Deeper than primes

[epix]

In "A = A" expression, "=" represents the observer and "A" represents the observed.

I still remember those times when '=' used to be "equals to" and we knew that both A's were identical to each other. Today, '=' is an "observer" that observes both A's. '1 + 1 observes' anything that comes after, like 3, 20, 1914, 1939, 2012 and so on.

 

[epix]

(please read http://www.scribd.com/doc/16542245/OMPT page 16).

Reading without understanding lacks purpose, and the purpose of the text suggested to read had to be implied. Your text issues several warning signs not to spend to much time reading, but otherwise it appears to be far more coherent than the hybrids that accumulate in your posts.

The increase in the engine power demands changes in the transmission design, as much as the processor power demands changes in the bus design. And so you have published your idea that relates to that. Why do you stress some "new thinking" is a mystery. Just leave this to the folks who will read your organic ways to bridge gaps and find it worth to implement. That's about it.

For the "other guy":

The solution is "doRon" -- smack in the middle. The bridging is symbolized in the text by the underscore; elements are symbolized by dots. That means the basic connection is ._. (dot, line, dot.) That creates the congruent complement: {doRon}=={moRse}, coz ._. is assigned to letter R in the Morse code. That should fix the gap between the L and Z arrays, right?

 

[doronshadmi]

C.N.0 suffers from circular reasoning,

No, "=" and "A" are different things that are related to each other without derive from each other, nothing is circular here.

 

[doronshadmi]

Let us use the empty set in order to define the concept "magnitude of existence".

Definition A: That has no successor has "the maximal magnitude of existence".

Definition B: That has no predecessor has "the minimal magnitude of existence".

The current scientific method, which developed since the 17th century, states that the researcher must be omitted form the research environment, in order to avoid results that are influenced by subjective tendencies of the researcher. It must be stressed that Aristotle determined 4 causes that sands at the basis of any existing thing, which are:

1) The material cause (from what material a given thing is made?).

2) The efficient cause (what are the natural forces that change a given thing?)

3) The formal cause (what is the "blueprint" in once mind that has an influence on a given thing?)

4) The final cause (what is the final goal in once mind, that has an influence on a given thing?)

The current scientific method uses only causes (1) and (2), in order to avoid any researcher's subjective influence on the result.

A question: Is it possible to return the researcher to the research environment and also avoid his\her subjective influence of the results?

My answer: I think that it is can be done if the "researcher" returns to the research environment as a general concept.

Let us use definitions A and B in order to demonstrate this notion.

{} describes the "researcher" in terms of definition A where what is between {} is the "researched" in terms of definition B (known also as "emptiness").

The outer "{""}" of {{}} describes the "researcher" in terms of definition A, where the inner "{""}" of {{}} describes the "researched" in terms of the model of the "researcher" that his\her "researched" subject is "emptiness".

At {{}} case "the magnitude of existence" of the "researched" is greater than "emptiness" (it has a predecessor) and smaller than the "researcher" (it has a successor).

Whether a non-empty collection is finite or infinite, it has both predecessor ("emptiness") AND successor ("researcher").

Anything that has both predecessor ("emptiness") AND successor ("researcher"), can't be reduced to "emptiness" AND can't be extended to "researcher". Because of this reason any given infinite collection can't have an exact Magnitude that is described by Cardinality.

If we symbolize these notions then: 0 < x < ∞, where ∞ represents the "the maximal magnitude of existence"("researcher") , 0 represents "the minimal magnitude of existence" ("emptiness"), and x represents "the magnitude of existence" that is > "emptiness" AND < "researcher" (any non-empty collection, whether it is finite or infinite).

By carefully research "the magnitude of existence" of an infinite collection, it is concluded that the universal quantifier "for all" has no meaning, because the accurate "magnitude of existence" of any given infinite collection can't be satisfied ( x < ∞). On the contrary, the universal quantifier "for all" has a meaning in the case of finite collections, because given any member of a finite collection it is defined as its final element, which in turn provides the accurate "magnitude of existence" that is described by an accurate Cardinality (A finite collection does not converge and does not diverge, which is a property that enables to determine its accurate cardinality).

In other words, if x is the cardinality of an infinite collection then x < ∞ prevents it accurate value.

Since the cardinality of any given infinite collection is inaccurate, then the 1-1 correspondence technique can't be used to determine any meaningful thing about the cardinality of such collections.

Furthermore, the Contor's diagonal upon decimal representation of irrational numbers, actually proves that it is impossible to determine the accurate value of x if x is related to an infinite collection.

Moreover, the ability to define a 1-1 correspondence between the natural numbers and a proper subset of them is a direct result of the impossibility to define the accurate cardinality of an infinite collection.

I wish to add that Russell's paradox does not hold that has cardinality ∞ can't be identical to any of its members, because any given member has at most x "magnitude of existence" and x < ∞ .

 

[The Man]

And yet the observed is not identical to the observer, otherwise there is no observation.

Simply nonsense

For example:

The observer is represented by the outer "{" "}", where the observed is represented by the internal "{""}", of observation "{{}}".

You are still just fixated on a particular representation of the members of a set which involves brackets.

In "A = A" expression, "=" represents the observer and "A" represents the observed.

Just your ‘relation/element’ dichotomy renamed.

This difference is known only if the observer gets its existence independently of any observed concept exactly as the empty set exists independently of its contents (it is not identical to emptiness).

Once again the empty set does not exist “independently of its contents” it is specifically defined as, and thus dependent on, having no members.

{} means that the observer exists independently of the observed (existence without thoughts).

No it doesn’t, it just represents the empty set.

{{}} means that the observer observes the concept of the empty set (a thought about {}, which is not identical to the observer (the outer "{""}")).

Actually it just represents a set whose only member is the empty set.

{{{}}} means the the observer observes the concept of non-empty set (a thought about {{}}, which is not identical to the observer (the outer "{""}")).

It just represents a set whose only member is set whose only member is the empty set

There is also a level that is beyond the observer, such that it is un-marked even as {}.

By using an analogy I call this level "The trunk", where the outer "{""}" is its Non-local aspect and the inner "{""}" is its Local aspect.

Non-locality and Locality are derive from the trunk but they are not derive from each other.

Because of this independency, thoughts are shareable among observers, and the mathematical science is a formal framework, which shares thoughts among observers, such that both the observer and the observed are independent and significant factors of that science, where the un-marked (un-manifested, if you will) is their origin.

Again, simply nonsense.

 

[The Man]

Observation is a result of the linkages among the observer and the observed.

So? The observer is already ‘linked’ to itself even when not ‘observing’ itself.

If the observer and the observed are identical, then there is no observation, and the expression "under observation" is false.

Simply nonsense.

Again, if there is no difference between the observer and the observed, then there is no observation.

Again simply nonsense.

In other words, Observation is at least {{}}, where the observer is the outer "{""}" and the observed is the inner "{""}", where the observer and the observed are derive from the un-manifested, and they do not derive from each other.

You are deliberately conflating a representation of a set whose only member is the empty set with some “un-manifested” dichotomistic nonsense that most likely can to you during some TM.

Because of this independency, the observer exists independently of the observed (existence without thoughts, that is notated as {}, exactly as the empty set exists independently of its contents (it is not identical to emptiness)), and if the observer is observed, then the observed is not the observer (we have an observer that observes itself as an observer without thoughts, which is a thought, and this case is notated as {{}}, which is different than {}, which is the observer without thoughts).

Doron this was nonsense before, it is still nonsense now and it will continue to be nonsense no matter how many times you repeat it. Has the thought never occurred to you that your “direct perception” and whatever thoughts that might have come to you during some TM were just nonsense?

 

[doronshadmi]

So? The observer is already ‘linked’ to itself even when not ‘observing’ itself.

Some problems to distinguish between Observer and Observation, The Man?

Once again the empty set does not exist “independently of its contents” it is specifically defined as, and thus dependent on, having no members.

Once again you can't distinguish between "defined by or as" and "identical to". After all flat-land is all you get, nothing has been changed all along this thread.


Here is more stuff that can't be comprehended from flat-land: http://www.internationalskeptics.com/forums/showpost.php?p=6347415&postcount=11584 .

 

[The Man]

Let us use the empty set in order to define the concept "magnitude of existence".

Definition A: That has no successor has "the maximal magnitude of existence".

Definition B: That has no successor has "the minimal magnitude of existence".

Both of these purported ‘Definitions’ specifically invoke your “concept "magnitude of existence", they do not define it. Also they give the same conditional reference “has no successor” to both your “maximal magnitude of existence” and “minimal magnitude of existence”.

The current scientific method, which developed since the 17th century, states that the researcher must be omitted form the research environment, in order to avoid results that are influenced by subjective tendencies of the researcher. It must be stressed that Aristotle determined 4 causes that sands at the basis of any existing thing, which are:

1) The material cause (from what material a given thing is made?).

2) The efficient cause (what are the natural forces that change a given thing?)

3) The formal cause (what is the "blueprint" in once mind that has an influence on a given thing?)

4) The final cause (what is the final goal in once mind, that has an influence on a given thing?)

The current scientific method uses only causes (1) and (2), in order to avoid any researcher's subjective influence on the result.

No Doron, we also use double blind protocols, control samples, peer review and independent repeatability to address the subjective aspects of some particular researcher.

A question: Is it possible to return the researcher the research environment and also avoid his\her subjective influence of the results?

Doron the researcher has never left the research environment, only the bias they might bring with them has been force out (under proper protocols).

My answer: I think that it is can be done if the "researcher" returns to the research environment as a general concept.

Let us use definitions A and B in order to demonstrate this notion.

{} describes the "researcher" in terms of definition A where what between {} is the "researched" in terms of definition B (known also as "emptiness").

The outer "{""}" of {{}} describes the "researcher" in terms of definition A, where the inner "{""}" of {{}} describes the "researched" in terms of the model of the "researcher" that his\her "researched" subject is "emptiness".

At {{}} case "the magnitude of existence" of the "researched" is greater than "emptiness" (it has predecessor) and smaller than the "researcher" (it has a successor).

Please pay attention where a non-empty collection is finite or infinite, it has both predecessor ("emptiness") AND successor ("researcher").

Now your just conflating a particular notation of a set with a "researcher" and the "researched"

Anything that has both predecessor ("emptiness") AND successor ("researcher"), can't be reduced to "emptiness" AND can't be extended to "researcher". Because of this reason any given infinite collection can't have an exact Magnitude that is described by Cardinality.

Again simply nonsense.

If we symbolize these notions then: 0 < x < ∞, where ∞ represents the "the maximal magnitude of existence"("researcher") , 0 represents "the minimal magnitude of existence" ("emptiness"), and x represents "the magnitude of existence" that is > "emptiness" AND < "researcher" (any non-empty collection, whether it is finite or infinite).

This still does not define what you mean by this “magnitude of existence” you refer to or how you determine its “magnitude” or “existence”

By carefully research "the magnitude of existence" of an infinite collection, it is concluded that the universal quantifier "for all", has no meaning because the accurate "magnitude of existence" of any given infinite collection can't be satisfied ( x < ∞). On the contrary, the universal quantifier "for all" has meaning in the case of finite collections, because given any member of a finite collection it is defined as its final element, which in turn provides the accurate "magnitude of existence" that is described by an accurate Cardinality.

Doron just making up crap does not constitute “carefully research "the magnitude of existence"”. Again what is this “magnitude of existence” you refer to? Your above assertions seem to indicate that it is just the cardinality of a set.

Doron if your "magnitude of existence" “can't be satisfied” as you claim, then that is just your problem.

In other words, if x is the cardinality of an infinite collection then x < ∞ prevents it accurate value.

In other words you can’t show that an infinite set is incomplete as you have claimed before?

Since the cardinality of any given infinite collection is inaccurate, then the 1-1 correspondence technique can't be used to determine any meaningful thing about the cardinality of such collections.

“inaccurate”? By how much?

Furthermore, the Contor's diagonal upon decimal representation of irrational numbers, actually proves that it is impossible to determine the accurate value of x if x is related to an infinite collection.

You’re not familiar with meaning of the word “accurate” are you?

Moreover, the ability to define a 1-1 correspondence between the natural numbers and a proper subset of them is a direct result of the impossibility to define the accurate cardinality of an infinite collection.

No Doron it just shows that they are accurately (to a 1-1 correspondence) the same size.

I wish to add that Russell's paradox does not hold that has cardinality ∞ can't be identical to any of its members, because any given member has at most x "magnitude of existence" and x < ∞

Really, so what is the maximum cardinality “any of its members” can have?

If you can cite a maximum, why that particular maximum?

 

[The Man]

Some problems to distinguish between Observer and Observation, The Man?

Nope, evidently you just have some problems distinguishing between the observed and an observation, Doron.

Once again you can't distinguish between "defined by or as" and "identical to". After all flat-land is all you get, nothing has been changed all along this thread.

Once again that is still just your nonsensical claim and not matter how many times you try to ascribe it to someone else it still remains entirely yours as does your fiat-land.

Here is more stuff that can't be comprehended from flat-land: http://www.internationalskeptics.com/forums/showpost.php?p=6347415&postcount=11584 .

That post, as usual Doron, simply shows the problems in comprehension to be just yours.

 

[epix]

If the observer and the observed are identical, then there is no observation, and the expression "under observation" is false.

A contradiction can be observed only in structures possessing a certain amount of coherency. Sometimes we get lucky:

a) We have an observer A and the relationship symbol '='

b) Observer and the observed are identical: A = A.

Apocalypse1: You call '=' an "observer" and a "non-local aspect." Since 'A' and "=" are different, they both cannot be observers.

Apocalypse2: If the observer and the observed are identical, then there must be '=' between them to define the relationship: A = A. Since '=' is also an observer by Organic Mathematics, then the observer is present smack in the middle of the A=A expression, and that means both A's are under observation, which contradicts your statement that there is no observation when A = A.

 

[doronshadmi]

A = A. Since '=' is also an observer by Organic Mathematics, then the observer is present smack in the middle of the A=A expression, and that means both A's are under observation, which contradicts your statement that there is no observation when A = A.

You have missed my claim.

My claim is that "=" and "A" are not the same thing ("=" represents the observer and "A" represents the observed) and because of this difference observation is possible.

 

[zooterkin]

A contradiction can be observed only in structures possessing a certain amount of coherency.

Oh, I don't know. Doron seems to produce plenty.

 

[doronshadmi]

Also they give the same conditional reference “has no successor” to both your “maximal magnitude of existence” and “minimal magnitude of existence”.

It was corrected during your reply.

But the "important" thing here that you read reply like a copy machine, without realize that it is a typo, and take this trivial typo, which anyone (but you) can immediately understand as a typo mistake, and use it as one of your arguments against OM.

No Doron, we also use double blind protocols, control samples, peer review and independent repeatability to address the subjective aspects of some particular researcher.

You mean to separate the subjective aspect of some particular researcher, from his/her scientific work (in this case the opinions, beliefs, and other subjective aspects of the researcher are clearly separated from his/her scientific research, or in other words, you reinforce my claim about the subjective-only approach of the modern science about the concept of the "researcher")

OM changes this subjective-only approach about the concept of the "researcher", by use it as a non-personal (general) concept, and the outer "{""}" of the concept of set, is one of the sufficient ways to express the non-personal (general) concept of the "researcher", which can't be grasped in flat-land, where the "researcher" is still a subjective-only concept.

Now your just conflating a particular notation of a set with a "researcher" and the "researched"

No, I use "A" or "{""}" to express the notion of sets, and in both cases "that has no successor" (the non-personal aspect of the "researcher") is involved, which is something that can't be comprehended from flat-land.

 

[doronshadmi]

Oh, I don't know. Doron seems to produce plenty.

You don't no also this.

 

[doronshadmi]

Nope, evidently you just have some problems distinguishing between the observed and an observation, Doron.

Evidently you have no clue what really observation is, The Man.

The reason: It can't be known from flat-land.

 

[doronshadmi]

Doron if your "magnitude of existence" “can't be satisfied” as you claim, then that is just your problem.

"Can't be satisfied" is a normal property of any framework, which is strong enough to deal with Arithmetic, so please give me a break (go learn Godel's incompleteness theorems).

 

[doronshadmi]

In other words, if x is the cardinality of an infinite collection then x < ∞ prevents it(s) accurate value.

In other words you can’t show that an infinite set is incomplete as you have claimed before?

No, in other words you do not understand that an inaccurate Cardinality means that the given collection is incomplete (its exact magnitude can't be satisfied).

 

[doronshadmi]

“inaccurate”? By how much?

Do you want the inaccurate or accurate value?

The Man, since you play this kind of game about infinite collections, then please tell us what is exactly the result of aleph1 - aleph0 ?

 

[jsfisher]

Do you want the inaccurate or accurate value?

The Man, since you play this kind of game about infinite collections, then please tell us what is exactly the result of aleph1 - aleph0 ?

Ok, so doesn't understand the term, inaccurate, either.

 

[doronshadmi]

Ok, so doesn't understand the term, inaccurate, either.

Exactly as you don't grasp a non-local number like 0.999...[base 10] (an example of infinite interpolation) and can't grasp that there is no definable result to aleph1 - aleph0 ( http://books.google.com/books?id=Jd...q=Cardinal arithmetic and subtraction&f=false )