Quote :

to I.A.1.: this is a subjective answer. The relevance of the argument A.1. is obvious, I think so. If "manhatten-distance" is an "argument" for both, than the  cells-example is also an "argument".

Stating that it is obvious has nothing to do with argumentation. The manhattan distance is an argument because this distance is used in tactical or strategical calculations. How useful is the ability to have integer calculuus of the number of spots in the whole board in terms of rings ? Answering to that question will demonstrate how relevant (or not) this argument is.

Quote :

to A.3: nobody is speaking of "proof", we speak of arguments. A.3 is an analogy and an analogy can be an "argument". One should show the inadequacy of the analogy and not denunciate an analgoy, since it is an analogy. This is too general, I think so.

An argument is a proof as long as it is logical. An analogy is everything but a logical argument. Thus, it can be use in order to try to convince someone but is quite invalid if the purpose is to demonstrate anything (demonstration relies on logical arguments).

Quote :

is a subjective feeling AND a presentable expression of many Players, to the "common Abalone-perception" - as I have written. If you dont think that this is the case, then you should show the opposite.

I'm interrested by objective, rational, logical facts allowing to chose between 4 rings+1 spot or 5 rings representation.

However, if you want me to show the opposite of "It seems obvious to me that the center is a spot, not a ring.
Therefore there are 4 rings with e5 at the center.", well it is quite easy : it seems obvious to me that the center is a ring - therefore there are 5 rings.

I don't think any discussion will go anywhere based on this kind of (pseudo-)argumentation.

Quote :

We dont speak of terms for Programming here

Well, you are partly right and partly wrong. You are right because, of course, we are not talking about programming. You are wrong because programming, IAs, algorithms and cognitive processes are highly connected.

If we agree that a general abalone theory will have, sooner or later, more to do with mathematics or algorithms than pure dialectics, then we should agree that a representation allowing simplier expression of equations or algorithms presents strong advantages.

If the purpose is to stay at a dialectic level, i agree that my point is irrelevant.

Quote :

"if one and only one should be chosen, then the rings only representation should be this one." I think this is your preference, probably because B1 and B2 have the strongest argument-weight for you.

Exactly.

In order to evaluate the weight of each argument, we have to find out the reasons why we want a normalized representation and all the consequences of such a representation. De facto, sooner or later, the 5 rings representation will be needed (unless we forget the concept of rings). So, it just makes sense to me that the 5 rings representation should be chosen if we want one and only one representation.

But why just bother with the concept of ring ? Because it is assumed that spots of the same rings share tactical or strategical properties and that a specific analysis can be made based on those properties.

I'm sure you will agree that the number of abstractions used has a direct impact on a system's complexity. By mixing different abstractions (4 rings + 1 spot), you are mixing diferent angles of analysis and introducing more complexity.  

--Last edited by chriscool on 2005-11-16 15:44:14 --

Hello,

I think first we have to understand some terms, because without terms we can not talk here in a fruitful way.
So first (I.) I try to introduce some terms "logical", "argument", "analogy", "content", strong/ low "argument-weight"

Then (II.) I will come back to the discussion.

-----------------------------------------------------------------

I. Terms

This is your understanding of "logical", "argument" and "analogy":

Quote :

An argument is a proof as long as it is logical. An analogy is everything but a logical argument.

I make a different suggestion for these terms:

a simple argument:

A -> B
A
-------
B

argument, logical
The "structure" (-> etc.) of the argument is "logical". This is the level of the "structure of the argument".
"Logic" is the science for this structure-level.

content and analogy:
The "content" of an argument are A,B, C ... or any other "facts".  There are "empirical sciences" to validate this contents/facts OR there has to be a discussion in a social sphere - for example like in this forum or in other social matters.

-> Of the point of view of this introduced terms:
You are  right, if you say: a analogy is everything but a logical argument. Yes, an analogy is not a structure of an argument (structure-level).
But this does not fit the level. The analogy can be a content of a argument (A, B,  C, ...). (content-level)
The content of an argument can be manhatten-distance, the obviousness of cells-counting, an analogy etc..

-------------------------------------------------------------

My suggestion for the term "argument-weight":

The sense of this topic is a "discussion" . In a discussion we can exchange arguments and everyone has to build his own opinion. What you say is your opinion and what I say is my opinion - everyone has the own measure. Everyone has his own "arguments" of his point of view - this is the personal point of view.
 
Finally, and this is decisive, WE have pretty to agree for a definition. I think, its not a personal task to say "this is true" and this is "objective fact". We have to agree in communication, this is the final goal.  
And this "We"-perspective is what I meant with "argument-weight".
Everyone can try to share this We-perspective. I think it is not fruitful to say "this is not a argument" on this level. "We" only have "to agree" in the argument-weight and in the strongest argument.

For example, we both agreed that the argument A3 has a low weight. There is no necessity to discuss, if this is a "rational, objective fact" or not. This is and should not be our point of view, I think so.

(By the way I have never seen any rational, objective fact, only ideas of this.)

---------------------------------------------------------------

I dont agree that the general theory will have to do with mathematics. It can, but there is no necessity.
This is the topic Glossary and this is the Forum of the General Theory - I thought all programmers here had realized this.

-------------------------------------------------------------

II. Back to the discussion:

Of my point of view the argument B2 has the strongest weight of all arguments.

Maybe you have realised that we both already agreed in the result.
We, nacre and mirror (eob) agreed with B1 (edited) as the strongest argument of the A1-4 and B1-3 arguments (- maybe eob will come back and will give us reasons for his proposal)

We only have to ask Abalekon and kopedito if they agree, too, because they had arguments for A, before nacre made his argument B1. Maybe Foxaphosphor and other members will write down their opinion, too.

I hope that WE will find a result here - its not a private decision, its beyond a personal task.  


Thank you.  

--Last edited by SilverSurfer on 2005-11-16 19:01:09 --

hello Frodo

Am I fool or could we say that B2 ("ring-n where 'n' is the set of marbles at distance 'n' to the 'center'") means 4 rings, am I??

I agree that my "A" opinions where not "arguments", just common sense.
Since I think it's not a matter of arguments but rather a matter of convention, I consider that both 0-based (4) or 1-based (5) conventions are acceptable.
Just one last word, is it possible to build a "theory" without the "center" terminology and hence treating the center as any other position? If this is the case, it could be challeging... but very interresting to get rid of that "center" attraction (side question: are there any successfull eval functions (or good players) not using e5 as a static reference in their strategy?).


kr.  

--Last edited by kopedito on 2005-11-16 18:04:03 --

Quote :

The sense of this topic is a "discussion" . In a discussion we can exchange arguments and everyone has to build his own opinion. What you say is your opinion and what I say is my opinion - everyone has the own measure. Everyone has his own "arguments" of his point of view - this is the personal point of view.   Finally, and this is decisive, WE have pretty to agree for a definition. I think, its not a personal task to say "this is true" and this is "objective fact". We have to agree in communication, this is the final goal.   And this "We"-perspective is what I meant with "argument-weight". Everyone can try to share this We-perspective. I think it is not fruitful to say "this is not a argument" on this level. "We" only have "to agree" in the argument-weight and in the strongest argument.

I strongly disagree with many points here.

First, i disagree with the meaning you seem to give to "discussion". It doesn't imply to me that anybody can say anything. At least, the interactivity and the ability for mutual understanding are fundamental. With life and all in it being experienced in a personnal manner, we have to articulate a discussion around something that would be commun. This is what you do when you try to give precise definitions of this or that term. I don't know many things being more common than logical expressions, which go far beyond language and culture (ie you can rely on logical expression even if the other contributors do not share the same culture).

I don't think it is possible to have real discussions without logical expressions. How can you discuss around an expression like "i feel that god exists, then it exists" ?

There is hardly any possibility to understand each other if we don't rely on logical expressions, particulary on internet. Without the ability to understand each other, i can hardly see any possible discussion.

So, i don't consider a discussion as just the expression of different opinions. Each opinion has to be argued on logical basis so that a discussion is possible.

As an exemple, if you say things like "i feel good", "i feel bad" or "i feel like god exists", there is not much to discuss about.

You said that everyone had one's own measure. The fact is that everyone has one's own experience, but we have to bring it to some more common (if not universal) measures in order to share it with others. As i said, i don't know any measure more universal than logical expressions. Particullary, the fact that it is unpersonnal allows to disagree without anyone feeling personnally attacked. I am more likely to accept your disagreement if you point out my logical errors that leads you to such a disagreement rather than by emitting opposite assertions.

There must be some interface between your assertions and mine. I don't know any better interface than logical expressions.

Without such an interface, there is nothing i could call a discussion.  

--Last edited by chriscool on 2005-11-16 18:14:47 --

Hello Kopedito,

ok, maybe we have to use your and chriscools argument-terms. I hope you can explain, what you mean with "argument" - I am very curious.

With my introduced terms, these were all arguments with a simple argument-structure. (argument-structure: logical level)
The difference of what you call the difference between "arguments" and "just common sense/opinions" is of this point of view the difference in "the validation-medium of the content of the arguments". (content-level)
I only know a argument-term with these two levels: structure (logic) and content (empirical). I never heard anything else - only in common sense, but not a well explained term, since a common-sense-term.

Hm, it was not B2, sorry, I have changed it now, it was B1:
"About ring terminology. I number rings from the center, this makes sense when you compare larger games (full board with side length 5) with smaller games (e.g a single group in the daisies, side length 2)”

I reagrad three points about the theory.
1. The term "centre" is very important. No doubt. I dont want to
pass on the term "centre".
2. But the possibility to compare structures is very important, too - this was the B1-argument.
3. There can be many "key-point" with more importance than the centre. The centre is often a important key-point (for example in many openings), but not always. Its a static point of view to take the centre as a general key-point, I think so, rather the real importance of the points is depending on the starting-position, the game-period and the actual position/structure.  


---------------------------------------------------------

And now again: Chriscool is claiming again for logic !
I dont know what you mean with your term "logic".  All what you say is in my ears not "logic".  
What do you mean with logic ? This sounds like "rational" in a common sense meaning. But what is this ? Have you any criteria ?

logical:

"i feel that god exists, then it exists"

A: I feel that god exists
B: my feeling is the proof for reality
C: good exists

A & B -> C

This is a "logic" "argument". No doubt! Isnt it ? (logic-level)

The only problem is the "content" of B and C. (content-level)

The problem is not the logical argument, but the validation of the content.
This are two different levels.


I never said, that we dont have to argue logical. (logical level)
I only said, we have to discuss the "argument-weight" (content-level)
Is this too difficult to understand ? It is too difficult to divide the logical level and the content level in an argumentation ?

I have introduced terms for logic, argument, etc. and I did not say, that we dont have to argue logical. More the contrary.

Can you please introduce what you mean with logic and argument, chris ?
I am very curious !


The term discussion:
I did not say that we can say everything in the discussion. I said, that the discussion-aim is to validate the arguments on the "WE-Level".


      argument
     /     \
    /       \
logical     content
              \
               --> validation of the content-level in the We-discussion         (Forum-Aim)  
             /
I         we
 \        /
  \      /
point of view  


The aim of the Forum is to validate the content in the discussion, I think so. The logical level was very simple in every argument.  

--Last edited by SilverSurfer on 2005-11-16 19:49:41 --

Quote :

We only have to ask Abalekon and kopedito if they agree, too, because they had arguments for A, before nacre made his argument B2.

I'm afraid I am not the right person to give a well-argued opinion about rings.  I'm just a not too bad player speaking the voice of common sense, and for me a spot is not a circle, you need many spots to make a circle.

Of course the answer to your problem may have implications on theory, IA, reckoning and so on, but I am not able to understand all that.

Ok, I try to give a last We-suggestion:

Than I abandon the ring-job, maybe kopedito or chriscool will be the "argumentation-term-Lord" - we will see  

nacre said:
" About ring terminology. I number rings from the center, this makes sense when you compare larger games (full board with side length 5) with smaller games (e.g a single group in the daisies, side length 2)
If you prefer 1 center + 4 rings, you can define the ring name from the radius of the ring, metric is manhattan distance = number of single-marble moves: ring 0 is the center marble, ring 4 is the outer ring."

chriscool said:
"My conclusion is that everyone should feel comfortable with both representations, but if one and only one should be chosen, then the rings only representation should be this one."

Kopedito said:
"Since I think it's not a matter of arguments but rather a matter of convention, I consider that both 0-based (4) or 1-based (5) conventions are acceptable."

Abalekon said:

"I'm afraid I am not the right person to give a well-argued opinion about rings.  I'm just a not too bad player speaking the voice of common sense, and for me a spot is not a circle, you need many spots to make a circle."

SilverSurfer said:
"A1-4 are expressions of common sense and intuitive views. This is very coherent to me.
But (B1) is a important technical analysis-view, I think so."


->> There was no agreement for one version. Therefore my proposal is that we keep both versions

4 rings and centre:            5 rings:          



Thank you,
Best Regards,
SilverSurfer  

--Last edited by SilverSurfer on 2005-11-16 19:39:00 --

or we could maybe use 2 terms like 'ring' and 'zone'?


(note: Silver, I used the term 'argument' in this context as a logical reasoning which would have validated one point while invalidating the other. As we can't obiously invalidate any point here, there are here in my sense no 'valid' arguments, only point of views... or except maybe in its second english meaning (quarrel), lol)

kr.

Hm, rings is the term for the 5 rings ? And zone for the centre ?

(I agree totaly that there are not strong valid arguments and we cant invalidate any arguments. The only question is, if we have to pass the term "argument" or can we keep it in combination with the term argument-weight and "a degree" of We-Validation. And my position is/was: yes.
But there is a difference between logical and empirical validation. And I think the arguments were all simple logical valid. The problem was/is the empirical-validation and the comparison of the weights of the several arguments.)  

--Last edited by SilverSurfer on 2005-11-16 22:02:29 --

lol, I would have expected 4 rings / 5 zones, here we go again...

ok, is this your argument?

If we take 4 rings and centre, than the ring-party will say, that you dont take the centre as a ring. But then you would answer: hey, we have 5 zones, isnt that enough ? The centre is maybe not a ring, but is certainly a zone!

This is the idea ?

Of my point of view, I would like to choose the 5 rings and the 5 zones solution. The ring-party has its rings and you can take the 5 zones  

--Last edited by SilverSurfer on 2005-11-16 21:30:32 --

the term zone is inadequat because it doesn't imply that all spots are at the same distance.

About what i call logic, well, just search google for deductive and inductive inferences, or just "valid argument" and you'll find, i think, clear explanations of what i am talking about.

In particular, logic is not a subjective concept.

And i have given a logical argumentation for using 5 rings rather than 4 rings+1 spot. I will sum it up :

1- Abstraction reduces complexity by providing less concepts to handle
=>
2- all other things being equal(*), handling one concept should provide less complexity than handling two concepts
=>
3- A 5 rings representation uses less concepts than 4 rings+1 spot. Then 5 rings should lead to a less complex representation.

This is a logical argumentation (deduction based).

(*) the restriction "all things being equal" means that if some advantages are found for a 4 rings+1 spot then this reasonning has to be re-evaluate.  

--Last edited by chriscool on 2005-11-16 20:43:55 --

I never said that logic is a subjective concept.
I said that there are different point of views - one of this is the I.

Quote :

argument      /     \     /       \ logical     content               \                --> validation of the content-level in the We-discussion         (Forum-Aim)                / I         we  \        /   \      / point of view

There is a "logic-level" and a "content-level" in the argumentation for validation. I think you speak of the logical validation, but this was not my question, rather the empirical validation.

I dont think that google does not agree with my terms.

My point of view is that you dont see that the validation is not only the task of the logic, independent of inductive or deductive inference.
You can creat a big logical tree: A-> B-> C_> etc.
But the empirical validation is independent of logic.  
If you have a inductive inference than you have true/false tabels and in the case of deductive you have the same problem of the validation of the content A,B,C. The logic is only a structure with a logical validation of logic-forms, far away of an empirical validation, but is depending on empirical validation. Empirical Validation is a task of empirical-methods or/and discussion.


And i dont agree that it is necessary for the term zone to have the same distance, more the contrary. Zone is a term, which allows different distances and this is very helpful.  


This is your logical-valid example:

Quote :

1- Abstraction reduces complexity by providing less concepts to handle => 2- all other things being equal(*), handling one concept should provide less complexity than handling two concepts => 3- A 5 rings representation uses less concepts than 4 rings+1 spot. Then 5 rings should lead to a less complex representation."

But the question is still, if the 1,2,3 are empircal-valid facts. And what weight has this argument (argument-weight) in the We-discussion.

All the time I speak of these two other points. It is not sufficient or even necessary to creat a logical-argument.
You can put everything in it.  


If you regard again this table:

 argument
     /     \
    /       \
logical    content
              \
               --> validation of the content-level in the We-discussion         (Forum-Aim)  
             /
I        we
 \        /
  \      /
point of view


With all your deductive and inductive logical-arguments you only get the logical level in this table. You creat a argument and this is logic for you and this is logical for all. So it is a logical-valid argument.
Maybe it is empircal-valid for you, too. But the question is, if
1. the argument is empircal-valid for all others
2. And what weight has this argument in a We-point-of-view.

You can creat 1000 logical and empirical valid arguments with contrary intentions. Finaly it is the question, which is the argument-weight of the We-point-of-view.

You neglect all the time the empirical-validation and the We-point-of-view of the discussion, I thnk so. The logical-world and the empirical point of view of one Ego is not enough!  

--Last edited by SilverSurfer on 2005-11-16 22:06:40 --

My earlier suggestion to name rings 0 to 4 was an attempt to cover both point-of-view: 5 rings (if you think of 0 as a ring) and 4 rings (think of 0 as the center).

If a 5-ring person says: "What happens if we place a marble in ring 3", he would be immediately understood by a 4-ring person, thinking "the 3rd ring, hm. that must he the one that is inside the outermost ring".

The only time they would disagree would be when they we discussing the center marble / center ring. In this case they agree on the marbles involved (the one in the center of the board) and only disagree on the name of this marble.