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

[Lonewolf]

I do beg your pardon?

 

[moshek]

For what Lonewolf ?

 

[Lonewolf]

"Organic mathematics", and an explanation of "Organic unity" is required before I can understand what the centre of it is.

 

[moshek]

Ok !

what do you understand from this qoute of Hilbert :


The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!

 

[Organic]

Hi Lonewolf,

Ok, how do you obtain the rationals, irrationals etc. out of this theory?

please read:
http://www.geocities.com/complementarytheory/NewDiagonalView.pdf

and this:

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

More can be found here:

http://www.geocities.com/complementarytheory/CATpage.html

 

[Organic]

Your link doesn't mean anything to me. All I see are the same diagrams I've been seeing for the past million posts, which still don't mean anything to me.

"If you understand their properties, then you can find by yourself how to play with them."

Yes, if I understand them. But I don't see any reason to put in the work to understand them. Why should I understand them? Where's Schrodinger's Equation? Where's the results?

http://www.physlink.com/Education/AskExperts/ae329.cfm

Schrodinger's Equation is based on a wave picture of QM.

My new nutural numbers are like wavicles.

Therefore if you use them, you get a natural picture of QM elements.

 

[matt grime]

Exactly in what context did I say you were wrong, organic? You are wrong about many things, but then you freely admit to not knowing much maths. You've not yet offered any reason as to why the strucuture of the natural numbers should be part of their definition - the axioms of a group (finite) do not say that the order of an element must divide the order of the group but that is part of the structure of group.

You have offered in the last few posts the first defintion of complementary pertaining to multiplication, but it didn't make much sense.

You might also care to explain why your definition of what the natural numbers ought to be doesn't agree with the usual definition. Some might consider that to be a problem. Not you.

So from first prinicples, why don't you demonstrate how, using the set of organic numbers, O, say that you obtain a meaningful system? You might be able to do so. Show how they can be used to solve an equation, model the flow of water round a sphere, be localized to form a field... Or even explain what they are used for. (there are many kinds of numbers organic, such as p-adic... any thoughts about that?)

 

[Organic]

Matt,

Multiplication and addition are complementary operations, which mean that each operation simultaneously defines and prevents the other operation.

"Pure" multiplication can be operated only among identical objects, where "pure" addition can be operated among unique objects.

[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]
...

If you understand this ordered relations between a multiset and a "normal" set, then you can see that these ordered elements can be used to construct an ordered table of infinitely many information forms, that can be used as fundamental building-blocks, that when connected to each other, can help us to research much more complex models than the conventional number system.

Please this time try to read all what I wrote here, and see for yourself a gate to complexity:

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

If this time you understand what I am talking about then try to connect this point of view to your knowledge and by this connection please tell me what do you find.

Thank you

Organic

 

[Hurkyl]

Why is there no ((1*2)*2) or ((1*2)*(1+1)) or ((1*(1+1))*(1+1)), et cetera?

 

[Organic]

In my system multiplication can be operated only between identical elements,
where id is both structural and quantitative.

For example:

((1*2)*2) = ((1*2)+(1*2)) = {{1,1},{1,1}}

((1*2)*(1+1)) does no exist because the internal information structure of (1*2) and (1+1) is different, for example:

(1*2) = {1,1}

(1+1) = {{1},1}

Shortly speaking multiplication cannot be operated between elements, which are not equal by their structural properties.

Please look again at page 7 (in the paper, not in the acrobat screen):

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

 

[Hurkyl]

But what if I wanted to compute ((1*2)*(1+1))? Normally, I'd get 4. Are you saying this expression cannot be handled by your system?

 

[Organic]

By my system we have ((1*2)+(1+1)).

Again my system is more sensitive that the conventional system that cares only for the quantitative result and omit the structural difference between the elements.

Please show me the difference between ((1*2)*(1+1)) and ((1*2)+(1+1)) by the convetional system.

 

[Hurkyl]

Please show me the difference between ((1*2)*(1+1)) and ((1*2)+(1+1)) by the convetional system.

The first expression has two multiples and an add, and the second expression has two adds and a multiply. Their parse trees would look like

((1*2)*(1+1))
   *
  / \
 *   +
/ \ / \
1 2 1 1

((1*2)+(1+1))
   +
  / \
 *   +
/ \ / \
1 2 1 1

And what about ((1*3)*(1+1))? Does that also not exist in your system? Note that, even if we're only concerned with the end result, ((1*3)*(1+1)) and ((1*3)+(1+1)) are different.


I have another question; in your system, how come we can't add by 2, and get something like (1+2) being a distinct structure?

 

[Organic]

Hurkyl,

((1*2)*(1+1))
   *
  / \
 *   +
/ \ / \
1 2 1 1

((1*2)+(1+1))
   +
  / \
 *   +
/ \ / \
1 2 1 1

In both cases you used a private case of some structure in quantity 4.

My system define these structures as general ordered information forms that existing in any given quantity, and only then each information form can be used in many ways, which one of them is the way you used it.

Again, in the first stage my system defines the ordered information forms that existing in any given quantity.

And only then they are used, but this time not just as arbitrary separated information forms, but as a part of ordered information forms, for example:

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

In your example you used shape (4,6).

 

[Hurkyl]

which one of them is the way you used it.

You just told me that ((1*2)*(1+1)) does not exist in your system. How can a parse tree then, be using your system? In fact, you said that you cannot multiply things that have different "internal information structure", but I can make a new expression by multiplying any two expressions.


And why can't you add by 2 in your system?

Or multiply two things that are both different from 1?

And what about ((1*3)*(1+1))?


And how is (2, 1) different from (2, 2)? And if there really is a difference, why don't we see something that looks like (3, 1) but with a similar difference?

 

[Organic]

Hurkyl,

You still don't understand me, so I'll try again.

You used this information structure:

    .
   / \
  .   .
 / \ / \
.  ..   .

This is a general information form and you used it by put your notations on it.

We can use this structure for infinitely many other purposes.

My system define the ordered universe of these information forms, and then
we can use them, but this time we can find the deep relations between them
Because thet are ordered, by my method.

 

[Hurkyl]

So, it seems your theory is not about +, *, or natural numbers; it is about binary trees.


I'm still puzzled about why some things are in your ETtable and others aren't. e.g. Why are these different:

| |
+-+--
|


| |
+-+
|

and why don't you have one like:

| | |
+-+ |
|   |
+---+---
|
|

?


P.S. the '+' symbols are diagrammatic; I don't mean for them to be labels or placeholders or anything.

 

[Organic]

By the way, you used the wrong information form, instead you have to use:

          b  b      
          #  #              
   {a, b, a, a}   
    .  .  .  .       
    |  |  |  |     
    |__|  |__|_ 
    |+    |*        
    |     |         
    |     |         
    |_____|____
    |   *                  
    {{{x},x},{x,x}} 
 
          b  b      
          #  #              
   {a, b, a, a}   
    .  .  .  .       
    |  |  |  |     
    |__|  |__|_ 
    |+    |*        
    |     |         
    |     |         
    |_____|____
    |   +                  
    {{{x},x},{x,x}}

and why don't you have one like:

| | |
+-+ |
|   |
+---+---
|
|

See by yourself:

[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]

So, it seems your theory is not about +, *, or natural numbers; it is about binary trees.

1) It is about the information forms that existing between the integral side and the differential side of any given natural number (in the first stage).

2) Binary trees are private cases in my universe.

 

[Hurkyl]

| | |
+-+ |
|   |
+---+---
|
|

is not an ETtree. Please see for yourself:

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

1) It is about the information forms that existing between the integral side and the differential side of any given natural number (in the first stage).

2) Binary trees are private cases in my universe.

But you said:

You used this information structure:

    .
   / \
  .   .
 / \ / \
.  ..   .

This is a general information form and you used it by put your notations on it.

We can use this structure for infinitely many other purposes.

My system define the ordered universe of these information forms, and then
we can use them, but this time we can find the deep relations between them
Because thet are ordered, by my method.

 

[cookiemonster]

http://www.physlink.com/Education/AskExperts/ae329.cfm

Schrodinger's Equation is based on a wave picture of QM.

Yes, thank you. I know what Schrodinger's Equation is.

My new nutural numbers are like w...ogen atom with your numbers? cookiemonster

 

[Organic]

Hi cookiemonster,

At this stage my system is a "pure" mathematical system.

If you understand the ordered redundancy_AND_uncertainty information forms model, then please use its products by yourself.

 

[cookiemonster]

So, at this instance in time but maybe or maybe not at some instance in the future, your numbers are 100% useless?

Good enough for me. Good day!

cookiemonster

 

[Organic]

So, at this instance in time but maybe or maybe not at some instance in the future, your numbers are 100% useless?

By your current understending of my system, the answer yes.

 

[cookiemonster]

"By my current understanding"? I have no understanding of your system. You have given me no reason to attempt to understand your system. I'm not against trying to understand your system if there is a reason, but you, the expert on and promoter of your system, have yet to provide one.

cookiemonster

 

[Organic]

cookiemonster,

My system is an ordered collection of infinitely many information forms that are ordered by their clarity degrees.

Shortly speaking, we have a Mendeleyev-like table of ordered information forms.

If we use these information forms as pert of our system, we get two benefits:

1) Local benefit: We have a concrete model of information form that we can research.

2) Global benefit: Because this information form belongs to an ordered universe, we can find the deep relations with another systems that are using these information forms as an "organic" part of them.

 

[cookiemonster]

My system is an ordered collection of infinitely many information forms that are ordered by their clarity degrees.

That's nice.

Shortly speaking, we have a Mendeleyev-like table of ordered information forms.

Again, that's nice.

If we use these information forms as pert of our system, we get two benefits:

Now we're getting somewhere.

1) Local benefit: We have a concrete model of information form that we can research.

A "model of information," huh. Really. "That we can research." Great, so I can figure out how many i's are in "information." Or maybe how many syllables are required to say "concrete."

A model of what kind of information? A model from which I can research what kind of knowledge? What kind of uses are we looking at? Your entire sentence is so cryptic and imprecise that it has no information.

2) Global benefit: Because this information form belongs to an ordered universe, we can find the deep relations with another systems that are using these information forms as an "organic" part of them.

"This information form." You still haven't mentioned what information form "this" is.

"An ordered universe." I don't believe our universe is perfectly ordered, and I'd wager that Quantum Theory agrees with me. Even when I scanned your webpage, I saw lots of mention of uncertainty.

"Deep relations." What?

"Another systems." Such as?

"'Organic' part of them." What?

What do these two reasons mean? Are they even saying anything? I mean, I'm not hard to fool here. I'm relatively uneducated in general and particularly unversed in your theory in specific. You could probably make something up that sounds good, is on the surface consistent, and makes sense and I'd buy it. But all you've said so far is that your system should be investigated "because it has things that should be investigated," which is hardly convincing.

Have you even arrived at any results, or have you been too busy drawing little diagrams? There's not much that's more convincing than results. If it works and I don't know why, then I'm relatively inclined to figure out why it does. But all your system is doing is sitting there doing nothing but stirring up matt and hijacking threads, and I don't know why, and I have no inclination to figure out why.

What's its purpose? What are you trying to accomplish with this? Are you striving toward some kind of goal? Have you gotten anywhere near that? Does your system satisfy that goal? If so, can we see this?

And for the third time, can you take any physical model of reality that has proven to be only an approximation, apply your numbers to it, and yield another physical model of reality that is a better approximation?

cookiemonster

 

[Hurkyl]

Perhaps you would care to draw a "redundancy / uncertainty" diagram for (5, 10)?


Why does "redundancy / uncertainty" never look like:

M  R  D
D  M  R

?

And what about ((1*3)*(1+1))?

 

[Organic]

Hurkyl,

My system is very accurate, and I show examples of it.

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

(1*3) means {1,1,1} and (1+1) means {{1},1}

Why does "redundancy / uncertainty" never look like:

M  R  D
D  M  R

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



Here is again examples of my system, and this time try to understand my game:


Let # be XOR

My system is an ordered collection of redundancy_AND_uncertainy information forms.

See by yourself:

[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]
...

also I showed that you used the wrong information form:

    b  b  b  b      
    #  #  #  #              
   {a, a, a, a}   
    .  .  .  .       
    |  |  |  |     
    |__|_ |__|_ 
    |     |         
    |     |         
    |     |         
    |_____|____
    |                      
    {{x,x},{x,x}}

instead you have to use:

          b  b      
          #  #              
   {a, b, a, a}   
    .  .  .  .       
    |  |  |  |     
    |__|  |__|_ 
    |+    |*        
    |     |         
    |     |         
    |_____|____
    |   *                  
    {{{x},x},{x,x}} 
 
          b  b      
          #  #              
   {a, b, a, a}   
    .  .  .  .       
    |  |  |  |     
    |__|  |__|_ 
    |+    |*        
    |     |         
    |     |         
    |_____|____
    |   +                  
    {{{x},x},{x,x}}

Each part of the graphic representation of it has an exact meaning, for example:

CR is Computational Root.

[u]A general graphic description of a CR[/u]

CD is Continuum AND Discreteness

RU is Rudandancy_AND_Uncertainty

AL is Association-Level

     .     .     .<------ D (Discreteness)
     |     |     |
     |     |     |
     |     |     |<------ The association between CD
     |     |     |
     |     |     |
     |_____|_____|__<---- RU marker
     |  ^
     |   \____ C (Continuum)
     |
     |<---- Next-AL marker

[url]http://www.geocities.com/complementarytheory/CATheory.pdf[/url] (page 7 - Indroduction (in the paper, not in the acrobat screen)).

You asked:

and why don't you have one like:

| | |
+-+ |
|   |
+---+---
|
|

My answer is:

If you use my system you have to follow my definitions, otherwise we are not talking about my system.

This form:

| | |
+-+ |
|   |
+---+---
|
|

has no meaning in my 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 unclear information of 3-system is the most left information's-tree, where each key has no unique value of its own, and vice versa:

<-Redundancy->
    M   M   M  ^<----Uncertainty
    R   R   R  |    R   R
    D   D   D  |    D   D   M       D   R   M
    .   .   .  v    .   .   .       .   .   .
    |   |   |       |   |   |       |   |   |
3 = |   |   |       |___|_  |       |___|   |
    |   |   |       |       |       |       |
    |___|___|_      |_______|       |_______|
    |               |               |

 

[matt grime]

Hurkyl,
My system is very accurate, and I show examples of it.
Plrease show me how can you define ((1*3)*(1+1)) when in my system
(1*3) means {1,1,1} and (1+1) means {{1},1}
Please give an example by using the lows of my system.

lows? Perhaps you are self aware after all.

Here is again examples of my system, and this time try to understand my game:

we can't because you won't explain what your "game" is or does.

This form:

| | |
+-+ |
|   |
+---+---
|
|

has no meaning in my system.

What, and the other things you write do mean something?