Deeper than primes

[epix]

A or B are non-composed things that have different qualities w.r.t each other.

If they are linked, then the result is a composed complexity.

If A and B cannot be linked, the condition is expressed as A, B. If A and B can be linked, then the condition is expressed as A B. If they are linked, the symbolic expression for the occassion is A_B, where '_' is the Hilderberg Line. Is it possible to prove or disprove the Hilderberg Conjecture?

 

[doronshadmi]

(Unfortunately, he usually insists on using examples which aren't atomic even within his very examples,.

Nope.

A line is an atomic element because no line is reducible into a point and still can be considered as a line.

Because of this simple fact, and the fact that a point is not nothing, a line is included NXOR excluded w.r.t a point (it is Non-local w.r.t it) and a point is included XOR excluded w.r.t a line (it is Local w.r.t it).

The line and the point are qualities that have to be generalized beyond the particular case of Metric space.

Only by this generalization one gets OM reasoning, which its result is a composed complexity that is derived from the Linkage among Non-local and Local aspects of the atomic self-state, which is un-manifested.

This diagram rigorously expresses exactly the same notion that is expressed by the string of symbols "Non-local\and Local Linkage":

 

[doronshadmi]

If A and B cannot be linked, the condition is expressed as A, B. If A and B can be linked, then the condition is expressed as A B. If they are linked, the symbolic expression for the occassion is A_B, where '_' is the Hilderberg Line. Is it possible to prove or disprove the Hilderberg Conjecture?

If A can't be linked with B, then the concept of Many, whether it is expressed by Letters or Words or Sentences or Paragraphs, or Pages or Chapters or Books or … is not expressed.

If there is a linkage, then the concept of Many (whether it is expressed by Letters or Words or Sentences or Paragraphs, or Pages or Chapters or Books or … ) is expressible.

So what you call Hilderberg Conjecture misses the generalization of the difference between A,B and A_B (the difference between One and Many).

 

[doronshadmi]

As for Mutual exclusion, A and ~A are different domains that are excluded w.r.t each other.

This difference is derived from the separate ID of each domain, which is possible because of the Independency aspect among A and ~A.

But this is only the Independence aspect among A and ~A.

The other aspect among A and ~A separate IDs is the Mutuality that enables the connection among A and ~A separate IDs.

In other words, Mutual exclusion is not less than Mutual-Independent framework, where Mutuality is its Non-local aspect and Independency is its Local aspect, exactly as shown by the following extended Venn-diagram:

A NXOR ~A or A XOR ~A are not less than Mutual-Independent framework, where A XOR ~A is focused on ID's independency and A NXOR ~A is focused on the Mutuality among A and ~A IDs.

People like The Man do not get the Mutual influence among different IDs, because they get only A, where ~A is A exclusion and therefore does not have its own ID.

This A-only limitation is called Local-only reasoning.

 

[epix]

Nope.

A line is an atomic element because no line is reducible into a point and still can be considered as a line.

The family of lines is divided on straight lines and curves. If a line is not a collection of points, then a tangent line cannot be drawn. Not only that, an area under such "irreducible" line cannot be computed.

Your pointless line is a useless abstract construct with no natural representation, but it can be considered as an exercise. You can create many strange abstract environments. They can be fun if you do it right.

 

[epix]

As for Mutual exclusion, A and ~A are different domains that are excluded w.r.t each other.

This difference is derived from the separate ID of each domain, which is possible because of the Independency aspect among A and ~A.

But this is only the Independence aspect among A and ~A.

The other aspect among A and ~A separate IDs is the Mutuality that enables the connection among A and ~A separate IDs.

In other words, Mutual exclusion is not less than Mutual-Independent framework, where Mutuality is its Non-local aspect and Independency is its Local aspect, exactly as shown by the following extended Venn-diagram:

[qimg]http://farm5.static.flickr.com/4077/4789944385_7e4d198597.jpg[/qimg]

A NXOR ~A or A XOR ~A are not less than Mutual-Independent framework, where A XOR ~A is focused on ID's independency and A NXOR ~A is focused on the Mutuality among A and ~A IDs.

People like The Man do not get the Mutual influence among different IDs, because they get only A, where ~A is A exclusion and therefore does not have its own ID.

This A-only limitation is called Local-only reasoning.

You are perfectly right about the A-only limitation. That's because A is a variable. If you attempt to assign non-abstract values to it, your construct falls apart.

 

[epix]

If A can't be linked with B, then the concept of Many, whether it is expressed by Letters or Words or Sentences or Paragraphs, or Pages or Chapters or Books or … is not expressed.

If there is a linkage, then the concept of Many (whether it is expressed by Letters or Words or Sentences or Paragraphs, or Pages or Chapters or Books or … ) is expressible.

So what you call Hilderberg Conjecture misses the generalization of the difference between A,B and A_B (the difference between One and Many).

I thought that your new concept would be able to handle the Hilderberg Conjecture, but it can't, coz your new concept includes the traditional perception of singular and plural. The generalization prevents indexing and so

Plural - Plural = Plural
Plural - Plural = 0
Plural - Plural = Singular

is true but not sufficient to prove the Hilderberg Conjecture.

 

[jsfisher]

A line is an atomic element because no line is reducible into a point and still can be considered as a line.

Excellent non sequitur! Well done.

Were a line atomic, then the line could not be divided into two half-lines or any number of line segments. That's what atomic means in this context: not able to be subdivided.

 

[zooterkin]

jsfisher

 

[jsfisher]

jsfisher

Thanks.

 

[The Man]

Nope.

You simply force "in" ("in the same domain", which is an inclusion-only approach) on the given framework, and as a result you get only B.

The given framework is not less than A and B domains w.r.t each other.

If A domain is "included NXOR excluded" w.r.t B domain, then A domain is (logically) Non-local w.r.t B domain.

If A domain is "included XOR excluded" w.r.t B domain, then A domain is (logically) Local w.r.t B domain.

As “excluded” was also clearly part of my statements you quoted “an inclusion-only approach” is again just one of your fantasies you are trying to “force” on anyone other than you.

Again…

This “w.r.t” nonsense of yours is still simply part of your endeavor, again apparently deliberately, not to be specific about the relationships you are considering. As a result you have invented this entire unspecific OM fantasy of yours. Evidently so that lack of specificity, at least to you, is not specifically yours.

 

[The Man]

Indeed, Happy Birthday jsfisher.

 

[doronshadmi]

Excellent non sequitur! Well done.

Were a line atomic, then the line could not be divided into two half-lines or any number of line segments. That's what atomic means in this context: not able to be subdivided.

Happy Birthday jsfisher.

A line segment is a composition of two kinds of atomic aspects, the Non-local aspect and the Local aspect.

 

[doronshadmi]

If a line is not a collection of points, then a tangent line cannot be drawn.

Nope.

A tangent line is a composition of two kinds or atomic aspects, the Non-local aspect and the Local aspect.

 

[doronshadmi]

You are perfectly right about the A-only limitation. That's because A is a variable. If you attempt to assign non-abstract values to it, your construct falls apart.

It is called free variable or a placeholder (a symbol that will later be replaced by some literal string) ( http://en.wikipedia.org/wiki/Free_variables_and_bound_variables ).

In other words, it is derived from Local notion.

 

[The Man]

The Man, a zero dimensional element (a point) cannot fully includ a one dimensional element.

No Doron, it can not include a one dimensional element or it would not be zero dimensional.

This is the reason of why a one dimensional element is included NXOR excluded w.r.t a zero dimensional element, or in other words, it is Non-local w.r.t a zero dimensional element.

As your assertion of some apparently partial inclusion of a one dimensional element by a zero dimensional element is false your “reason” and “Non-local w.r.t” simply fails.

You still do not distinguish between no dimension and zero dimension

You obviously just do not distinguish between one dimension and zero dimensions.

(for example: the cardinality of {} (=0) is not the same
as the "content" of {} (= nothing),

Actually it is the same thing, that “the cardinality of {} (=0)” is representative of the fact that “{}” has no content (contains no elements).

or in other words: {} ≠ {0}).

On the contrary, a zero dimensional element is included XOR excluded w.r.t a one dimensional element, exactly as you wrote here:

One (“{}”) includes no content, which excludes even a partial content, while the other (“{0}”) contains an element. Just as a zero dimensional element includes no dimensions, which excludes even a partial dimensional element, but does not preclude that zero dimensional element being part of a one dimensional element. Nothing “On the contrary” about it, “{}” can include no content just as a zero dimensional element can include no dimensional elements. However “{}” can be included as an element of another set (like {{}}) just as a zero dimensional element can be included as an element of some dimensional element.

and actually this is all you can get all along this thread, which is called Local-only reasoning.

What ever you want to call it, it is still only your own failed “reasoning” that you simply try to ascribe to others.

 

[jsfisher]

A line segment is a composition of two kinds of atomic aspects, the Non-local aspect and the Local aspect.

So, your non-composed thing is composed.

 

[doronshadmi]

As “excluded” was also clearly part of my statements you quoted “an inclusion-only approach” is again just one of your fantasies you are trying to “force” on anyone other than you.

Again…

The Man, by your "in the same domain" nonesense, domain A is forced to be in domain B.

 

[The Man]

Nope.

You simply can't grasp the notion of A or B as non-composed things that have different qualities w.r.t each other.

Doron you simply can’t seem to understand that it is specifically your “non-composed things” that requires you try to imagine all this self-contradictory and unspecific OM nonsense. Again that requirement as a result of your own deliberate “non-composed” limitation is still simply just yours, as is the nonsense.

 

[doronshadmi]

So, your non-composed thing is composed.

A line segment is a composed result of two non-composed things, which are the non-local quality of a line and the local quality of a point.

Again, non-locality or Locality are not limited to Metric space.