Deeper than primes

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MosheKlein said:
Hi ddt,

Really a great work !
Thank you for the 5 hours of computing or(n).
You are the leader today of this computation on the planet of Earth..

Did you have in advance the program for the partitions ?
No, I didn't have that in advance. So I've been tinkering with how to do that efficiently. My first algorithm just generated a big list of all partitions, but that ran out of heap space at n=64. So as a next try, I made a version with a recursive generator that ran in a separate thread - so that one still had O(n^2) space requirements. My third try was an iterative version of that without the multi-threading but still with the O(n^2) space requirement because of the emulation of the stackframes, and in my fourth try I eliminated the stackframes and so I got the O(n) space requirement - which is also the minimum possible.

I also tried another algorithm I found on the internet, which claims to be the most time efficient, but that one runs actually slower than the one I made - basically because it constructs a partition in as a list 4 = 2 + 1 + 1, whereas your algorithm needs it in the form (2, 1, 0, 0). The conversion between the two makes it 50% slower. So my algorithm is actually very fast :). I did some profiling and I conclude from that that the actual calculations are dwarfed, in terms of the time used, by the function calls. :jaw-dropp

But I'm glad that Java has BigIntegers, so I don't have to program those. :D
(oh, and a little optimization I overlooked: skipping the g(Or(i), a_i) factors where a_i == 0 cuts execution time in half :)).
Click to expand...
Click to expand...
 
jsfisher said:
ddt,

www.site.uottawa.ca/~ivan/F49-int-part.pdf
Click to expand...

Yep, that's the one I found. I implemented algorithm ZS1, and it was slower than my own :(

First, some Java technicalities: I implemented it using the Iterator interface. That means you have to make two methods:
1) hasNext() which reports if there's a next element in the list;
2) next() which actually gives the next element.
I put all the actual calculation in hasNext(); if it finds a next partition, it reports 'true', but it also has that next partition prepared and well. The implementation of next() only entails returning that partition, and two checks before that if one was found or if we first have to find the next one (in case next() is called twice in a row without a hasNext() in between).

So color me skeptical when the built-in Java profiling said he spent equal amount in both methods. Then I put in time counters myself in the code, and this is what it reported for a run calculating partitions of 75:
time in hasNext: 10828831745 8118265
time in next: 10659977218 8118263​
The first number is the nanoseconds, the second the number of calls.

My implementation of the ZS1 algorithm from the paper gives:
time in convert: 10953318714 8118263
time in hasNext: 10293843313 8118265
time in next: 10072671076 8118263​
The extra method 'convert' is needed to convert the result to the right format.
For the partition 4 = 2 + 1 + 1, the ZS1 algorithm gives the list (2, 1, 1), and I have to convert that to the list (2, 1, 0, 0). As you see, that costs equal time to any of the other two methods.

My conclusion of this is, that the time needed for the actual calculations are trifle compared to the overhead of the function calls. It would be a nice experiment to rewrite the stuff in C or C++ to see if that works better :).

Oh, and I already threw out most of the other overhead. The partitions I return are simple integer arrays, no fancy objects.
 
Look, folks, Doron believes he had found the SECRET OF MATHEMATICS, the one which had eluded Euclid, Gauss, Galois, Euler, and all the rest. They were all idiots. He's a genius.

Yes, Doron's "math" (such as it is) is wrong, as any first-year undergrad in math (at the latest) can tell. Actually, in most cases it isn't even wrong -- it is just meaningless gibberish. "2+2=5" can be proven wrong. "The invariant vector over the doronistic field of the super new triangular mathematic eigenvalue always has a doron-logic super-truth value of 17" (or the equivalent) cannot be proven wrong, since it's completely meaningless, and a statement has to mean something to be either right or wrong. (This, by the way, is the real reason cranks always proclaim proudly that "nobody has them wrong".)

But there is no arguing doron out of it any more than there is arguing with a psychotic and explaining to him the alien reptilians aren't really out to get him. Every counter-argument is just dismissed as either the work of midgets, too stupid to understand his towering genius, or else the works of those in the conspiracy, of envious mathematicians out to rob him of his just reward as the founder of REAL mathematics.

Logic and evidence are all on your side, of course, but they are, as is well known, completely powerless against self-delusion. Doron will, with all probability, go to his grave still believing he is the greatest mathematician who ever lived, and that he only failed to get recognized due to the envy and stupidity of his unappreciating age.
 
Skeptic said:
Look, folks, Doron believes he had found the SECRET OF MATHEMATICS, the one which had eluded Euclid, Gauss, Galois, Euler, and all the rest. They were all idiots. He's a genius.
Click to expand...

Many of your other fellow posters have managed to actually bring reasoned argumentation to this discussion with informative feedback. You would do well to do the same. If you've no substantive input of your own to add to this discussion keep your asinine jeering to yourself.
 
Skeptic said:
Look, folks, Doron believes he had found the SECRET OF MATHEMATICS, the one which had eluded Euclid, Gauss, Galois, Euler, and all the rest. They were all idiots. He's a genius.

Yes, Doron's "math" (such as it is) is wrong, as any first-year undergrad in math (at the latest) can tell. Actually, in most cases it isn't even wrong -- it is just meaningless gibberish. "2+2=5" can be proven wrong. "The invariant vector over the doronistic field of the super new triangular mathematic eigenvalue always has a doron-logic super-truth value of 17" (or the equivalent) cannot be proven wrong, since it's completely meaningless, and a statement has to mean something to be either right or wrong. (This, by the way, is the real reason cranks always proclaim proudly that "nobody has them wrong".)

But there is no arguing doron out of it any more than there is arguing with a psychotic and explaining to him the alien reptilians aren't really out to get him. Every counter-argument is just dismissed as either the work of midgets, too stupid to understand his towering genius, or else the works of those in the conspiracy, of envious mathematicians out to rob him of his just reward as the founder of REAL mathematics.

Logic and evidence are all on your side, of course, but they are, as is well known, completely powerless against self-delusion. Doron will, with all probability, go to his grave still believing he is the greatest mathematician who ever lived, and that he only failed to get recognized due to the envy and stupidity of his unappreciating age.
Click to expand...


Hi Skeptic,

Organic Mathematics is an extension to the discovery of Galois about unification of construction of drawing with a ruler and a compass.Now apply to all Mathematics branches in term of locality and non locality . I am glad that today it is possible to have open discussion about the value of OM. As you know Galois die in the age of 21 without recognition.

Have you seen already my presentation at Sweden ?

Moshe:boxedin:
 
ddt said:
MosheKlein said:
Hi ddt,

Really a great work !
Thank you for the 5 hours of computing or(n).
You are the leader today of this computation on the planet of Earth..

Did you have in advance the program for the partitions ?
No, I didn't have that in advance. So I've been tinkering with how to do that efficiently. My first algorithm just generated a big list of all partitions, but that ran out of heap space at n=64. So as a next try, I made a version with a recursive generator that ran in a separate thread - so that one still had O(n^2) space requirements. My third try was an iterative version of that without the multi-threading but still with the O(n^2) space requirement because of the emulation of the stackframes, and in my fourth try I eliminated the stackframes and so I got the O(n) space requirement - which is also the minimum possible.

I also tried another algorithm I found on the internet, which claims to be the most time efficient, but that one runs actually slower than the one I made - basically because it constructs a partition in as a list 4 = 2 + 1 + 1, whereas your algorithm needs it in the form (2, 1, 0, 0). The conversion between the two makes it 50% slower. So my algorithm is actually very fast :). I did some profiling and I conclude from that that the actual calculations are dwarfed, in terms of the time used, by the function calls. :jaw-dropp

But I'm glad that Java has BigIntegers, so I don't have to program those. :D
(oh, and a little optimization I overlooked: skipping the g(Or(i), a_i) factors where a_i == 0 cuts execution time in half :)).
Click to expand...

This is really beautiful ddt
Do you want to write a common paper with me
about the formula and your algorithm.

Best
Moshe:blush:
Click to expand...
Click to expand...
 
MosheKlein said:
Hi Skeptic,

Organic Mathematics is an extension to the discovery of Galois about unification of construction of drawing with a ruler and a compass.Now apply to all Mathematics branches in term of locality and non locality . I am glad that today it is possible to have open discussion about the value of OM. As you know Galois die in the age of 21 without recognition.

Have you seen already my presentation at Sweden ?

Moshe:boxedin:
Click to expand...

Don't bother, Moshe, not everyone on JREF is nice. Skeptic isn't here to participate in an actual discussion.
 
jsfisher said:
Ok, now having waded through the Sweden presentation videos, I think I understand what MosheKlein means by distinction. Let me play this back to MosheKlein for his reaction:

First off, the concept of number being used here has some underlying reference to things, often implicit. You don't just consider 3 as an abstract mathematical construct; there must be 3 things of one sort or another. Beads on a string has been the frequent example in this thread.

Each thing is presumed to have some identity, but the identity may be unknown to use. Distinction refers to the possible ways in which we can distinguish (or not) among those things.

Let's say we have 2 things, with identities A and B. If we don't know which is which, the best we can say is one is either A or B and the other is either B or A. (This would be the superposition of identities that's been mentioned once or twice in this thread.) If we know the identity of one of the things, then by the process of elimination we know the identity of the other.

So, for 2 things, there are 2 distinctions: (AB, AB) and (A, B).

For 3 things, the claim is there are 3 distinctions, ranging from knowing nothing, something, or everything: (ABC, ABC, ABC), (A, BC, BC), and (A, B, C).


How am I doing, MosheKlein?
Click to expand...

You are doing great !
I am glad that I made the travel to Sweden !

sincerely
Moshe:p
 
jsfisher said:
Since this would be a part of the material you already admitted you don't understand, there's really no reason to believe you know what it does or does not explain, now is there?
Click to expand...

jsfisher,



n=2 to ∞

k=n-1

For each partition of the form (k+1) the +1 part is always a unique id.



In order to understand it let us start from n=2

(1+1)
(2,2)
((1),1)

You can see that under partition (1+1) of n=2, there are two cases.

One is non-distinct and represented by (2,2), and the other is the case (k+1) and it is
represented as ((1),1).



Now let us examine n=3

(1+1+1)
(3,3,3)

(2+1) is the (k+1) case of n=3
(2,2,1)
(((1),1),1)



The (k+1) case holds for any n>1.

Therefore the +1 of partition (3+1) of n=4 represents a unique id, and it is consistent with partition (1+1) of n=2, and with partition (2+1) of n=3.

Here is partition (3+1) of n=4

(3+1)
((3, 3, 3), 1)
(((2, 2), 1), 1)
((((1), 1), 1), 1)

If you read very carefully this post, I believe that you will get the consistency of partition (k+1) for any given n.
 
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Skeptic said:
Look, folks, Doron believes he had found the SECRET OF MATHEMATICS, the one which had eluded Euclid, Gauss, Galois, Euler, and all the rest. They were all idiots. He's a genius.

Yes, Doron's "math" (such as it is) is wrong, as any first-year undergrad in math (at the latest) can tell. Actually, in most cases it isn't even wrong -- it is just meaningless gibberish. "2+2=5" can be proven wrong. "The invariant vector over the doronistic field of the super new triangular mathematic eigenvalue always has a doron-logic super-truth value of 17" (or the equivalent) cannot be proven wrong, since it's completely meaningless, and a statement has to mean something to be either right or wrong. (This, by the way, is the real reason cranks always proclaim proudly that "nobody has them wrong".)

But there is no arguing doron out of it any more than there is arguing with a psychotic and explaining to him the alien reptilians aren't really out to get him. Every counter-argument is just dismissed as either the work of midgets, too stupid to understand his towering genius, or else the works of those in the conspiracy, of envious mathematicians out to rob him of his just reward as the founder of REAL mathematics.

Logic and evidence are all on your side, of course, but they are, as is well known, completely powerless against self-delusion. Doron will, with all probability, go to his grave still believing he is the greatest mathematician who ever lived, and that he only failed to get recognized due to the envy and stupidity of his unappreciating age.
Click to expand...

Enjoy your uniqueness.
 
AkuManiMani said:
Don't bother, Moshe, not everyone on JREF is nice. Skeptic isn't here to participate in an actual discussion.
Click to expand...

Dear AkuManiMani ,

Thank you !

During ICM2006 F.Gauss was chosen by the members of IMU as the great Mathematicians of all time !

For more then 2000 years there was an interesting problem in Mathematics. Is it possible to divide an angel to 3 equal parts by using of a ruler and a compass. E.Galois notices that by construction with a ruler and a compass we solve quadratic or linear equation. Using this unification he could prove that it is impossible to divide an angel of 60 degrees to 20 degrees since cos(20) solve equation of degree 3 which can't be reduce to degree 2. Despite this great discovery he could not accepted to high study in mathematics !

OM discover that it is possible to unify all area of Mathematics ( Set, Logic, Topology , etc ) in term of locality and non locality. The first step is accepting the new notion :"The distinction of a number".

Sincerely
Moshe:blush:
 
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Apathia said:
Generous of you, Moshe, but I have no relation with a local kindergarten which would welcome your demonstration.

So perhaps you could share a typical interaction via a simple dialog.
For example what I did in the Paddy Post.
You describe your set up then give Paddy's response to each situation.

That way you could illustrate the typical way a pre-schooler thinks and how that relates to OM.

If you could do this, it would certainly be more economic and less time consuming than you flying to America. Also you'd be able to cut to the chase rather than waiting for little kids to make the demonstration you expect.
Click to expand...


I don't understand, what is the problem to fly to America( I will be in a vocation from the kindergardens in July / August) for a good meeting with young childrens concerning Mathematics. And please don't worry about the money..;)
 
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MosheKlein said:
You are doing great !
I am glad that I made the travel to Sweden !
Click to expand...


Ok, then you and I have reached a common understanding of what you mean by distinction.

Why isn't (AB, AC, BC) among the possibilities for 3?

Why isn't (AB, ABC, ABC) among the possibilities for 3?
 
jsfisher said:
Ok, then you and I have reached a common understanding of what you mean by distinction.

Why isn't (AB, AC, BC) among the possibilities for 3?

Why isn't (AB, ABC, ABC) among the possibilities for 3?
Click to expand...

very good jsfisher !


Because the real identity of the beads ( in my sweden presentation)
is not important in the sense of permutation:

(a,b,c)=(b,a,c) etc

so (AB,AC,BC) have no real meaning in distinction.

Did I made myself clear to you ?

Moshe:blush:
 
MosheKlein said:
very good jsfisher !


Because the real identity of the beads ( in my sweden presentation)
is not important in the sense of permutation:

(a,b,c)=(b,a,c) etc

so (AB,AC,BC) have no real meaning in distinction.

Did I made myself clear to you ?
Click to expand...

(AB, AC, BC) isn't a permutation of any of your cases. Nor is (AB, ABC, ABC). Both examples illustrate cases where some information is known about the identity of each bead. Why are these not valid distinctions?
 
jsfisher said:
Ok, then you and I have reached a common understanding of what you mean by distinction.

Why isn't (AB, AC, BC) among the possibilities for 3?

Why isn't (AB, ABC, ABC) among the possibilities for 3?
Click to expand...

Jsfisher,

You can invent your Organic Numbers if you wish.

All you have to do is to define a consistent way to use Distinction as their property.

In my case, I used Distinction by construct the next n forms with the previous forms that belong the values that are less than n, starting from n=2 and moving forward according to a certain principle (that can be replaced by another principle, or even mixed up with several principles).

The principle of my construction is clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=4852892&postcount=4112 and an explanation about (3+1), which is consistent with my construction case, is given in http://www.internationalskeptics.com/forums/showpost.php?p=4853391&postcount=4131 .


By using Distinction, you can invent different Organic Numbers, as follows:

n=2

(1+1)
(2,2)
((1),2)
((1),1)



n=3

(1+1+1)
(3,3,3)

(2+1)
((2,2),3)
((2,2),2)
((2,2),1)
(((1),2),3)
(((1),2),2)
(((1),2),1)
(((1),1),3)
((1),1),2)
((1),1),1)

I leave you to draw n=4 according to this construction, but also in this more complex case, Distinction is used as a main principle, and this is the essence of Organic Numbers, weather they are constructed as I first introduced them, or they are constructed differently from my first introduction of them.
 
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jsfisher said:
Thanks, but I neither seek nor require your permission.
Click to expand...

I hope now you get why the particular discussed recursive function is not the important thing here.

Distinction is important, and any particular construction of it can be used for different purpose (where my first construction is nothing but an example of such construction).
 
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The introduced Or(n) only provides the serial case of my particular construction of Organic Numbers.
 
MosheKlein said:
I don't understand, what is the problem to fly to America( I will be in a vocation from the kindergardens in July / August) for a good meeting with young childrens concerning Mathematics. And please don't worry about the money..;)
Click to expand...

I'm glad an international flight isn't an economic difficulty for you.

The difficulty is that I have no connections with a local kindergarten or teacher local who would be interested in or allow a guest to come in and work with the kids.

Also it's clear there is a language barrier.

It would most likely suffice for me if you just gave me some simple dialogs where a child exhibits the way of thinking you have worked into a more complex math-like presentation.

Let's start with Anthony. (the boy in my avatar)
He's shown three American coins. Let's say quarters.
All three are brand new and minted in the same state, so they look exactly alike.

Now let's ask Anthony to "count" them.

Here we begin a simple, concrete story that could get at the heart of the mind of OM.

That's what I'm after. I want to understand the way of thinking,
I'm not a mathematician (The only calculus I was ever able to pass was renal.
The last maths course I took was Set Theory & Logic.)
I'm not into so intersted in the algorithm. I want to know the why of it, what its for, and how it has any practical value in integrating mathmatics and ethics.

So let's start with Little Anthony. He knows nothing of algorithims of partitions.
But you believe he has a special insight, don't you.
Please show me how he expresses that.
First we'll use the coins and then move onto the toys.
 
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doronshadmi said:
It is a fundamental mistake to think that Ethical considerations cannot be an inseparable property of the scientific real-time tools of the exact sciences, and OM's goal is to develop exactly such tools that will give the scientist the needed Ethical aspects directly through his scientific tools.

If such a goal is achieved, then we do not need politicians or religious leaders in order to decide what to do with a destructive technology, simply because such a technology will not be developed by scientists that are aware of Ethics and Logics\Technologic aspects as built-in properties of their scientific tools.
Click to expand...
...OK, let's consider how that will apply to a hypothetical scientist in your brave new world. He(she) gets up, has breakfast, goes to the lab, studies the reactivity profiles of protiens folded in different ways as part of blue-sky research with potential pharmaceutical applications. After work, it's back home, a meal, leisure time, then bed. The research work involves ovens and incubators and freezers and fridges, and centrifuges and scales and glassware and liquids and machines, and paperwork and rigid protocols, and a well-defined work flow. Oh, and a tool based on Organic Mathematics that will give our scientist the ethical aspects of his work. How do you see this tool working? Is it some piece of 'smart' software? if so, what are its inputs? its outputs? Is this tool a mental approach, a methodology? What do you see it as, and how will it involve or integrate ethics and morality into this researcher's protien folding study?

Perhaps the study is funded by a charity looking for a cure for malaria. Perhaps the charity is indirectly 80% funded by a pharmaceutical company looking to make big bucks with a new anti-malaria treatment. Perhaps the pharmaceutical company has a close association with a state military agency that sees the possibility using this research to produce an anti-toxin to protect their troops from the toxins they wish to use. A complex but not totally unrealistic tangle of moral and ethical considerations - with many unknowns.

How do you see Organic Numbers fitting into this scenario? how will they help? where and how will they be used? Where does the ethical and moral bridge manifest? Explain the tool that allows our researcher to integrate ethics and morality into her work. What about the bigger picture? The politicians and power-brokers that run and fund research? the people who make practical use of it? where does the Organic Number philosophy get involved, and how?
 
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MosheKlein said:
Hi Man,

I think that you got the point !
best
Moshe
:boxedin:
Click to expand...



Well unfortunately I’m sorry to hear that, thought I am pleased at your apparent openness, honesty and candor. However it does not bode well for OM and I’m at a loss to see the usefulness of simply introduction arbitrary observer induced distinctions particularly in some of the examples I gave where the intent is to minimize potential observe influence. It seems useful in keeping ddt’s computer occupied though (something to be said there) and certainly Doron finds it useful as he can introduce such ‘distinctions’ then claim them as some underlying independent aspects that he also claims can not be researched independently.

As I see jsfisher is taking a more direct approach on this issue, I’ll see how that pans out.
 
doronshadmi said:
OK The Man, I get your point, you simply wish not to get the Symmetric\Non-symmetric model and instead you rambling around the Person's personal life, his health problems, his relations with his parents, etc. etc. …

My suggestion to you is: go have a life …
Click to expand...


What? “Symmetric\Non-symmetric model”? “the Person's personal life”? “his health problems”? “his relations with his parents, etc. etc. ? What never ending sphincter are you pulling all of that out of? Seriously Doron that post is far more bizarre then even your usual fare.
 
AkuManiMani said:
At the risk of draggin the HPC debate into this thread [please forgive me >_<] I'd say that to be conscious is to observe something. Cutting of a particular sensory channel wouldn't change this. Even if one has their optic nerves severed, is rendered deaf, and loses connection to their bodily sensations, if they are still have thoughts, emotions, and mental imagery they are still observing.
Click to expand...


Indeed but do those isolated observation need to be or can they be (other then by mere happenstance) consistent with common observations, like the glass being on my left when I open my eyes that is indistinguishable from when I closed my eyes for me but not for others?
 
MosheKlein said:
very good jsfisher !


Because the real identity of the beads ( in my sweden presentation)
is not important in the sense of permutation:

(a,b,c)=(b,a,c) etc

so (AB,AC,BC) have no real meaning in distinction.

Did I made myself clear to you ?

Moshe:blush:
Click to expand...


Just to add to jsfishers question, why are ordering distinctions excluded particularly if one is going though the trouble of identifying each bead individually or uniquely? It would seem to me that uniqueness of ordering would be just as, if not more, significant since the higher the number of elements go you are going to have a greater number of unique orderings compared to just unique associations.
 
dlorde said:
Is it some piece of 'smart' software?
Click to expand...

Yes, it is both software and hardware called the researcher, which is aware of how to save and enrich complexity\simplicity interactions as a phenomenon of a one ecosystem during his real-time work. By using Organic Numbers the researcher is an aware organ of the ecosystem, that will do his best in order to avoid any potential harmful action against the ecosystem, simply because any damage to the ecosystem is a damage to the researcher himself, and Organic Numbers do not let the researcher to forget during his real-time work, that he is an organ of the ecosystem.
 
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My first construction of Organic Numbers ( please see http://www.internationalskeptics.com/forums/showpost.php?p=4850095&postcount=4039 ) is the minimal consistent way of using Distinction as a main property of some collection of elements.

On top of this minimal construction there can be infinitely many different constrictions that are not the minimal construction, but all these constructions have a one thing in common, they extend Distinction beyond a single id for each element, as we find in the case of Set's membership or Category's Morphisms.

Here are two detailed examples of the minimal costruction of partitions (4+3+2) and (3+3+3) of n=9:

432_333.jpg
 
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doronshadmi said:
Yes, it is both software and hardware called the researcher, which is aware of how to save and enrich complexity\simplicity interactions as a phenomenon of a one ecosystem during his real-time work. By using Organic Numbers the researcher is an aware organ of the ecosystem, that will do his best in order to avoid any potential harmful action against the ecosystem, simply because any damage to the ecosystem is a damage to the researcher himself, and Organic Numbers do not let the researcher to forget during his real-time work, that he is an organ of the ecosystem.
Click to expand...


Oh is that what they do? Here I was just starting to think that all they could do was to keep ddt’s computer busy. You seem to have a rather bizarre interpretation of an ecosystem (of course bizarre interpretations are noting new for you). You do realize the proper functioning of an ecosystem generally involves some organisms consuming others. Even now certain organisms are working away quite busily trying to consume you. So how do you define damage to an ecosystem particularly one well on it’s way to consuming you? Do organic numbers also remind a researcher when he is the particular organism about to be consumed in given ecosystem or that the ecosystem he might be researching is more harmful to him then he is to that ecosystem. Unfortunately our ecosystem in general does not have the humanistic fixation you appear to have. That’s understandable as we are generally at the top of the macro biological food chain. Microbiology is something different though and we are, for the most part, still dinner on the table. Even in a macro biological sense there are plenty of places around the world where the ecosystem will consume you just as readily as any other food source. I’ll say this for you Doron you have at least one unflappable consistency, your knowledge of biology and ecosystems is right on par with your knowledge of math, physics, philosophy, ethics, morality and any of the other topics that you display absolutely no understanding of or at best a very rudimentary and naive understanding of and at worst a complete confabulation that exists only in your mind.
 
While I am waiting for MosheKlein to answer the question I posed to him, maybe Doron will grace up with the logical follow-on question regarding this:

doronshadmi said:
(A, B, ABCD, ABCD) means: the distinct from of 2 within form 4 ( it is under the partition (2+1+1) ).
Click to expand...

Doron, you are still telling me how you got it, not what it means. I offered a working definition for distinction, and both you and MosheKlein accepted it:

In short: Distinction refers to all the different ways a number of things can be distinguished (or not) from each other.

I introduced the notation which you accepted and latched onto. In that notation, (A, B, ABCD, ABCD) means there are 4 things. The first has been identified as A, the second as B, and the last two could each be A or B or C or D.

That's what the notation says. Is that what you meant? If not, what did you mean?
 
doronshadmi said:
...Organic Numbers do not let the researcher to forget during his real-time work, that he is an organ of the ecosystem.
Click to expand...
From what I've seen, Organic Numbers are just a way of enumerating the 'distinctions' of the partitions of a number - how do they make the user any more aware of his ecosystem that any other obscure exercise in mathematics? and how are they used in practice?

Still waiting for even a hypothetical example of their practical use and how ethics and morals are automatically a part of their use.
 
jsfisher said:
(AB, AC, BC) isn't a permutation of any of your cases. Nor is (AB, ABC, ABC). Both examples illustrate cases where some information is known about the identity of each bead. Why are these not valid distinctions?
Click to expand...

Well jsfisher,I have never thought about this possibility of distinction, thank you. Maybe it is possible ! I will think about it and come back when I will have something more to say.

Moshe:eek:
 
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The Man said:
Just to add to jsfishers question, why are ordering distinctions excluded particularly if one is going though the trouble of identifying each bead individually or uniquely? It would seem to me that uniqueness of ordering would be just as, if not more, significant since the higher the number of elements go you are going to have a greater number of unique orderings compared to just unique associations.
Click to expand...

My first and intuitive answer to you is that ordering of distinction in significant in serial observation like {......} and not significant in parallel observation of {____} is that help you in some sense ?

Moshe:boggled:
 
Apathia said:
I'm glad an international flight isn't an economic difficulty for you.

The difficulty is that I have no connections with a local kindergarten or teacher local who would be interested in or allow a guest to come in and work with the kids.

Also it's clear there is a language barrier.

It would most likely suffice for me if you just gave me some simple dialogs where a child exhibits the way of thinking you have worked into a more complex math-like presentation.

Let's start with Anthony. (the boy in my avatar)
He's shown three American coins. Let's say quarters.
All three are brand new and minted in the same state, so they look exactly alike.

Now let's ask Anthony to "count" them.

Here we begin a simple, concrete story that could get at the heart of the mind of OM.

That's what I'm after. I want to understand the way of thinking,
I'm not a mathematician (The only calculus I was ever able to pass was renal.
The last maths course I took was Set Theory & Logic.)
I'm not into so intersted in the algorithm. I want to know the why of it, what its for, and how it has any practical value in integrating mathmatics and ethics.

So let's start with Little Anthony. He knows nothing of algorithims of partitions.
But you believe he has a special insight, don't you.
Please show me how he expresses that.
First we'll use the coins and then move onto the toys.
Click to expand...

ok you got it.

I will ask Anthony: "what do you see on the table?"

can you imagine his answer ?

Moshe:blush:
 
jsfisher said:
In short: Distinction refers to all the different ways a number of things can be distinguished (or not) from each other.
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No: Distinction refers to the amount of levels a thing is distinct.


Each Organic number is a one organism (a one thing) and this is the reason of why the different forms are connected by a line, for example ON 4 (the minimal case):

ON4.jpg


Each form is both local and global case of the entire organism.

Again:

Instead of ABCD we use 4 in order to represent 4 possible ids (no matter what they are, as long as they are forms of n=1 to 4).
Instead of ABC we use 3 in order to represent 3 possible ids (no matter what they are, as long as they are forms of n=1 to 4).
Instead of AB we use 2 in order to represent 2 possible ids (no matter what they are, as long as they are forms of n=1 to 4).
Instead of A we use 1 in order to represent 1 possible ids (no matter what they are, as long as they are forms of n=1 to 4).

By using this generalization, case 4 looks like this:

(1+1+1+1)
(4, 4, 4, 4)

(2+1+1)
((2, 2), 4, 4)
(((1), 1), 4, 4)

(2+2)
((2, 2), (2, 2))
(((1), 1), (2, 2))
(((1), 1), ((1), 1))

(3+1)
((3, 3, 3), 1)
(((2, 2), 1), 1)
((((1), 1), 1), 1)
 
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