Deeper than primes

[doronshadmi]

Once again you simply misrepresent the notion of cardinality.

Once again you ignore Complexity as inspirable property of the ability to measure Cardinality, and as a result you artificially limit this measurement to the first level of the existence of each measured member, as if it is the one and only one ability to measure it.

All ignorance is conditional, specificaly upon that which is being ignored and why it can be ignored in some specifc consideration.

The consideration to ignore something is meaningless if you do not first have a wider view of the researched subject. This is not the case with the standard approach about Cardinality, that has no understanding of the Complexity of the measured entities.

Incomplete proportions?

No, proportions are invariant property that is not changed by the amount of infinitely many elements, where this amount is not fixed (like a finite amount) and therefore incomplete (no one of the considered elements is a finite element of the considered collection).

Are you forgetting that you notion of “any collection” includes “the stage”? remember…

The stage is not one of the players, and this is where you fail to understand stage\players linkage.

If any such “collection” “has a successor” then so too does that particular “stage” you used “to collect players”.

Again you look at the stage as one of the players.

Well the further investigation on this thread continues to demonstrate your notions as both inconsistent and invalid, particularly when addressing that “standard approach”.

Further reading of your replies demonstrated that you can’t get the difference between stage and player.

 

[doronshadmi]

... until you can establish what you specifically mean by “existence” or “exists” your questions simply remain without meaning.

The Man,

You reject the notion that a line is made by points.

I agree with you, and in that case the existence of a line is independent of the existence of points.

An existing thing has some properties that enable us to recognize it, and if a line is not made of points then it may have some properties that are different than a point.

Please see http://www.internationalskeptics.com/forums/showpost.php?p=5130111&postcount=5994 for better understanding of this subject.

 

[Apathia]

Dear Apathia,

When we close things under definitions we have to ask ourselves how they are still related to each other.

But doesn't definition entail relationship.
When I assign an identity to an individual (The kind of identity as an instance of a certain class of things) that sets out a relationship to that individual and the other individuals of its class.

So a definition does not close things to relation.
Unless we define in such a way as to exclude from other relationships.

Of course your program is not about living without definition, boundaries, or fences, but to insure that there is some kind of openess.
An analogy you might use comes from Flatland.
In the 2-dimensional world there is a square. It's closed on all sides.
But from the perspective of a third dimension, all its contents are open to view.

I have some follow up on my previous post, but I don't have time this morning.
Later.

 

[doronshadmi]

But doesn't definition entail relationship.
When I assign an identity to an individual (The kind of identity as an instance of a certain class of things) that sets out a relationship to that individual and the other individuals of its class.

So a definition does not close things to relation.
Unless we define in such a way as to exclude from other relationships.

Of course your program is not about living without definition, boundaries, or fences, but to insure that there is some kind of openess.
An analogy you might use comes from Flatland.
In the 2-dimensional world there is a square. It's closed on all sides.
But from the perspective of a third dimension, all its contents are open to view.

I have some follow up on my previous post, but I don't have time this morning.
Later.

If definition is the tendency to limit things, then relation is the tendency to connect things.

Both tendencies are factors of a one framework.

 

[Apathia]

If definition is the tendency to limit things, then relation is the tendency to connect things.

Both tendencies are factors of a one framework.

They are inseperable.
Where you get one you always find the other.
Like the peaks and troughs of waves, remember?

 

[The Man]

Once again you ignore Complexity as inspirable property of the ability to measure Cardinality, and as a result you artificially limit this measurement to the first level of the existence of each measured member, as if it is the one and only one ability to measure it.

Once again you simply misrepresent the concept of cardinality. If you want your Doronality to measure what you refer to as “Complexity” then you need to define what you are referring to as “Complexity” and how you intend to measure it.

As an example my car is a complex collection of parts, however simply collecting all the relevant parts does not result in the same complexity of my car. Complexity depends on the relationships of the members not simply a collection of those members.

The consideration to ignore something is meaningless if you do not first have a wider view of the researched subject. This is not the case with the standard approach about Cardinality, that has no understanding of the Complexity of the measured entities.

As noted above that is because complexity deals with relationships not simple membership as cardinality does. Your continued ignorance of that distinction between those two does not make them, well, indistinguishable.

No, proportions are invariant property that is not changed by the amount of infinitely many elements, where this amount is not fixed (like a finite amount) and therefore incomplete (no one of the considered elements is a finite element of the considered collection).

Thus incomplete proportions.

The stage is not one of the players, and this is where you fail to understand stage\players linkage.

You have noted that “linkage” as the “collection” requiring both your “players” and your “stage”. Thus any “successor” to that “collection” is a “successor” to those “players” and that “stage”. Once again the failure is simply yours, even to understand your own assertions.

Again you look at the stage as one of the players.





Further reading of your replies demonstrated that you can’t get the difference between stage and player.

Again you demonstrate your failure to understand your own asserted “linkage”.

 

[The Man]

The Man,

You reject the notion that a line is made by points.

Again a line segment is defined by points.

I agree with you, and in that case the existence of a line is independent of the existence of points.

No you do not, unless you agree that a line segment is defined by points and thus is not “independent” of those points.

An existing thing has some properties that enable us to recognize it, and if a line is not made of points then it may have some properties that are different than a point.

Defined by does not mean “made of”, but it does mean that the definition of a line segment is not independent from a definition of those defining points. Likewise that a line segment is defined by points does not limit the properties of a line segment to those of a point.

Please see http://www.internationalskeptics.com/forums/showpost.php?p=5130111&postcount=5994 for better understanding of this subject.

Seen it already and it simply displays your usual self inconsistent “understanding” .

 

[doronshadmi]

They are inseperable.
Where you get one you always find the other.
Like the peaks and troughs of waves, remember?

Locality (limitation) and Non-locality (non-limitation) existence are mutually independent of each other like two axioms, yet they define a realm, which is the offspring of the their linkage and under this realm any existing thing is not totally local and not totally non-local, or in other words: they are inseparable under linkage.

 

[doronshadmi]

Once again you simply misrepresent the concept of cardinality. If you want your Doronality to measure what you refer to as “Complexity” then you need to define what you are referring to as “Complexity” and how you intend to measure it.

As an example my car is a complex collection of parts, however simply collecting all the relevant parts does not result in the same complexity of my car. Complexity depends on the relationships of the members not simply a collection of those members.

We have no argue about the inability of Cardinality to represent Complexity ( see http://www.internationalskeptics.com/forums/showpost.php?p=5016057&postcount=5824 ).

I am talking about the cardinality of the things of a given collection including the number of the level of connections within a given thing. By this approach Cardinality is both parts+levels.

Standard Math cares only about the first level of the considered things, where OM can also consider the levels as a legitimated value of Cardinality’s measurement.

Furthermore, even by Stndard Math the Cardinality of the first-level is based on the ability to distinguish between the levels of each measured thing.

As noted above that is because complexity deals with relationships not simple membership as cardinality does. Your continued ignorance of that distinction between those two does not make them, well, indistinguishable.

No The Man,

You simply reduce membership to first-level measurement and as a result you get a partial measured realm, but this is your must have limitation, not mine.

Thus incomplete proportions.

No, proportion is an invariant property even if infinitely many elements are involved, where no element is final element of the non-finite collection.

You have noted that “linkage” as the “collection” requiring both your “players” and your “stage”. Thus any “successor” to that “collection” is a “successor” to those “players” and that “stage”. Once again the failure is simply yours, even to understand your own assertions.

No, the result of the linkage (which is a collection) has predecessor and successor.

Nothing (the empty stage) has no predecessor and the stage has no successor.

The existence of any player is between nothing and stage.

Again you demonstrate your failure to understand your own asserted “linkage”.

Again you demonstrate that you do not get player's existence.

 

[doronshadmi]

Again a line segment is defined by points.

A line segment is partially limited by points because it both belong and does not belong to them.

No you do not, unless you agree that a line segment is defined by points and thus is not “independent” of those points.

If we are talking about the existence of a line segment, then a line segment is independent of the existence of the points because it is non-local (can belong AND not to belong to some domain) .

Defined by does not mean “made of”, but it does mean that the definition of a line segment is not independent from a definition of those defining points. Likewise that a line segment is defined by points does not limit the properties of a line segment to those of a point.

I agree with you. A line that is partially limited by points, is not limited (local) like a point. As I show in http://www.internationalskeptics.com/forums/showpost.php?p=5130111&postcount=5994, definition does not deal with the existence of things.

Form the level of existence. a line segment's existence is independent of the existence of points because a line segment has also non-local existence and a point has only local existence (it must be in a one state of membership that is: belong XOR not belong).

For example: the point between the domains belongs XOR does not belong to the them, where the line belongs AND does not belong to the two domains:

+------+
|     \|
|      \
|      |\
+------+-\----+
       |  \   |
       |      |
       |      |
       +------+

Seen it already and it simply displays your usual self inconsistent “understanding” .

Please provide more details about your argument here.

 

[Apathia]

Locality (limitation) and Non-locality (non-limitation) existence are mutually independent of each other like two axioms, yet they define a realm, which is the offspring of the their linkage and under this realm any existing thing is not totally local and not totally non-local, or is other words: they are inseparable under linkage.

This is, of course, the unique and crucial feature of your Organic Mathematics.
Two linguistic concepts are made fundamental principles in a metaphysical or almost Platonic existence outside language and independent of each other.

An assumption in Mathematics for the last two millennia is that these are not entities outside of language. Arising in mathematical discourse, they have a more symbiotic relationship and are able to interpenetrate each other.
For example, since the Finite and the Infinite are not mutually independent, metaphysical entities, the infinite can be found nestled in the finite as it is limits, convergences, and fractals.

This entails paradoxes you'd like to save mathematics from. But suffering and coping with them may have destroyed the dreams of Fomalists, but has made mathematics a very remarkable tool kit that can do things your OM is never going to be able to do because it disallows so much of the foundation of analysis (unless you wink your eye and let the mathematicians play with their serial numbers in their own little realm of expression.).

"The set of all whole numbers between 2 and 4"
The traditional mathematician wants to say that it is complete in containing only the number 3.
You want to tell him he has limited reality, for in reality the set contains no end of numbers. (or at least all the elements of the Redundancy/Uncertainty linkage tree.)
You say he's limiting himself by missing and not acknowledging what's there.
Non-Locality, as you see it is the totality of all the numbers ever and everywhere present.

I said somewhere before that traditional mathematics doesn't live as if there were no Non-Locality. It's just that Non-Locality is not an entity full of content but an empty place holder or template upon which temporary sets come and go.
If a mathematician wants to exclude or include, she defines a new set. And with each new set there is a new quantity created. The quantity isn't prior to the definition of the set.
If I want to include Barak Obama and George Bush in the same set, I don't use the race set or the Democrat set and assert that George Bush is also black or a democrat, but I use a classification that naturally includes both. Human, Presidents, Americans.

This is the utility of mathematics. It assumes the Non-Local is not a metaphysical entity full of quantity content, but an empty tablet upon which everything can be drawn and erased.

You tell the mathematician that he limits by excluding what is already there.
But he could turn around and tell you, you limit by trying to cram in what's not there.

I understand. You want to liberate mathematics from what you see as cages.
Meanwhile the mathematicians aren't seeing them as cages but creations and temporary dwellings.

Consider for a moment that you may have created your own iron ball and chain.

 

[!Kaggen]

This is, of course, the unique and crucial feature of your Organic Mathematics.
Two linguistic concepts are made fundamental principles in a metaphysical or almost Platonic existence outside language and independent of each other.

An assumption in Mathematics for the last two millennia is that these are not entities outside of language. Arising in mathematical discourse, they have a more symbiotic relationship and are able to interpenetrate each other.
For example, since the Finite and the Infinite are not mutually independent, metaphysical entities, the infinite can be found nestled in the finite as it is limits, convergences, and fractals.

This entails paradoxes you'd like to save mathematics from. But suffering and coping with them may have destroyed the dreams of Fomalists, but has made mathematics a very remarkable tool kit that can do things your OM is never going to be able to do because it disallows so much of the foundation of analysis (unless you wink your eye and let the mathematicians play with their serial numbers in their own little realm of expression.).

"The set of all whole numbers between 2 and 4"
The traditional mathematician wants to say that it is complete in containing only the number 3.
You want to tell him he has limited reality, for in reality the set contains no end of numbers. (or at least all the elements of the Redundancy/Uncertainty linkage tree.)
You say he's limiting himself by missing and not acknowledging what's there.
Non-Locality, as you see it is the totality of all the numbers ever and everywhere present.

I said somewhere before that traditional mathematics doesn't live as if there were no Non-Locality. It's just that Non-Locality is not an entity full of content but an empty place holder or template upon which temporary sets come and go.
If a mathematician wants to exclude or include, she defines a new set. And with each new set there is a new quantity created. The quantity isn't prior to the definition of the set.
If I want to include Barak Obama and George Bush in the same set, I don't use the race set or the Democrat set and assert that George Bush is also black or a democrat, but I use a classification that naturally includes both. Human, Presidents, Americans.

This is the utility of mathematics. It assumes the Non-Local is not a metaphysical entity full of quantity content, but an empty tablet upon which everything can be drawn and erased.

You tell the mathematician that he limits by excluding what is already there.
But he could turn around and tell you, you limit by trying to cram in what's not there.

I understand. You want to liberate mathematics from what you see as cages.
Meanwhile the mathematicians aren't seeing them as cages but creations and temporary dwellings. Consider for a moment that you may have created your own iron ball and chain.

I am not so sure about that.
The mathematicians in these threads
http://www.internationalskeptics.com/forums/showthread.php?t=151854
http://www.internationalskeptics.com/forums/showthread.php?t=152910
are pretty adamant that mathematics is not an invention.

 

[The Man]

We have no argue about the inability of Cardinality to represent Complexity ( see http://www.internationalskeptics.com/forums/showpost.php?p=5016057&postcount=5824 ).

I am talking about the cardinality of the things of a given collection including the number of the level of connections within a given thing. By this approach Cardinality is both parts+levels.

Standard Math cares only about the first level of the considered things, where OM can also consider the levels as a legitimated value of Cardinality’s measurement.

Furthermore, even by Stndard Math the Cardinality of the first-level is based on the ability to distinguish between the levels of each measured thing.

Once again you simply misrepresent the notion of cardinality, as your post you cited demonstrates. That cardinality does not specifically itself deal with complexity, does not mean that it can not be used to represent complexity in certain circumstances, it simply depends on the set being considered.

Using my car as an example again: a set of all the parts for my car is the same whether those parts are assembled as my car or simply in a pile. Thus the difference in complexity between a pile of the same parts and my car is not apparent. However, a set containing the operations required to assemble those parts into a simple pile and another representing the operations needed to assemble those parts into my car would clearly demonstrate that my car is significantly more complex then simply a pile of the relevant parts. The point is that such comparison of complexity is due to the definition of the sets being examined and not in the notion of cardinality itself.

No The Man,

You simply reduce membership to first-level measurement and as a result you get a partial measured realm, but this is your must have limitation, not mine.

No Doron the limitation is specifically yours by you attempting to limit cardinality to your Doronality or as a measure of “existence” and “complexity”.

No, proportion is an invariant property even if infinitely many elements are involved, where no element is final element of the non-finite collection.

No, the result of the linkage (which is a collection) has predecessor and successor.

Nothing (the empty stage) has no predecessor and the stage has no successor.

Such an infinite set is closed under the operation of succession, meaning the successor to any member of that set is also a member of that set by the definition of that set. However, that collection itself can have a successor meaning it is a successor to the entire collection and not specifically any one element in that collection. Thus it is a successor to both your “players” (the members of the set) and your “stage” (the definition of that set which determines what constitutes a member) of that specific collection.

The existence of any player is between nothing and stage.



Again you demonstrate that you do not get player's existence.

Once again you depend upon the fact that your use of the word “existence” remains without any meaning given by you in this discussion.

 

[Apathia]

I am not so sure about that.
The mathematicians in these threads
http://www.internationalskeptics.com/forums/showthread.php?t=151854
http://www.internationalskeptics.com/forums/showthread.php?t=152910
are pretty adamant that mathematics is not an invention.

Well, in my inprecise context, I'm not addressing the same issue as they are.
Perhaps some of them would be more comfortable with Doron's insistance on Infinity as a metaphysical entity.

As far as I'm concerend, the development of mathematics is both a process of creation and discovery.

But all the mathalogs in the threads you reference, would more likely see a given set with it's quantity as a creation at the moment, as oppsed to being a permenant, metaphysical container with a fixed quantity of zero or infinity with any other quantity being a limitation of its metaphysical content.

 

[Apathia]

Well, in my inprecise context, I'm not addressing the same issue as they are.
Perhaps some of them would be more comfortable with Doron's insistance on Infinity as a metaphysical entity.

As far as I'm concerend, the development of mathematics is both a process of creation and discovery.

But all the mathalogs in the threads you reference, would more likely see a given set with it's quantity as a creation at the moment, as oppsed to being a permenant, metaphysical container with a fixed quantity of zero or infinity with any other quantity being a limitation of its metaphysical content.

I'm going to get into trouble with Doron about the above, because it is his insistance that no set can contain on completetion all of the infinity of numbers.
So asserting this, he gores on to assert that any given set is not complete because you can drop any other number into it, and they all belong to it in virtue of their Non-Locality.
So, the empty set contains no elements locally speaking but infinity non-locally speaking.

Yes, I know that contradicts the assertion that no set can be complete.

I suppose Doron will then parse a potential infinity as opposed to an absolute Infinity.

 

[The Man]

A line segment is partially limited by points because it both belong and does not belong to them.

Well this returns us to the already exacerbated discussion of closed and open intervals. That a closed interval includes the limits as members of that interval and an open one does not, in no way alters then fact that those are the de facto defined limits of that interval.

If we are talking about the existence of a line segment, then a line segment is independent of the existence of the points because it is non-local (can belong AND not to belong to some domain) .

There is that word “existence” again. Any chance of you giving your use of it any actual meaning anytime soon?

I agree with you. A line that is partially limited by points, is not limited (local) like a point. As I show in http://www.internationalskeptics.com/forums/showpost.php?p=5130111&postcount=5994,

No you do not agree with me. Claiming that you do agree with me and then giving a statement in direct opposition to what I said, simply demonstrates that you do not agree with me. A line segment is entirely limited by its endpoints, whether an interval describing that segment is open or closed.

definition does not deal with the existence of things.

Form the level of existence. a line segment's existence is independent of the existence of points because a line segment has also non-local existence and a point has only local existence (it must be in a one state of membership that is: belong XOR not belong).

As long as your use of the word “existence” remains undefined it continues to remain without any meaning in this discussion.

For example: the point between the domains belongs XOR does not belong to the them, where the line belongs AND does not belong to the two domains:

+------+
|     \|
|      \
|      |\
+------+-\----+
       |  \   |
       |      |
       |      |
       +------+

As apparently indicated by your representation a segment of that line does in fact “belong” to one domain and another segment of that line to the other “domain”. The third middle segment apparently “belongs” to nether domain. The point where the domains appear to intersect could belong to either or both depending on how those domains are defined. Your entire concept appears to based upon a simple lack of definition, but only in considerations that you specifically choose not to define.

Please provide more details about your argument here.

No problem, as I am sure it was readily obvious to everyone but you.

If we translate the word “definition” to Hebrew we get the word “hagdara”.

“hagdara” is based on the root g.d.r that is common with the Hebrew word “gader” .

The translation of the word “gader” to English is “fence”, where the abstract meaning in this case is “the thing that is used for limitation”.

By following this notion, a definition is a limitation of already existing thing that enables us to use it for our purpose.

By following this reasoning the current mathematical activity does not deal with the existence of things but with the possible manipulations of already existing things.

Here you specifically limit the meaning of “definition” to a singular application that suits your purpose, apply some equally limited and utterly false “reasoning” (as you call it) and assert that limitation as being something other then simply yours.

OM is a pre-definition framework because it deals with the existence of things.

From this pre-definition view a non-local thing has the property to belong AND not to belong to a given limitation (some domain) where a local thing has the property to belong XOR not to belong to a given limitation (some domain).

The minimal representation of Locality is a point and if it is used as a common thing for at least two different things, then it must belong to both of them.

This is not the case with a line, which can belong AND not to belong to these two different things, even if it is common for both of them, for example:

+------+
|     \|
|      \
|      |\
+------+-\----+
       |  \   |
       |      |
       |      |
       +------+

The linkage between Non-locality and Locality stands at the basis of the researchable mathematical entities.

Here you begin by claiming “OM is a pre-definition framework” which Apathia referred to as “oxymoronic“, I would refer to it as simply moronic and self-inconsistent. You then proceed to define the ‘properties’ “From this pre-definition view” and thus limitations of your “local” and “non-local” ’things’ required for your “pre-definition framework”. Your problem is clearly not with limitations in general, as you specifically limit your “atoms” to having no sub-elements and to not being “researchable“ independently. Your problem simply seems to be with limitations and definitions not specifically imposed by you, as the problems with your notions are specifically the limitations and definitions (what few there have been) you impose even just for yourself. The lack of self-consistency demonstrated by the above posts simply exemplifies such a lack of self-constancy as one of the major failures of your proposed OM notions.

 

[!Kaggen]

I'm going to get into trouble with Doron about the above, because it is his insistance that no set can contain on completetion all of the infinity of numbers.
So asserting this, he gores on to assert that any given set is not complete because you can drop any other number into it, and they all belong to it in virtue of their Non-Locality.
So, the empty set contains no elements locally speaking but infinity non-locally speaking.

Yes, I know that contradicts the assertion that no set can be complete.

I suppose Doron will then parse a potential infinity as opposed to an absolute Infinity.

I have said it before in this thread and by pm to Moshe Klein.
I believe Projective Geometry's conception of infinity is much more user friendly than what OM proposes as it is both potential and absolute due to the principle of duality. The problems of infinite measure/numbers are avoided since it is a fundamental non-metric geometry.

 

[The Man]

I said somewhere before that traditional mathematics doesn't live as if there were no Non-Locality. It's just that Non-Locality is not an entity full of content but an empty place holder or template upon which temporary sets come and go.
If a mathematician wants to exclude or include, she defines a new set. And with each new set there is a new quantity created. The quantity isn't prior to the definition of the set.
If I want to include Barak Obama and George Bush in the same set, I don't use the race set or the Democrat set and assert that George Bush is also black or a democrat, but I use a classification that naturally includes both. Human, Presidents, Americans.

Indeed correct Apathia and which gives mathematics both flexibility and a definitive nature that OM apparently lacks.

This is the utility of mathematics. It assumes the Non-Local is not a metaphysical entity full of quantity content, but an empty tablet upon which everything can be drawn and erased.

Well that is part of the problem Apathia, in mathematics as well as physics ‘Non-local’ has specific definitions depending upon the application. Doron’s OM simply uses that term in an indefinite fashion to represent his concept of that “empty tablet upon which everything can be drawn and erased”.

You tell the mathematician that he limits by excluding what is already there.
But he could turn around and tell you, you limit by trying to cram in what's not there.

I understand. You want to liberate mathematics from what you see as cages.
Meanwhile the mathematicians aren't seeing them as cages but creations and temporary dwellings.

Consider for a moment that you may have created your own iron ball and chain.

An excellent point Apathia, and Doron not wanting to be constrained by his own ball and chain simply results in his notions being self-inconsistent.

 

[Apathia]

I have said it before in this thread and by pm to Moshe Klein.
I believe Projective Geometry's conception of infinity is much more user friendly than what OM proposes as it is both potential and absolute due to the principle of duality. The problems of infinite measure/numbers are avoided since it is a fundamental non-metric geometry.

I feel you have a point there.
I say I feel, because I haven't thought through that perspective (so to speak).

 

[Apathia]

Well that is part of the problem Apathia, in mathematics as well as physics ‘Non-local’ has specific definitions depending upon the application. Doron’s OM simply uses that term in an indefinite fashion to represent his concept of that “empty tablet upon which everything can be drawn and erased”.

As usual we have in "non-locality" a term of a number of different usages.
What I'm trying to express myself is non-locality as not a meta-locality (as if seems Doron does), but an abscence of any fixed or absolute locality.