Deeper than primes

[doronshadmi]

Since the unit circle has r=1, one dimension is already assumed and therefore it takes only 1 coordinate (the angle) to locate a point drawn on the unite circle.

It is like as if you say:

Coordinate x is already assumed and therefore it takes only 1 coordinate to locate a point drawn on the unite circle.

As for a circle w.r.t a plane, if a circle is taken as a dimension 1 element w.r.t to a given plane, then the given plane is at and beyond the magnitude value of dimension 1 element, exactly as dimension 1 has a room for one or many dimension 0 elements, dimension 2 has a room for one or many dimension 0 and dimension 1 elements, etc ... ad infintum.

 

[doronshadmi]

if your “line” can not be completely covered by points (or locations if you will) or composed with the least upper bound property and no gaps between those elements (a Linear_continuum) then it is a discete space.

Nope.
http://en.wikipedia.org/wiki/Least_upper_bound_property

If the supremum exists, it is unique,

where uniqness along the real line is equivalent to an exact location along the real line.

Being exact location along the real line means that given at least pair of arbitrary locations, where each one of them is unigue, the least expression is "x locstion ≠ ~x location", or "~x location ≠ location", such that "~x ≠ x" or "x ≠ ~x" is a constant expression, where "x" and "~x" are its local aspect and "≠" is its non-local aspect, and this expression is constant exactly because it does not change upon infinitely many scale levels.

"x" or "~x" are at least dimension 0 elements and "≠" is at least dimension 1 element.

"No dimension" means that there is nothing to be valued, not as Magnitude and not as Multitude.

 

[doronshadmi]

a point remains zero dimensional even when embedded in a one or multi-dimensional space.

Exactly, the magnitude of a point is not changed by the number of values that are related to it, in order to determine the exact location of 0 dimensional element (a point) w.r.t a given dimensional space.

If the term is "0 dimensional element" = "no dimensional element" then no values are related to any element, no coordinates are measured, and the concept of Location (whether it is local or non-local) get's off stage.

n=1 to ∞
k=0 to n-1

X = "Dimensional space"

Y = "Dimensional element"

n_X - k_Y = (n-k) coordinates that are used to determine k_Y location w.r.t n_X

k_X - k_Y = 0 coordinates that are used to determine k_Y location w.r.t k_X

By k_X - k_Y = 0, where 0 coordinates (which is a Multitude's expression) are used to determine k_Y location w.r.t k_X,
no matter if k magnitude >= 0 (it is clealr that if 0 coordinates are used, then no location of a local element w.r.t k_X is defineable).

No_X - k_Y is an invalid mathematical expression.

Persons like you do not understand the difference between the k_X and No_X.

 

[doronshadmi]

Here are some corrections of post http://www.internationalskeptics.com/forums/showpost.php?p=6246920&postcount=11222.


Being exact location along the real line means that given at least pair of arbitrary locations, where each one of them is unique, the least expression is "x location ≠ ~x location", or "~x location ≠ x location", such that "~x ≠ x" or "x ≠ ~x" is an invariant expression, where "x" or "~x" are its local aspect and "≠" is its non-local aspect, and this expression is invariant exactly because it does not changed upon infinitely many scale levels.

"x" or "~x" are at least dimension 0 elements and "≠" is at least dimension 1 element.

"No dimension" means that there is nothing to be valued, not as Magnitude and not as Multitude


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


Here are some corrections of http://www.internationalskeptics.com/forums/showpost.php?p=6247085&postcount=11223.


By k_X - k_Y = 0, 0 coordinates (which is a Multitude's expression) are used to determine k_Y location w.r.t k_X,
no matter if k magnitude >= 0 (it is clear that if 0 coordinates are used, then no location of a local elements w.r.t k_X is definable).

 

[Little 10 Toes]

Here are some corrections of post http://www.internationalskeptics.com/forums/showpost.php?p=6246920&postcount=11222.


Being exact location along the real line means that given at least pair of arbitrary locations, where each one of them is unique, the least expression is "x location ≠ ~x location", or "~x location ≠ x location", such that "~x ≠ x" or "x ≠ ~x" is an invariant expression, where "x" or "~x" are its local aspect and "≠" is its non-local aspect, and this expression is invariant exactly because it does not changed upon infinitely many scale levels.

"x" or "~x" are at least dimension 0 elements and "≠" is at least dimension 1 element.

"No dimension" means that there is nothing to be valued, not as Magnitude and not as Multitude

No. Remember, if you label a single point with a location of X, then ALL other points that are on the line are not at location X. If I have a plane and a point X, then ~X are all the other points in that plane.

 

[doronshadmi]

No. Remember, if you label a single point with a location of X, then ALL other points that are on the line are not at location X. If I have a plane and a point X, then ~X are all the other points in that plane.

I was talking about at least pair of arbitrary locations.

 

[doronshadmi]

The simultaneous existence of opposites in a one framework without eliminating each other, means that they are manifestations of that is beyond them.

 

[The Man]

Too bad that the Wikipedia contributor uses the term "unit circle" instead of "a circle" pointing the difference out, coz "unit circle" assumes given radius (one polar co-ordinate) and therefore it suffices to locate or define a point on the circumference with only one, the angular coordinate. But the usage of polar coordinates is limited, coz x=sin(0)= 0 or x=cos(0)=1 and that is where the first point of the circle appears. If you want to draw a circle on a plane with its center at x=10 and y=12, for example, you need to draw two semicircles using y1 = f(x) and y2 = -f(x), (or use parametric functions). That circle has always dimension 2 with no consideration of dimension 1, unless you offset its center to suit its definition expressed in the polar coordinates. It's a jungle out there . . . and Doron fevereshly works on converting it into a wasteland.

True the reference is to a specific circle, but the point remains that the dimensionality of that object is independent of the dimensionally of the space you might need to draw a specific one in that space. You can always pick your origin and in polar coordinates it becomes the center of infinite an number of concentric circles.

So Doron shouldn't be severely punished for manipulating the text the way he did, only for the analogy that he commited shortly thereafter.

Yes, but we have been over the one dimensionally of a circle with him before.

I can't follow Doron in such a detail as you can, but that's a mistake easy to make. When it gets down to kinda abstract, esoteric stuff, impeccable definitions are a must, otherwise goulash. Since Doron's defining terms and his construction of definitions is an example of advanced cryptography, he also misdefines his own stuff here and there. Where exactly is the dificult part of Doronetics.

Sure it is easy to make mistakes, but when you just keep coming back to the same nonsense it is no longer just a mistake but an intent. The difficult part is only for Doron, and evidently deliberately so.

 

[The Man]

Nope.
http://en.wikipedia.org/wiki/Least_upper_bound_property

where uniqness along the real line is equivalent to an exact location along the real line.

Being exact location along the real line means that given at least pair of arbitrary locations, where each one of them is unigue, the least expression is "x locstion ≠ ~x location", or "~x location ≠ location", such that "~x ≠ x" or "x ≠ ~x" is a constant expression, where "x" and "~x" are its local aspect and "≠" is its non-local aspect, and this expression is constant exactly because it does not change upon infinitely many scale levels.

"x" or "~x" are at least dimension 0 elements and "≠" is at least dimension 1 element.

"No dimension" means that there is nothing to be valued, not as Magnitude and not as Multitude.

Again these “dimension 0” and “dimension 1” are just your fantisies. Again if you think just a point has a location then give us the location of just your “dimension 0” “point”.

Perhaps this can help

The origin in a two dimensional space has two coordinates

(0,0)

As a set it is

{0,0}

This set has a cardinality of 2

The origin of a one dimensional space has one ordinate.


(0)

As a set it is

{0}

This set has a cardinality of 1

The origin of a zero dimensional space (a point) has no ordinate or coordinates (because it technically has no origin)

()

As a set it is, well, empty

{}

This set has a cardinality of 0.


It is still simply you Doron who can not distigush (and evidently diliberatly so) {0} from {}.

Exactly, the magnitude of a point is not changed by the number of values that are related to it, in order to determine the exact location of 0 dimensional element (a point) w.r.t a given dimensional space.

If the term is "0 dimensional element" = "no dimensional element" then no values are related to any element, no coordinates are measured, and the concept of Location (whether it is local or non-local) get's off stage.

n=1 to ∞
k=0 to n-1

X = "Dimensional space"

Y = "Dimensional element"

n_X - k_Y = (n-k) coordinates that are used to determine k_Y location w.r.t n_X

k_X - k_Y = 0 coordinates that are used to determine k_Y location w.r.t k_X

By k_X - k_Y = 0, where 0 coordinates (which is a Multitude's expression) are used to determine k_Y location w.r.t k_X,
no matter if k magnitude >= 0 (it is clealr that if 0 coordinates are used, then no location of a local element w.r.t k_X is defineable).

No_X - k_Y is an invalid mathematical expression.

Persons like you do not understand the difference between the k_X and No_X.

Persons like you do not, evidently deliberately, understand the difference between the dimensionality of an object and the space it may be embedded in.

 

[doronshadmi]

(being comprised of your “dimension 0” and your “dimension 1”)

You still count things instead of understanding the difference of the magnitude of a point w.r.t a line or the magnitude of a line w.r.t a point.

A point is 0 dimensional element and it has an exact location w.r.t 1 dimensional space (dimension of a line) where a line is located at AND beyond the given point.

Your "No dimension" = "Dimension 0" is the core of your invalid reasoning.

 

[doronshadmi]

Again these “dimension 0” and “dimension 1” are just your fantisies. Again if you think just a point has a location then give us the location of just your “dimension 0” “point”.

Please show where exactly a claim that a point has a location, which is not w.r.t at least a line.

You simply do not understand the following:

n=1 to ∞
k=0 to n-1

X = "Dimensional space"

Y = "Dimensional element"

n_X - k_Y = (n-k) coordinates that are used to determine k_Y location w.r.t n_X

k_X - k_Y = 0 coordinates that are used to determine k_Y location w.r.t k_X

By k_X - k_Y = 0, 0 coordinates (which is a Multitude's expression) are used to determine k_Y "location" w.r.t k_X,
no matter if k magnitude >= 0 (it is clear that if 0 coordinates are used, then no location of local elements w.r.t k_X is definable).

No_X - k_Y is an invalid mathematical expression.

Persons like you do not understand the difference between the k_X and No_X and http://www.internationalskeptics.com/forums/showpost.php?p=6247928&postcount=11229 is a Strew Man (which is a better name than The Man, according the considered subject).

 

[doronshadmi]

The origin in a two dimensional space has two coordinates

(0,0)

It is called two dimensional space, because the exact location of 0 dimensional element w.r.t the considered space, is given by two values that are related to the 0 dimensional element.

The origin of a one dimensional space has one ordinate.


(0)

It is called one dimensional space, because the exact location of 0 dimensional element w.r.t the considered space, is given by one value that are related to the 0 dimensional element.

The origin of a zero dimensional space (a point) has no ordinate or coordinates (because it technically has no origin)

()

It is called zero dimensional space, because the exact location of 0 dimensional element w.r.t the considered space, is given by no values that are related to the 0 dimensional element.

It does not mean that 0 dimensional element or 0 dimensional space are not considered.

On the contrary in the case of No-dimension, dimensional element or dimensional space are not considered at all.

 

[zooterkin]

It is called two dimensional space, because the exact location of 0 dimensional element w.r.t the considered space, is given by two values that are related to the 0 dimensional element.

What do you mean, "related to"? Related to in what way?

ETA: And by "0 dimensional element", do you mean "point"?

 

[epix]

True the reference is to a specific circle, but the point remains that the dimensionality of that object is independent of the dimensionally of the space you might need to draw a specific one in that space.

Yes, you are right. The height/dimension of a person doesn't depend on his location -- the person is still 6 feet tall in the kitchen or in the bedroom. I always think in terms of how many coordinates it takes to draw/define n-multidimensional object on a specific plane. So if you have that person measured while he is walking through a room 4 feet from the floor to the ceiling, you don't not get the right measurement unless you adjust the coordinate system. He is going to bend his back and you need to add one coordinate: from "I (one) coordinate system" to "L" (two) coordinate system. Under that condition, the person is not 6 feet tall but 4+2 feet tall. (Kinda sounds like an exerpt from Chapter 42 of "The Joy of Doronetics." LOL.)

You can always pick your origin and in polar coordinates it becomes the center of infinite an number of concentric circles.

That's the idea: there is only one parametric change necessary to draw multitude of distinct circles to demonstrate the single dimensionality of a circle. The first point drawn is shared by the multitude of the drawn circles.

The single-dimensionality doesn't limit itself to the circle; it can be any object defined by polar coordinates, like this "flower" on the tOMbstone.

http://www.calculator-grapher.com/graphing-calculator.html

 

[doronshadmi]

That's the idea: there is only one parametric change necessary to draw multitude of distinct circles to demonstrate the single dimensionality of a circle. The first point drawn is shared by the multitude of the drawn circles.

According to this reasoning, also a ball has a single dimensionality.

Actually any dimension that is > 0 has single dimensionality, such that there are infinitely many elements for any dimension > 0 w.r.t a given point.

But this is not the case with 0 dimension, which has exactly one element w.r.t the given location, because 0 dimensional element is the locality where any given dimensional element > 0, is non-local w.r.t to it.

 

[Little 10 Toes]

Thank you for answering my previous message so quickly. Perhaps you can answer these questions, that I'm asking for the EIGHTH TIME or are they to hard for you to answer?

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.

What are "non-composed things"? What qualities are we examining? What is "linked"? What "result"?

 

[doronshadmi]

Thank you for answering my previous message so quickly. Perhaps you can answer these questions, that I'm asking for the EIGHTH TIME or are they to hard for you to answer?

1) Not composed by sub-elements.

2) The non-local and local qualities.

3) Vanished into and derive from the un-manifested, without being components of each other.

4) Complexity.

 

[The Man]

You still count things instead of understanding the difference of the magnitude of a point w.r.t a line or the magnitude of a line w.r.t a point.

A point is 0 dimensional element and it has an exact location w.r.t 1 dimensional space (dimension of a line) where a line is located at AND beyond the given point.

Your "No dimension" = "Dimension 0" is the core of your invalid reasoning.

You still do understand, or evidently want to understand the difference between the dimensionality of some space and that of some object that might be embedded in that space.

Please show where exactly a claim that a point has a location, which is not w.r.t at least a line.

Please show where exactly such a claim of a claim was made?

Are you asserting now that a point does not have a location unless embedded in some >0 dimensional space?

You simply do not understand the following:

n=1 to ∞
k=0 to n-1

X = "Dimensional space"

Y = "Dimensional element"

n_X - k_Y = (n-k) coordinates that are used to determine k_Y location w.r.t n_X

k_X - k_Y = 0 coordinates that are used to determine k_Y location w.r.t k_X

By k_X - k_Y = 0, 0 coordinates (which is a Multitude's expression) are used to determine k_Y "location" w.r.t k_X,
no matter if k magnitude >= 0 (it is clear that if 0 coordinates are used, then no location of local elements w.r.t k_X is definable).

No_X - k_Y is an invalid mathematical expression.

Persons like you do not understand the difference between the k_X and No_X and http://www.internationalskeptics.com/forums/showpost.php?p=6247928&postcount=11229 is a Strew Man (which is a better name than The Man, according the considered subject).

It is quite obvious that you simply do not understand it, dimension or a “strawman”. Though K-Y is an appropriate designation for that nonsense you strewed about above, since you are just using it to jerk yourself around.

It is called two dimensional space, because the exact location of 0 dimensional element w.r.t the considered space, is given by two values that are related to the 0 dimensional element.

It is called one dimensional space, because the exact location of 0 dimensional element w.r.t the considered space, is given by one value that are related to the 0 dimensional element.

So now your counting the number of ‘values’ “that are related to the 0 dimensional element”?

Guess your pervious assertion...

You still count things instead of understanding the difference of the magnitude of a point w.r.t a line or the magnitude of a line w.r.t a point.

was just one of your “Strew” men.

It is called zero dimensional space, because the exact location of 0 dimensional element w.r.t the considered space, is given by no values that are related to the 0 dimensional element.

See I figured that would help you, at least somewhat.

It does not mean that 0 dimensional element or 0 dimensional space are not considered.

Well of course they are “considered” and specifically in that latter case that “0 dimensional element” is the entire space being “considered”. That’s why it has no location and thus no dimension.

On the contrary in the case of No-dimension, dimensional element or dimensional space are not considered at all.

Well, you’re still confusing, again perhaps deliberately, the lack of dimension with the lack of a concept of dimension. Once again even if you have no apple you can still have a concept of an apple and in fact need that concept of an apple in order to determine that you indeed have no apple.

 

[doronshadmi]

What do you mean, "related to"? Related to in what way?

ETA: And by "0 dimensional element", do you mean "point"?

Related in order to define the exact location of 0 dimensional element w.r.t a given dimensional space.

 

[doronshadmi]

Well of course they are “considered” and specifically in that latter case that “0 dimensional element” is the entire space being “considered”. That’s why it has no location and thus no dimension.

Again your local-only reasoning airs its limited view, and now it is done about the concept of dimension.

EDIT:
Look how the number of values (the multitude) that are needed in order to define the exact location of 0 dimesional element (which is local w.r.t any given dimension > 0) is a direct result of magnitude > 0 - magnitude 0, or in other words, the multitude is based on the magnitude, in this case.

Well, you’re still confusing, again perhaps deliberately, the lack of dimension with the lack of a concept of dimension. Once again even if you have no apple you can still have a concept of an apple and in fact need that concept of an apple in order to determine that you indeed have no apple.

If you accept the notion that No dimension is still a dimension, then we agree with each other.