Deeper than primes

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ddt said:
Before you get too elated about Apathia's post, a small forewarning. Apathia's tried to do this before, and invariably, sooner or later he got burned when it turned out that his interpretation was not what Doron meant. So don't get your hopes too high up.
Click to expand...
It's OK, I've been here before. At some point I'll realise I've wrung all the interest out of it and move on ;)
 
dlorde said:
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?
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These the whole point dlorde.

The real world is not out there and you are not just an observer of it.

The real world is here and right now within and out of you, where a tool like Organic Number is a direct reflection of you also as an active participator of any calculation that is based on it (also computers are agents of your mind).

Please read again very carefully http://www.geocities.com/complementarytheory/OMPT.pdf pages 18-20, but this time please do not exclude yourself and be an inseparable factor of your experience of understanding during your real-time research.

Organic Mathematics is the presence of the researcher's awareness as an inseparable property of the research, and this aware presence is where the bridge between Ethics and Logic\Technology is developed, by using education methods.
 
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"...where Distinction is a first-order property."​

This phrase continues to appear with great regularity in the stuff we have seen of your work. So far, we don't have a satisfactory explanation of what the phrase means. Perhaps you can provide one, MosheKlein.

What do you mean by the word, distinction? Your word choice suggests it should have something to do with the word, distinct, in English, but then it would have to be relative to something else, not a property of a single thing. A is distinct from B.

What aspect makes it first-order? I hope you realize first-order has a specific mathematical meaning having to do with predicates and quantification, so I am curious how distinction (whatever that really means) takes on first-order characteristics.


By the way, MosheKlein, there is something you should know. Your Organic Mathematics concepts may be crystal clear to you, but they are very poorly expressed in your writings. People here in this Forum can be a great resource for moving your ideas into legitimate mathematical expression. We'd very much like to help, but first we need to understand what it is your are trying to say.

If you react positively to the help provided here, people will react very positively to you. If, instead, to blame everyone else, as Doron has been doing, for any communication problems, don't expect people to be always friendly.
 
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jsfisher said:
"...where Distinction is a first-order property."​

This phrase continues to appear with great regularity in the stuff we have seen of your work. So far, we don't have a satisfactory explanation of what the phrase means. Perhaps you can provide one, MosheKlein.

What do you mean by the word, distinction? Your word choice suggests it should have something to do with the word, distinct, in English, but then it would have to be relative to something else, not a property of a single thing. A is distinct from B.

What aspect makes it first-order? I hope you realize first-order has a specific mathematical meaning having to do with predicates and quantification, so I am curious how distinction (whatever that really means) takes on first-order characteristics.


By the way, MosheKlein, there is something you should know. Your Organic Mathematics concepts may be crystal clear to you, but they are very poorly expressed in your writings. People here in this Forum can be a great resource for moving your ideas into legitimate mathematical expression. We'd very much like to help, but first we need to understand what it is your are trying to say.

If you react positively to the help provided here, people will react very positively to you. If, instead, to blame everyone else, as Doron has been doing, for any communication problems, don't expect people to be always friendly.
Click to expand...

http://www.internationalskeptics.com/forums/showpost.php?p=4850095&postcount=4039
 
doronshadmi said:
... please do not exclude yourself and be an inseparable factor of your experience of understanding during your real-time research.
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I don't - I'm very aware of myself and my experience of understanding when doing research. I know that the results of my research are my interpretation of the data, and this is why I try to understand it from as many points of view as I can.

Organic Mathematics is the presence of the researcher's awareness as an inseparable property of the research
Click to expand...
I don't see how any research can be done without the researcher's awareness being present and inseparable from it - the researcher's awareness performs the research.

... and this aware presence is where the bridge between Ethics and Logic\Technology is developed, by using education methods.
Click to expand...
What education methods are these? how are they used? Please give an example.
 
doronshadmi said:
Hello my dear friend,

:welcome4 to the forum.
Click to expand...

Dear Doron,

Thank you for the invitation to be in this forum !
I was looking from time to time on this discussion
Now I can be more involve

Maybe it can be a good place to share
that we meet during 2002.


Moshe:)
 
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Apathia said:
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?
Click to expand...


Hi Apathia,

In the sort movie ( I will sent the link soon) you can see working with young children with : permutation, partition and the pentagon, concerning the discovery by Hipasus of irrationality in the days of Pythagoras.

We have movie of working on distinction ( the main issue for understanding OM) but we did not edit them yet.

When I will come to County Cork the first question I will ask the children's is
what there's more in the world : people or eyes ?
since I know that at list 50% ( in age 4-5) will answer "people" than I will enjoy to listen to there explanation to the answer.
And I will no correct them, as we use to do.


Moshe:)
 
The Man said:
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.
Click to expand...


Thank you The man !

I hope I can satisfy part of your expectation concerning me in this discussion.

Moshe:p
 
jsfisher said:
"...where Distinction is a first-order property."​

This phrase continues to appear with great regularity in the stuff we have seen of your work. So far, we don't have a satisfactory explanation of what the phrase means. Perhaps you can provide one, MosheKlein.

What do you mean by the word, distinction? Your word choice suggests it should have something to do with the word, distinct, in English, but then it would have to be relative to something else, not a property of a single thing. A is distinct from B.

What aspect makes it first-order? I hope you realize first-order has a specific mathematical meaning having to do with predicates and quantification, so I am curious how distinction (whatever that really means) takes on first-order characteristics.


By the way, MosheKlein, there is something you should know. Your Organic Mathematics concepts may be crystal clear to you, but they are very poorly expressed in your writings. People here in this Forum can be a great resource for moving your ideas into legitimate mathematical expression. We'd very much like to help, but first we need to understand what it is your are trying to say.

If you react positively to the help provided here, people will react very positively to you. If, instead, to blame everyone else, as Doron has been doing, for any communication problems, don't expect people to be always friendly.
Click to expand...


Dear jsfisher,

Thank you for your insisting that I will be part of this discussion
you know little about myself so I will be glad to know little about you ( If you want to share)

I am glad that you really consider to help us by moving our idea to legitimate mathematical expression. This will be very kind from you !

Aloud me in first stage a very sort explanation only as a start point to our dialog

The Distinctions are the colors between two polarities in our stae of mind
( black @white )


{1,1,1,1} and {1,2,3,4}


what do you think ?

Do you got something from this ?

Sincerley
Moshe:)
 
MosheKlein said:
The Distinctions are the colors between two polarities in our stae of mind
( black @white )


{1,1,1,1} and {1,2,3,4}


what do you think ?
Click to expand...

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.

So, it sounds like you are saying distinction is a relation, not a property.

Now, what about this first-order aspect? Would you claim that distinction is a first-order relation? And what do you think first-order means in this context?
 
MosheKlein said:
Hi Apathia,

In the sort movie ( I will sent the link soon) you can see working with young children with : permutation, partition and the pentagon, concerning the discovery by Hipasus of irrationality in the days of Pythagoras.

We have movie of working on distinction ( the main issue for understanding OM) but we did not edit them yet.

When I will come to County Cork the first question I will ask the children's is
what there's more in the world : people or eyes ?
since I know that at list 50% ( in age 4-5) will answer "people" than I will enjoy to listen to there explanation to the answer.
And I will no correct them, as we use to do.
Moshe:)
Click to expand...

Good! Let's explore ths. I believe it will take us to the core issue with Organic Numbers.

Now I hope those little one's are not having some of the same diagrams I've struggled with presented to them.
I'm kind of hoping you can regard us as elementary school kids and give us the core of OM in the ordinary way we'd naturally encouter it.
Abstract presentations haven't helped us in the least.

I'm Little Paddy. Help me put in words the two kinds of distinction. Help me to learn arithmatic when there are more people than eyes.

Aloud me in first stage a very sort explanation only as a start point to our dialog

The Distinctions are the colors between two polarities in our stae of mind
( black @white )


{1,1,1,1} and {1,2,3,4}
Click to expand...

Now I'm pretty sure I know what you're driving at here, but if we were back at Doron's first thread, I'd not have a clue from this.
Please break out the blocks and rods.
 
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jsfisher said:
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.

So, it sounds like you are saying distinction is a relation, not a property.

Now, what about this first-order aspect? Would you claim that distinction is a first-order relation? And what do you think first-order means in this context?
Click to expand...


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:boxedin:
 
MosheKlein said:
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.
Click to expand...

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.

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" ?
Click to expand...

I am not familiar with Frege's writings.
 
Apathia said:
Good! Let's explore ths. I believe it will take us to the core issue with Organic Numbers.

Now I hope those little one's are not having some of the same diagrams I've struggled with presented to them.
I'm kind of hoping you can regard us as elementary school kids and give us the core of OM in the ordinary way we'd naturally encouter it.
Abstract presentations haven't helped us in the least.

I'm Little Paddy. Help me put in words the two kinds of distinction. Help me to learn arithmatic when there are more people than eyes.



Now I'm pretty sure I know what you're driving at here, but if we were back at Doron's first thread, I'd not have a clue from this.
Please break out the blocks and rods.
Click to expand...

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

Following the cave legacy of Plato in a world that there are more people then eyes you need a new "Dialog Mathematics" which will make the other the possibility to see to two eyes of the one you are in dialog with..

One eyes is the objective
Seconded eyes is the subjective

This can create for us the three dimension of our perception.

I am very glad that you can see/understand more now !

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


Best regards
Moshe:idea:
 
MosheKlein said:
I think that in 2 more Posts I may be aloud here
to put the link of the You Tube Movie.
Click to expand...

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.
 
MosheKlein said:
With the very young children's we work only.. up to organic number 3
Click to expand...

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?
 
jsfisher said:
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.
Click to expand...

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:blush:
 
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jsfisher said:
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.
Click to expand...


thank you ! I got it.

Now try to imagine my English before I made the spelling in Word program..:jaw-dropp

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 :rolleyes:
 
Apathia said:
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?
Click to expand...


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:)
 
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MosheKlein said:
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:boxedin:
Click to expand...
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
 
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jsfisher said:
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.
Click to expand...
Unless property is used to say something about the framework, where both relations and elements are involved.
 
MosheKlein said:
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.
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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(n) space :D. 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?

MosheKlein said:
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
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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 said:
Unless property is used to say something about the framework, where both relations and elements are involved.
Click to expand...

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:

DISTIN.jpg


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.
 
MosheKlein said:
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:boxedin:
Click to expand...


doronshadmi said:
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.
Click to expand...

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.
 
jsfisher said:
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.
Click to expand...

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.
 
MosheKlein said:
Apathia, these are not permutations - maybe you can call them partitions.
Click to expand...

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 !
Click to expand...

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..)
Click to expand...
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.
Click to expand...

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

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?
The Man said:
As such would relate to the properties of the observer
Click to expand...
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.

The Man said:
Generally conditions like control groups, double blind procedures and independent verification are used to isolate arbitrary aspects of the observer from the observed.
Click to expand...
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.
 
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MosheKlein said:
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.
Click to expand...

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.
 
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AkuManiMani said:
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.
Click to expand...

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.
 
jsfisher said:
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.
Click to expand...

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

http://www.internationalskeptics.com/forums/showpost.php?p=4851725&postcount=4074
 
The Man said:
... Generally conditions like control groups, double blind procedures and independent verification are used to isolate arbitrary aspects of the observer from the observed.
Click to expand...
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.
 
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