Deeper than primes - Continuation

[doronshadmi]

By using abstraction, an infinite curvature has exactly 0-dimesional space, where 0-dimensional space can be at one and only one location w.r.t a give domain.

This is not the case about 1-demensional space (weather it is curved or straight), because by define it as an element (an atom) w.r.t a given domain like 0-dimnsional space, it can be at AND not at the given 0-dimnsional space location (where the given 0-dimnsional space is also an atom).

I used the words "host" (for the relation of 1-demensional space w.r.t a given 0-dimnsional space) and "hosted" (for the relation of 0-demensional space w.r.t a given 1-dimnsional space) in order to clarify that these dimensions are verbally_symbolically defined as non-local\local w.r.t each other, but they are not made of each other visually_spatially since they are elements (atoms).

So, the "host" AND "hosted" notion actually known only by using verbal_symbolic AND visual_spatial skills in order to really define the relations among different dimensional spaces.

Verbal_symbolic-only skill(ers)' reasoning can't get the invariance of the atomic state of the relations among different dimensional spaces.

Furthermore, they force their context-dependent-only "packed in boxes" reasoning on the entire population, at least for the past 500 years.

One of the devastating results of context-dependent-only "packed in boxes" reasoning is its built-in inability to grasp and develop a unified comprehensive and balanced framework for our ethical and logical\technological skills.

The results of this inability are daily seen by the race after mass destruction weapon, exactly because of the non-unified and imbalanced framework among our ethical and logical\technological skills.

Take, for example, the Iran case.

If it is fulfilled, then you can say good-bye to the rest of the life-supporting technological results of the past 5000 years.

Another devastating results are the technological developments, winch harm planet Earth's Ecosystem, exactly because these technologies are based on imbalanced minds, which can't comprehend the development of the unified framework among our ethical and logical\technological skills, which can't be achieved without using verbal_symbolic AND visual_spatial skills as a one comprehensive framework.

After 9 years of discussion over the internet, it is clear that the current community of mathematicians uses almost only verbal_symbolic skills and as a result they can't comprehend http://www.internationalskeptics.com/forums/showpost.php?p=7676943&postcount=5 or this post.

Without Cross-contexts AND Context-dependent framework development, we are going to be impacted very quickly by the imbalanced framework that was developed for the past 5000 years mostly by verbal_symbolic_only skill(ers) (this imbalanced development was accelerated for the past 500 years).

 

[epix]

Well, I live in rural New York, though I did have to study mechanics of materials (compression, elongation, stress, strain and such physical attributes that you allude to) before I was employed as a mechanical engineer.

That's why it's unlikely that the ladder slips under you.

 

[epix]

By using abstraction, an infinite curvature has exactly 0-dimesional space, where 0-dimensional space can be at one and only one location w.r.t a give domain.

Abstraction is of no use here. One really needs to wait for the autopsy to learn in what degree of mental decomposition the above idea actually is. "...An infinite curvature has exactly 0-dime[n]sional space..."

 

[doronshadmi]

Verbal_symbolic-only skill(ers) do not have the needed skills in order to realize that Non-locality and Locality are the primary properties among mathematical or physical dimensional spaces, exactly because they wrongly get these dimensional spaces by their secondary properties.

For example, they try to define mathematical or physical dimensional spaces in terms of secondary property like curvature.

By using verbal_symbolic AND visual_spatial skills, as done by the following diagram:

one really understands that a 1-dimesional space is non-local w.r.t any given curvature's degree along it, including infinite curvature, known as 0-dimesional space (in this example, 1-dimensional space is at AND not at w.r.t to any curvature degree along it, or in other words, Non-locality is a primary property w.r.t to curvature's property).

Again, by using an example used by set theory, no collection of different "hosted" curvatures reaches the power of the continuum (the non-locality) of a given "host" mathematical or physical space, such that {|(collection of all possible curvatures)|} < |{(collection of all possible curvatures)}|, as explained in http://www.internationalskeptics.com/forums/showpost.php?p=7665090&postcount=16566 and http://www.internationalskeptics.com/forums/showpost.php?p=7666664&postcount=16568 (and can't be known by verbal_symbolic-only skill(ers)).

This understanding is generalized to all possible mathematical or physical dimensional spaces, such that all dimensional spaces > 0 are non-local w.r.t all dimensional spaces that are smaller than them AND all smaller dimensional spaces are local w.r.t these greater dimensional spaces, no matter what curvature degree is considered among all smaller and greater dimensional spaces, exactly because curvature degree is a secondary property among mathematical or physical dimensional spaces (again, this fact is known only by using verbal_symbolic AND visual_spatial skills, something that verbal_symbolic-only skill(ers) can't do).

 

[epix]

By using verbal_symbolic AND visual_spatial skills, as done by the following diagram:

[qimg]http://www.math.brown.edu/help/discontinuities%203.gif[/qimg]

one really understands that a 1-dimesional space is non-local w.r.t any given curvature's degree along it, including infinite curvature, known as 0-dimesional space (in this example, 1-dimensional space is at AND not at w.r.t to any curvature degree along it, or in other words, Non-locality is a primary property w.r.t to curvature's property).

In case someone may wonder what the graph is actually all about, here is a brief explanation of the broad kind: By monitoring the behavior of some object under Condition A, we receive data. When we organize the data, they form a curve. When Condition A is no longer in effect, the behavior of the object is theorized to change and indeed it is so, as the data organization results in the straight line. What draws both lines are functions:

Condition A ~ "function that draws a curve"
Condition not A ~ "function that draws a straight line"

Since there is only one object displaying certain property under two different conditions - the property we are interested about - there is also only one function, but divided into two parts. Such a function f(x) is called "piecewise function." This type of function can have many parts depending on the number of conditions under which the studied object behaves. Here is another example of piecewise function y:

You can use piecewise function to monitor the speed of a car over certain distances. For example, when a car accelerates to a certain speed and then keeps going at that constant speed, the result is a curve and a straight line, coz curves describe acceleration of an object, whereas straight lines describe the speed of an object moving at a constant speed.

 

[doronshadmi]

By understating the "host"\"hosted" principle, one understands that given any mathematical or physical space, no collection of "hosted" spaces is the "host" space.

For example, a given function is the "host" space of the collection of all the possible "hosted" results, where being "host" means that the function is at AND not at the domain of all possible results, exactly because it is an invariant rule w.r.t to all the possible results.

Verbal_symbolic-only skill(ers) get only the collection of all possible results but they don't understand the invariant and non-local property of the rule, which is the "host" space of all the "hosted" results, such that being "host" space means that it is defined but not made of the "hosted" spaces (the collections of particular results).

 

[doronshadmi]

In addition to http://www.internationalskeptics.com/forums/showpost.php?p=7754750&postcount=146 , for example, the collection of all natural numbers is not the "host" class, where the "host" class is at AND beyond all natural numbers, otherwise the natural numbers (the "hosted" objects) are not gathered by a common rule.

The "host" class is at the domain of the "hosted" objects, such that the terms "host" and "hosted" are defined w.r.t each other AND it is also not at the domain of the "hosted" objects, because it is not made of the "hosted" objects (for example: 1-dimensional space is not made of 0-dimensional spaces, yet it is defined as the "host" space w.r.t 0-dimensional spaces, where 0-dimenrsional spaces are defined as "hosted" spaces w.r.t 1-dimensional space).

In terms of Cardinality aleph-0 is related but also beyond all natural numbers (and so is the case with all transfinite cardinals w.r.t to the classified objects).

Cantor missed the notion of the non-locality of transfinite cardinality, exactly because he used verbal_symbolic-only skills in order to get them.

 

[jsfisher]

Cantor missed the notion of the non-locality of transfinite cardinality, exactly because he used verbal_symbolic-only skills in order to get them.

Such an odd and baseless thing for Doron to claim. But, then again, most of what Doron has to say is odd and baseless.

Cantor's concepts still work so he must have done something right. Doron's, not so much, and it is reasonably certain he has yet to do anything right.

 

[epix]

Cantor missed the notion of the non-locality of transfinite cardinality, exactly because he used verbal_symbolic-only skills in order to get them.

The agreement between plurals

Cantor missed the notion of the non-locality of transfinite cardinality, exactly because he used verbal_symbolic-only skills in order to get them.

suggests that Cantor used verbal_symbolic-only skills in order to get verbal_symbolic-only skills.

Note that the term "non-locality of transfinite cardinality" is rendered in its verbal_only form, like any other Doron's idea that cannot be meaningfully visualized without invoking the work of Hieronymus Bosh.
http://2.bp.blogspot.com/_wafnR4B40ak/TNISO9yXukI/AAAAAAAACMU/3_XERNexeUk/s1600/Hieronymus+Bosch.jpg

 

[The Man]

Verbal_symbolic-only skill(ers) do not have the needed skills in order to realize that Non-locality and Locality are the primary properties among mathematical or physical dimensional spaces, exactly because they wrongly get these dimensional spaces by their secondary properties.

So the “primary properties among mathematical or physical dimensional spaces” aren’t their, well, dimensionality but just some deliberately ill defined “Non-locality and Locality” that you also deliberately (later in your post) associate directly with their dimensionality? You continue to amaze only yourself Doron.

For example, they try to define mathematical or physical dimensional spaces in terms of secondary property like curvature.

By using verbal_symbolic AND visual_spatial skills, as done by the following diagram:

[qimg]http://www.math.brown.edu/help/discontinuities%203.gif[/qimg]

one really understands that a 1-dimesional space is non-local w.r.t any given curvature's degree along it, including infinite curvature, known as 0-dimesional space (in this example, 1-dimensional space is at AND not at w.r.t to any curvature degree along it, or in other words, Non-locality is a primary property w.r.t to curvature's property).

Wait, “1-dimesional space is non-local w.r.t any given curvature's degree along it”, so your “1-dimesional space” is “non-local w.r.t” to itself, since that is what has the curvature? “Non-locality is a primary property w.r.t to curvature's property”? So your “0-dimesional space” is “non-local w.r.t” to itself as you use what you call “infinite curvature” as the defining attribute. Can you ever even just agree with yourself Doron? Again until you can no one can ever possibly agree with you. Please tell use what exactly has “infinite curvature” in your “0-dimesional space”.

Again, by using an example used by set theory, no collection of different "hosted" curvatures reaches the power of the continuum (the non-locality) of a given "host" mathematical or physical space, such that {|(collection of all possible curvatures)|} < |{(collection of all possible curvatures)}|, as explained in http://www.internationalskeptics.com/forums/showpost.php?p=7665090&postcount=16566 and http://www.internationalskeptics.com/forums/showpost.php?p=7666664&postcount=16568 (and can't be known by verbal_symbolic-only skill(ers)).

What “example used by set theory” makes such claims?

This understanding is generalized to all possible mathematical or physical dimensional spaces, such that all dimensional spaces > 0 are non-local w.r.t all dimensional spaces that are smaller than them AND all smaller dimensional spaces are local w.r.t these greater dimensional spaces, no matter what curvature degree is considered among all smaller and greater dimensional spaces, exactly because curvature degree is a secondary property among mathematical or physical dimensional spaces (again, this fact is known only by using verbal_symbolic AND visual_spatial skills, something that verbal_symbolic-only skill(ers) can't do).

And now here we come full circle with you now directly linking your “non-local” and “local” to the dimensionality of your “dimensional spaces”. Of course with your assertions before of your “1-dimesional space is non-local wrt any given curvature’s degree along it,” and your “infinite curvature, known as 0-dimesional space”. Your “curvature” is also thrown into the deliberately ill defined, self-contradictory and jumbled up mix. If you’re as concerned about the state of the world and nuclear proliferation as you allude to before, then stop wasting your time with this self-contradictory nonsense, learn something, get involved and make a difference instead of just pretending that more nonsense is what such a situation would require.

 

[epix]

So the “primary properties among mathematical or physical dimensional spaces” aren’t their, well, dimensionality but just some deliberately ill defined “Non-locality and Locality” that you also deliberately (later in your post) associate directly with their dimensionality? You continue to amaze only yourself Doron.

Doron is just lazy to explain the concept of the locality using both types of skills that basically relate to the verbal AND the visual rendering. Take for example the Newton Laws. You can translate the formulas using a descriptive language, but if you see the actual demonstration at the same time, then everything can be easily understood. But as far as the locality is concerned, there is a need for a third element that would enter the explaining: verbal AND visual AND host (the concept that Doron is now very particular to). Not everyone can demonstrate the locality w.r.t. Newton Laws though. In the following video - it's in the middle of the page - the locality, which has fascinated Doron and very likely interested even Isaac Newton, appears at 12:30 of the video. Since the locality is superbly hosted, no other question should follow.
http://www.ceskatelevize.cz/porady/10319921345-rande-s-fyzikou/211563230150003-newtonovy-zakony/

 

[doronshadmi]

Verbal_symbolic-only skill(ers) get the phrase “1-dimesional space is non-local w.r.t any given curvature's degree along it” as if 1-dimesional space is non-local w.r.t itself, exactly because they get 1-dimesional space in terms of collection of particular (and therefore limited domains of) curvatures (again, it has to be stressed that dimensional spaces are defined but not made of each other, which is a fact that verbal_symbolic-only skill(ers) can't comprehend).

But all curvatures have their own values, where 1-dimesional space is not any particular value (it is at AND not at any particular curvature along it, whether this curvature is finite or not).

In other words, it is non-local w.r.t the property of curvature, where each given curvature is some local case w.r.t 1-dimesional space.

Verbal_symbolic-only skill(ers) claim that they can define two distinct infinite curvatures without any finite curvature between them.

By avoiding the finite curvature between the infinite curvatures, they miss the non-locality of the 1-dimesional space w.r.t the different curvatures along it, which is at AND not at the domain of any particular curvature, where each particular curvature (finite or not) is local w.r.t it.

Once again, Non-locality and Locality are defined by each other, but they are not made of each other exactly as 1-dimensioal space is not made of the particular (and therefore limited domains of) curvatures along it.

Furthermore, the terms "host" and "hosted" is used in order to clarify that different given spaces are defined but not made of each other.

If one takes Curvature as the primary property of dimensional spaces, then one actually claims that, for example, 0-curvature is made of a collection of infinitely many infinite curvatures, which is a wrong notion.

 

[epix]

If one takes Curvature as the primary property of dimensional spaces, then one actually claims that, for example, 0-curvature is made of a collection of infinitely many infinite curvatures, which is a wrong notion.

If one takes Curvature as the primary property of dimensional spaces, then he won't be able to use this primary property to locate the primary components of constructions called points. That's why one doesn't take Curvature as the primary property of dimensional spaces and choses something else instead:

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it.

The second reason why one doesn't take Curvature as the primary property of dimensional spaces is that such a choice lacks any meaning when visualized, as opposed to the common sense definition of dimension.
http://en.wikipedia.org/wiki/File:Dimension_levels.svg (No pun intended with the in the link. It's a part of ':' followed by D[imension]).

Once again, we see that Doron's inventions can't become a feast for the "visual_spacial skill(ers)." Not a complete loss though, coz the blah_blah_blah_blah_only skill(ers) will be fed.

 

[The Man]

Verbal_symbolic-only skill(ers) get the phrase “1-dimesional space is non-local w.r.t any given curvature's degree along it” as if 1-dimesional space is non-local w.r.t itself, exactly because they get 1-dimesional space in terms of collection of particular (and therefore limited domains of) curvatures (again, it has to be stressed that dimensional spaces are defined but not made of each other, which is a fact that verbal_symbolic-only skill(ers) can't comprehend).

What “limited domains of) curvatures” are you restricting your fantasy “Verbal_symbolic-only skill(ers)” to? Again if for some reason you just don’t like the limits you place on your own fantasies, then you should strive to at least have better fantasies.

But all curvatures have their own values, where 1-dimesional space is not any particular value (it is at AND not at any particular curvature along it, whether this curvature is finite or not).

As other “dimesional space”s can have zero and/or non-zero curvature your “1-dimesional space” is a particular value of “dimesional space”s that can have zero and/or non-zero curvature. Oh and your “straight line” is a “1-dimesional space” with a very “particular value” of curvature, 0.

In other words, it is non-local w.r.t the property of curvature, where each given curvature is some local case w.r.t 1-dimesional space.

Again the curvature of a line is specifically a property of that line so you just claim your “line” is “non-local w.r.t” to itself.

Verbal_symbolic-only skill(ers) claim that they can define two distinct infinite curvatures without any finite curvature between them.

By avoiding the finite curvature between the infinite curvatures, they miss the non-locality of the 1-dimesional space w.r.t the different curvatures along it, which is at AND not at the domain of any particular curvature, where each particular curvature (finite or not) is local w.r.t it.

Again if you have problems with your fantasy “Verbal_symbolic-only skill(ers)” you should probably try to have fantasies that are less problematic for you.

Once again, Non-locality and Locality are defined by each other, but they are not made of each other exactly as 1-dimensioal space is not made of the particular (and therefore limited domains of) curvatures along it.

As already noted many times before that just makes your purported “Non-locality and Locality” ‘definitions’ circular.

Furthermore, the terms "host" and "hosted" is used in order to clarify that different given spaces are defined but not made of each other.

If one takes Curvature as the primary property of dimensional spaces, then one actually claims that, for example, 0-curvature is made of a collection of infinitely many infinite curvatures, which is a wrong notion.

No one but you has made such a claim, too bad for you then.

 

[doronshadmi]

Verbal_symbolic-only skill(ers) do not get their own phrases.

For example let's take the phrase:

"Again the curvature of a line is specifically a property of that line"

This phrase actually means that the property of curvature is context dependent ("specifically a property of that line"), such that no measured curvature is the one and only one possible curvature of the 1-dimesional space.

In other words, the 1-dimensional space is the "host" (cross-contexts) w.r.t all infinitely many particular (specifically) "hosted" (context-dependent) curvatures along it.

Furthermore, being dimensional space is cross-contexts w.r.t to all particular (and therefore context-dependent) dimensional spaces, such that no particular (specifically) dimensional space is, by definition, the one and only one possible dimensional space.

So is the case about Set, it is cross-contexts w.r.t to all classified (and therefore context-dependent cases) where, for example, being empty set or non-empty are particular (specifically) context-dependent w.r.t to the cross-contexts concept of Set.

In other words, any given framework (no matter what concept is used) is not less than Cross-contexts AND Context-dependent.

The terms "host" and "hosted" is used in order to clarify that different given mathematical or physical spaces are defined but not made of each other, such that being "host" is cross-contexts or non-local w.r.t being "hosted", where being "hosted" is context-dependent or local (specifically) w.r.t being "host".

 

[doronshadmi]

A phrase like:" “1-dimesional space” is a particular value of “dimesional space”s that can have zero and/or non-zero curvature." clreary demostrate that AND among different curvatures is possible exactly becuse 1-dimesional is cross-context w.r.t the different curvatures along it.

Varbal_symbolic-only skill(ers) simply can't get it.

 

[epix]

A phrase like:" “1-dimesional space” is a particular value of “dimesional space”s that can have zero and/or non-zero curvature." clreary demostrate that AND among different curvatures is possible exactly becuse 1-dimesional is cross-context w.r.t the different curvatures along it.

Varbal_symbolic-only skill(ers) simply can't get it.

Well, they can do something that really matters - something that Doron can't do: they can actually compute the curvature of the line. And that, as opposed to Doronetics, is the primary object of not only the topic but the whole of mathematics.

 

[doronshadmi]

No matter how many times Cross-context AND Context-dependent framework is introduced to Context-dependent-only skill(er), he\she will get only by its Context-dependent accept.

Because of this limitation they can't comprehend non-local numbers like 0.111...₂ or calculation like 0.111...₂ + 0.000...1₂ = 1

 

[doronshadmi]

Some verbal_symbolic-only skill(er) claims: "“1-dimesional space” is a particular value of “dimesional space”"

He is right, 1-dimesional space is some particular (context-dependent or local) form of the Cross-contexts concept of Dimensional space w.r.t its all particular (context-dependent or local) forms.

Once again Cross-contexts AND Context-dependent holds, but Context-dependent-only skill(ers) get only its Context-dependent accept.

 

[The Man]

Verbal_symbolic-only skill(ers) do not get their own phrases.

For example let's take the phrase:

"Again the curvature of a line is specifically a property of that line"

This phrase actually means that the property of curvature is context dependent ("specifically a property of that line"), such that no measured curvature is the one and only one possible curvature of the 1-dimesional space.

In other words, the 1-dimensional space is the "host" (cross-contexts) w.r.t all infinitely many particular (specifically) "hosted" (context-dependent) curvatures along it.

Furthermore, being dimensional space is cross-contexts w.r.t to all particular (and therefore context-dependent) dimensional spaces, such that no particular (specifically) dimensional space is, by definition, the one and only one possible dimensional space.

So is the case about Set, it is cross-contexts w.r.t to all classified (and therefore context-dependent cases) where, for example, being empty set or non-empty are particular (specifically) context-dependent w.r.t to the cross-contexts concept of Set.

In other words, any given framework (no matter what concept is used) is not less than Cross-contexts AND Context-dependent.

The terms "host" and "hosted" is used in order to clarify that different given mathematical or physical spaces are defined but not made of each other, such that being "host" is cross-contexts or non-local w.r.t being "hosted", where being "hosted" is context-dependent or local (specifically) w.r.t being "host".

So you still just don’t (or just don’t want to) understand context. Whatever your fantasy “Verbal_symbolic-only skill(ers)” may or may not get, the statement “Again the curvature of a line is specifically a property of that line" is explicit. By all means, please, tell us what other curvatures (other than 0) your “straight line” has?


So which is it Doron, your “straight line” is not entirely straight (given your history you claiming your “straight line” does not involve being straight wouldn’t surprise anyone) or your claim that “the property of curvature is context dependent ("specifically a property of that line"), such that no measured curvature is the one and only one possible curvature of the 1-dimesional space.” is just nonsensical gibberish that you don’t even agree with?


If all this blather is just intended to assert that different lines can have different curvatures then once again you simply belabor the trivial just as different lines can have the same curvature.