Deeper than primes

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doronshadmi said:
Are forms like:

(A,A), (B,B)

(A,A,A), (B,B,B), (C,C,C)

etc.. are also valid in your ONs game?
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No. That would violate the definition laid out for distinction. I know you don't worry about consistency, but it is one of those important aspects fo Mathematics.
 
dlorde said:
Operators and operands are well defined and well understood.
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No, they are not understood as REI (Relation Element Interaction), where Distinction, Non-locality and Locality play main roles.

In order to understand REI you have to read http://www.geocities.com/complementarytheory/OMPT.pdf pages 15-17.

It will help you to think about Relation as a line, and about en Element as a point, where a result that is not 0 is an interaction between a line and point(s) (negative results are simply a mirror image of some REI).
 
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jsfisher said:
No. That would violate the definition laid out for distinction. I know you don't worry about consistency, but it is one of those important aspects fo Mathematics.
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Here is the definition:

Distinction refers to the amount of the distinct levels of a thing.

Please explain how (A,A,A) etc... violates this definition.

(A,A,A) ... and so on, is simply the case where Distinction is based on Redundancy without Uncertainty.

On the contrary (ABC) ... and so on, is simply the case where Distinction is based on Uncertainty without Redundancy.

(A,A,A) is shown in http://www.internationalskeptics.com/forums/showpost.php?p=4859114&postcount=4198 .

x is an element.

Definition 1:
Identity is a property of x, which allows distinguishing among it.

Definition 2:
Copy is a duplication of a single identity.

Definition 3:
If x has more than a single identity, then x is called Uncertain.

Definition 4:
If x has more than a single copy, then x is called Redundant.

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

Until now ONs are played on Uncertainty\Redundancy matrix, but you can add more Axis if you like.

But the important thing here that no matter what ONs' games you play, they are all based of Distinction, Non-locality and Locality as their main principles, where the player is a significant factor of any game.
 
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jsfisher said:
Yes, you are wrong.

The Fibonacci sequence can be defined by:

F(1) = 1
F(2) = 1
F(n+2) = F(n+1) + F(n)

The first two parts of this definition are necessary to the recursion. It cannot work without it. Moreover, there is nothing in the definition that makes one part contradict any other part.

For your definition of Or(n), you included unnecessary components. Worse, those unnecessary component contradict other components. Your definition for Or(n) is not self-consistent.

For Or(1), your formula devolves to a summation over an empty set and requires no explicit definition for value. The definition for Or(1), therefore, is unnecessary. Worse, the definition doesn't agree with the formula.

Also, the Fibonacci sequence recursion requires two "starting values" because of its formulation. Your recursion for Or(n), just by its form, doesn't require two starting values.

To be proper, your starting values for a recursion must be (1) necessary and (2) consistent. Yours are neither.
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Hi jsfisher,

I have read the answer of Doron and accept it

http://www.internationalskeptics.com/forums/showpost.php?p=4857707&postcount=4185

2=1+1 is a special case
it include the most uncertainty case n=1+1+..+1
and the case when the first id of and element is appear

only in 3 there is a real separation between them

3=1+1+1
3=2+1

this explane why 2 is unique in or(n)

So my algorithm should start to work only at 3.

Sorry
Moshe:D
 
The Man said:
No problem let my try to make it clearer. For the value 4 it is apparently being claimed that this must be 4 ‘things’ which may or may not be distinct from each other. So we label these things as A, B, C and D, giving the each distinct identifications. As there is only 1 A, 1 B 1 C and 1 D in this case of complete distinction then when we sum these things we get 4 in total. At lower levels of distinction we may have 2 As 1 B and 1 C but still only 4 total items. The problem is ordering is another type of distinction that specifically comes into play the more independent those individual distinctions become. In fact ordering distinctions become the most significant in the first instance I gave of complete distinctions. Now ordering is not that critical when simply discussing math or specifically summation, but that is not what we are talking about here. We are talking about things, specifically potentially uniquely identifiable things, and in that respect ordering can be an important if not essential factor. Let’s add some very specific identification to those things and see what we get when we change ordering. If we take 1 slab of butter, 1 slice bread, 1 slice of cheese and 1 application of heat we have lunch as a grilled cheese sandwich. If we gather, combine or add these things together then we are ready to eat. However if we do not gather them in a suitable order we do not end with the same “total” (lunch) but still have brought together 4 items in total. If we add the heat to the butter or cheese with out having gathered the bread first we just end up with mess to clean up and our elements go into the trash instead of in our stomachs. Other orderings might not be as unpalatable as this but still will not result in the same total of a grilled cheese sandwich. The proper ordering would be gather beard, add butter to bread add cheese then add heat. We can reverse the butter and cheese ordering without much consequence, so some identities can require more specific or singular ordering while others do not.


If you are just going to start assigning distinctions to possible elements of 4 then you must consider all the ramification of such assignment otherwise that assignment is just arbitrary and insignificant. If you are going to specifically base such assignments on the possibility or insistence that they must represent real things then again the consequences of complete consideration are required invoked. Otherwise there is absolutely no point in making such distinctions and any 1 is no different then any other 1. When you do make such distinctions particularly such that some 1 is some how different then some other 1 then ordering distinctions must come into play otherwise you are simply claiming that this particular 1 is no different then that particular 1 and your ascribed distinctions have absolutely no meaning.
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Dear Man

haven't you understand already
that I am dyslectic in English.
It's like a black board for me
many red colors in the speller of word..

can't you explain yourself much shortly
what is the main problem ?

Sincerely
Moshe:con2:
 
MosheKlein said:
2=1+1 is a special case
it include the most uncertainty case n=1+1+..+1
and the case when the first id of and element is appear

only in 3 there is a real separation between them

3=1+1+1
3=2+1

this explane why 2 is unique in or(n)
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No, it doesn't. It is just backpedaling and hand-waving. You also didn't address the arbitrary rule introduced for 1. Apparently, though, we all agree the whole organic number scheme is inconsistent and founded on special cases and exceptions. How is this useful?
 
The Man said:
No problem let my try to make it clearer. For the value 4 it is apparently being claimed that this must be 4 ‘things’ which may or may not be distinct from each other. So we label these things as A, B, C and D, giving the each distinct identifications. As there is only 1 A, 1 B 1 C and 1 D in this case of complete distinction then when we sum these things we get 4 in total. At lower levels of distinction we may have 2 As 1 B and 1 C but still only 4 total items. The problem is ordering is another type of distinction that specifically comes into play the more independent those individual distinctions become. In fact ordering distinctions become the most significant in the first instance I gave of complete distinctions. Now ordering is not that critical when simply discussing math or specifically summation, but that is not what we are talking about here. We are talking about things, specifically potentially uniquely identifiable things, and in that respect ordering can be an important if not essential factor. Let’s add some very specific identification to those things and see what we get when we change ordering. If we take 1 slab of butter, 1 slice bread, 1 slice of cheese and 1 application of heat we have lunch as a grilled cheese sandwich. If we gather, combine or add these things together then we are ready to eat. However if we do not gather them in a suitable order we do not end with the same “total” (lunch) but still have brought together 4 items in total. If we add the heat to the butter or cheese with out having gathered the bread first we just end up with mess to clean up and our elements go into the trash instead of in our stomachs. Other orderings might not be as unpalatable as this but still will not result in the same total of a grilled cheese sandwich. The proper ordering would be gather beard, add butter to bread add cheese then add heat. We can reverse the butter and cheese ordering without much consequence, so some identities can require more specific or singular ordering while others do not.


If you are just going to start assigning distinctions to possible elements of 4 then you must consider all the ramification of such assignment otherwise that assignment is just arbitrary and insignificant. If you are going to specifically base such assignments on the possibility or insistence that they must represent real things then again the consequences of complete consideration are required invoked. Otherwise there is absolutely no point in making such distinctions and any 1 is no different then any other 1. When you do make such distinctions particularly such that some 1 is some how different then some other 1 then ordering distinctions must come into play otherwise you are simply claiming that this particular 1 is no different then that particular 1 and your ascribed distinctions have absolutely no meaning.
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The Man, one of the first things that are needed is to define the basic environment (the playground) where the game takes place.

In this case the environment is nxn matrix, where one axis measures the uncertainty of the played element(s) and the other axis measures the redundancy of the played element(s).

The game is considered as a one thing with many different situations that are measured by the nxn matrix, where each salutation is both local and global case of the game. Also all along the game the player is a significant factor of the game.

But the most important thing is to define the invariant properties that are not changed even if the playgrounds, the games (they rules), or the players are changed.

And this is exactly what OM is all about, where its invariant properties are Distinction, Non-locality and Locality.

You and Jsfisher looking only on the "branches" of the ecosystem (playgrounds, games' rules (in your case you ignore the players)), and totally ignore its "trunk" (these invariant properties that are not changed even if the playgrounds, the games (they rules), or the players are changed).

You still continue to ignore it, and as a result you continue not to get OM.

Nobody but you can help you to get OM's ecosystem as a one complex organism, which is the result of Non-locality\Locality Intercation.

EDIT:

I wish to add that your analogies are limited to the macro realm and ignore QM micro realm.
 
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jsfisher said:
That's not a usable definition. Keep trying, though.
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I admire your patience. The generation of Organic Numbers is now referred to as 'a game' that takes place in a 'playground', and the rules for generating them are not fixed. It's like pinning jelly to the wall.

Truly a construction built on shifting sands - or perhaps a game played with moving goalposts :D
 
dlorde said:
I admire your patience. The generation of Organic Numbers is now referred to as 'a game' that takes place in a 'playground', and the rules for generating them are not fixed.
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No, the rules for generating them are determined by the player's agreed principles , the playground properties and the invariant properties of the ecosystem (where the ecosystem is both abstract or non-abstract realm).

Do you think that Standard Math is different (the words of God or something)?

By using Distinction, Non-locality and Locality as "trunk" properties, I clearly show that Standard Math gets only the "branches" (it does not have any "trunk" principles) and as a result it has no real fundamental understanding of that "branches", exactly as an inability to understand a tree if one ignore its trunk.
 
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Little 10 Toes said:
Are we talking about shapes, size (not cardinality), area, volume, or something else?
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What ever you wish (abstract or not) that can work separately or together .

Let us provide even a better definition:

Distinction refers to the amount of the identified states of a thing, that can be used both as globel and local property of a given system.
 
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Let us do it even better:

Distinction refers to the identified states of a thing, that can be used both as globel and local property of a given system.


Now all is needed is at least a n-Uncertainty x n-Redundancy matrix, and let your play begin, according to some consistant rules.


We can play a game called "all possible identified states of a given n-Uncertainty x n-Redundancy matrix".

My first introduction of Organin Numbers uses n-Uncertainty x n-Redundancy matrix but it does not play the game of "all possible identified states of a given n-Uncertainty x n-Redundancy matrix", because I use my first untroduction only as an example, where Distinction, Non-locality and Locality are used as the invariant properties (the "trunk" properties) and my OMPT paper is dedicated to the "trunk"\"branches" intercation in general, and not to the particular ONs example.
 
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jsfisher said:
No, it doesn't. It is just backpedaling and hand-waving. You also didn't address the arbitrary rule introduced for 1. Apparently, though, we all agree the whole organic number scheme is inconsistent and founded on special cases and exceptions. How is this useful?
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One is the only case were there is no real distinction.
So 1 in OM is the same as in Euclidian Mathematics.
OM will help us/you to have a direct perception of Mathematics !
Intuitive and not formalist what P.Erdos name as the book of God
for the most simple prove to a theorem.

Moshe:boxedin:
 
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doronshadmi said:
Distinction refers to the amount of the identified states of a thing.
...Think about the most geneal notion of "identified states".
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Are you talking about uniquely identifying properties (unique identifiers) ? Distinction being the number of unique identifiers an object has?

So the number 4 can be uniquely identified by its value, the character '4' by its shape, this particular character '4' by its position in this piece of text... ?

So a collection of four objects can be uniquely identified in a number of ways, depending on the identities of the objects that comprise it, and the OM of four objects is the sum of the different ways this collection can be uniquely identified - according to a set of rules that arbitrarily exclude certain ways ?

So how does this introduce morals and ethics into science, exactly?
And how are they used in any practical way (examples welcome) ?

Didn't I ask this before? Wasn't I studiously ignored?
 
dlorde said:
Are you talking about uniquely identifying properties (unique identifiers) ? Distinction being the number of unique identifiers an object has?

So the number 4 can be uniquely identified by its value, the character '4' by its shape, this particular character '4' by its position in this piece of text... ?

So a collection of four objects can be uniquely identified in a number of ways, depending on the identities of the objects that comprise it, and the OM of four objects is the sum of the different ways this collection can be uniquely identified - according to a set of rules that arbitrarily exclude certain ways ?

So how does this introduce morals and ethics into science, exactly?
And how are they used in any practical way (examples welcome) ?

Didn't I ask this before? Wasn't I studiously ignored?
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please look at http://www.internationalskeptics.com/forums/showpost.php?p=4859722&postcount=4217 .

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.

The mathematician talk about mathematical "branches", but they have no answer about the "trunk" of this science.

Please tell me how can one talks about the "branches" of a thing if he is ignorant about its "trunk"?

People like jsfisher will tell you that Consistency is the "trunk's" principle, but there are "branches" like "Paraconsistent Logic" ( http://en.wikipedia.org/wiki/Paraconsistent_logic ) which are weaker than Classical Logic, but still ar considered as a valid branch of the mathematical science. So Consistency is not a "trunk's" principle.

Also Logic has many branches that some of them have no common principles, so also Logic is not a "trunk's" principle of the mathematical science.

OM defines Distinction, Non-locality and Locality as common properties of the mathematical science, where the mathematician's cognition is a significant and real-time factor of that science.

Furthermore, by using Non-Locality it shows that things that are considered as contradiction from a local point of view are not a contradiction from a non-local point of view.

In order to get it please read http://www.geocities.com/complementarytheory/OMPT.pdf pages 22-30.

jsfisher and his friends can't grasp this new stuff because they never learned this novel knowledge and their standard knowledge can't help them to comprehend it.

Instead they are using their standard knowledge and techniques on particular technical aspects of it, and by this behavior they miss time after time the novel OM's "trunk" knowledge.

To tell you the true, I am getting tiered of their inabilities to get things beyond their :boxedin:
 
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