Deeper than primes

[Apathia]

Welcome Mr. Klein!

Pehaps tomorrow I'll be asking you a simple question about "sets" in OM just to gauge if I'm on the right track with a point Doron has made a number of times and to see what your way of explianing things is like.

I'm also very interested in how you'd go about presenting Organic Numbers to an elementary school kid.
I've very much need that kind of simple approach, as I am not a mathematician but a word slinger.

 

[MosheKlein]

Don't you mean the results of your function are 1,2,3,9,24,76,236,785?

Most of the mathematical function equations are above me, but why doesn't the number 5 produce six results? According to doronshamdi, I can "write" the number five like so:
1+1+1+1+1 or 2+1+1+1 or 2+2+1 or 3+1+1 or 3+2 or 4+1

This is based on the "way" he provides the permiutations of 4: 1+1+1+1, 2+2, 1+3, 2+1+1.

Yes , here is all what we calculate until today

1, 2, 3, 9, 24, 76, 236, 785, 2634, 9106, 31870, 113371 ,...


as you understand we don't use for calculation the partition n=n

but 2=1+1 bring two distinctions

2=(1)+(1) we don't know the identity of the two elements.
2= (1)+1 we know the identity of the two elements.

so it is more complicate then the known partition function.
and much dipper then the primes..

 

[MosheKlein]

Hi Apathia,

A very basic different in OM concerning set theory is that we permit an element to appear several of times.

Ex: A= { 1,2,2,3,4,4,5}

Since I am a new member here, I can't sent you yet the link to a sort You Tube movie
of myself working with preschool childrens with Organic Mathematics ideas.

Maybe Doron will do that.

Best
Moshe

p.s : I like your moving fingers

 

[catbasket]

Welcome to the forum, MosheKlein.

 

[ddt]

First of all, welcome, MosheKlein!

Yes , here is all what we calculate until today

1, 2, 3, 9, 24, 76, 236, 785, 2634, 9106, 31870, 113371 ,...

And it goes on like this?

Or(1) = 1
Or(2) = 2
Or(3) = 3
Or(4) = 9
Or(5) = 24
Or(6) = 76
Or(7) = 236
Or(8) = 785
Or(9) = 2634
Or(10) = 9106
Or(11) = 31870
Or(12) = 113371
Or(13) = 407438
Or(14) = 1479526
Or(15) = 5415700
Or(16) = 19970119
Or(17) = 74096864
Or(18) = 276466199
Or(19) = 1036598162
Or(20) = 3903844089

when I read your formulae right?

In post #3906 in this thread, Doron posted an explanation of yours how the formulae work.

as you understand we don't use for calculation the partition n=n

That's clear. But why do you ignore it?

And shouldn't, then, in point (5), the definition of D, the product go up to n-1 instead of n?

but 2=1+1 bring two distinctions

2=(1)+(1) we don't know the identity of the two elements.
2= (1)+1 we know the identity of the two elements.

So what does this "distinction" mean? The partition part is clear, function g is clear, but then you define D and Or, mutually recursive, and I have no idea what is going on here. I can calculate it all right, but what is the meaning behind these formulae? What does it signify. The above two lines don't really help me.

 

[ddt]

Since I am a new member here, I can't sent you yet the link to a sort You Tube movie
of myself working with preschool childrens with Organic Mathematics ideas.

Just put some spaces in the URL and then you fool the newbie filter, like this:

www . youtube . com / ...

 

[MosheKlein]

Hi ddt,

1) Very nice calculation ! How did you made it so fast. Did you use a computer?
I let you know that there is a sequences named A056198 ( you can find it in the internet) which being exactly like Or. So I check with Or(20) as in your calculation and it's fit but I am not sure that it will be so forever.

[an open problem in OM..]

2) The case n=n will lead to problem and infinite recursion

3) Since we add with GAMA- ( all partition without n=n) it's good also

4) The distinction answer to the question how the number appear in the mind of the observer so its a kind of Quantum theory inspiration in the base of OM.

If you understand/ agree with n=2 it can be really great.

2=(1)+(1)
2=(1)+1


5) Thank you for the idea. So I can add the link to the you tube Movie ( I will do that later )


Best regards
Moshe

 

[MosheKlein]

Welcome to the forum, MosheKlein.

Thank you catbasket !

I will do my best here to share my understanding of OM
I have B.A in Mathematics ( 1980), MA in education of Mathematics ( 1998) and quite long experience in Kindergarten education ( 1988 - today )

Moshe

 

[AkuManiMani]

'Ello, Moshe. Welcome to the JREF!

 

[Apathia]

ddt asked

So what does this "distinction" mean? The partition part is clear, function g is clear, but then you define D and Or, mutually recursive, and I have no idea what is going on here. I can calculate it all right, but what is the meaning behind these formulae? What does it signify. The above two lines don't really help me.

MosheKlein answered:

4) The distinction answer to the question how the number appear in the mind of the observer so its a kind of Quantum theory inspiration in the base of OM.

If you understand/ agree with n=2 it can be really great.

2=(1)+(1)
2=(1)+1

This upstages the question I was going to ask, because it is by far the most important one.
So, we are going to keep asking you it till there is a clear answer.
I'm afraid your answer above simply says it's all an answer to another question.
Now we not only don't have an answer to ddt's question, but there's an added question we don't know.

What concept or meaning does an organic number express that a traditional number doesn't?
Perhaps the formula you've created has some structural similarities to aspects of quantum behavior. But the big question is what the asperagus is an organic number?
What is "Distinction?"

 

[doronshadmi]

Thank you jsfisher !

I think that the main new idea for us here is to begin with is to observe a number n as a superposition of its partitions Pr. Recently I have develop an algorithm to calculate the number of distinctions of a number Or . The sequences started with 1,2,3,9,24,76,236,785, …( we calculate it until or(12))

I made some correction following your remarks – thank you !

Do you have some more remarks?

Moshe Klein

Sorry for my English..

Hello my dear friend,

to the forum.

 

[The Man]

Okey, good. I got some other questions

Once, I asked my HS geometry teacher "If there are two rods that are infinitely long but one is 2 ft wide and the other only 1ft wide, is one bigger than the other?" He just kinda shook his head and said that was a question for philosophers >_<

Got a more satisfactory answer for me?

Satisfaction is not guaranteed, but I'll give it a shot.

Clearly one rod is bigger in width (or diameter for a rod) thus cross sectional area, yet both would encompass an infinite volume. Were we to create sets containing the locations of a specific finite volume element for each rod. Both sets would be infinite, but there would not be a one to one correspondence (bijection) between the sets and thus they would have a different cardinality (the relative size of sets). Alternatively if we make the finite volume elements proportional to the rods there would be a one to one bijection between the sets of the locations of those volume elements. However since the elements are scaled from one rod to the other again the difference in size or volume of the elements is clear. Finally we can use specific finite area elements of infinite length thus infinite volume elements. Of which one rod would have more such elements then the other. So no matter how you slice it one rod is bigger then the other, more clearly seen in width and cross sectional area then length or volume.

And my other questions are: How many points are there in a line segment 3 units long? And does a line segment with more than 3 units have more points?

There are always an infinite number of points in any finite length. Thus a line segment with more then three units does not have more points then one of just three units.


Please see cardinality.

http://en.wikipedia.org/wiki/Cardinality

Cardinal arithmetic can be used to show not only that the number of points in a real number line is equal to the number of points in any segment of that line, but that this is equal to the number of points on a plane and, indeed, in any finite-dimensional space. These results are highly counterintuitive, because they imply that there exist proper subsets and proper supersets of an infinite set S that have the same size as S, although S contains elements that do not belong to its subsets, and the supersets of S contain elements that are not included in it.

The difference between the infinite rods and the finite line segments examples is that one is infinite and refers to size while the other finite and refers to the number of points. You will note the use of finite dimensional volumes or finite dimensional areas in comparing the relative ‘sizes’ of the rods. While the segments are already of finite dimension thus directly comparable and in one to one correspondence with the real number line.

I hope that is satisfactory.

 

[The Man]

Oh and by the way, welcome to the forum MosheKlien.

I'm sorry to say that I have some errands to run right now, but I look forward to your input on this thread.

 

[doronshadmi]

ddt asked



MosheKlein answered:


This upstages the question I was going to ask, because it is by far the most important one.
So, we are going to keep asking you it till there is a clear answer.
I'm afraid your answer above simply says it's all an answer to another question.
Now we not only don't have an answer to ddt's question, but there's an added question we don't know.

What concept or meaning does an organic number express that a traditional number doesn't?
Perhaps the formula you've created has some structural similarities to aspects of quantum behavior. But the big question is what the asperagus is an organic number?
What is "Distinction?"

Let us take number 2, and let us use only whole numbers and * or + operations in order to calculate it.

Under these restrictions Standard Math cares only about the quantitative result.

So by Standard Math 1*2=1+1=2

This is not the only case under OM framework if the distinction of the elements is not ignored, for example:

We use 1*2 only if the elements are identical: •• = 1*2 = 2

We use 1+1 only if the elements are not identical: •• = 1+1 = 2

 

[doronshadmi]

Let us show my calculations that stand at the basis of Moshe's Or function.

1) Organic Number n is the all possible states of Distinction between n elements, where order has no significance.

2) In n=1 there is only one state of distinction, so Or=1.

3) In n=2 the are two possible states of distinction, for example: •• and ••, so Or=2.

4) From n=3 and further Or value is based on the following:

a) First we take the partitions of n which are not of the form n+0, for example:

If n=3 we take 1+1+1, 2+1 and ignore 3+0
If n=4 we take 1+1+1+1, 2+1+1, 2+2, 3+1 and ignore 4+0
Ect. …

b) Now we are using the recursion function D on each partition of some n (the case n+0 is ignored), for example let us take n=3:

The calculated partitions of n=3 are D(1+1+1) and D(2+1) (D(3+0) is not calculated, because if we calculate D(n+0) we enter into a non-finite loop of recursion).

Since 1 has only one case of distinction, then D(1+1+1)=1
Since 2 has only two cases of distinction, then D(2+1)=2

So, Or(3)=D(1+1+1)+D(2+1)=3

The calculated partitions of n=4 are D(1+1+1+1), D(2+1+1), D(2+2) and D(3+1) (D(4+0) is not calculated, because if we calculate D(n+0) we enter into a non-finite loop of recursion).

Since 1 has only one case of distinction, then D(1+1+1)=1
Since 2 has only two cases of distinction, then D(2+1+1)=2
The case of any partition of the form (2,2,2,…) is calculated by D as the result of the amount of the repetitions of number 2 in the partition+1, for example:
D(2+2)=3, D(2+2+2)=4, D(2+2+2+2)=5 , etc. …
So in the case of n=4 the result of the recursion D on partition (2+2) is D(2+2)=3
Since 3 has only three cases of distinction, then D(3+1)=3

So, Or(3)=D(1+1+1)+D(2+1+1)+ D(2+2)+ D(3+1)=9

5) The further calculations of D that are not based on (2+2+…) partitions, are as follows:

a) If the elements of a given partition are distinct - for example partition (3+2) of n=5 – then the value of D(3+2) = Or(3)*Or(2)=6. In general D(n1,n2,n3,…)= Or(n1)*Or(n2)*Or(n3)* …

b) If the elements of a given partition are non-distinct - for example partition (3+3) of n=6 – then the value of D(3+3) = (Or(3)+(Or(3)-1)+Or(3)-2)+(Or(2)+Or(2)-1)+(Or(1)) = (3+2+1)+(2+1)+(1)=10. D(3+3+3) = ((3+2+1)+(2+1)+(1)) + ((2+1)+(1)) + ((1)) = 15 (partition (3+3+3) belongs to n=6)

6) The partition is a mixing of distinct and non-distinct elements (for example partition (3,3,2) of n=8) the we first calculate 3 according (b) and then multiply the result of (b) with the result of Or(2).

In the case of partition (3,3,2,2) of n=10, we first calculate 3 and 2 cases according to (b) and then we mutably the results.

I hope that I did not make mistakes here, but it there are mistakes, I'll fix them later.

 

[Apathia]

Let us take number 2, and let us use only whole numbers and * or + operations in order to calculate it.

Under these restrictions Standard Math cares only about the quantitative result.

So by Standard Math 1*2=1+1=2

This is not the only case under OM framework if the distinction of the elements is not ignored, for example:

We use 1*2 only if the elements are identical: •• = 1*2 = 2

We use 1+1 only if the elements are not identical: •• = 1+1 = 2

OK, I'm trying to get this.
OM shows the aspect of a number as a distinct entity independent of quantification.

Can the concept of number be independent of quantity?

Are "+" and "*" arithmetic opperations? (If so, we have quantities.)

But I think get your drift in this example:

We have a series of two pictures of a banana.
if we regard this as the self same banana repeated, copied, or cloned, we must exclusively use the times opperator.
If we take regard the bananas as different objects (albeit both of the same class of object), we must exclusively use the addition opperator.

Ordinary math throws both these regards into the same intellectual pot,
But in OM, depending on how an element is being regarded,
1*2 may not necessarily equal 1+1, because we may or may not have the mere instance of the self same unique object.

 

[Apathia]

Let us show my calculations that stand at the basis of Moshe's Or function.

1) Organic Number n is the all possible states of Distinction between n elements, where order has no significance.

2) In n=1 there is only one state of distinction, so Or=1.

3) In n=2 the are two possible states of distinction, for example: •• and ••, so Or=2.

4) From n=3 and further Or value is based on the following:

a) First we take the partitions of n which are not of the form n+0, for example:

If n=3 we take 1+1+1, 2+1 and ignore 3+0
If n=4 we take 1+1+1+1, 2+1+1, 2+2, 3+1 and ignore 4+0
Ect. …

b) Now we are using the recursion function D on each partition of some n (the case n+0 is ignored), for example let us take n=3:

The calculated partitions of n=3 are D(1+1+1) and D(2+1) (D(3+0) is not calculated, because if we calculate D(n+0) we enter into a non-finite loop of recursion).

Since 1 has only one case of distinction, then D(1+1+1)=1
Since 2 has only two cases of distinction, then D(2+1)=2

So, Or(3)=D(1+1+1)+D(2+1)=3

The calculated partitions of n=4 are D(1+1+1+1), D(2+1+1), D(2+2) and D(3+1) (D(4+0) is not calculated, because if we calculate D(n+0) we enter into a non-finite loop of recursion).

Since 1 has only one case of distinction, then D(1+1+1)=1
Since 2 has only two cases of distinction, then D(2+1+1)=2
The case of any partition of the form (2,2,2,…) is calculated by D as the result of the amount of the repetitions of number 2 in the partition+1, for example:
D(2+2)=3, D(2+2+2)=4, D(2+2+2+2)=5 , etc. …
So in the case of n=4 the result of the recursion D on partition (2+2) is D(2+2)=3
Since 3 has only three cases of distinction, then D(3+1)=3

So, Or(3)=D(1+1+1)+D(2+1+1)+ D(2+2)+ D(3+1)=9

5) The further calculations of D that are not based on (2+2+…) partitions, are as follows:

a) If the elements of a given partition are distinct - for example partition (3+2) of n=5 – then the value of D(3+2) = Or(3)*Or(2)=6. In general D(n1,n2,n3,…)= Or(n1)*Or(n2)*Or(n3)* …

b) If the elements of a given partition are non-distinct - for example partition (3+3) of n=6 – then the value of D(3+3) = (Or(3)+(Or(3)-1)+Or(3)-2)+(Or(2)+Or(2)-1)+(Or(1)) = (3+2+1)+(2+1)+(1)=10. D(3+3+3) = ((3+2+1)+(2+1)+(1)) + ((2+1)+(1)) + ((1)) = 15 (partition (3+3+3) belongs to n=6)

6) The partition is a mixing of distinct and non-distinct elements (for example partition (3,3,2) of n=8) the we first calculate 3 according (b) and then multiply the result of (b) with the result of Or(2).

In the case of partition (3,3,2,2) of n=10, we first calculate 3 and 2 cases according to (b) and then we mutably the results.

I hope that I did not make mistakes here, but it there are mistakes, I'll fix them later.

The math people may find some details to correct, but I get the purpose.
I also think I get your Redundancy/Uncertainty thing now.

While I'm waiting for Mosheklein to give his answers, I'll offer a little theatre to focus in on the kindergarten scene.

Somewhere in County Cork:

Sister Mallory shows Little Paddy a page in his coloring book.
Typically it shows a series of three drawings of a potato that all look the same.

Sister Mallory: How many potatoes are there, Paddy?
Paddy: One.
Sister Mallory: Wrong! (She whacks his fingers with her ruler.)
Paddy: But it's the same potato!
Sister Mallory: (she whacks him again.)

Somewhere in County Cork after Sister Mallory is packed off to foreign monastery:

Sister Goodwin: Paddy, How many potatoes are there?
Paddy: One
Sister Goodwin: Right. Same Potato, huh? How many pictures of the potato are there?
Paddy: Three.
Sister Goodwin: Excellent!

Now what will happen when Moshe Kline comes to County Cork?
And green bagels, anyone?

 

[doronshadmi]

Oppsss...

 

[doronshadmi]

Some corrections of http://www.internationalskeptics.com/forums/showpost.php?p=4849130&postcount=4035 typo mistakes:

Let us show my calculations that stand at the basis of Moshe's Or function.

1) Organic Number n is the all possible states of Distinction between n elements, where order has no significance.

2) In n=1 there is only one state of distinction, so Or=1.

3) In n=2 there are two possible states of distinction, for example: •• and ••, so Or=2.

4) From n=3 and further Or value is based on the following:

a) First we take the partitions of n which are not of the form n+0, for example:

If n=3 we take 1+1+1, 2+1 and ignore 3+0
If n=4 we take 1+1+1+1, 2+1+1, 2+2, 3+1 and ignore 4+0
etc. …

b) Now we are using the recursion function D on each partition of some n (the case n+0 is ignored), for example let us take n=3:

The calculated partitions of n=3 are D(1+1+1) and D(2+1) (D(3+0) is not calculated, because if we calculate D(n+0) we enter into a non-finite loop of recursion).

Since 1 has only one case of distinction, then D(1+1+1)=1
Since 2 has only two cases of distinction, then D(2+1)=2

So, Or(3)=D(1+1+1)+D(2+1)=3

The calculated partitions of n=4 are D(1+1+1+1), D(2+1+1), D(2+2) and D(3+1) (D(4+0) is not calculated, because if we calculate D(n+0) we enter into a non-finite loop of recursion).

Since 1 has only one case of distinction, then D(1+1+1)=1
Since 2 has only two cases of distinction, then D(2+1+1)=2
The case of any partition of the form (2,2,2,…) is calculated by D as the result of the amount of the repetitions of number 2 in the partition+1, for example:

D(2+2)=3, D(2+2+2)=4, D(2+2+2+2)=5 , etc. …
So in the case of n=4 the result of the recursion D on partition (2+2) is D(2+2)=3
Since 3 has only three cases of distinction, then D(3+1)=3

So, Or(4)=D(1+1+1)+D(2+1+1)+ D(2+2)+ D(3+1)=9

5) The further calculations of D that are not based on (2+2+…) partitions, are as follows:

a) If the elements of a given partition are distinct - for example partition (3+2) of n=5 – then the value of D(3+2) = Or(3)*Or(2)=6.
In general, D(n1,n2,n3,…)= Or(n1)*Or(n2)*Or(n3)* …

b) If the elements of a given partition are non-distinct - for example partition (3+3) of n=6 – then the value of
D(3+3) = (Or(3)+(Or(3)-1)+Or(3)-2)+(Or(2)+Or(2)-1)+(Or(1)) = (3+2+1)+(2+1)+(1)=10.
D(3+3+3) = ((3+2+1)+(2+1)+(1)) + ((2+1)+(1)) + ((1)) = 15 ( (3+3+3) is a partition of n=9 ).

6) If the partition is a mixing of distinct and non-distinct elements (for example partition (3,3,2) of n=8) then we first calculate 3 according (b) and then multiply the result of (b) with the result of Or(2).

In the case of partition (3,3,2,2) of n=10, we first calculate 3 and 2 cases according to (b) and then we *multiply\add the results.

*(I still have to check if in a case like (3,3,2,2) we multiply the results of 3,3 with the results of 2,2, or we add the results of 3,3 with the results of 2,2).

EDIT: I'v chacked it, it is multiply, so D(3,3,2,2)=30

 

[dlorde]

The partical example starts at the moment that you get that Number is the result of Memory\Object interaction, exactly as explained in http://www.geocities.com/complementarytheory/OMPT.pdf pages 18-20.

Well I get the idea, as Apathia explained it, and, as I already said, it seems to fit with what's in the document, but I would like to see a worked example of a real-world situation to which this language has been applied to analyse and/or resolve a mathematical/scientific problem with its moral and ethical implications.

Again: I would like to see a worked example of a real-world situation to which this language has been applied to bridge science and ethics.

It's surely not much to ask, as this is exactly the task the language is designed for?