Deeper than primes

[MosheKlein]

Well actually no, the question wasn’t how ordering distinctions differ from associative distinctions in OM, but why are they excluded. So really you have just switched the question to why are serial distinctions excluded when, particularly for larger numbers, there are going to be more ordering (serial) distinctions then associative (parallel) distinctions? Again I must say that I am glad to see someone willing and capable of giving clear and concise answers on the subject, but unfortunately it did not answer the question asked.

Hi Man,

I have some difficulties to understand your question
Maybe because of my English..
Can we concentrate on a specific example?
for example the case 4=2+2 bring to 3 different distinction since we delete one case
Because of symmetry


Can this be related to your question?

Best
Moshe

 

[MosheKlein]

I'm not really sure if my algorithm for generating partitions is very interesting. I don't even know if it's new . For the rest, I just implemented your algorithm and put some thought into what intermediate results are worth caching (see Memoization^WP).

Hi ddt,

Following your computation Or : n=1..100
is equal to the sequences A5069.. ( don't remember it's number)
So we can present in the paper an nice open problem
if it will continue forever , What do you think ?

Moshe

 

[MosheKlein]

Thank you Moshe.

Now we're assuming some things, of course.

1.) There are three quarters on the table. (Again "quarter is the name of an American coin value of 25 cents.)

2.) They are new coins and look alike. You'd have to look very hard to tell them apart.

3.) First off they are in a neat little row.

4.) I began with the suggestion that Athony count the coins.
You are asking him what he sees. So let's go there.

I imagine Anthony knows what quarters are and has seen them in action.
His answer could likely be, "A row of quarters." And he mighty just tell us "three quarters" without our asking.

But If our Anthony has never before seen quarter in his life, then there's a row of round things.
An if he doesn't know counting words, he's not going to tell us there are three round things.

What does he see?
Perhaps a row of individual objects.
Perhaps a row of duplicates of the same thing.

Shall we make something of that?

Maybe I shouldn't have chosen coins that look alike, but seperate fruit items.
like an orange, an apple, and a banana.



(Just a note:
Objects
Duplicates
Both are plural.
Both are its of third person discourse.
Anthony might "see" something entirely different, if he weren't reporting things he saw.)


Now you'll begin correcting me about what Anthony might have seen.
Please do. That's going to tell me a lot.

Hi Apathia,

I can see that you see two children's Anthony and Michel everyone say something else so let make the distinction between them.

Michel says : "I see a fruit."
Anthony says: "I see an orange, an apple, and a Banana."

So I can asked them both : Do you see the same thing ?

What do you think can be there answer ?


Best
Moshe

 

[MosheKlein]

MosheKlein,

While you are thinking about (AB, BC, AC) and (AB, ABC, ABC) as missing distinctions for 3, pardon me for adding more fuel to the fire: For both 1 and 2, you invoke special rules.

For 1, you use the partition 1=1 to get 1 distinction. However, 1=1 is one of those n=n cases you said to ignore. You are therefore applying a special rule for 1 to get Or(1)=1. (Interestingly, too, you seldom show one of those stick drawings for the distinctions of 1 case like you do for all the other numbers.)

For 2, you omit the 2=2 partition (as you should, at least according to your rules), but somehow you generate two distinctions from the 2=1+1 partition. For all other numbers, the 1+1+...+1 case yields only one distinction. You are therefore applying a special rule for 2 to get Or(2)=2.

These very same inconsistencies exist in your formula for Or, too. You "define" Or(1) to be 1 and Or(2) to be 2. However, if you were to just calculate Or(1) from your formula directly, ignoring the defined value, you get Or(1)=0. So, on the one hand the definition for Or(1) is unnecessary, but on the other hand the definition you provided is inconsistent with the formula. You are therefore introducing a special rule for 1 to get Or(1)=1.

Similarly, if we were to accept Or(1)=1 and calculate Or(2) directly from the formula, we get Or(2)=1. Again, the definition for Or(2) is unnecessary, but the definition you provided is inconsistent with the formula. You are therefore introducing a special rule for 2 to get Or(2)=2.


What does all this mean? Well, from my point of view it means what was supposed to be a simple, elegant observation about the structure of the positive integers starts out with two inconsistencies followed by the wrong answer (for 1, 2, and 3, respectively).

Hi jsfisher,

I don't understand the problem
every recursion need initialization
For example the Fibonacci sequences

1,1,2,3,5,8,13

you define :

a1=1
a2=1

you don't have to explain the beginning

or(1)=1
or(2)=2

am I wrong ?

Moshe

 

[doronshadmi]

Hi jsfisher,

I don't understand the problem
every recursion need initialization
For example the Fibonacci sequences

1,1,2,3,5,8,13

you define :

a1=1
a2=1

you don't have to explain the beginning

or(1)=1
or(2)=2

am I wrong ?

Moshe

Hi Moshe,

There is a simple explanation of why your function gets on stage only for any n>2.

1) Your function ignores n+0 case, so it does not work for partition 1+0, which is the only partition of n=1

2) Your function does not work in partition 1+1 of n=2 because partition 1+1 is used for both the non-distinct case (AB,AB)=(2,2) and for the distinct case (A,B)=((1),1):

n=2

(1+1)
(AB,AB)=(2,2)
(A,B)=((1),1)


3) Your function works for any n>2 because only from n=3 to ∞ the partition of the form (1+1+1+…) is clearly used only for the non-distinct form for any n>2, for example, in n=3:

n=3

(1+1+1)
(ABC,ABC,ABC)=(3,3,3) (the non-distinct case of n=3)

(2+1)
(AB,AB,C)=((2,2),1)
(A,B,C)=(((1),1),1)

 

[doronshadmi]

4 is simply a representation of a value,

I am talking about:

1) 4 as a cardinal of a collection, that does not provide any information about the level of distinction of the elements of that collection.

2) 4 as a distinct value (what you call "4 is simply a representation of a value").

Then ABC, ACB, BCA, BAC, CBA and CAB are all distinct orderings of an A,B,C association and
are “distinctions based simply on ordering” that you must “include”.

(A,B,C)=(((1),1),1)
(ABC,ABC,ABC)=(3,3,3) and it is a superposition of 3 ids and not a permutation of 3 ids.

A permutation of 3 ids is based on the particular distinct case (A,B,C)=(((1),1),1) of ON3, and on this basis we have ABC, ACB, BCA, BAC, CBA and CAB premutation.

In general, the minimal case of ON3 is:

(ABC,ABC,ABC)=(3,3,3) (superposition of 3 ids)
(AB,AB,ABC)=((2,2),1) (superposition of 2 ids within n=3)
(A,B,C)=(((1),1),1) (distinct ids of n=3)

where the order of the symbols has no significance.

Unless as usual you are simply claiming that you only “include distinctions based simply on ordering” that you have arbitrarily selected.

The Man I am sorry to tell you that after more than 4000 posts you simply do not understand Organic Numbers and how they use Distinction.

You do not understand how uncertainty and redundancy are used by them, in order to determine the ids of the gathered elements.

There is no use to continue the dialog with you on this case, because all you wish to do is to show what is wrong in my head, instead of using your head in order to understand what you read.

Your kind of criticism is sterile and boring, and any further reply to you (as long as you continue this style of criticism) is a waste of energy.

 

[jsfisher]

Hi jsfisher,

I don't understand the problem
every recursion need initialization
For example the Fibonacci sequences

1,1,2,3,5,8,13

you define :

a1=1
a2=1

you don't have to explain the beginning

or(1)=1
or(2)=2

am I wrong ?

Yes, you are wrong.

The Fibonacci sequence can be defined by:

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

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, you included unnecessary components. Worse, those unnecessary component contradict other components. Your definition for Or 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, 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.

 

[The Man]

(A,B,C)=(((1),1),1)
(ABC,ABC,ABC)=(3,3,3) and it is a superposition of 3 ids and not a permutation of 3 ids.

A permutation of 3 ids is based on the particular distinct case (A,B,C)=(((1),1),1) of ON3, and on this basis we have ABC, ACB, BCA, BAC, CBA and CAB premutation.

In general, the minimal case of ON3 is:

(ABC,ABC,ABC)=(3,3,3) (superposition of 3 ids)
(AB,AB,ABC)=((2,2),1) (superposition of 2 ids within n=3)
(A,B,C)=(((1),1),1) (disdinct ids of n=3)

where the order of the symbols has no significance.

By labeling “(((1),1),1)” as “(A,B,C)” it is distinctions that you have established yourself. The orders of the symbols has significance by those distinctions you just established yourself. That fact that you simply ignore this particular type of distinction only goes to further demonstrate the arbitrary nature of your so called distinctions

The Man I am sorry to tell you that after more than 4000 posts you simply do not understand Organic Numbers and how they use Distinction.

After 4000 posts Doron you still do not know what it is you are doing by individually labeling your “1”s as either A, B , or C. You gave those indpendent distinctions which gives ordering distinctions like ABC, BAC and CAB validity. That you simply ignore those ordering and independent distinctions you gave them yourself only goes to show the insignificance of your so called distinctions even just to yourself.

You do not understand how uncertainty and redundancy are used by them, in order to determine the ids of the gathered elements.

You still do not understand that it is all a bunch of arbitrary nonsense that you specifically admitted in your last post that it is not from any information provided by the “number”

There is no use to continue the dialog with you on this case, because all you wish to do is to show what is wrong in my head, instead of using your head in order to understand what you read.

Your kind of criticism is sterile and boring, and any further reply to you (as long as you continue this style of criticism) is a waste of energy.

We have all heard that before Doron.

 

[jsfisher]

Moshe's formula gets on stage only for any n>2.

You have already told us you don't understand MosheKlein's formula, and I am confident you were truthful in that statement. I am also confident you don't understand the inadequacy of your explanation.

 

[doronshadmi]

By labeling “(((1),1),1)” as “(A,B,C)” it is distinctions that you have established yourself

No, it is not:

(((1),1),1) is the general form for (A,B,C), (A,C,B), (B,C,A), (B,A,C), (C,B,A) and (C,A,B) and you simply do not get it.

The "1"+"()" simply represent a unique id, no matter what value it has.

 

[doronshadmi]

You have already told us you don't understand MosheKlein's formula, and I am confident you were truthful in that statement. I am also confident you don't understand the inadequacy of your explanation.

Your confidence can't help you to undertand ONs, and why Moshe's formula is efective only for any n>2.

If you wish to undertand it, it is in http://www.internationalskeptics.com/forums/showpost.php?p=4857707&postcount=4185 .

 

[Apathia]

It is an interesting question. For many pre-K youngsters, the answer to "What do you see?" would be just one of the fruit as a one-word response. "What else?" would get you the other two, but only one at a time.

For post-K youngsters, the compound answer would be more likely than the single fruit response, but I wouldn't think you would get the "I see some fruit" response (without prompting) until about middle school.

For the typical kindergartener, though, I'd guess most would respond with just one of the fruit.

YMMV.

Your right. The kid would name whichever one his or her attention was upon.

Of course I'm going on a fishing trip with Moshe here.
I want to see just what bait he's going to put on the line, and what answers he thinks are significant.
It will get me to what's concrete to him about Organic Numbers.
Then, hopefully, I'll be able to communicate with him about the concept.

 

[jsfisher]

Of course I'm going on a fishing trip with Moshe here.

In our own ways, we both are.

 

[The Man]

Hi Man,

I have some difficulties to understand your question
Maybe because of my English..
Can we concentrate on a specific example?
for example the case 4=2+2 bring to 3 different distinction since we delete one case
Because of symmetry


Can this be related to your question?

Best
Moshe

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.

 

[The Man]

No, it is not:

(((1),1),1) is the general form for (A,B,C), (A,C,B), (B,C,A), (B,A,C), (C,B,A) and (C,A,B) and you simply do not get it.

The "1"+"()" simply represent a unique id, no matter what value it has.

Doron your “general form” again only demonstrates that you ignore your ascribed A, B and C distinctions and the ordering distinctions that creates. You might as well just make it (A,A,A) if you are going to simply ignore your own distinctions.


Only 15 minutes from my last post after you said.

There is no use to continue the dialog with you on this case, because all you wish to do is to show what is wrong in my head, instead of using your head in order to understand what you read.

Your kind of criticism is sterile and boring, and any further reply to you (as long as you continue this style of criticism) is a waste of energy.

I think that has got to be my best time yet in getting you to reply after you saying you would not.

 

[dlorde]

The amount of a thing needs elements and something that gather then into a one thing. I call the gathered "the local aspect of that thing" and I call the gatherer ""the non-local aspect of that thing", for example in lisp language expression (+ 1 2 76.890 pi) "+" is the non-local aspect and "1 2 76.890 pi" is the local aspect.

So the 'non-local aspect' is the operator and the 'local aspect' is the operands... so why not use conventional nomenclature? Operators and operands are well defined and well understood. Local and non-local are not, in this context. Or perhaps you're just trying to hitch a ride on the idea of quantum 'non-locality' by using the same terminology (for something quite different) ?

 

[jsfisher]

How curious.

Using the meaning of distinction MosheKlein conveyed in his recent presentation in Sweden, I've tried to generate by hand the distinctions for the first 4 positive integers. My results are presented below. Since hand-generation is error-prone, by confidence in the correctness and completeness of these is low; however, I do note the following:

For 1, there is 1! distinction.
For 2, there are 2! distinctions.
For 3, there are 3! distinctions.
For 4, there are 4! distinctions.

I claim this observation, although highly tentative, is far more interesting than much else we have seen in this thread.

1:
(A)

2:
(A,  B)
(AB, AB)

3:
(A,   B,   C)
(A,   BC,  BC)
(AB,  ABC, ABC)
(AB,  AC,  BC)
(AB,  AC,  ABC)
(ABC, ABC, ABC)

4:
(A,    B,    C,    D)
(A,    B,    CD,   CD)
(A,    BC,   BCD,  BCD)
(A,    BC,   CD,   BD)
(A,    BC,   CD,   BCD)
(A,    BCD,  BCD,  BCD)
(AB,   AB,   CD,   CD)
(AB,   ABC,  ABCD, ABCD)
(AB,   ABC,  ABD,  ACD)
(AB,   ABC,  ABD,  ABCD)
(AB,   ABC,  ACD,  BCD)
(AB,   ABD,  ACD,  BCD)
(AB,   ABCD, ABCD, ABCD)
(AB,   BC,   ABCD, ABCD)
(AB,   BC,   ACD,  ACD)
(AB,   BC,   CD,   AC)
(AB,   CD,   ABC,  ABD)
(AB,   CD,   ABCD, ABCD)
(ABC,  ABC,  ABCD, ABCD)
(ABC,  ABC,  ABD,  ABD)
(ABC,  ABCD, ABCD, ABCD)
(ABC,  ABD,  ACD,  ABCD)
(ABC,  ABD,  ABCD, ABCD)
(ABCD, ABCD, ABCD, ABCD)

 

[doronshadmi]

Doron your “general form” again only demonstrates that you ignore your ascribed A, B and C distinctions and the ordering distinctions that creates. You might as well just make it (A,A,A) if you are going to simply ignore your own distinctions.

You can do that, but (A,A,A) (which is, by the way, redundancy with no uncertainty) is not a form of the minimal introduction of ONs, for example:

Let us see (((1),1),1) general form of the minimal introduction of ONs:

A *  .  .                                                                               
  |  |  |                                                                               
B .  *  . = (A,B,C) , (C,B,A)                                                           
  |  |  |                                                                               
C .__.__*                                                                               
                                                                                        
                                                                                        
A .  *  .                                                                               
  |  |  |                                                                               
B *  .  . = (B,A,C) , (C,A,B)                                                           
  |  |  |                                                                               
C .__.__*                                                                               
                                                                                        
                                                                                        
A *  .  .                                                                               
  |  |  |                                                                               
B .  .  * = (A,C,B) , (B,C,A)                                                           
  |  |  |                                                                               
C .__*__.                                                                               
                                                                                        
                                                                                        
                                                                                        
You can play another game, where redundancy with no uncertainty is valid, 
for example:   
                                                                                        
                                                                                        
A *  *  *                                                                               
  |  |  |                                                                               
B .  .  . = (A,A,A)                                                                     
  |  |  |                                                                               
C .__.__.

In my first introduction of ONs ucretainty and redundancy levels are equal, for example:

0

1

2

3

4 and 5

Uncertainty\Redundancy matrix:

In other words The Man, it will be much more fruitful if you start to think abstract and general, instead of use your energy in order to show what is wrong in my head.

 

[doronshadmi]

How curious.

Using the meaning of distinction MosheKlein conveyed in his recent presentation in Sweden, I've tried to generate by hand the distinctions for the first 4 positive integers. My results are presented below. Since hand-generation is error-prone, by confidence in the correctness and completeness of these is low; however, I do note the following:

For 1, there is 1! distinction.
For 2, there are 2! distinctions.
For 3, there are 3! distinctions.
For 4, there are 4! distinctions.

I claim this observation, although highly tentative, is far more interesting than much else we have seen in this thread.

1:
(A)

2:
(A,  B)
(AB, AB)

3:
(A,   B,   C)
(A,   BC,  BC)
(AB,  ABC, ABC)
(AB,  AC,  BC)
(AB,  AC,  ABC)
(ABC, ABC, ABC)

4:
(A,    B,    C,    D)
(A,    B,    CD,   CD)
(A,    BC,   BCD,  BCD)
(A,    BC,   CD,   BD)
(A,    BC,   CD,   BCD)
(A,    BCD,  BCD,  BCD)
(AB,   AB,   CD,   CD)
(AB,   ABC,  ABCD, ABCD)
(AB,   ABC,  ABD,  ACD)
(AB,   ABC,  ABD,  ABCD)
(AB,   ABC,  ACD,  BCD)
(AB,   ABD,  ACD,  BCD)
(AB,   ABCD, ABCD, ABCD)
(AB,   BC,   ABCD, ABCD)
(AB,   BC,   ACD,  ACD)
(AB,   BC,   CD,   AC)
(AB,   CD,   ABC,  ABD)
(AB,   CD,   ABCD, ABCD)
(ABC,  ABC,  ABCD, ABCD)
(ABC,  ABC,  ABD,  ABD)
(ABC,  ABCD, ABCD, ABCD)
(ABC,  ABD,  ACD,  ABCD)
(ABC,  ABD,  ABCD, ABCD)
(ABCD, ABCD, ABCD, ABCD)

jsfisher,

This is simply great!!

Are forms like:

(A,A), (B,B)

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

etc.. are also valid in your ONs game?

I think that if you use Uncertainty\Redundancy matrix ( shown in http://www.internationalskeptics.com/forums/showpost.php?p=4859114&postcount=4198 )
you can improve your ONs game(s).

 

[ddt]

Hi ddt,

Following your computation Or : n=1..100
is equal to the sequences A5069.. ( don't remember it's number)
So we can present in the paper an nice open problem
if it will continue forever , What do you think ?

Moshe

The sequence number is A056198. Well, I've only shown that the first 30 numbers are the same. Just the conjecture that they're the same seems not very appealing - at least to me. Somewhere, there's gotta be a proof for that. I haven't taken a close look at the definition of the sequence (and I don't have Maple so I can't try that one out), but it says:

Recurrence suggested by that for A000669

and the latter is a graph problem. I have no idea how it is "suggested" from A000669, but with the combinatorial nature of the OR definition, I wouldn't be surprised if it's not already simply in there.

BTW, I've also implemented algorithm ZS2 for generating partition lists from the paper jsfisher mentioned. It blows ZS1 out of the water with roughly a factor 2 . Execution times for a C, C++ and Java variant are nearly identical: around 2 seconds for n=100. Execution time for OR(100) is down to ca. 40 minutes . Clearly, generating the list of partitions isn't the bottleneck (any more).