Deeper than primes

[epix]

On the contrary, OM enables to deal with both cases of Membership, where the traditional Membership deals with complexities, and the novel aspect deals with non-composed elements that share a common property.

The novel aspect of Membership goes beyond the limitations of the traditional approach of the concept of Membership.

Here is the part that clearly shows how the traditional approach can't deal with Membership among ur-elements (which is something that OM enables to do, in addition to the standard Membership among sets):

http://en.wikipedia.org/wiki/Urelemen

It only clearly shows that you misspelled the term "ur-element" and that's why Wiki reference no worky.

OM claims to posses tools that enable Man to answer the most profound question regarding the innermost property of the Universe: There is time t-zero when one of the ur-elements morphs into UR-crazy. What is the time t-zero when the unit of measurement is furlong * parsec^-2?

 

[doronshadmi]

So how do you define your “degrees of freedom”?

An extension of a given element is another element, which shares a given concept with the given element and also has an additional property of that concept.

Degrees of freedom is the number of extensions of a given dimensional space under the concept of Dimension.

0 dimensional space has 0 extensions of the concept of Dimension.

1 dimensional space has 1 extensions of the concept of Dimension.

2 dimensional space has 2 extensions of the concept of Dimension.

3 dimensional space has 3 extensions of the concept of Dimension.

Etc ... ad infinitum ...

 

[doronshadmi]

OM claims to posses ...

No, OM claims to extend the universe under a given concept, where the concepts can be, for example:

Membership, Dimension, Reasoning, Locality, Number, etc ...

 

[epix]

No, OM claims to extend the universe under a given concept, where the concepts can be, for example:

Membership, Dimension, Reasoning, Locality, Number, etc ...

That's nice, Doron. Any attempt to come up with novel methods to expand our knowledge of the universe is commendable, even though complex systems may not work when applied for the first time. It just a matter of some debugging. We do it some other time, coz the atheists have been chasing me around and I gotta run. Just don't venture elsewhere. Oh, maaan... LOL.

 

[doronshadmi]

Any attempt to come up with novel methods to expand our knowledge of the universe is commendable

In this case the extension is the concept of Membership also among urelements, which is based on sharing a common concept with other urelements without being composed by them, as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6276966&postcount=11362 under the concept of Dimension.

For example, no amount of dimensional spaces that have 1 extensions of the concept of Dimension, can be a dimensional space that has 2 extensions of the concept of Dimension.

This is a matter of Magnitude and not a matter of Multitude, and one of the results of this notion is the inability of any amount of 0 dimensional spaces to be a 1 dimensional space (or in other words, no collection of points can fully cover a line).

Also no amount of convergent magnitudes like 0.9+0.09+0.009+... = 0.999...[base 10] have the magnitude of 1 dimensional space.

 

[The Man]

An extension of a given element is another element, which shares a given concept with the given element and also has an additional property of that concept.

Extension? How, to where? “another element,?” So you’re extending some element by adding some additional element or just "additional property" (which would be an additional element)? Sounds like a hair extension. However, this would go against your “non-composed” requirement.

As amusing as your ‘hair extension’ nonsense is, it still does not define your “Degrees of freedom”.

How exactly do you determine the number of your “Degrees of freedom” for some given space?

Degrees of freedom is the number of extensions of a given dimensional space under the concept of Dimension.

0 dimensional space has 0 extensions of the concept of Dimension.

Nope, it just has 0 dimension as you have already given it as being, well, “0 dimensional”. Your ‘extended’ nonsense is simply and demonstrably superfluous as usual.

1 dimensional space has 1 extensions of the concept of Dimension.

Nope, it just has 1 dimension as you have already given it as being, well, “1 dimensional”. Your ‘extended’ nonsense is simply and demonstrably superfluous as usual.

2 dimensional space has 2 extensions of the concept of Dimension.

Nope, it just has 2 dimensions as you have already given it as being, well, “2 dimensional”. Your ‘extended’ nonsense is simply and demonstrably superfluous as usual.

3 dimensional space has 3 extensions of the concept of Dimension.

Nope, it just has 3 dimensions as you have already given it as being, well, “3 dimensional”. Your ‘extended’ nonsense is simply and demonstrably superfluous as usual.

Etc ... ad infinitum ...

Etc ... ad infinitum ...


What “concept of Dimension” are you referring to now, and how exactly do you give it an ‘extension’, other than simply with your superfluous and extensive nonsense.

Evidently your “Degrees of freedom” are just the number of dimensions of some given space that you simply wish you could extend into your nonsense.

 

[The Man]

In this case the extension is the concept of Membership also among urelements, which is based on sharing a common concept with other urelements without being composed by them, as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6276966&postcount=11362 under the concept of Dimension.

For example, no amount of dimensional spaces that have 1 extensions of the concept of Dimension, can be a dimensional space that has 2 extensions of the concept of Dimension.

This is a matter of Magnitude and not a matter of Multitude, and one of the results of this notion is the inability of any amount of 0 dimensional spaces to be a 1 dimensional space (or in other words, no collection of points can fully cover a line).

Again as it is your own self–imposed limitation, Doron, it is simply and entirely just your problem. Again if you think “no collection of points can fully cover a line” then identify some location on that line not covered by points. That is something you simply can not do, as in identifying that location you simply demonstrate that it can in fact and must be covered by points and by not identifying such a location your claim of “no collection of points can fully cover a line” is simply without merit. You simply do not want a line to be fully covered by a collection of points and you have invented your extended nonsense thinking it will accommodate your goal. However, as both the goal and the imposed limitations (to that end) are entirely of your own making the resulting ambiguity, lack of utility and self-contradictions of this contrivance of yours are again simply and entirely yours.

Also no amount of convergent magnitudes like 0.9+0.09+0.009+... = 0.999...[base 10] have the magnitude of 1 dimensional space.

Doron they are already 1 dimensional as line segments. Is that simply your problem, your inability to distinguish a 0 dimensional space or object like a point from a 1 dimensional space or object like a line segment?

 

[epix]

What “concept of Dimension” are you referring to now, and how exactly do you give it an ‘extension’, other than simply with your superfluous and extensive nonsense.

Evidently your “Degrees of freedom” are just the number of dimensions of some given space that you simply wish you could extend into your nonsense.

I think Doron is trying to adjust the fundamentals of Degrees of Freedom to fit OM:

FUNDAMENTAL NOTIONS

•The most basic conception of dimension is as a degree of freedom.

•A point is an object with no properties other than location.

•A space is a collection of locations.

•Spaces can be characterized by their degrees of freedom.


The concept of dimension is, in its most basic and intuitive form, the concept of measuring certain aspects of an object independently from all of its other aspects. This idea of dimension is also known as "degrees of freedom." If an object has three degrees of freedom—height, width, and length, let's say—that means that it is able to "change" in any one of those three ways, and a change in one has no effect on the other two. So, if we are navigating the streets of a city laid out on a grid system, for instance, we are free to change our east-west position or our north-south position, depending on whether we're moving along an avenue or a street. These are our two degrees of freedom. In a city whose grid system is perfectly oriented to the four cardinal directions, going north on an avenue does not affect your east-west position.

The concept lives in the abstraction realm only as necessary; this geometry was designed to be applied in the fields like robotics, for example. Mechanical systems maybe restricted in some ways -- a robotic arm has a certain degree of freedom to operate. So the task of this type of geometry is to maximize the modus operandi of mechanical objects. The math is done within 3-D, for obvious reasons. The extension to higher dimensions lacks purpose for the engineers -- unless Doron finds a killer app for it.

I think Doron works the opposite way, coz math has been almost always subordinate to the purpose of idealizing the real into a manageable form. Doron creates concepts that are "superordinate" to the real; OM seems to be subordinate to the task of understanding an artificial universe. That's a very interesting concept: a tool creates an object, and the same tool is used to understand the properties of the object.

I think Doron is on the right track to develop OM into something practical:

OM ---- development -----> OM(NISCIENCE)

God didn't create Man to his own image and likeness; it was just his intention, and he let Man to complete the task. I think someone is working on it...

 

[doronshadmi]

Your ‘extended’ nonsense is simply and demonstrably superfluous as usual.

Let us see: “0 extensions” is superfluous exactly “0 members” is superfluous in the case of the empty set.

“1 extensions” is superfluous exactly “1 members” is superfluous in the case of non-empty set.

You don’t get the generalization of these notions.

(which would be an additional element)?

No the man, it would be an additional property which distinguishes between at least two kinds of building-blocks, where building-blocks are called elements (element is non-composed).

However, this would go against your “non-composed” requirement.

Certainly not, each dimensional space that is represented by whole values is a building-block that has its own magnitude, and yet these building-blocks share the same concept (Dimension, in this case).

For example: 1 dimensional space + 1 dimensional space ≠ 2 dimensional space, because no 1 dimensional space (and you can add infinitely many 1 dimensional spaces) has the magnitude of 2 dimensional space (which is a building-block).

Again if you think “no collection of points can fully cover a line” then identify some location on that line not covered by points.

You actually say: “identify some location (use 0 dimensional space) on that line (on 1 dimensional space) not covered by points (not covered by 0 dimensional spaces)” .

Again, it is a matter of different magnitudes.

For example: 0 dimensional space + 0 dimensional space ≠ 1 dimensional space, because no 0 dimensional space (and you can add infinitely many 1 dimensional spaces) has the magnitude of 1 dimensional space (which is a building-block).

As a result given infinitely locations (where each location is 0 dimensional space) upon infinitely many scale levels, there is always a 1 dimensional space at AND beyond any given 0 dimensional space, because 1 dimensional space extends the magnitude of 0 dimensional spaces.

 

[doronshadmi]

Evidently your “Degrees of freedom” are just the number of dimensions of some given space that you simply wish you could extend into your nonsense.

“just the number of dimensions of some given space” requires magnitude X that enables more than 0 degrees of freedom for any given magnitude X w.r.t any given magnitude < magnitude X.

0 dimensional space has magnitude A.

0 dimensional space has 0 extensions of the concept of Dimension because there is at most 0 degrees of freedom of Magnitude A w.r.t Magnitude A.

1 dimensional space has magnitude B.

1 dimensional space has 1 extensions of the concept of Dimension, which is resulted by at most 1 degrees of freedom of Magnitude B w.r.t Magnitude A.

2 dimensional space has magnitude C.

2 dimensional space has 2 extensions of the concept of Dimension, which is resulted by at most 2 degrees of freedom of Magnitude B w.r.t Magnitude A.

Etc ... ad infinitum ...

a) 1 dimensional space + 1 dimensional space = 2 dimensional spaces of at most 1 degrees of freedom for each dimensional space.

b) 2 dimensional spaces of at most 1 degrees of freedom for each dimensional space ≠ 2 dimensional space that has 2 degrees of freedom.

 

[doronshadmi]

Doron they are already 1 dimensional as line segments.

You still do not get the notion that a line segment is a composed result of dimensional spaces, which its magnitude > 0 AND < 1, and in the case of 0.999...[base 10], this intermediate dimensional space is > 0 dimensional space and < 1 dimensional space by 0.000...1[base 10], which is the inaccessibility of magnitude of 0.999...[base 10] to magnitude 1, where both 0.999...[base 10] and 0.000...1[base 10] are fogs (non-local numbers, where summation is essentially not their property).

Is that simply your problem, your inability to distinguish a 0 dimensional space or object like a point from a 1 dimensional space or object like a line segment?

Is that simply your problem, your inability to distinguish a 0 non-composed dimensional space (a point) from a 1 non-composed dimensional space (a line) , which are the building-blocks of a composed result like a line segment?

 

[doronshadmi]

Some correction of http://www.internationalskeptics.com/forums/showpost.php?p=6279815&postcount=11369 last part.

Instead of:

For example: 0 dimensional space + 0 dimensional space ≠ 1 dimensional space, because no 0 dimensional space (and you can add infinitely many 1 dimensional spaces) has the magnitude of 1 dimensional space (which is a building-block).

It has to be:

For example: 0 dimensional space + 0 dimensional space ≠ 1 dimensional space, because no 0 dimensional space (and you can add infinitely many 0 dimensional spaces) has the magnitude of 1 dimensional space (which is a building-block).

 

[Little 10 Toes]

Asking a simple question for the fifth time:

Domain is "that is researched".

What is researched?

Define researched.

A measurable realm.

What is "a measurable realm"?

A realm where the measured and the measurer are interacted.

Since you want to play little games.

Your mom has an apple. She wants to know the weight of the apple. She places the apple on the scale. When she places the apple (the measured object) on the scale, it will give her a measurement. Who is the measurer?

Question bolded.

And don't worry. I'll do this same process with "What is interacted" too.

Here's a rhetorical question, if a domain, according to doronshadmi, is "[A] realm where the measured and the measurer are interacted [sic]", why even reply "that is researched [sic]"?

 

[doronshadmi]

Asking a simple question

http://www.internationalskeptics.com/forums/showpost.php?p=6271554&postcount=11336

 

[doronshadmi]

However, this would go against your “non-composed” requirement.

The Man.

There is a distinction between the magnitude of a line segment, which is a composed object with certain or uncertain length, and the magnitude of a given dimensional space (which is a non-composed element).

For example:

If we take a line as a dimensional space of magnitude 1, then along it there can be finitely or infinitely many line segments (composed objects), where their magnitudes is less than 1 because each line segment is the result of an intermediate magnitude of value > 0 AND < 1.

 

[Little 10 Toes]

http://www.internationalskeptics.com/forums/showpost.php?p=6271554&postcount=11336

Avoidance noted. I ask a simple question of who/what is the measurer and it's something that you can't answer.

Edit: Why does it matter who asked the question?

 

[The Man]

I think Doron is trying to adjust the fundamentals of Degrees of Freedom to fit OM:

Heck, why should degrees of freedom remain unscathed by the indefinite onslaught of OM? It just shows once again, as I’ve said before, that although he calls it a new paradigm for math it actually just resembles a typical ameba paradigm that simply ingests everything into some amorphous blob.

The concept lives in the abstraction realm only as necessary; this geometry was designed to be applied in the fields like robotics, for example. Mechanical systems maybe restricted in some ways -- a robotic arm has a certain degree of freedom to operate. So the task of this type of geometry is to maximize the modus operandi of mechanical objects. The math is done within 3-D, for obvious reasons. The extension to higher dimensions lacks purpose for the engineers -- unless Doron finds a killer app for it.

I think Doron works the opposite way, coz math has been almost always subordinate to the purpose of idealizing the real into a manageable form. Doron creates concepts that are "superordinate" to the real; OM seems to be subordinate to the task of understanding an artificial universe. That's a very interesting concept: a tool creates an object, and the same tool is used to understand the properties of the object.

I think Doron is on the right track to develop OM into something practical:

OM ---- development -----> OM(NISCIENCE)

God didn't create Man to his own image and likeness; it was just his intention, and he let Man to complete the task. I think someone is working on it...

Hey Doron can create his own universe, God, OM or whatever in any image he wants. As I’ve said before if he would simply present it that way I doubt I would be here to debate the issue. What he does not get to do is to simply recreate well established, well defined, and useful concepts in his own ill defined, obscure, self-contradictory and useless image while pretending he understands current mathematics.

 

[doronshadmi]

Heck, why should degrees of freedom remain unscathed by the indefinite onslaught of OM? It just shows once again, as I’ve said before, that although he calls it a new paradigm for math it actually just resembles a typical ameba paradigm that simply ingests everything into some amorphous blob.





Hey Doron can create his own universe, God, OM or whatever in any image he wants. As I’ve said before if he would simply present it that way I doubt I would be here to debate the issue. What he does not get to do is to simply recreate well established, well defined, and useful concepts in his own ill defined, obscure, self-contradictory and useless image while pretending he understands current mathematics.

The Man, it is clearly seen that you have no ability to get novel view of already agreed framework.

For example, you simply can't grasp the novel notion about Membership among non-composed elements, because you can't grasp the idea of shared concept among different magnitudes that are not components of each other.

As a result you can't grasp the notion of dimensional spaces as non-composed elements that have different extensions of the same concept, where each extended state is not a collection of the previews extensions.

Again, 1-D space is not a collection of 0-D spaces, because no matter how many 0-D spaces there are along it, no one of them has the extension of 1-D space.

n = 1 to ∞
k = 0 to n-1

In general, n-D space is not a collection of k-D spaces, because no matter how many k-D spaces there are, no one of them has the extension of n-D space.

You still do not get that the "trunk" level (not composed AND not non-composed) of Y form is not defined as a collection of the "branches" level.

As for the concept of Dimension, all you get is the number of different values (known as co-ordinates) that are related to 0-dimensional space w.r.t extended and non-composed states of the concept of Dimension.

By doing that you get the concept of Dimension only in terms of naturally local elements like 0-dimensional spaces, which is again a signature of your local-only reasoning that stands at the basis of any notion that is "developed" in your mind.

For example, you define a 1-D space in terms of a collection of 0-D spaces.

The Man, no direct-perception extension (whether it is infinite extrapolation or interpolation of a direct-perception) and say "bye bye" to real development.

 

[epix]

Asking a simple question for the fifth time:

How about adjusting to the circumstances by changing your nickname to "Little 10 Times?" Otherwise I don't know how to draw attention from Doron apart from pointing out slight inconsistencies in his theorems.

 

[The Man]

Let us see: “0 extensions” is superfluous exactly “0 members” is superfluous in the case of the empty set.

“1 extensions” is superfluous exactly “1 members” is superfluous in the case of non-empty set.

Let’s see: your “0 extensions” is superfluous in the case of the empty set having exactly, well, “0 members”.

Likewise your ““1 extensions” is superfluous in the case of a set with exactly “1 members” being, well, non-empty.

Got any more exactly superfluous comparisons you’d like to make?

You don’t get the generalization of these notions.

You still don’t get that just making up whatever (extended or otherwise) crap you want does not constitute a “generalization”.

No the man, it would be an additional property which distinguishes between at least two kinds of building-blocks, where building-blocks are called elements (element is non-composed).

In a set of the properties of your “building-blocks” those properties are elements of that set as those properties are also elements of your “building-blocks”.

Certainly not, each dimensional space that is represented by whole values is a building-block that has its own magnitude, and yet these building-blocks share the same concept (Dimension, in this case).

Again what “concept (Dimension, in this case)” are you referring to?

So your properties are not elements of your “building-blocks”?

For example: 1 dimensional space + 1 dimensional space ≠ 2 dimensional space, because no 1 dimensional space (and you can add infinitely many 1 dimensional spaces) has the magnitude of 2 dimensional space (which is a building-block).

Well of course no 1 dimensional space has two dimensions or it would be, well, 2 dimensional. However this restriction of yours that two 1 dimensional spaces do not comprise a 2 dimensional space restricts only you.

Wait, so now you can have a set of “infinitely many 1 dimensional spaces”?

You actually say: “identify some location (use 0 dimensional space) on that line (on 1 dimensional space) not covered by points (not covered by 0 dimensional spaces)” .

I actually say what I actually said. Although your attempt to paraphrase did far better this time than you usually do. However to be precise your paraphrasing should read ‘identify some location (a 0 dimensional object) on that line (in 1 dimensional space) not covered by points (not covered by 0 dimensional objects).

So have you found such an ‘uncovered’ location yet.

Again, it is a matter of different magnitudes.

No Doron it is specifically a matter of dimension. A point has none while two points defines one.

For example: 0 dimensional space + 0 dimensional space ≠ 1 dimensional space, because no 0 dimensional space (and you can add infinitely many 1 dimensional spaces) has the magnitude of 1 dimensional space (which is a building-block).

Doron, once again two points define a line segment which is one dimensional. Your simple and continued ignorance of that fact does not change that fact.

As a result given infinitely locations (where each location is 0 dimensional space) upon infinitely many scale levels, there is always a 1 dimensional space at AND beyond any given 0 dimensional space, because 1 dimensional space extends the magnitude of 0 dimensional spaces.

Again if you think a line or line segment is not completely covered by points then indentify the locations on that line or line segments you claim to be not covered by points.

“just the number of dimensions of some given space” requires magnitude X that enables more than 0 degrees of freedom for any given magnitude X w.r.t any given magnitude < magnitude X.

0 dimensional space has magnitude A.

A 0 dimensional space or object has no “magnitude” as it has no dimension.

0 dimensional space has 0 extensions of the concept of Dimension because there is at most 0 degrees of freedom of Magnitude A w.r.t Magnitude A.

“extensions”?, How and to where?

1 dimensional space has magnitude B.

1 dimensional space has 1 extensions of the concept of Dimension, which is resulted by at most 1 degrees of freedom of Magnitude B w.r.t Magnitude A.

2 dimensional space has magnitude C.

2 dimensional space has 2 extensions of the concept of Dimension, which is resulted by at most 2 degrees of freedom of Magnitude B w.r.t Magnitude A.

Etc ... ad infinitum ...

“extensions”?, How and to where?

Etc ... ad infinitum

a) 1 dimensional space + 1 dimensional space = 2 dimensional spaces of at most 1 degrees of freedom for each dimensional space.


b) 2 dimensional spaces of at most 1 degrees of freedom for each dimensional space ≠ 2 dimensional space that has 2 degrees of freedom.

Your assertion, so simply your restrictions.

You still do not get the notion that a line segment is a composed result of dimensional spaces, which its magnitude > 0 AND < 1, and in the case of 0.999...[base 10], this intermediate dimensional space is > 0 dimensional space and < 1 dimensional space by 0.000...1[base 10], which is the inaccessibility of magnitude of 0.999...[base 10] to magnitude 1, where both 0.999...[base 10] and 0.000...1[base 10] are fogs (non-local numbers, where summation is essentially not their property).

You still don’t get the notion that your fogs are deliberate and simply just yours. Still that does not change the fact that they are one dimensional as line segments.

Is that simply your problem, your inability to distinguish a 0 non-composed dimensional space (a point) from a 1 non-composed dimensional space (a line) , which are the building-blocks of a composed result like a line segment?

Nope as those are your restrictions it remains just your problem.

The Man.

There is a distinction between the magnitude of a line segment, which is a composed object with certain or uncertain length, and the magnitude of a given dimensional space (which is a non-composed element).

Doron, a line segment can be “a given dimensional space” or it can just be a object in some space with at least one dimension.

For example:

If we take a line as a dimensional space of magnitude 1, then along it there can be finitely or infinitely many line segments (composed objects), where their magnitudes is less than 1 because each line segment is the result of an intermediate magnitude of value > 0 AND < 1.

Again this deliberate ‘indeterminism’ is simply and entirely yours.

You seem to be confusing, again perhaps deliberately, the 1 dimensionality of a line and of lines segment with its length.

So now you can have a set of “infinitely many line segments”.