Doron's naive view of things leads him to define a "pointless curve" as some closed curve that we did not specify a collection of specific coordinates on it. In his mind the closed curve is an entity on its own and is not composed of other elements nor does it contain "by default" any other elements. He is not really aware of the mathematical nature of things, he tries to take things out of his day to day experience and talk about them in mathematical jargon. For example, he takes a string, closes it by tying a knot, or welding or whatever, and thinks that it is a representation of a mathematical closed curve. Just as the string is not composed of "points" or "dots" he thinks that the closed curve does not contain a subset of coordinates by its own existence.
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Doron's naive view of things leads him to define a "pointless curve" as some closed curve that we did not specify a collection of specific coordinates on it. In his mind the closed curve is an entity on its own and is not composed of other elements nor does it contain "by default" any other elements. He is not really aware of the mathematical nature of things, he tries to take things out of his day to day experience and talk about them in mathematical jargon. For example, he takes a string, closes it by tying a knot, or welding or whatever, and thinks that it is a representation of a mathematical closed curve. Just as the string is not composed of "points" or "dots" he thinks that the closed curve does not contain a subset of coordinates by its own existence.
realpaladin
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Yes, but if you can manage to read the whole backlog of posts, I have gone over this with him even to the concept of Planck time, just to show there are 'smallest' units.
Yes, but the fact that this has been pointed to him does not mean he acknowledges/understands that. All I am saying is that there is a communication problem here. No real dialog will take place unless all parties agree on the terms used.
jsfisher
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Aye, there's the rub. Doron does not / cannot define his terms. Doron abuses established terminology without warning or excuse. All attempts so far to help him understand established terminology or to help him define his own unique concepts and usages have failed.
You are welcome to give it another shot, though.
Actually I tried several times and regretted it every single time. I completely agree with your observation. Doron has a counter productive (and annoying) tendency to knowingly redefine terms since he does not agree with the existing definition (we all know in most cases he simply does not understand the definition). A recent example is his new interpretation for the term "all". He asserts that this term should only be used for finite collections. What he does not realize (since he has no formal training) is that this actually makes this term redundant - if the term "all" can only be used for finite collections, well then, instead of using the term "all" just enumerate all the elements...
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realpaladin
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Well, to be honest, the main reason for me to return to this thread is that it actually feels like a sitcom. Doron being Archie and me the long-haired meatball
Nothing changes until either 'we get it' (i.e. concede) or Doron figures out a way to show what his brainchild can actually 'do'.
Because, even though to date Doron has not shown anything with OM that can not be done with a conventional toolkit of maths, it just may be that he really really sees it, but that he is unable get it into the right verbage to make us see it.
If Doron could establish a consistent framework (not the 0-dim/1-dim nonsense, or the trying to find faults with other mathematicians works) then we might be able to slowly work our way towards an end.
That might be a good idea. Let me try and let's just see what we get:
Doron,
mind you, these are only definitions I got from your posts. We just define things, no talk about proof, or how got to them.
- Your OM has 0-dim and 1-dim elements. How can we refer to them, measure them and how do we define relations amongst them?
Let's, please, just refer to 0-dim and 1-dim elements as O and I. This way I am not tempted to talk about how to see what the size of 1-dim is.
- I propose that, to differentiate between different 1-dim types, we class them with a 'dimensional class' (could be the size, we do not define that, ok?) and 'dimensional type' (could be the curve, could be angular, we do not define that, ok?). So we would have O and Int
About the O and I elements we can state the following:
- Any Int is bounded by exactly 2 O. It can not be less, because then n would be infinite. It can not be more because then I would be more than 1-dimensional. This takes care of that no infinite O's can be on any I.
- Any Int can be curved, angular, whatever, on a 2-dim plane, but we do not care about that, that is the property of the class 't'. It has no points.
- Any collection of O can never have an infinite number of elements.
- Any collection of Int can never have an infinite number of elements.
- Therefore any collection of O and Int can never have an infinite number of elements.
- A collection is called 'complete' if all elements, be they O or Int are both the beginning and the end of the collection.
So, in this vein, Doron, can you complete this?
Well, to be honest, the main reason for me to return to this thread is that it actually feels like a sitcom. Doron being Archie and me the long-haired meatball
Nothing changes until either 'we get it' (i.e. concede) or Doron figures out a way to show what his brainchild can actually 'do'.
Because, even though to date Doron has not shown anything with OM that can not be done with a conventional toolkit of maths, it just may be that he really really sees it, but that he is unable get it into the right verbage to make us see it.
If you enjoy posting on this thread, and debating with Doron - well, then this a perfectly good reason to continue posting. For others who are interested in actually broadening their mathematical horizons, I suspect this is not the place... Doron will not give you any practical use for his "theory" simply because there is not such. He is convinced that the entire mathematical science and science in general for that matter stems out of his "work". Mind you that the only solid mathematical content of his "work" is the graphical representations of integer partitions.
realpaladin
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I know, I even read all his info on other forums, his pdf's and had skirmishes with his sidekick (where is he gone? Or was that but a sockpuppet).
We will see.
The Man
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Well it is more his contrived view of things that leads him to need to separate his “closed curve” from the points that define it as both a curve as well as closed. Without that deliberate separation Doron has nothing to recombine into his “complex”. Indeed “naïve” is the best description of both his use of language and his conceptual notions, which of coarse goes hand in hand with the “day to day experience” references you remark to. However most of us already know how naïve concepts and use of language fail in strict applications. This is why tremendous efforts were put it to and effective results obtained by formalizing the notations, language and concepts we employ regularly today. Doron claims he wants to formalize his notions, but continues to fall back on and hide behind naïve use of language and interpretations, indicating that he would prefer to keep his notions as naïve rather then potentially losing them as formalization might require.
well put.
The Man
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Well, to be honest, the main reason for me to return to this thread is that it actually feels like a sitcom. Doron being Archie and me the long-haired meatball
That’s “Meathead”, you long-haired meatball.
The Man
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Thanks
realpaladin
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Honest! I think I am going to apply for the MDC today! This is the 3rd YT I caused to be used as a reply to me in 1 day!
But thanks
Little 10 Toes
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To save time I'll combine my two "threads" of this post.
Edited/Reformated Recap 1
Edited/Reformated Recap #2
I notice that you never answered my request for proof on how a finite collection is circular. My set or collection of vowels in the English alphabet, {a,e,i,o,u} has nothing to do with a line. If you want me to forget Geometry, why do you ask me to put it on "a closed curve", a.k.a. a circle? Do you want me to put them on a circle so that you can then claim that the collection is circular? When a set is created, there is typically an obvoius relationship between all elements of the set (blue objects, valued less than $5.23, cubes, picked at random, bitter, denser than mercury, bigger than a breadbox, comic books I still have hermetically sealed, and watched by more than 100 people are some relationships). Typically, the creation of the set comes before finding out cardinality of the set. I have now demonstrated that I can make a set without needing to first use cardinality. Once I have my set, I then use cardinality to determine the size of the set, or more specifically, the number of elements in the set.
Edited/Reformated Recap 1
Edited/Reformated Recap #2
I notice that you never answered my request for proof on how a finite collection is circular. My set or collection of vowels in the English alphabet, {a,e,i,o,u} has nothing to do with a line. If you want me to forget Geometry, why do you ask me to put it on "a closed curve", a.k.a. a circle? Do you want me to put them on a circle so that you can then claim that the collection is circular? When a set is created, there is typically an obvoius relationship between all elements of the set (blue objects, valued less than $5.23, cubes, picked at random, bitter, denser than mercury, bigger than a breadbox, comic books I still have hermetically sealed, and watched by more than 100 people are some relationships). Typically, the creation of the set comes before finding out cardinality of the set. I have now demonstrated that I can make a set without needing to first use cardinality. Once I have my set, I then use cardinality to determine the size of the set, or more specifically, the number of elements in the set.
Because as in any good Zen koan, hwadu, or story, dependence on rational classification and comparison are shattered.
There can be no similitude between the boy's finger and the master's finger till the boy's finger has gone non-local.
More and more I find my best responce to your perspective and its vocabulary is to channel either Zen Master Im Do-Son or Film Director David Lynch. I know better now than to try to fit all that you say into some consistant rational frame. I just go with the impression.
In terms of mathematical expectations, your departure from common property based reasoning is as dramatic and painful as having a finger cut off.
doronshadmi
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Little 10 Toes said:
First, thank you for giving us and example of a collection that has nothing in common between its elements except the fact that it is a finite collection of distinct elements.
By generalization all we care is about the number of distinct elements of a given collection.
Form this general notion if any arbitrary element of a collection of distinct elements is both a beginning AND an end of that collection, then the cardinality of that collection is determined.
Otherwise, the cardinality is undetermined.
It is easily understood that an arbitrary element of a given collection of distinct elements is both a beginning AND an end of the given collection only if the collection is finite.
It is also easily understood that an arbitrary element of a given collection of distinct elements is NOT both a beginning AND an end of the given collection only if the collection is infinite.
doronshadmi
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If the collection of points is infinite, then you can't return to the beginning X arbitrary point on the circle, because there is always another point Y' between Y and X that prevents the comparison between Y and X, etc… ad infinituum …
If X and Y are compared, you get a finite collection.
So if the collection is infinite than X and Y are not compared.
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doronshadmi
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Sorry to cut off your line, but the Zen koan reasoning fits much better to the claim that there is a complete infinite collection.
doronshadmi
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This is just the Local aspect of QM story. The other aspect is Non-locality.
doronshadmi
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No jsfisher, you simply can't get the notion of a pointless closed curve.
doronshadmi
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It is called determined cardinality, where the cardinality of an infinite collection is undetermined.
Simple as that.
doronshadmi
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As the minimal representations of the building-blocks of Complexity.
Can you do that?
It suits better the position that there is no ontological or metaphysical Infinity.
I one respect it agrees with you that there is no absolute all.
The word "all" is used in a realtivre sense only.
The mathematical concept you find abhorant because Infinity must be pure is that we can speak in terms of relative infinities that are relatively complete.
A set can be complete relative to the class of objects which defines it.
But I realize you try to speak of the essense of a set as not relative to a class or a property, but in terms of how its an interaction of the absolute all and the absolute none.
Which is of course different from the philosophical tradition behind zen, that has no such ontological building blocks.
jsfisher
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Prove me wrong, then. Define something, define one of these terms you misuse so arbitrarily.
doronshadmi
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A set is a collection of distinct elements, whether the number of classes is less or equal to the number of the elements of a given collection.
Since this is the case, all we care is the number of the elements, where class has no significance.
From this general view, only quantity matters, where in the case of a finite quantity any arbitrary given element of some collection is both a beginning AND an end of that collection of distinct elements, and we get a determined cardinality.
This is not the case with an infinite collection because no arbitrary given element of that collection is both a beginning AND an end of that collection of distinct elements, and we get an undetermined cardinality.
doronshadmi
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A pointless closed curve.
Ok, give us the definition for that.
doronshadmi
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It is the definition: "a pointless closed curve"
Your inability to get http://www.internationalskeptics.com/forums/showpost.php?p=5509335&postcount=8014 is your problem.
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No, it is your inabilty to understand English words; in this case, "definition".
doronshadmi
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In the case that you still do not get it, by closed curve I mean any closed form.
In examples 1,2,3 below we can see that there is more than a one closed version for cardinality 2,3,4 along a given closed form (you can play by yourself and find the closed versions for cardinalities 5,6,7,8 … etc.):
It is clearly understood that that there is no closed version (in the sense that any arbitrary point is both a beginning AND an end) for infinite collection of points.
In examples 1,2,3 below we can see that there is more than a one closed version for cardinality 2,3,4 along a given closed form (you can play by yourself and find the closed versions for cardinalities 5,6,7,8 … etc.):
It is clearly understood that that there is no closed version (in the sense that any arbitrary point is both a beginning AND an end) for infinite collection of points.
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ddt
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Yep. A definition defines something in other (more primitive) terms. Say:
"An A is a B which is also a C and has D".
But I have the idea that trying to explain this to you is as pointless as this whole thread. You're not here to listen to anything we say.
Well, those pictures are interesting. I'll leave it to the mathematically qualified to comment in more detail. It does surprise me that you are visiting the points on the circle in different orders, which suggests you are ignoring the curve itself.
Regardless of that, it's still not a definition.
The Man
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Again patently false, comparing X with Y places no resections on a collection and you have demonstrated no such restriction. Again you simply claiming something as part of your notions restrict only you and your notions. So claiming that “if the collection is infinite than X and Y are not compared” makes your OM restricted to making comparative assertion about finite collections only. This also belies your pervious statements about any element being a beginning of an infinite collection. You now assert that you can make no claims as to whether some infinite collection has a beginning as that would be comparison between X (beginning element) and Y (not beginning element). Once again Doron the greatest opposition to your notions is simply you, in expressing those notions.
doronshadmi
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doronshadmi
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No The Man,
X is a beginning but not an end if the collection is infinite.
All you have to do is to grasp http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152.
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The Man
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Then you can not claim it is an "infinite collection" as that would constitute your determining it to be at least not a finite collection. Infinite is a determination much as you would like to deliberately not to accept it as one. If your cardinality is in fact “undetermined” then it could just as well be finite as well as infinite. Once again your deliberate ignorance places restrictions on you and your notions only.
The Man
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I said nothing about "an end if the collection is infinite", put your strawman away. All you have to do is to grasp that determining "X is a beginning" is a comparative assertion with Y as not the beginning. As you claim you can not compare "X and Y" in your infinite collection you are asserting absolutely no basis to claims "X is a beginning" in just your own notions about an infinite collection.
doronshadmi
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http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152 clearly shows that X is a beginning AND an end point only if the collection is finite.
If the collection is infinite then X is a beginning-only point exactly because no Y is comparable with it (if it was true that Y is comparable with X, then X was both a beginning AND an and of the given infinite collection).
EDIT: You do not understand that each time that you compare Y (which is not X) with X, you get a closed form of finite amount of points.
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