Deeper than primes

[The Man]

EDIT:

Let us get it this way:

An element of a given universe has the most basic property of that universe.

The property can be "Apple", "Dimension", … etc …

------------------------

By following your argument:

Where did I ever make such a ridiculous “argument”? Again Doron stop trying to just pawn off asspects of your own failed reasoning onto others.

If "no apples" is not the lack of the most basic property of the universe of apples (because, afrer all, the term "apples" is used), then this universe has an empty set as one of its members, known as "no apples".

If "no dimension" is not the lack the most basic property of the universe of dimensions (because, afrer all, the term "dimension" is used), then this universe has an empty set as one of its members, known as "no dimension".

--------------------------

In that case there is an exclusive empty set for each given universe, which is a false claim, because empty set is not an exclusive element of any given universe.

What the heck are you talking about? The empty set is by definition, well, empty becouse it excludes all "elements". This “exclusive empty set for each given universe” is just some ridiculous aspect of your own failed reasoning that again you're just trying to attribute to someone else.

--------------------------

Let us follow your argument about a point:

An element that has "no dimension" is equivalent to empty set under the universe of dimensions, and a point is such an element.

--------------------------

No Doron the set of an ordinate or coordinates locating a point, when the space is that point, is the empty set. This has been explained to your several times yet you still simply ignore it. If you are going to assert “ Let us follow your argument about a point:” then at least try to follow that argument and not some imaginary nonsense you simply want to attribute to someone eles.

But this is a false claim because empty set is not an exclusive element of any given universe, and since "no dimension" is an exclusive element then a point is not equivalent to empty set.

Too bad, it’s your claim, if you think it is false then the problem lies simply with you.

A point (which is not equivalent to empty set) and a line are elements of the universe of dimensions, where a point is a dimensional element that has 0 degrees of freedom and a line is a dimensional element that has more than 0 degrees of freedom.

Nope again a point is specifically an “element” without dimension.

Again if you think just a point has dimension then give us a set of the ordinate or coordinates to locate that point in itself and give us the cardinality of that set (and thus the dimensionality of your "point" with dimension)

By getting this simple fact, a point is located XOR not-located w.r.t to a given line, where a line is located NXOR not-located w.r.t a given point.

Simply changing from "included" and "excluded" to “located” and “not-located” does not help you. “located NXOR not-located w.r.t a given point” is still always FALSE as “located” and “not-located” are mutually exclusive.

The Man, in addition to post http://www.internationalskeptics.com/forums/showpost.php?p=6270709&postcount=11327 :

{} is not equivalent to {no apples}

Who ever said it was?

{} is not equivalent to {no dimension} is equivalent to {.}

Doron “{no dimension}” or “{.}” are still not a set of the ordinate or coordinates needed to locate a point in that point. You’re still just jerking yourself around claiming apples aren’t the same as oranges.

 

[The Man]

It doesn't go like that. The number of dependent variables defines the dimensionality of drawn objects:

f(x,y) = 0 draws a 2D object:


[qimg]http://a.imageshack.us/img693/2578/2dplane.jpg[/qimg]


f(x) = 0 draws a 1D object -- a horizontal line

Now, which function would draw the 0-D object, which the point?

It's a function with no dependent variable. But such a function doesn't exist and therefore a point cannot be drawn at a specified location, coz there is no function to do so. But a point can be located by a set of two functions. A point of intersection, for example, is a a solution of f(x) - g(x) = 0. Points are just imaginary reference points.

You need to be careful though when you go the other way. Remember that

y = f(x)
z = f(x,y)

and so on.

When you start to manipulate the independent variables the dimensional objects will respond according to the dependent variable y, z, and so on. The changes can be detected with the help of co-ordinates y, z, and so on. Here is an example:


[qimg]http://a.imageshack.us/img834/5913/ekklund1.jpg[/qimg]


Looks familiar?


If you rewrite the equation in the graph to satisfy certain conditions that exist in the Gamma-Rho phase space, then . . .


[qimg]http://a.imageshack.us/img227/7767/ekklund2.jpg[/qimg]


Yep. It's the four-legged mischievous demon Ekklund.

The higher dimensions are virtually infested with deities of peculiar varieties, so be careful -- unless you are an atheist with limited, local-only reasoning that is closed to the isomorphic algebra of multi-dimensional manifolds.

Nice one epix. Say, that guy does look familiar. Wasn’t he in that movie “Pirates of the Caribbean Plain: The Curse of the Buckled Surface“?

 

[epix]

EDIT:

Let us get it this way:

An element of a given universe has the most basic property of that universe.

The property can be "Apple", "Dimension", … etc …

I don't think so. That universe, as any other universe, develops a very dense objects that generate such a strong gravitational pull that even the photon cannot overcome, so the very dense object is invisible. But there is no black juice, is there?

 

[epix]

A pair of coordinates is related to 0 dimensional space under 2 dimensional space, so?


A single ordinate is related to 0 dimensional space under 1 dimensional space (where the term "horizontal" is insignificant), so?

So?
Well, an "inductive reasoning" leads you to a conclusion that no ordinate is related to a point. Since the specific relation means, and has always meant, 'ordinate <--> variable' you can't draw a point at a specified location. But a line is a collection of points organized according to y=f(x). That means a property of a point can be established only when it exist in a multitude. A point is not a free particle like the neutrino; it manifest itself only through a 1-D object. It is like investigating the property of a quark which manifest itself only when proton forms an imaginary line by travelling fast inside a particle collider where it collides with another proton. The high energy fender-bender releases a quark. Now you can see the property of the quark/point.

You can see the lines where two protons were traveling along, and the point of impact is the point of intersection. The impact releases a quark/point so you can see it and investigate its property. You are establishing the property of a point through some philosophies foreign to this universe. By doing so, you are missing the very concept that the existence of Higgs boson relies upon.

 

[epix]

You’re still just jerking yourself around claiming apples aren’t the same as oranges.

Are they?

 

[epix]

Say, that guy does look familiar. Wasn’t he in that movie “Pirates of the Caribbean Plain: The Curse of the Buckled Surface“?

Who? The mischievous demon Ekklund?
I think he got a cameo in the sequel "Pirates of the Caribbean Plain: The Curse of the Swashbuckled Surface."

 

[doronshadmi]

No Doron the set of an ordinate or coordinates locating a point, when the space is that point, is the empty set.

No The Man, you ignore the fact that a point is an existing element of the set of dimensional spaces, where the amount of its coordinates is 0.

This set looks like this:

{0,1,2,3,4,5,..}, where each value is the number of ordinates or coordinates that is related to each existing dimensional space.

Before you jump and replace each number by a set ( for example: {{},{{}},{{},{{}}}, …} ) be aware that according to OM each dimensional space is a non-composed element (or ur-element, if you wish) which is not a set, so the whole idea of Membership as defined among sets, is changed to Membership as defined among ur-elements, where this membership is based on sharing a common property ("Dimension", in this case).

EDIT:

A point and a line are ur-elements that shares the proprty of Dimension.

By understanding the Membership among ur-elements, which is based on shared property, a point is included XOR excluded w.r.t a line and a line is included NXOR excluded w.r.t a point (where no one of them is the component of the other).

A point is an existing dimensional space that has 0 degrees of freedom (0 coordinates are related to points).

A line is an existing dimensional space that has 1 degrees of freedom (singletons of ordinates are related to points).

A plan is an existing dimensional space that has 2 degrees of freedom (pairs of coordinates are related to points).

A sphere is an existing dimensional space that has 3 degrees of freedom (triples of coordinates are related to points).

Etc... ad infinituum.

Doron “{no dimension}” or “{.}” are still not a set of the ordinate or coordinates needed to locate a point in that point.

Here it is:

{0, ...} , where 0 ( which is a member of {0,1,2,3,4,5,..} ) is the number of ordinates or coordinates needed to locate a point in 0 dimensional space.

The dimensional spaces can be also represented as { . , __ , ... } but we have a problem to represent dimensional spaces > 3 in this way.

By the way, by understanding a dimensional space and its related coordinates, we are able to get the notion of Mutual Independency, because each value of pair of, triple of (or any greater finite amount of) coordinates can be changed independently of each other, and yet they are all related to given dimensional spaces (which is the property of mutuality), which have 2 or more degrees of freedom (where a point and its related values under a given dimensional space, is the local aspect of this dimensional space).

 

[zooterkin]

No The Man, you ignore the fact that a point is an existing element of the set of dimensional spaces, where the amount of its coordinates is 0.

Let me stop you there. You appear to be still confused about what co-ordinates are. They tell you where the point is, not its size or extent. The number of (co-)ordinates needed to specify where a point (or anything else) is depends on the number of dimensions of the space it is located in, not the number of dimensions the point has.

 

[doronshadmi]

Let me stop you there. You appear to be still confused about what co-ordinates are. They tell you where the point is, not its size or extent. The number of (co-)ordinates needed to specify where a point (or anything else) is depends on the number of dimensions of the space it is located in, not the number of dimensons the point has.

EDIT:

You appear to be still confused about what co-ordinates are. A dimensional space that has 0 degrees of freedom has an amount of coordinates that are derive from the difference of degrees of freedom that each dimensional space has w.r.t it.

But this is the particular case that is derive from the difference of dimensional spaces with more than 0 degrees of freedom w.r.t a dimensional space that has 0 degrees of freedom.

The arithmetic of this case is very simple:

Abs (0 degrees of freedom – 0 degrees of freedom) = 0 amount of (co-)ordinates.

Abs (1 degrees of freedom – 0 degrees of freedom) = 1 amount of (co-)ordinates.

Abs (2 degrees of freedom – 0 degrees of freedom) = 2 amount of (co-)ordinates.

Abs (3 degrees of freedom – 0 degrees of freedom) = 3 amount of (co-)ordinates.

Etc … at infinitum …

In general, the amount of (co-)ordinates is derive from the absolute difference among the degrees of freedom of dimensional spaces.

Another particular case defines the number of (co-)ordinates of dimensional spaces w.r.t themselves, and as we see the result is 0 amount of (co-)ordinates.

Also the arithmetic of this case is very simple:

Abs (0 degrees of freedom – 0 degrees of freedom) = 0 amount of (co-)ordinates.

Abs (1 degrees of freedom – 1 degrees of freedom) = 0 amount of (co-)ordinates.

Abs (2 degrees of freedom – 2 degrees of freedom) = 0 amount of (co-)ordinates.

Abs (3 degrees of freedom – 3 degrees of freedom) = 0 amount of (co-)ordinates.

Etc … at infinitum …

 

[epix]

EDIT:

You appear to be still confused about what co-ordinates are.…

Co-ordinates are called "degrees of freedom" in phase space, which is a geometry concept that enables engineers to better understand the mechanics of object assembly -- among other things. The purpose of drawing co-ordinates is to locate a point. But in phase space, co-ordinates are basically lines to be followed. In 3-D space, you have 3 degrees of freedom to move along. So what would you do?

It depends on circumstances. For example, if you have your back against the record machine then you . . . ?

 

[The Man]

No The Man, you ignore the fact that a point is an existing element of the set of dimensional spaces, where the amount of its coordinates is 0.

So now you’re now claiming a point has no dimension(s) since you claim it has no coordinates?

This set looks like this:

{0,1,2,3,4,5,..}, where each value is the number of ordinates or coordinates that is related to each existing dimensional space.

Related how, specifically?

Before you jump and replace each number by a set ( for example: {{},{{}},{{},{{}}}, …} ) be aware that according to OM each dimensional space is a non-composed element (or ur-element, if you wish) which is not a set, so the whole idea of Membership as defined among sets, is changed to Membership as defined among ur-elements, where this membership is based on sharing a common property ("Dimension", in this case).

Again as this “each dimensional space is a non-composed element (or ur-element, if you wish)” is just your own imposed limitation, it restricts only you.

Please tell us what “elements” the empty set “{}” is “composed” of? How many elements are in the set of coordinates for just a point? Your assertion above says “0”, thus it would be the empty set.

No ordinate or coordinates, no dimension(s) Doron.

EDIT:

A point and a line are ur-elements that shares the proprty of Dimension.

Again a point specifically has no dimension(s) thus “the proprty of Dimension” it has is specifically, well, lacking.

By understanding the Membership among ur-elements, which is based on shared property, a point is included XOR excluded w.r.t a line and a line is included NXOR excluded w.r.t a point (where no one of them is the component of the other).

Once again as “each dimensional space is a non-composed element (or ur-element, if you wish)” is just your own imposed limitation, it restricts only you. Still, this does not help you as “a line is included NXOR excluded w.r.t a point” is still always FALSE as included and excluded are mutually exclusive.

Again how does your “point” specifically “include” your “line” or your “line” specifically “include” your “point” when you claim both are “a non-composed element”?

A point is an existing dimensional space that has 0 degrees of freedom (0 coordinates are related to points).

Thus it has no dimension(s) as no “coordinates are related to” that point.

A line is an existing dimensional space that has 1 degrees of freedom (singletons of ordinates are related to points).

A plan is an existing dimensional space that has 2 degrees of freedom (pairs of coordinates are related to points).

A sphere is an existing dimensional space that has 3 degrees of freedom (triples of coordinates are related to points).

Etc... ad infinituum.

“related to points”, how, specifically?

Particularly considering that by your own restriction they are “non-composed element (or ur-element, if you wish)”. My recommendation would be that you simply stop ‘wishing’ that.

How are any of your "spaces" "dimensional" if they do not specifically "include" points?

Again…

So please tell us how many dimensions you have when your have “0 points”?

How are your 2 and 3 “dimensional” spaces 2 or 3 dimensional if they are not “composed” of those, well, dimensions?

Here it is:

{0, ...} , where 0 ( which is a member of {0,1,2,3,4,5,..} ) is the number of ordinates or coordinates needed to locate a point in 0 dimensional space.

So now you’re now claiming a point has no dimension(s) as no ordinate or coordinates can locate that point when the space is that point?

The dimensional spaces can be also represented as { . , __ , ... } but we have a problem to represent dimensional spaces > 3 in this way.

Too bad, as it’s simply your nonsense it’s just your problem.

By the way, by understanding a dimensional space and its related coordinates, we are able to get the notion of Mutual Independency, because each value of pair of, triple of (or any greater finite amount of) coordinates can be changed independently of each other, and yet they are all related to given dimensional spaces (which is the property of mutuality), which have 2 or more degrees of freedom (where a point and its related values under a given dimensional space, is the local aspect of this dimensional space).

By the way, you simply not understanding or just refusing to try to understand dimension does not imbue your pervious “Mutual Independency” nonsense with any validity.

Here it is:

Once again you simply try to substitute your deliberate misuse of a phrase like “Mutual Independency”, your unspecific “related to” and “included” ascriptions, your own self imposed “ur-element” restriction, your always FALSE “included NXOR excluded” assertion, your superfluous “degrees of freedom” and your continued, evidently deliberate, obfuscation of the empty set for the ordinate or coordinates of just a point for an actual understanding and direct discussion of dimension.

 

[The Man]

EDIT:

You appear to be still confused about what co-ordinates are. A dimensional space that has 0 degrees of freedom has an amount of coordinates that are derive from the difference of degrees of freedom that each dimensional space has w.r.t it.

But this is the particular case that is derive from the difference of dimensional spaces with more than 0 degrees of freedom w.r.t a dimensional space that has 0 degrees of freedom.

The arithmetic of this case is very simple:

Abs (0 degrees of freedom – 0 degrees of freedom) = 0 amount of (co-)ordinates.

Abs (1 degrees of freedom – 0 degrees of freedom) = 1 amount of (co-)ordinates.

Abs (2 degrees of freedom – 0 degrees of freedom) = 2 amount of (co-)ordinates.

Abs (3 degrees of freedom – 0 degrees of freedom) = 3 amount of (co-)ordinates.

Etc … at infinitum …

In general, the amount of (co-)ordinates is derive from the absolute difference among the degrees of freedom of dimensional spaces.

Another particular case defines the number of (co-)ordinates of dimensional spaces w.r.t themselves, and as we see the result is 0 amount of (co-)ordinates.

Also the arithmetic of this case is very simple:

Abs (0 degrees of freedom – 0 degrees of freedom) = 0 amount of (co-)ordinates.

Abs (1 degrees of freedom – 1 degrees of freedom) = 0 amount of (co-)ordinates.

Abs (2 degrees of freedom – 2 degrees of freedom) = 0 amount of (co-)ordinates.

Abs (3 degrees of freedom – 3 degrees of freedom) = 0 amount of (co-)ordinates.

Etc … at infinitum …

Absolutely ridiculous, this superfluous subtracting nonsense of yours did not work for you before and it is no different now that you have just substituted the words “degrees of freedom” for your “k_X - k_Y” designations.

Your own absolutely ridiculous and superfluous subtracting nonsense still shows no coordinates (in both of your ‘cases’) for just a point and thus no dimension(s). Your really are without a clue when even your own absolutely ridiculous and superfluous subtracting nonsense still proves you wrong.

 

[doronshadmi]

So now you’re now claiming a point has no dimension(s) since you claim it has no coordinates?

No, I claim that a point has 0 degrees of freedom, and any measured case that has 0 degrees of freedom does not have any (co-)ordinates that are related to it.

Yet it is not equivalent to the empty set because any given dimensional space is non-composed (also known as ur-element), where the Membership among ur-elements is not based on being sub-elements, but by sharing a common property, where in the case of dimensional spaces, the common property is being a dimension.

Traditional Math gets the concept of Membership only in terms of sets, and as a result the member must be a component (sub-set) of a given set, which is a limitation of the concept of Membership.

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

One way is to work in a first-order theory with two sorts, sets and urelements, with a ∈ b only defined when b is a set. In this case, if U is an urelement, it makes no sense to say

X ∈ U

 

[doronshadmi]

Absolutely ridiculous, this superfluous subtracting nonsense of yours did not work for you before and it is no different now that you have just substituted the words “degrees of freedom” for your “k_X - k_Y” designations.

Your own absolutely ridiculous and superfluous subtracting nonsense still shows no coordinates (in both of your ‘cases’) for just a point and thus no dimension(s). Your really are without a clue when even your own absolutely ridiculous and superfluous subtracting nonsense still proves you wrong.

The Man, you are stuck with the notion of sets, and can't get any reasoning which goes beyond it.

The ridiculous and superfluous nonsense is a direct result of forcing your limited reasoning (which is stuck with the notion of sets) on OM's reasoning.

The fact is this:

1) Dimensional spaces do not need (co-)ordinates in order to be defined.

2) Dimensional spaces need degrees of freedom in order to be defined and here is the set of degrees of freedom of dimensional spaces:

{0,1,2,3,4,5,...}

 

[zooterkin]

OM's reasoning.

Something yet to be demonstrated.

 

[zooterkin]

No, I claim that a point has 0 degrees of freedom, and any measured case that has 0 degrees of freedom does not have any (co-)ordinates that are related to it.

So by your logic, since a point has no co-ordinates, it cannot be at any location?

Of course, the whole statement is nonsense anyway. I'll repeat, just in case that should have an effect; the co-ordinates tell you where the point is, not anything about its size (which is not surprising, since it has none).

Yet it is not equivalent to the empty set because any given dimensional space is non-composed (also known as ur-element), where the Membership among ur-elements is not based on being sub-elements, but by sharing a common property, where in the case of dimensional spaces, the common property is being a dimension.

What does the empty set have to with the location of a point?

 

[doronshadmi]

“related to points”, how, specifically?

By the difference of degrees of freedom among dimensional spaces.

 

[doronshadmi]

So by your logic, since a point has no co-ordinates, it cannot be at any location?

Any dimensional space w.r.t itself in not local AND not non-local.

the co-ordinates tell you ...

The co-ordinates are the result of the difference of degrees of freedom among dimensional spaces.

 

[epix]

The dimensional spaces can be also represented as { . , __ , ... } but we have a problem to represent dimensional spaces > 3 in this way.

We?

And who is the other guy who has a hard time to realize that there are other punctuation marks apart from the period and the comma?

Doron, put your human waste together or you won't be able to sneeze again. Never. Ever. You hear?

 

[The Man]

No, I claim that a point has 0 degrees of freedom, and any measured case that has 0 degrees of freedom does not have any (co-)ordinates that are related to it.

So how do you define "degrees of freedom"?

Yet it is not equivalent to the empty set because any given dimensional space is non-composed (also known as ur-element), where the Membership among ur-elements is not based on being sub-elements, but by sharing a common property, where in the case of dimensional spaces, the common property is being a dimension.

Again if you claim the set of coordinates for just a point is not the empty set then give us those coordinates.

Traditional Math gets the concept of Membership only in terms of sets, and as a result the member must be a component (sub-set) of a given set, which is a limitation of the concept of Membership.

No Doran the definition of what constitutes a member is specifically the limitation of membership, it is what limits something (even a set) to, well, its members.

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.

On the contrary, Doron, the demonstrative evidence is that your “OM” has not enabled you to deal with anything.

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

No Doron it simply makes membership meaningless because that limitation (mutual exclusion) of membership is specifically what makes something a member and something else not a member. Your simple and deliberate ignorance of membership is not a "novel aspect".

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

Doron “ur-elements” is a membership (A classification of some elements), the only one who evidently can’t deal with that (or evidently just can't understand what he quotes from some reference) is you.

The Man, you are stuck with the notion of sets, and can't get any reasoning which goes beyond it.

The ridiculous and superfluous nonsense is a direct result of forcing your limited reasoning (which is stuck with the notion of sets) on OM's reasoning.

Doron you are still just stuck in your fantasies and the resulting ridiculous and superfluous nonsense you spew is a direct result of you forcing your fantasies onto terminology of actual mathematics.

The fact is this:

1) Dimensional spaces do not need (co-)ordinates in order to be defined.

Then define your “Dimensional space” without “(co-)ordinates”.

2) Dimensional spaces need degrees of freedom in order to be defined and here is the set of degrees of freedom of dimensional spaces:

{0,1,2,3,4,5,...}

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

By the difference of degrees of freedom among dimensional spaces.

“related to points” “By the difference of degrees of freedom among dimensional spaces.” how, specifically?

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