Deeper than primes

[jsfisher]

I think that in 2 more Posts I may be aloud here
to put the link of the You Tube Movie.

We all understand English is not your native tongue, so please accept my correction as instructive: The word you meant was allowed.

Aloud means to talk or think in a way that everyone else can hear you. Allowed means to be permitted to do something.

Read the text aloud.
You are allowed to ask questions.

 

[Apathia]

With the very young children's we work only.. up to organic number 3

Yes, I see. Well before organic number 50, it becomes too cumbersome for even an adult to keep in mind all those permutations.

Do these children learn serial numerals and how to count serialy?

 

[MosheKlein]

Ok, good. I am more comfortable with distinction not being a property. I think this observer/object interaction aspect is more philosophic than mathematical, so maybe Apathia should have first crack at it.



I am not familiar with Frege's writings.

I am glad with that . As a mathematician Please remember
that philosophy is the mother of Mathematics !
We are talking here about a kind of "Socrates Mathematics".

No problem.Prege is consider the great logician after Aristotle
His fundamental book establish the concept of first order property
Unfortanatly he himself was not recognize during his life time.
It was L.Wittgenstein who bring to his great recognition today.

If you can see his book you will see very similar notion to Doron Organic number tree. ( not exactly but very similar)

Best wishes
Moshe

 

[MosheKlein]

We all understand English is not your native tongue, so please accept my correction as instructive: The word you meant was allowed.

Aloud means to talk or think in a way that everyone else can hear you. Allowed means to be permitted to do something.

Read the text aloud.
You are allowed to ask questions.

thank you ! I got it.

Now try to imagine my English before I made the spelling in Word program..

I just came back from a conference in Sweden were I gave a lecture on OM
can you arrange ( of course later ) a presentation for us somewhere

 

[MosheKlein]

Yes, I see. Well before organic number 50, it becomes too cumbersome for even an adult to keep in mind all those permutations.

Do these children learn serial numerals and how to count serialy?

Apathia, these are not permutations - maybe you can call them partitions.

concernig the children, we are talking about new pedagogy which we named "The pedagogy of the unknown" you see I really study Organic Mathematics togheter with the childrens !

Were are you from ? ( In earth..)

I try now ( after 15 post ) to put a link to my web-site

http://www.omath.org.il

I see that it's work !!!

the link to the sort video is the first in the Hebrew page.


best wishes
Moshe

 

[Little 10 Toes]

You are right. Distinction is not a property of something. Also it is not a relation between two objects. It is something completely new. It may be defined as a level of interaction between the observer and the object.

Concerning the first order issue : Have you study the book written by Gottlob Frege : "Conceptual notation, a formal language modeled on that of arithmetic, for pure thought" ?

Moshe

Link to the book: http://en.wikipedia.org/wiki/Begriffsschrift

Author's wikipedia page and discussion of said book:
http://en.wikipedia.org/wiki/Gottlob_Frege#Work_as_a_logician

 

[doronshadmi]

Link to the book: http://en.wikipedia.org/wiki/Begriffsschrift

Author's wikipedia page and discussion of said book:
http://en.wikipedia.org/wiki/Gottlob_Frege#Work_as_a_logician

Please look at http://www.geocities.com/complementarytheory/ONN3.pdf in order to undertand better OM\Begriffsschrift relations.

 

[doronshadmi]

Ok, good. I am more comfortable with distinction not being a property. I think this observer/object interaction aspect is more philosophic than mathematical, so maybe Apathia should have first crack at it.

Unless property is used to say something about the framework, where both relations and elements are involved.

 

[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.

Yes, of course I used a computer. The large numbers involved pose all kind of interesting optimization questions, both w.r.t. time and space. I now have a generator for the list of partitions of n which runs in O space . Your algorithm gives:

Or(100) = 2199516347439237513754580009632686701940043714513581388093

(okay, that one still took 5 hours of computer time).

I've seen the sequence at the OEIS. It seems to be the same - at least for the first 30 numbers of that sequence that are listed. Have you tried proving they are the same? Have you submitted your formula to the OEIS?

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

Technically, your definition of D:
D(alpha) = Prod (i=i..n) ...
still leads to an infinite recursion. If you restrict that one to
D(alpha) = Prod(i=1..n-1)
it doesn't matter if the sum in the definition of Or includes the partition n=n or not.

But that's a technical argument and not a conceptual one. There should be a rationale behind the formulae, and why the partition n=n is included or not. I'll have a look later at your other posts.

 

[doronshadmi]

Unless property is used to say something about the framework, where both relations and elements are involved.

Distinction is a property of some framework if we use both Relations and Elements in order to define it under the investigated framework.

For example, let us look at this diagram:

There are two persons in that diagram that seating around a circled table, and on the table there are two glasses such that no person knows what glass to use.

This is the non-distinct state of the Persons\Glasses framework.

If one of the persons chooses a glass, the other person uses the other glass.

This is the distinct state of the Persons\Glasses framework.

In both cases Distinction is a property of the investigated framework, and not a property of any particular relation or element of that framework.

In this case we say that Distinction is a first-order property of this framework.

 

[The Man]

You are right. Distinction is not a property of something. Also it is not a relation between two objects. It is something completely new. It may be defined as a level of interaction between the observer and the object.

Concerning the first order issue : Have you study the book written by Gottlob Frege : "Conceptual notation, a formal language modeled on that of arithmetic, for pure thought" ?

Moshe

Distinction is a property of some framework if we use both Relations and Elements in order to define it under the investigated framework.

For example, let us look at this diagram:

[qimg]http://www.geocities.com/complementarytheory/DISTIN.jpg[/qimg]

There are two persons in that diagram that seating around a circled table, and on the table there are two glasses such that no person knows what glass to use.

This is the non-distinct state of the Persons\Glasses framework.

If one of the persons chooses a glass, the other person uses the other glass.

This is the distinct state of the Persons\Glasses framework.

In both cases Distinction is a property of the investigated framework, and not a property of any particular relation or element of that framework.

In this case we say that Distinction is a first-order property of this framework.

It would seem to me then that what your are referring to as ‘distinction’ is simply an arbitrary choice made by the observer. As such would relate to the properties of the observer. In fact that such distinction is not inherently part of the object, the possible distinctions to select from is also something simply arbitrarily imposed by said observer. Thus as opposed to an observer not ignoring his relation with the observed you seem to be simply imposing additional arbitrary relationships that are not inherently part of the specific observation, but simply a matter of happenstance and arbitrary selection on the part of the observer. As the general purpose of observation is to determine characteristics about the observed, such imposed arbitrary aspects simply on the part of the observer detract from that. It would seem that if the focus was on the act of observation itself and specifically on the aspects the observer could bring to that observation that such consideration might have validity as opposed to simply detracting from a focus on what is observed. Generally conditions like control groups, double blind procedures and independent verification are used to isolate arbitrary aspects of the observer from the observed.

 

[AkuManiMani]

It sounds like you are not discussing a property at all. Properties are inherent characteristics in something, independent of other things. As soon as you bring in a second something, you have left the realm of property and moved into relations.

Not really. There are different categories of properties. For instance there are intrinsic properties that are inherent to a thing in question [e.g. mass] and extrinsic properties that come from its relation to other things [e.g. weight]. Of course, one could split the categories even further, but the point is that the properties of an entity need not be inherent, per se.

 

[Apathia]

Apathia, these are not permutations - maybe you can call them partitions.

Yes, you're right, not permutations or iterations, but quite an increasing load of fract-thingies to bear in mind.

concernig the children, we are talking about new pedagogy which we named "The pedagogy of the unknown" you see I really study Organic Mathematics togheter with the childrens !

I think it would remove a lot of mystery about OM, if we could bring in a 5 year old to demonstrate her grasp of counting numbers.

Were are you from ? ( In earth..)

Not County Cork.
I'm an American, born in the State of Florida.

I try now ( after 15 post ) to put a link to my web-site

http://www.omath.org.il

I see that it's work !!!

the link to the sort video is the first in the Hebrew page.

Thank's
Too bad I don't speak Hebrew.
The situation speaks for itself though.
I wish you could set us down with the toy cars and the dots and show us in concrete the mathematic conceptions of pre-schoolers.

 

[doronshadmi]

It would seem to me then that what your are referring to as ‘distinction’ is simply an arbitrary choice made by the observer.

What do you mean arbitrary?

These are the only two states (uniquely chosen or not-uniquely chosen) that can be under this particular Persons\Glasses framework, so?

As such would relate to the properties of the observer

The word "observer" has no meaning if the observed is not in the same framework with the observer. In other words, the property belongs to the framework and not to any particular relation or element under this framework.

Generally conditions like control groups, double blind procedures and independent verification are used to isolate arbitrary aspects of the observer from the observed.

If the observer is totally isolated from the observed, then both words have no meaning.

What give them their meaning are the properties of the framework, where both of them are inseparable factors of it.

 

[doronshadmi]

But that's a technical argument and not a conceptual one. There should be a rationale behind the formulae, and why the partition n=n is included or not. I'll have a look later at your other posts.

The reasoning behind the function can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=4850095&postcount=4039 .

 

[jsfisher]

Prege is consider the great logician after Aristotle
His fundamental book establish the concept of first order property
Unfortanatly he himself was not recognize during his life time.
It was L.Wittgenstein who bring to his great recognition today.

I think we can agree, then, that Frege deserves some credit as the father of first order logic. However, that doesn't answer my question. I know what first-order means in Mathematics. I will assume you do, too. My question to you, MosheKlein, is how to express "distinction is a first-order property" (or relation or whatever) as a first-order predicate.

Such a predicate and a functional definition of distinction are necessary to understand what you mean by distinction in a more formal way.

 

[jsfisher]

Not really. There are different categories of properties. For instance there are intrinsic properties that are inherent to a thing in question [e.g. mass] and extrinsic properties that come from its relation to other things [e.g. weight]. Of course, one could split the categories even further, but the point is that the properties of an entity need not be inherent, per se.

As a mathematical term, property is usually restricted to yes/no propositions. This may seem like an unnecessary nit-pick, especially since I did say it was only usually true, but the phrasing first-order property puts it into the realm of always true.

 

[doronshadmi]

I think we can agree, then, that Frege deserves some credit as the father of first order logic. However, that doesn't answer my question. I know what first-order means in Mathematics. I will assume you do, too. My question to you, MosheKlein, is how to express "distinction is a first-order property" (or relation or whatever) as a first-order predicate.

Such a predicate and a functional definition of distinction are necessary to understand what you mean by distinction in a more formal way.

http://www.internationalskeptics.com/forums/showpost.php?p=4851637&postcount=4070

http://www.internationalskeptics.com/forums/showpost.php?p=4851725&postcount=4074

 

[Little 10 Toes]

Once again doronshadmi, the question is not directed to you.

 

[dlorde]

... Generally conditions like control groups, double blind procedures and independent verification are used to isolate arbitrary aspects of the observer from the observed.

This appears to be a deliberate attempt to integrate/amalgamate the observer and the observed into a complex and subjective relational 'entity'. Quite how this provides practical benefit is unclear, as is also how it avoids throwing out the baby of (scientific) objectivity with the bathwater.