal" sets, we can see that the internal structure of n+1 > 1 ordered forms, constructed by using all previous n > 1 forms:

[b]1[/b]
(+1) = {1}

[b]2[/b]
(1*2)    = {1,1}
((+1)+1) = {{1},1}

[b]3[/b]
(1*3)        = {1,1,1}
((1*2)+1)    = {{1,1},1}
(((+1)+1)+1) = {{{1},1},1}

[b]4[/b]
(1*4)               = {1,1,1,1} <------------- Maximum symmetry-degree, 
((1*2)+1*2)         = {{1,1},1,1}              Minimum information's 
(((+1)+1)+1*2)      = {{{1},1},1,1}            clarity-degree
((1*2)+(1*2))       = {{1,1},{1,1}}            (no uniqueness) 
(((+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)
[b]5[/b]
...

 

[Organic]

Dear Hurkyl,

I want to correct my previous answers to your questions.

Standard Math using only the 0_redunduncy_AND_0_uncertainty information forms.

For example, the information form, which is used in ((1*3)*(1+1)) is:

    a  b
    .  .        
    |  |      
    |__| 
    |

and when this building-block repeating within itself in two level, we get:

    1  3  1  1   
    .  .  .  .       
    |  |  |  |     
    |__|  |__| 
    |*    |+        =      ((1*3)*(1+1))   
    |     |         
    |     |         
    |_____|
    |  * 
    |

So, as you can see, my system is a first-order system of information forms, which existing within any given n.

Shortly speaking, first we define the information forms building-blocks, for example:

http://www.geocities.com/complementarytheory/ETtable.pdf

and only then we can use these building-blocks to construct our model.

Standard Math using only the last form of each collection that existing within any given n, for example:

      [b]0[/b]
      [b].[/b]
1 =   [b]|    
      *[/b]


    1   1
    0   0     [b]0   1[/b]
    .   .     [b].   .[/b]
    |   |     [b]|   |[/b]
2 = |___|_    [b]|___|[/b]
    |         [b]| *[/b]


    2   2   2
    1   1   1       1   1
    0   0   0       0   0   2       [b]0   1   2[/b]
    .   .   .       .   .   .       [b].   .   .[/b]
    |   |   |       |   |   |       [b]|   |   |[/b]
3 = |   |   |       |___|_  |       [b]|___|   |[/b]
    |   |   |       |       |       [b]|       |[/b]
    |___|___|_      |_______|       [b]|_______|[/b]
    |               |               [b]|   *[/b]

    
    -------------->>>
    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           1  1
    0  0  0  0     0  0  0  0     0  1  0  0     0  0  0  0     0  1  0  0
    .  .  .  .     .  .  .  .     .  .  .  .     .  .  .  .     .  .  .  .
    |  |  |  |     |  |  |  |     |  |  |  |     |  |  |  |     |  |  |  |
    |  |  |  |     |__|_ |  |     |__|  |  |     |__|_ |__|_    |__|  |__|_
    |  |  |  |     |     |  |     |     |  |     |     |        |     |
    |  |  |  |     |     |  |     |     |  |     |     |        |     |
    |  |  |  |     |     |  |     |     |  |     |     |        |     |
    |__|__|__|_    |_____|__|_    |_____|__|_    |_____|____    |_____|____
    |              |              |              |              |
 
4 =                2  2  2
                   1  1  1        1  1
    0  1  0  1     0  0  0  3     0  0  2  3     [b]0  1  2  3[/b]
    .  .  .  .     .  .  .  .     .  .  .  .     [b].  .  .  .[/b]
    |  |  |  |     |  |  |  |     |  |  |  |     [b]|  |  |  |[/b]
    |__|  |__|     |  |  |  |     |__|_ |  |     [b]|__|  |  |[/b]
    |     |        |  |  |  |     |     |  |     [b]|     |  |[/b]
    |     |        |__|__|_ |     |_____|  |     [b]|_____|  |[/b]
    |     |        |        |     |        |     [b]|        |[/b]
    |_____|____    |________|     |________|     [b]|________|[/b]
    |              |              |              [b]|   *[/b]

The bold forms that notated by * are number system representations, based on Peano axioms (Standard Math information forms).

All the other first-order information forms, are new forms, which are not used (yet) by Standard Math language as building-blocks of natural numbers.

Why does "redundancy / uncertainty" never look like:

    M   R   D    
    D   M   R    
    .   .   .      
    |   |   |     
    |   |   |     
    |   |   |     
    |___|___|_   
    |

A complete state of Redundancy_AND_uncertainty within quantity 3 cannot be less then 3 different possibilities for each discrete element.

If we use again the example of transformations between multisetes and "normal" sets, we can see that the internal structure of n+1 > 1 ordered forms, constructed by using all previous n > 1 forms:

[b]1[/b]
(+1) = {1}

[b]2[/b]
(1*2)    = {1,1}
((+1)+1) = {{1},1}

[b]3[/b]
(1*3)        = {1,1,1}
((1*2)+1)    = {{1,1},1}
(((+1)+1)+1) = {{{1},1},1}

[b]4[/b]
(1*4)               = {1,1,1,1} <------------- Maximum symmetry-degree, 
((1*2)+1*2)         = {{1,1},1,1}              Minimum information's 
(((+1)+1)+1*2)      = {{{1},1},1,1}            clarity-degree
((1*2)+(1*2))       = {{1,1},{1,1}}            (no uniqueness) 
(((+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)
[b]5[/b]
...