Deeper than primes

[zooterkin]

http://www.internationalskeptics.com/forums/showpost.php?p=6267040&postcount=11318

Sorry, I'm not going to aim at a moving target.

 

[doronshadmi]

Sorry, I'm not going to aim at a moving target.

He does seem to have a propensity for introducing more errors when trying to make a correction.

Nonsense. You don't use the point as a co-ordinate, the co-ordinates tell you where the point is.

By dragging the point, you are defining, for example, a line, which is 1-dimensional.

This reasoning has infinitely many errors.

The right reasoning is this:

A point is an existing dimensional space that has 0 degrees of freedom (no 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.

So why you are using the nonsense of "dragging a point" in order to define a line?

 

[Little 10 Toes]

Asking for the second 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.

So after several times of you having to clarify what your previous answer is, we're at the point where your definition of a domain is "A realm where the measured and the measurer are interacted". Clear as mud.

Define "interacted".

If I use a tool to measure the measured, what/who is the measurer? For example, I have a book with a unknown weight. When I place the book (the measured object) the scale will give me a measurement. Who is the measurer?

You went back and edited several posts and you had problems understanding the word "I" so I ask the same questions without using the word I.

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?

 

[The Man]

Let's do it clearer



You still miss it.

If a set that containing a point has cardinality 1 it means that the contained is not nothing even if the considered universe is Dimension.

Again…

Who ever said a point or a set containing a point it was “nothing”?

The set that containing no apples has cardinality 0 if the considered universe is Apples.

So a set containing no dimensions would have a “cardinality 0 if the considered universe” is dimension?

In other words, “0 apples” is equivalent to “0 points”, but “0 points” is not equivalent to “0 dimension”, so your “0 apples” argument does not hold water.

Again the analogy was “0 apples” to “0 dimensions”. If you want it to be “0 apples” to “0 points” that‘s a different analogy as I addressed in my pervious post.

Again..

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

I thought you said you were going to try to “do it clearer”, not just repeat the same claims I addressed in my previous post?

That is why a point is an existing thing that has 0 dimension.

OK so now your “point” does not have “a dimension” as you claimed before?

Since 0 dimensional element and 1 dimensional element are both existing things under the universe of Dimensions, then 1 dimensional element is included NXOR excluded w.r.t 0 dimensional element under that universe, and 0 dimensional element is included XOR excluded w.r.t 1 dimensional element under that universe.

Furthermore, there is a difference between “element”, which is a non-composed thing, and “object” that can be a composed thing (in both cases we are talking about existing things, where contained existing things of some set is resulted by cardinality > 0 of the considered set).

A line segment is a composed result of 0 and 1 non-composed dimensional spaces.

So you think simply repeating the same things from your pervious post, verbatim, is doing “it clearer”?

You simply can’t grasp the notion of existing and non-composed things, because you do not understand differences that are based on magnitudes.

Your “direct perception” has failed you yet again.

The one who enables to get differences that are based on magnitudes (where Magnitude is defined according to “How much?” question, which is essentially different than “How many?” question) , immediately grasps the difference of the existing 0 dimensional element and 1 dimensional element w.r.t each other.

Doron if the answer to how much (by mass) of a 1 kg apple pie is apples, is 0.75 kg and each apple used was about 0.125 kg (excluding the core, skin and seeds), how many apples were used in that pie?

In case you haven’t realized it yet the answer to how much of the apple pie is apples (by mass) is answered both by how many apples were used and how much mass (excluding the core, skin and seeds) each had. How much mass each apple has is represented by how many kgs of matter each contains (excluding the core, skin and seeds). So how much is directly dependent on how many of some given units of measure, whether it be apples, kgs or whatever.

How much apple can your pie have when how many apples you have is 0?

Doron, “How much” is just a question of “How many” of some unit representation.

How much (in apples) of an apple is apple? How many apples is that? Take half of that and how much (in apples) is that now? How many apples would that be now?

No, I am claiming that a point is an existing element and the cardinality of a set that includes it as a member, clearly demonstrates it.

So you still simply have not or can not answer the question of how many dimensions your “point” has.

Start by fixing your reasoning's abilities (for example: the difference between “How much?” and “How many?” questions).

Start by gaining some reasoning abilities yourself and stop just fixating on your OM fantasies.

Some exercises:

The same “exercises” for you, that you have as yet to directly answer.

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

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)

How much size a point has?

Size is an aspect of dimension, as a point has no dimension(s) it thus has no size.

Does an element that has 0 size exists?

A point is an abstract concept with no dimension and thus no size, it “exists” specifically as that abstract concept.

What is the cardinality of a set that have at least a point as its member?

A set with only one member has a cardinality of one, so “a set that have at least a point as its member” has a cardinality of at least one. You still seem to be, perhaps deliberately, ignoring that it is a set containing the ordinate or co-ordinates of some point that represents dimension (in this consideration) not a set containing a point. So I guess you’re simply not done comparing apples to oranges.

Nope.

There is a difference between “How many?” (apples) and “How much?” (size).

So how much (in apples) of an apple is apple? More specifically to your assertion above, what is the “size” of an apple in apples? How many apples is that? Take half of that and what is the “size” of that in apples? How many apples is that now?

A point is an existing element with 0 size, and if it is the only thing that included in some set, then the cardinality of that set is at least 1.

Again dimension is represented (in this consideration) by a set containing the ordinate or coordinates needed to located that point in some space or object, not a set containing just a point. Your continued and apparently deliberate ignorance of the fact does not change that fact.

This is not the case with no apples because no apples is not an existing thing, so if no apples are the only thing that is included in a given set, then the cardinality of that set is 0.

You still seem to be confusing, most likely deliberately, no dimension with no point.

Yes, a point is an existing element exactly a line is an existing element, and both of them are exiting things under the concept of Dimension.

Yes, to what? That now your “point” is 0 dimensional?

Would this “concept of Dimension” of yours be similar to the one that is defined by points, specifically the ordinate or coordinates needed to locate some point in a given space or object?

By understanding this fact a point is included XOR excluded w.r.t a line and a line is included NXOR excluded w.r.t a point.

Again “included NXOR excluded w.r.t a point” is always false as inclusion and exclusion are mutually exclusive.

You seem to be ignoring the obvious fact that a point is not the building-block of a line and as a result a point and a line are different and existing magnitudes that have different properties if compared w.r.t each other, and they are comparable under the concept of Dimension.

You still seem to be ignoring the obvious fact , again apparently deliberately so, that it is the ordinate or coordinates needed to located a point in some space or object that defines dimension (in this consideration).

Nothing was shifted. A point is an existing element under the concept of Dimension, and if some set includes elements of that concept,
then |{.}| = 1 where cardinality 1 indicates the existence of a point as an element of the concept of Dimension.

Doron, the ‘elements’ “of the concept of Dimension” are again the ordinate or coordinates needed to located a point in some space or object. Having no ordinate or coordinates does not infer no point, but it does define no dimension(s). Again you shifted your “universe based on dimension” to one based on point(s), which again means that you might actually be learning some geometry in spite of yourself.

A point is an existing element under the universe of Dimensions exactly as some apple is an existing element under the universe of apples.

If the universe of apples has no apples, then we deal with the empty set.

If the universe of dimensions has no elements (where a point is one of the elements of this universe) then we deal with the empty set.

See there you go again you specifically claim if your “universe of apples has no apples, then we deal with the empty set” yet for your “universe of dimensions” you do not specifically state if it “has no” dimension“, then we deal with the empty set”. Once again you are simply trying to infer no point from no dimension when a point is specifically defined as having no dimensions.

EDIT:

There is no element that lacks the property of apple under the universe of apples.

So now your “empty set” that has no apples in your “universe of apples” has a “property of apple”?

There is no element that lacks the property of dimension under the universe of dimensions.

Yet you still do not specifically assert the empty set for “no dimension” in your “universe of dimensions” as you did for your “universe of apples”. Once again you are simply ignoring no dimension in your “universe of dimensions” while proclaiming the empty set for no apples in your “universe of apples”.

Since a point is an element under the universe of dimensions that has exactly "0 dimension", then "0 dimension" is not the same as "no dimension", because an element that has "no dimension" is not under the universe of dimensions.

Yet “no apples” is under your “universe of apples” as the empty set. Once again you are simply ignoring “no dimension" as the empty set in your “universe of dimensions”. Once again you seem to be confusing, and at this point it can only be deliberate, a set containing a point with the definition of dimension (in this consideration) as the (or a set containing the) ordinate or coordinates need to locate a point in some space or object. As I said before a point is a defining element of dimesion, specifically the ordinate or coordinates need to locate a point in some space or object. So no point means no dimension(s) as there is nothing to locate. However, having just a single point also means no dimension(s) as although you now have something to locate you have no way of locating it (the ordinate or coordinates of that point is the empty set). In order to locate it you need at least one other point in a discrete space and if your space is continuous then between those two points are an infinite number of points, both giving a dimension with in which to locate that point or any of those points.

 

[epix]

Doron, “How much” is just a question of “How many” of some unit representation.

Do you have any evidence to support your claim? (The notorious Q. LOL.)

How much money do I need to buy a pipe like that?

26 dollars and 99 cents plus tax.

Hmm. I guess you do.

 

[epix]

This reasoning has infinitely many errors.

The right reasoning is this:

A point is an existing dimensional space that has 0 degrees of freedom (no 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.

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:

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:

Looks familiar?


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

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.

 

[doronshadmi]

See there you go again you specifically claim if your “universe of apples has no apples, then we deal with the empty set” yet for your “universe of dimensions” you do not specifically state if it “has no” dimension“, then we deal with the empty set”. Once again you are simply trying to infer no point from no dimension when a point is specifically defined as having no dimensions.

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:

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.

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

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.

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

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.

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.

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.

 

[doronshadmi]

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

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

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

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

 

[zooterkin]

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, once again, you demonstrate your ignorance.

What, exactly, is "0 dimensional space"? Is that just you struggling to understand what a point is? As epix says, a point is just an imaginary reference point; you specify it with co-ordinates; it is a location.

 

[doronshadmi]

Yet “no apples” is under your “universe of apples” as the empty set. Once again you are simply ignoring “no dimension" as the empty set in your “universe of dimensions”.

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

{} is not equivalent to {no apples}

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

 

[doronshadmi]

a point is just an imaginary reference point

You can't use the word "point" as a part of its definition ("a point is just an imaginary reference point"), because you get a circular reasoning, which is invalid.

 

[zooterkin]

You can't use the word "point" as a part of its definition ("a point is just an imaginary reference point"), because you get a circular reasoning, which is invalid.

You'll be the expert on what constitutes a definition, then?

Yes, you are correct, a different word should be used; I was quoting epix, and missed the reuse of the word. Does that stop you from understanding what a point is, though, or a co-ordinate?

 

[doronshadmi]

You'll be the expert on what constitutes a definition, then?

Yes, you are correct, a different word should be used; I was quoting epix, and missed the reuse of the word. Does that stop you from understanding what a point is, though, or a co-ordinate?

You get the notion of point under the universe of dimensional spaces:

A point is an existing dimensional space that has 0 degrees of freedom (no 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.


EDIT:

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).

 

[Little 10 Toes]

Asking for the third 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.

So after several times of you having to clarify what your previous answer is, we're at the point where your definition of a domain is "A realm where the measured and the measurer are interacted". Clear as mud.

Define "interacted".

If I use a tool to measure the measured, what/who is the measurer? For example, I have a book with a unknown weight. When I place the book (the measured object) the scale will give me a measurement. Who is the measurer?

You went back and edited several posts and you had problems understanding the word "I" so I ask the same questions without using the word I.[/QUOTE]

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?

 

[zooterkin]

A point is an existing dimensional space that has 0 degrees of freedom (no coordinates are related to points).

No.

 

[doronshadmi]

so I ask the same questions without using the word I.

Who is I that asks the same questions without using the word I?
http://www.internationalskeptics.com/forums/showpost.php?p=6267027&postcount=11316

 

[doronshadmi]

No.

Some details that support your "No", please.

 

[zooterkin]

Some details that support your "No", please.

What would be the point?

 

[doronshadmi]

What would be the point?

Maybe you tell us.

Also be aware of the fact that

Sorry, I'm not going to aim at a moving target.

AND

By dragging the point, you are defining, for example, a line, which is 1-dimensional.

is a contradiction.

 

[Little 10 Toes]

Fourth time asking a very simple question:

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?

Maybe you tell us.

Also be aware of the fact that

AND

is a contradiction.

Not answering your ever changing posts (That is what zooterkin is referring to in the second quoted message) and dragging a point (the third quoted message) is not a contradiction.

Are you sure that English is a second language for you? The way you can't comprehend it makes me wonder.