Exploring Non-Commutative Natural Numbers

In summary, Standard Math does not understand the concept of a number, and so numbers cannot be defined in terms of these structures.
  • #71
Matt,

1) there is no meaning to mirror images when we want to represent redundancy_AND_uncertainty variations.

If you don't think so, please show us how redundancy_AND_uncertainty are changed by a mirror image.

2) Please this time show the detailed trees of 2,3 and 4 without mirror images.

3) Please explain the relations between multiplication and addition in your system.
 
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  • #72
For a bloody joke this is getting out of hand.

NateTG, if you want to define other operations please do so, I don't care in the slightest, but I was attempting to get the silliest defintions I could.

Organic, why would I require uncertainty and redundancy to change under mirror images? I don't in my system, which I won't justify becuase I don't have to.

The realtiohsip between + and * is given to you in the definition of * as repeated +.

No, I can'be be bothered to draw out the diagrams, why should I? I don't actually think this idea is useful or interesting to anyone but you. It is a silly and pointless exercise I cooked up in a couple of minutes. I'm sure if I felt like it I could construct a system doing exactly what you require, but as you never explain what you require clearly it would be a tiresome exercise - after all, why are you now saying mirror images must alter redundancy and uncertainty? I don't remember you saying that ever before (you didn't mention mirror images) so how do I know you won't change your mind again?
 
  • #73
Matt,

By using "\" "|" and "/" symbols I can represent 1,2,3 and 4 in this way:
Code: 
|


      |
\/    |


            |
      |     |
\|/   |/    |

                                                 |
                                                 |
            |            |     ||          |     |
\\//  \///  |//   \/\/   |\/   ||   \|//   |//   |
There are no left-right switches or mirroring changes in my system.

Now, please use the same three basic symbols to represent your trees, without left-right switches or mirroring changes.

Here is an example of left-right switches:
Code: 
\/||    |\/|
Here is an example of mirroring changes:
Code: 
|     |
|/   \|
 
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  • #74
fine, delcare all mirror image trees to be identified, i don't really care. most of the things you drew aren't trees cos they don't have a root, but that could jst be the restrictions of html coding, and you've repeated lots of them too.
 
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  • #75
Matt,

If you can't draw your detailed trees, we can understand that you have no method to define them.

So, you did not succeed to produce any system where multiplication and addition are complementary operations.
and you've repeated lots of them too.
Please give an example
 
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  • #76
No, I can't be bothered to draw them. If you cannot draw all trees with 4 edges and so on then that's your problem. As you have not said what it means for addition and multiplication to be complementary the second assertion is a little moot, isn't it?

To draw a tree/directed graph. Pick a base point. Draw arrows out of the base point, from the tip of each arrow draw more arrows going out that do not touch any other arrows. Repeat.

the elements of degree n are all the diagrams you can draw with n arrows, I require you to order the edges leaving a node so that you can differentiate between certain trees. You've declared that you ought not to do that, but why? I disagree, and you cannot prove I'm wrong.

It is not clear what

\\// \/\/ \||/

etc that you drew are, seeing as they all have depth 1 and should all thus be the same tree - where is the root point?

You do know that a tree is a (directed) graph without loops?
 
  • #77
This is my system:
Code: 
[b]
0
|
[/b]
1
[b]

11
00   1|
\/   0|
[/b]
1     2

[b]
222
111   11    2|
000   002   1|
\|/   \//   0|
[/b]
 1     2     3

[b]
3333     33     33
2222     22     22                        222           3|
1111   1111     11   1111     11          111    11     2|
0000   0000   1|00   0000   1|00   1||1   0003   0023   1|
\\//   \///   0|//   \/\/   0|\/   0||0   \|//   \///   0| 
[/b]
  1      2      3      4      5     6      7      8      9
and it cannot be represented by "\" , "/" and "|" notations (as you choosed to do) because, for example, in a given quantity 4, tree-2 has the same shape as tree-8.

So it is not so trivial as you think.

Now, please find an accurate way to draw your trees, and please explain what data you give to each branch, as I did.
 
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  • #78
I am assigning no data to my diagrams; I didn't say yours was trivial (it isn't very interesting, but that's different); I have noi desire to draw out these things, they aren't interesting, useful or of any point what so ever, just like yours. You said there was nothing maths LIKE your theory. There is. As you've never bothered to explain your theory accurately it's only a reasonabl approximation, the best we can do when there is incomplete information.
 
  • #79
Code: 
(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)
All left-right variations are ignored, please see the examples below:

{1,1,1,1}

{{1,1},1,1} (left-right {1,{1,1},1} and {1,1,{1,1}} are ignored)

{{{1},1},1,1} (left-right {1,{{1},1},1} and {1,1,{{1},1} and {1,{1,{1}},1} and {1,1,{1,{1}}} are ignored)

{{1,1},{1,1}}

{{{1},1},{1,1}}

{{{1},1},{{1},1}}

{{1,1,1},1}

{{{1,1},1},1}

{{{{1},1},1},1}

The first one is a multi set {1,1,1,1}

The last one is a normal set {{{{1},1},1},1}

All other collections between them are the ordered collections of hybrid sets.

Can you use this to show your system?
 
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  • #80
Please excuse my interjections, as I have only briefly followed this thread and the related one from the Math section.
Organic, I am a little confused as to the thrust of your arguments due to all the rambling. Could you re-state them?
 
  • #81
Hi pallidin,

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.

Code: 
[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]
...

Please show what is not understood in the above example.
 
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  • #82
OK.

Well, I understand what you have shown, but not sure of the point.
 
  • #84
Matt

How you write correctly in english "tranjuction " point.
I mean by this a "the point of the big change".

thank you
Moshek
 
  • #85
I think I'm going to let myself be dragged into this for just about exactly one post...

Organic, do you have a concrete example of the use of your system? I see lots of you arguing with matt about how he's wrong and you're right and he's obtuse and you're not, etc., etc. And I see lots of little diagrams which have no meaning to me, which is probably my own fault. And I see lots of claims that this may or may not have use to physical theories that require some uncertainty.

I'll be honest with you. I really haven't cared a bit about your theory because I haven't seen its use. To me, math isn't a whole lot more than a tool or a game. It'd probably take me a lot of work to go through and try to understand what you're getting at (no offense, but your explanations seem to be exactly the same, which means it won't help the second time if it didn't the first), and unless it's worthwhile, I don't want to waste my time.

So can you show me it's worthwhile? Can you show an example? Can you throw your numbers at the classical expression for U + T = E and have Schrodinger's Equation appear? Or is this an unfair comparison between your numbers and the currently established numbers? If so, is there a fair comparison?

cookiemonster
 
  • #86
Hi cookiemonster

I hope that you will find the cookies that you like here:

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

My theory of numbers is also new tools for new games.

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

I see lots of you arguing with matt about how he's wrong and you're right and he's obtuse and you're not, etc., etc.
I don't say that Matt is wrong (he says this about me) all what I say is that because he ignores the structural/quantitative relations as fundamental point of view of the NUMBER concept, he cannot understand my number-system.
 
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  • #87
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?

cookiemonster
 
  • #88
To Organic
with his new numbers system:


----------------------------------------------


For Mathematics

The current big-band
His here real Glory.
Milky way is around us.
A solar system was created.

Everything is a number
Said Pythagoras
While he could hear
The music of the spheres.

But so many water
Cover the head of Hipasus
After he discovery
The secret of irrationality.


Maybe Euclids hide the story
For the protecting the axiom
Of the parallels
To establish his own mathematics.

While Newton calculate
The end of the world
Leibniz with the monads believed
A unify language must exist.

Goethe could see here
With the generic type
But he just did not
like or know mathematics

Hilbert was staying
So misunderstood
With his list of 23 problems
and the organic unity.


A.Connes with
Noncomutativs geometry
100 to Hilbert end with
some new understanding.

M.Athiya for his Index
And K theory
Talk about here
As some Enigma.

I Stuart with his vision
Share her flexibility
In his Epilog
The nature of numbers

Wittgenstein say
We should be Aliens
To see here in
The bottle of Klein.


From the top mountain
Of the Rieman hypothesis
We can see the real mount Analog
And Hear its’ sixth symphony. ’


Einstein did a real
First step of a child
When he ask how we
measure a length.

Only if we could See again
The world Like children
We will count again
Now from the beginning 1. 2. 3.




Moshe Klein 4.4.04
 
  • #89
Ok, how do you obtain the rationals, irrationals etc. out of this theory?
 
  • #90
Only by Analogy no definition:

Since the relation between irrational number to rational numbers
Is like "Organic mathematic" with here new center of the organic unity of mathematics to the Euclidian mathematics where the center there was logic.
 
  • #91
I do beg your pardon?
 
  • #92
For what Lonewolf ?
 
  • #93
"Organic mathematics", and an explanation of "Organic unity" is required before I can understand what the centre of it is.
 
  • #94
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!
 
  • #96
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.
 
  • #97
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?)
 
  • #98
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.

Code: 
[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
 
  • #99
Why is there no ((1*2)*2) or ((1*2)*(1+1)) or ((1*(1+1))*(1+1)), et cetera?
 
  • #100
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
 
  • #101
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?
 
  • #102
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.
 
  • #103
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

Code: 
((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?
 
  • #104
Hurkyl,

Code: 
((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).
 
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  • #105
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?
 
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